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Bayesian Optimization for Design of Multiscale Biological Circuits

Cite this: ACS Synth. Biol. 2023, 12, 7, 2073–2082
Publication Date (Web):June 20, 2023
https://doi.org/10.1021/acssynbio.3c00120

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Abstract

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Recent advances in synthetic biology have enabled the construction of molecular circuits that operate across multiple scales of cellular organization, such as gene regulation, signaling pathways, and cellular metabolism. Computational optimization can effectively aid the design process, but current methods are generally unsuited for systems with multiple temporal or concentration scales, as these are slow to simulate due to their numerical stiffness. Here, we present a machine learning method for the efficient optimization of biological circuits across scales. The method relies on Bayesian optimization, a technique commonly used to fine-tune deep neural networks, to learn the shape of a performance landscape and iteratively navigate the design space toward an optimal circuit. This strategy allows the joint optimization of both circuit architecture and parameters, and provides a feasible approach to solve a highly nonconvex optimization problem in a mixed-integer input space. We illustrate the applicability of the method on several gene circuits for controlling biosynthetic pathways with strong nonlinearities, multiple interacting scales, and using various performance objectives. The method efficiently handles large multiscale problems and enables parametric sweeps to assess circuit robustness to perturbations, serving as an efficient in silico screening method prior to experimental implementation.

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 Special Issue

Published as part of the ACS Synthetic Biology virtual special issue “AI for Synthetic Biology”.

1. Introduction

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The design of molecular circuits with prescribed functions is a core task in synthetic biology. (1) These circuits can include components that operate across various scales of cellular organization, such as gene expression, signaling pathways, (2) or metabolic processes. (3) Computational methods are widely employed to discover circuits with specific dynamics, (4−6) and, in particular, optimization-based strategies can be employed to search over design space and single out circuits predicted to fulfill a desired function. (7−10) However, circuit design requires the specification of circuit architecture, i.e., the circuit “wiring diagram”, as well as the strength of interactions among molecular components. Since circuit architectures are discrete choices and molecular interactions depend on continuous parameters such as binding rate constants, circuit design leads to mixed-integer optimization problems that can be notoriously difficult to solve. (11) Moreover, when circuits operate across multiple scales, their computational models become numerically stiff, (12) resulting in extremely slow simulations that make their mixed-integer optimization challenging or even impossible to solve.
Previous work on computational circuit design has largely focused on genetic circuits that operate in isolation from other layers of the cellular machinery (Figure 1A). A range of techniques have been employed to identify functional circuits, including exhaustive search, (4−6,13) computational optimization, (7,8) systems theoretic approaches, (14−18) Bayesian design, (19,20) and machine learning. (9,21) While these methods differ on their specific modeling strategies and assumptions, they all require computational simulations at many locations, typically thousands to millions, in the design space. But since multiscale systems often cannot be simulated at such scale, the computational costs limit the applicability of current optimization methods.

Figure 1

Figure 1. Bayesian optimization for the design of circuit architectures and parameters. (A) Previous optimization methods have focused on genetic circuits in isolation from other cellular processes. For multiscale circuits, optimization approaches become infeasible due to the difficulty of simulating stiff dynamical systems in many locations of the design space; a common example of such multiscale systems are gene circuits that control metabolic production. (3) We propose the use of Bayesian optimization (BayesOpt) for efficient optimization of architectures and parameters in multiscale circuits. (B) Schematic of a mixed-integer Bayesian optimization loop; the objective function is regarded a random variable to be optimized over an input space comprised of continuous parameters and a set of discrete circuit architectures. At each iteration, the algorithm computes the value of the objective function from the solution of an ordinary differential equation (ODE) model at a single location in the input space. The algorithm learns the shape of the objective landscape using a nonparametric statistical model, (37) which is employed to propose a new location in the input space through an acquisition function designed to balance exploration and exploitation of the input space; more details in the Methods. The algorithm iteratively learns the shape of the performance landscape until convergence to a global optimum. (C) Example metabolic pathway under gene regulation. We consider three negative feedback architectures plus open loop control; the architectures are named based on the net effect of the metabolite on gene expression. The intermediate X1 binds a transcription factor (TF) that controls the expression of pathway enzymes, either as an activator or repressor. Vin is the constant influx to the engineered pathway from native metabolism. The TF dose-response curve (at right) is described by three parameters, ki, θi, and ni, where i = 1, 2. The aim is to find designs with optimal architecture and dose-response parameters (ki, θi); for simplicity the Hill coefficient was fixed to ni = 2. (D) Performance landscapes of the four feasible circuit architectures. We exclude architectures with positive feedback loops as these are prone to multistability. (47) The shape of the performance landscape defined in eq 3 shows substantial variation across the four architectures. This leads to a highly nonconvex mixed-integer optimization problem. Heatmaps show the value of the objective J computed on a regular grid of the indicated parameters. (E) Comparison of BayesOpt against other strategies using the toy model as a benchmark; lower objective function values are better. Shown are the results for random sampling (N = 1,000 samples), grid search (N = 40,000), a genetic algorithm (55) (N = 100 individuals, N = 1,000 generations), and a gradient-based optimizer to find optimal continuous parameter values for each architecture. (48)

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A notable example of this challenge appears in genetic circuits for dynamic control of metabolic pathways. (22−26) These systems are receiving substantial attention thanks to several successful implementations that improved yields as compared to classic techniques in metabolic engineering. (27,28) The key principle is to put enzymatic genes under the control of metabolite-responsive mechanisms that couple heterologous expression to the concentration of a pathway intermediate. (3) This creates feedback loops between enzyme expression and pathway intermediates that allow the control of pathway activity in response to upstream changes in growth conditions or precursor availability. Such dual genetic-metabolic systems are particularly challenging to simulate efficiently because metabolites and enzymes vary in different time scales, from milliseconds (enzyme kinetics) to minutes (enzyme expression), and they also appear in vastly different concentrations; in bacteria enzymes are typically expressed in nanomolar concentrations, while metabolites are found typically above the millimolar range. (29) Moreover, the implementation of these systems is costly and requires substantial experimental fine-tuning. As a result, a central task prior to implementation is the choice of a suitable feedback control loop between metabolites and enzymatic genes, and the strength of interactions between metabolites and actuators of gene expression such as transcription factors (30) or riboregulators. (31) The design of control architectures is particularly important, because there are many ways of building similar control loops, (32) for example by employing combinations of transcriptional activators and repressors, (33,34) that may differ in their performance and cost of implementation.
Here, we present a fast and scalable machine learning approach for optimization of multiscale circuit architectures and parameters (Figure 1A). The method is based on Bayesian optimization coupled with differential equation models, and we highlight its utility in various models of metabolic pathways under genetic feedback control. (35) Using a toy example for a simple pathway, we first show that the method converges rapidly and outperforms other optimizers by a substantial margin. We then consider real world models of metabolic pathways in Escherichia coli for the production of several relevant precursors: glucaric acid, (36) fatty acids, (33) and p-aminostyrene. (34) We use these pathways to illustrate how the speed of our method enables screening optimal designs in realistic design tasks that would otherwise be infeasible to compute, including the impact of uncertain enzyme kinetic parameters, the use of layered architectures that combine metabolic and genetic control, and the optimization of a complex model with 23 differential equations, 27 candidate control architectures, and 16 parameters to be optimized. The method can help speed up the design of synthetic biological circuits and presents a novel approach to explore the design space ahead of implementation.

2. Results

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2.1. Bayesian Optimization for Joint Optimization of Circuit Architecture and Parameters

In general, a circuit design task can be stated as the following mixed-integer optimization problem:
min p d , p c ⁡ J ( x , p c , p d ) subject to : d x / d t = h ( x ) p c ∈ C , ⁣ p d ∈ D
(1)
where J(x, pc, pd) is a performance objective to be optimized over a space of continuous parameters pc and a discrete set of circuit architectures pd. The ordinary differential equation (ODE) in eq 1 describes the temporal dynamics of circuit components and are typically built from mass balance relations comprised in the nonlinear function h(x). Common examples of continuous parameters in applications are binding affinities between DNA and regulatory proteins, or the strength of protein-protein interactions. Conversely, circuit architecture would typically involve various combinations of positive and negative feedback loops among molecular species. We have stated the problem as minimization of J, but similar formulations can be posed as a maximization problem.
In this paper, we propose to solve the design problem in eq 1 with Bayesian optimization (BayesOpt), a class of algorithms designed for problems with objective functions that are expensive to compute. BayesOpt is a global optimization technique that treats the objective function as a random variable with a prior distribution on it. The algorithm creates a statistical model of the objective through subsequent evaluations, which are employed to build a posterior distribution and determine the next set of inputs to evaluate (Figure 1B). A typical application of BayesOpt is in design of experiments (35) where the objective function requires measuring data with costly and/or slow experimental work. In deep learning, BayesOpt is widely employed for model selection, as traditional grid search approaches require large compute resources to train many architectures with combinations of various layer sizes and other hyperparameters. (37,38)
For the circuit design task in eq 1, when the biological system has multiple scales the computation of objective J requires solving a stiff ODE at many locations of the mixed-integer search space, which can rapidly become infeasible. To illustrate the utility of BayesOpt in a range of design problems, we focus on genetic control circuits for metabolic pathways that synthesize high-value products. In this case, the ODE in eq 1 contains two sets of equations:
d s / d t = f ( s , e ) − λ s d e / d t = u ( s , p c , p d ) − λ e
(2)
where s and e are vectors of metabolite and enzyme concentrations, respectively. The term f(s, e) describes the biochemical reactions between pathway intermediates, while the parameter λ models the dilution effect by cell growth. The vector u(s, pc, pd) describes the enzyme expression rates controlled by some pathway intermediates, and typically take the form of sigmoidal dose-response curves that lump together processes such as metabolite-TF or metabolite-riboregulator interactions. (30) The continuous parameters pc model the dose-response curves of the feedback mechanisms, whereas the discrete parameters pd specify the gene control architecture. The number of heterologous enzymes determines the number of genes in the control circuit. In pathways under dynamic control as in eq 2, both sets of species change in different time scales; metabolic reactions operate in the millisecond range or faster, (39) while enzyme expression changes in the scale of minutes or longer. Moreover, metabolites and enzymes are also present in different ranges of concentrations, from nM for enzymes to mM and higher for metabolites. (29) As a result, simulation of the ODE in eq 2 is computationally expensive, particularly when this has to be done many times as part of an optimization-based search.
The performance objective J can be flexibly used to model common design goals such as production flux, yield or titer, as well as cost-benefit tasks that balance production with the deleterious impact of the pathway on the physiology of the host. To first establish a baseline for the performance of our method, we employed a simple toy pathway model that displays common features found in real metabolic pathway (Figure 1C). The model includes a metabolic branch point through a heterologous pathway with two enzymatic steps. As a performance objective we considered the minimization of
J = α 1 J prod + α 2 J cost
(3)
where Jprod was designed so that its minimization is equivalent to maximization of the production flux, and Jcost penalizes total amount of enzyme expressed during the culture. The parameters α1 and α2 are positive weights used to control the balance between the costs and benefits of expressing the heterologous pathway. Details on the objective function can be found in the Supporting Information.
We considered the four control architectures shown in Figure 1C, which include open loop control as well as three different implementations of negative feedback control using a metabolite-responsive transcription factor. Negative feedback is widely employed in gene circuits as it has substantial benefits in terms of robustness and performance, and their properties have been extensively studied in the literature. (40−42) To illustrate the challenge of jointly optimizing circuit architecture and parameters, in Figure 1D we show a schematic of the design space. The four control architectures under consideration reside at different discrete points in the architecture space. Within each architecture, we observe substantial variations in the shape of the performance landscape J as a function of the dose-response parameters pc. There are cases with convex landscapes with a clear optimum (e.g. dual control) and landscapes with flat basins where most optimization algorithms would struggle to find the optimum (e.g. downstream activation). When searching over the space of architectures and parameters simultaneously, the problem becomes a mixed-integer, nonconvex optimization that is extremely challenging to solve with traditional approaches.
We implemented a BayesOpt routine to jointly compute the architecture (pd) and dose-response parameters (pc) that minimize the performance objective in eq 3. We benchmarked its performance against several other methods, including a random search, an exhaustive grid search, a gradient based method, and a genetic algorithm (Figure 1E). The algorithm was able to compute optimal solutions rapidly (average 27 seconds per run across 100 runs) and robustly (standard deviation less than 2.5% of the mean optimal objective function value). BayesOpt runs significantly faster than the other methods, and provides a 30-fold improvement over a genetic algorithm. The accuracy of the optimum, quantified by the minimal value of the objective function, is on average 11.4% worse than the genetic algorithm, but this falls within the variation of the latter across several runs. We also note that the traditional gradient-based optimizer proved unreliable and failed to converge on 14.5% of runs.
A key advantage of Bayesian methods is that they are not gradient-based, and therefore are not constrained to navigate the space smoothly in the direction of steepest descent. Gradient-based methods can get trapped in local minima and struggle to find the global optimum, especially in highly nonconvex landscapes like the ones presented here. In contrast, BayesOpt does not converge by chasing minima directly but rather by modeling the entire objective function landscape, which results in rapid and reliable results. The method can perform multiple “jumps” between distant locations in the discrete-continuous search space, where each subsequent sample is selected to maximize the expected improvement on the best sample found so far.
The speed of our approach enables the computation of large solution ensembles under model perturbations such as sweeps of key model parameters. In addition, our method can search high-dimensional mixed-integer design spaces. We next illustrate the versatility of the approach in a range of relevant real world pathways that require solving the optimization problem for large samples of parameter values.

2.2. Robustness of Control Circuits to Uncertainty in Enzyme Kinetic Parameters

A challenge in building pathway models is the substantial uncertainty on the enzyme kinetic parameters; this is particularly critical for pathways that include regulatory mechanisms such allostery or product inhibition, which are often poorly characterized. Databases such as BRENDA (43) often have insufficient data on enzyme kinetics for a particular host strain or substrate of interest. Since pathway dynamics can strongly depend on enzyme kinetics, the parametric uncertainty requires extensive sweeps of kinetic parameters to determine the robustness of a specific control architecture deemed to be optimal.
We focused on a pathway for synthesis of glucaric acid in E. coli (Figure 2A), a key precursor for many downstream products. (36) The pathway branches from glucose-6-phosphate (g6p) in upper glycolysis and contains three enzymatic steps (Ino1, SuhB, and MIOX). Doong and colleagues implemented a dynamic control circuit using the dual transcriptional regulator IpsA which responds to the intermediate myoinositol (MI). (26) The pathway enzyme MIOX is allosterically activated by its own precursor, and one intermediate (MI) can be exported to the extracellular space. We employed a previously developed ODE model (10) that was parametrized using a combination of enzyme kinetic data and omics measurements, and considered the same four control architectures as in the previous example, including various alternative implementations of negative feedback control.

Figure 2

Figure 2. Robustness of optimal circuits to parameter uncertainty. (A) Schematic of a dynamic pathway for production of glucaric acid in Escherichia coli. (26) The pathway includes allosteric inhibition and export of an intermediate to the extracellular space. The core pathway components myoinositol (MI) and glucaric acid (GA) are modeled explicitly, as are the enzymes Ino1 and MIOX. The enzyme SuhB is not rate-limiting and is not modeled explicitly. Vin is the constant influx to the engineered pathway from native metabolism. As in Figure 1C, the architectures are named based on the net effect of the metabolite on gene expression. (B) Sample run of the BayesOpt algorithm for 1,000 iterations of the loop in Figure 1B. Black line shows the descent on the value of the objective function. Dots show all samples colored by architecture; pie charts show the fraction of architectures explored by the algorithm, and the fraction of samples taken from the majority architecture (dual control). The first quarter of the run had the most exploration of architectures other than dual control, with 38.6% of samples coming from nonmajority architectures. This percentage steadily decreased over the iterations but did not drop below 20%, illustrating the global nature of the optimization routine. (C) To examine the robustness of the optimal solutions to parameter uncertainty, we computed optimal solutions for many perturbed parameters of the allosteric activation of MIOX by its substrate myoinositol (MI). Strip plot shows the best objective function values achieved for background and perturbed kinetic parameters (Vm,MIOX, aMIOX, ka,MIOX) in eq 4. Kinetic parameters were perturbed using Latin Hypercube sampling (56) in the range (−100%, +100%) of the nominal values (Supporting Information). We observed little difference between background and perturbed values; dashed line denotes the mean value of the objective function. Only one of the N = 100 runs for perturbed parameters failed to converge the optimum. (D) Optimal architectures across runs with background and perturbed parameter values. Both background and perturbed systems resulted in over 80% of runs selecting dual control as the optimal architecture. (E) Average dose-response curves and distribution of optimal parameters for the dual control architecture with perturbed allosteric parameters. The repressive and activatory loops have substantially different dose-response curves on average. The distributions of the dose-response parameters (right) show important variations in their mean and dispersion. The parameter ki and θi determine the maximal enzyme expression rate and regulatory threshold, respectively.

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The results in Figure 2B show a typical run of the optimizer when using the cost-benefit objective in eq 3 (details in Supporting Information), together with the fraction of samples in which the algorithm explored each control architecture across the successive iterations. The optimal architecture (dual control in this case) was found quickly and the algorithm was able to further decrease the value of the objective function by exploring the space of dose-response parameters of IpsA. We observe that as the iterations progress, the algorithm shows a remarkable ability to explore other architectures despite their larger objective function values, thus highlighting the global nature of the algorithm.
To explore the impact of uncertain enzyme kinetics, we perturbed the parameters of the rate-limiting MIOX allosteric reaction:
V MIOX = V m,eff MI k m,MIOX + MI given V m,eff = V m,MIOX 1 + a MIOX MI k a,MIOX + MI
(4)
where Vm,MIOX is the maximum rate of reaction, km,MIOX is the Michaelis-Menten constant, and ka,MIOX and aMIOX are allosteric activation constants. We solved the optimization problem for 1,000 combinations of these three parameters, which took under 16 hours on a Macbook Air with Apple M1 processor and 8 GB of RAM running MacOS Monterey. Perturbing the kinetic parameters of the glucaric acid pathway did not significantly affect the minimum objective function value achieved, indicating that the optimum is robust to uncertainty in the kinetic parameters (Figure 2C). However, the mean optimal objective function value was not significantly higher among the perturbed samples. We found that the dual control architecture was chosen as optimal in more than 85% of samples (Figure 2D). We thus sought to examine the optimal dose-response parameters of this architecture in more detail.
The maximal enzyme expression rates (k) and regulatory thresholds (θ) control the shape of the dose-response curves. As shown in Figure 2E, we found that the upstream repressive loop and downstream activatory loop had different optimal dose-response curves, corresponding to different optimal values of the continuous parameters. Optimal values of the upstream repression threshold θ1 are low (mean value 0.64) and compressed into a narrow range as compared to the larger standard deviation of the downstream repression threshold θ2 (mean value 7.24). This is reflected on a larger variation in the shape of the dose response curve for the downstream loop. Experimental fine-tuning of a dual control circuit might target parameters with optimal values with a wide range, such as k1, as varying these parameters is less likely to impair circuit function. Overall, these results show the robustness of the glucaric acid dual control system to kinetic parameter uncertainty and demonstrate the possibilities enabled by the speed of BayesOpt.

2.3. Exploration of Alternative Objective Functions

In the previous case studies we employed a cost-benefit objective designed to account for the trade-off between heterologous production and the cost of expressing pathway enzymes, as in eq 3. To demonstrate the flexibility of the method with other objective functions, here we consider the optimization of the temporal trajectories of pathway metabolites.
We focused on the joint optimization of the rise time and overshoot in a model of a fatty acid production pathway considered previously in the literature. (33) Fatty acids are an essential energy source and cellular membrane component. In addition, hydrocarbons derived from fatty acids have attracted attention as a potential biofuel source. (24,44) Recent work engineering metabolic and genetic control loops showed that negative feedback control could speed up the rise to steady-state conditions. (33) The pathway built in literature expressed a thioesterase under transcriptional control, shown as the negative metabolic loop (NML) architecture in Figure 3A. In addition to transcription-factor mediated negative feedback loops, this model also includes individually implemented direct genetic loops where a repressor is expressed on the same promoter as the enzyme. These two different scales of loops interface with different levels of cellular organization. We explore several control architectures previously proposed in the literature (33) (Figure 3A).

Figure 3

Figure 3. Optimization of metabolite dynamics in a fatty acid synthesis pathway. (A) Pathway diagrams with various control architectures implemented in Escherichia coli. (33) The metabolic loop employs a metabolite-responsive transcription factor, whereas the gene loop includes only a repressor expressed on the same promoter as the enzyme. (B) Representative run of BayesOpt with cost-benefit objective showing the best objective function value (black line). All samples are colored by their architecture. Pie charts of each quarter of the run show continued exploration of all architectures despite clear stratification in losses. (C) Optimal trade-off curve between overshoot and rise time. The objective weight α was swept from α = 0.01 to α = 10,000 and BayesOpt was run for 100 iterations at each α value. The optimal parameter values were used to compute the rise time and overshoot for visualization. The inset shows three sample trajectories illustrating how different optimal architectures navigate the trade-off between overshoot and rise time.

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We first considered a similar objective function as in eq 3 so as to compare convergence against the previous case studies. We implemented a modified production flux objective which takes the reciprocal of the product flux to convert the optimization to a minimization problem. The pathway cost Jcost is measured by summing the expression of all heterologous enzymes and varies across the different architectures. Details on the objective function can be found in the Supporting Information. A representative optimization run for this objective (Figure 3B) shows that the negative gene loop (NGL, green) and negative metabolic loop (NML, orange) architectures perform, on average, better than the other two architectures. BayesOpt samples taken from the open-loop architecture were, on average, 2 orders of magnitude worse than samples taken from NML and NGL architectures. Despite such hierarchy of loss values across the four architectures, the method effectively explores all architectures throughout the optimization run.
We next considered the optimization of percent overshoot and rise time presented in the literature. (33) The percent overshoot objective, Jos, measures the maximal deviation of product from its steady state concentration and is defined as the percent difference between the maximum fatty acid concentration and the steady state fatty acid concentration. The rise time, Jrt, is a measure of how fast fatty acid production rises to steady state and is defined as the first time point where the fatty acid concentration reaches 50% of the steady state value, normalized by the total integration time. We minimized the sum of the overshoot and rise time with a scaling weight α:
J = α J rt + J os
(5)
Adjusting α balances the relative importance of the two optimization criteria; details on the calculation of rise time and overshoot are in the Supporting Information. Higher values of α correspond to optimal circuits with low rise times, while lower values of α prioritize circuits with low overshoot. Rise time is a measure of circuit speed, while overshoot is a measure of circuit accuracy. We found that when α is varied across several orders of magnitude, the optimal circuits form a optimal trade-off curve (Figure 3C). Different architectures occupy different parts of the optimal trade-off curve and display markedly different dynamics. The NML optima occupies a single point in the loss space, indicating that multiple continuous parameter values give the same loss function value for multiple values of α. The NML also has the lowest absolute loss function value of all the architectures considered. The NGL and layered negative metabolic loop (LNML) architectures occupy larger ranges on the curve, with NGL giving a low overshoot and LNML a low rise time. The optimal NML circuit has no overshoot but the slowest rise time, while the LNML has a rapid rise time but overshoots the steady-state value by more than double. These opposing trade-offs demonstrate the importance of balancing multiple circuit design objectives.

2.4. Scalability to Large Pathway Models

Our previous case studies have been limited to circuits with a single metabolite controlling gene expression and a relatively small number of control architectures. We now study a large model for the synthesis of p-aminostyrene (p-AS), an industrially relevant vinyl aromatic monomer, in E. coli (Figure 4A) (45) using a cost-benefit objective similar to eq 3 tailored to the specific pathway (details in Supporting Information). This model has two possible metabolites that can regulate gene expression, namely p-amminocinnamic acid (p-ACA) and p-aminophenylalanine (p-AF), both of which can act as ligands for aptazyme-regulated expression device (aRED) transcription factors, (46) and three genes to be controlled. The aRED transcription factors can also act as dual regulators (activators or repressors) on any of the three promoters involved in the pathway. For simplicity, we limit the design space to control architectures without positive feedback loops, as these are prone to bistability. (47) This results in 27 possible control architectures and 16 continuous parameters to be optimized. The model also has a number of additional complexities. It contains operon-based gene expression commonly found in bacterial systems (genes papA, papB, and papC are expressed on the papABC operon), it includes a detailed description of mRNA dynamics and protein folding, which results in a large model with 23 differential equations, and it can also display oscillatory dynamics.

Figure 4

Figure 4. Bayesian optimization in a complex pathway. (A) Schematic of pathway for production of p-aminostyrene. (34) Two intermediates can act as ligands for metabolite-dependent riboregulators, and three promoter sites of control. The optimization problem has 16 continuous decision variables and 27 circuit architectures. The substrate S is converted by enzymes A, B, and C to X1, which is then converted by E to X2. The toxic substrate X2 is then pumped out of the cell via an efflux pump to form the product P. Both X1 and X2 can act on the transcription factors TF1 and TF2. Vin is the constant influx to the engineered pathway from native metabolism. (B) Representative run of the BayesOpt algorithm; the method samples many architectures before settling on the optimal one. Pie charts show continued exploration of a large number of architectures. The winning architecture is shown in the inset. (C) The p-aminostyrene pathway has several forms of substrate, protein, and enzyme toxicity expressed via a toxicity factor τ (see eq 6). To explore the effects of protein and metabolite toxicity, we perturbed the toxicity factor. Metabolite-induced toxicity was perturbed on the nominal range (1 × 10–3, 1 × 10–4) and protein-induced toxicity on the range (1 × 10–4, 1 × 101) respectively. Both ranges were selected to match the ranges provided in the literature. (34) Latin Hypercube sampling was used to generate N = 100 perturbed parameter values, and the optimal solutions were compared to an equal number of background solutions using the nominal parameter values. (D) Visualization of the optimal solutions; scatter plot of principal components of the optimal parameter values for the model with perturbed toxicity parameters (N = 100). Contour plots show the background distribution of parameter values.

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In addition to expression of heterologous enzymes, the accumulation of toxic intermediates is another major source of genetic burden to host organisms. The p-AS model has several sources of toxicity present in the pathway. (34,45) The intermediate p-ACA and the efflux pump used to remove p-ACA from cells are both cytotoxic, while another intermediate, p-AF, leaks from cells. (34) The pathway enzyme L-Amino Acid Oxidase (LAAO) depletes key aromatic amino acid metabolites and creates toxic hydrogen peroxide as a byproduct. The model incorporates these various types of toxicity in the form of a toxicity factor τ. This toxicity factor is of the form
τ = k i k i + pACA t a + P efflux t p + LAAO t l
(6)
where tl, ta, and tp are chemical-specific toxicity factors. Enzyme-induced toxicity tl scales the key metabolite depletion rate driven by the enzyme LAAO. Metabolite-induced toxicity ta scales the impact of toxic intermediate p-ACA concentration. Finally, protein-induced toxicity tp reflects the toxicity caused by efflux pump expression. The toxicity factor acts as a scaling coefficient on the pathway synthesis, degradation, and folding reaction rates.
Despite the complexity and size of the p-AS model, we observe that BayesOpt explores many of the 27 possible architectures and converges to a low value of the objective function (Figure 4B); this was also achieved at a reasonable computational cost (mean run time under 2 min). The best architecture selected in the sample run was a double upstream repression, single downstream activation loop controlled by p-AF (Figure 4B, inset), but there is no clear best architecture when the optimization is run many times. No architecture is optimal for more than 15% of test runs, demonstrating that there are combinations of architectures and parameter values that achieve a similar optimal loss. We also found that several architectures can display oscillatory solutions, which we chose to exclude from the search by applying a peak detection algorithm (48) and adding a large regularization term to the loss.
To investigate the robustness to chemical toxicity, we perturbed the metabolite-induced toxicity ta and protein-induced toxicity tp in eq 6. The optimal loss values were found to be comparable between perturbed and background systems (Figure 4C). Additionally, when projected onto a 2-dimensional space using principal component analysis, the distribution of background parameter values was similar to the distribution of perturbed solutions, indicating that the perturbation did not significantly affect the optimal parameters selected (Figure 4D). (49) The p-AS pathway lies at the far end of what is currently possible to build experimentally and thus illustrates the broad applicability of BayesOpt to realistic design tasks in metabolic engineering.

3. Discussion

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Progress in synthetic biology allows the construction of circuits of increased complexity across various levels of biological organization. However, large design spaces and multiple scales can become substantial challenges for the design of functional systems. In this paper, we presented the use of Bayesian optimization for the design of biological circuits. The method can rapidly find circuit architectures and parameters that optimize a performance objective that captures the target circuit functionality.
The method is particularly well suited for cases in which the multiple scales prevent efficient simulation of ODE models. Gene circuits designed to control metabolic pathways are an excellent example of such multiscale systems, as they combine fast metabolic time scales with the much slower dynamics of gene expression. Moreover, the choice of regulators, control points, and control architectures adds multiple degrees of freedom that are infeasible to explore experimentally. Previously implemented metabolic control systems have been built primarily based on application-specific knowledge of pathway features. (27,50) We have shown that Bayesian optimization can aid the design of such systems prior to implementation and serve as tools for in silico screening of competing designs that may have similar performance but entail different cost of wetlab implementation. We showed the efficiency and scalability of the method in several real world case studies from metabolic engineering. In particular, the p-aminostyrene pathway is more complex than systems typically implemented in literature so far, which suggests that the method is applicable across a range of relevant design tasks.
We anticipate several novel applications of this work to other problem areas where discovery or tuning of multiscale circuits has been previously infeasible. For instance, this method could be employed to fit temporal circuit dynamics to data or discern which of several discrete circuit mechanisms most closely matches observed behavior. As with other design strategies based on ODE models, a challenge of our approach is the significant domain knowledge required to construct models for a target pathway, both in terms of the enzyme kinetics and the downstream metabolic processes that affect pathway activity. Machine learning has already proved useful in a range of metabolic engineering tasks (51) and is gaining substantial interest in other areas of synthetic biology. (52,53) In this paper we have shown how such methods can also benefit dynamic pathway engineering by using optimization as a means to navigate the design space prior to system prototyping.

4. Methods

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4.1. Bayesian Optimization

We employed the Bayesian optimization routine implemented in the Python HyperOpt package. (37) Bayesian optimization is commonly employed for hyperparameter tuning in deep neural networks. We employed Expected Improvement as an acquisition function and a tree-structured Parzen estimator (TPE) as a nonparametric statistical model for the loss landscape. We performed a grid search over the TPE hyperparameter γ which controls the balance between exploration and exploitation but found little impact on the algorithm performance; we thus used the default value of γ = 15 (Supplementary Figure S1).
Constraints on the continuous and discrete decision variables were incorporated directly into the HyperOpt search space. At each run of the Bayesian optimization routine, the initial guess for the continuous decision variables were sampled from uniform distributions, with upper and lower bounds were taken from literature. (10,34,44) Architectures were chosen uniformly from the set of architectures without positive feedback loops.

4.2. Model Pathways

We considered four exemplar pathways modeled via ordinary differential equations (ODEs): the toy system in Figure 1C, the glucaric acid pathway in Figure 2A, the fatty acid pathway in Figure 3A, and the p-aminostyrene pathway in Figure 4A. Table 1 contains a summary of the four considered models. In all cases, pathway models include ODEs for both metabolites and pathway enzymes. In each case, we define the various control architectures and incorporate them as discrete decision variables in the optimization problem, i.e., pd in eq 1; the continuous decision variables, i.e., pc in eq 1, appear in the expression rates of the pathway enzymes. For the toy model and the glucaric acid pathway, enzyme expression was parametrized using a lumped Hill equation model to describe the interaction between a regulatory metabolite and a transcription factor. For the fatty acid and p-aminostyrene pathways, expression rates were parametrized with bespoke nonlinear functions describing specific biochemical processes. The discrete control architectures were defined in two different ways. For the toy, glucaric acid, and p-aminostyrene models, the architectures were defined using a binary matrix to encode the mode of transcriptional control. For the fatty acid model we instead defined each architecture as a categorical choice and switched between model functions correspondingly. We note that the p-aminostyrene pathway also contains ODEs for mRNA abundance and folded/unfolded proteins. All models and their parameters are described in the Supporting Information.
Table 1. Summary of Pathway Models Studied in This Paper. The ODEs in the p-Aminostyrene Pathway Also Include mRNA and Folding Dynamics
product parameters (pc) architectures (pd) metabolites enzymes ODEs
toy pathway 4 4 2 2 4
glucaric acid (10,26) 4 4 3 2 5
fatty acid (33) 2 4 1 2 3
p-aminostyrene (34) 16 27 7 6 23
The ODE models were solved with scikit-odes, a Python wrapper for the SUNDIALS suite of solvers. (54) In all cases, the initial concentrations of heterologous pathway enzymes were assumed to be zero. Initial concentrations for native metabolites were determined by first solving a model without the heterologous enzymes up to steady state. Simulation times and initial conditions are detailed in the Supporting Information for each model.

4.3. Loss Function

In all cases the loss function J in eq 3 was instanced to each pathway. Generally, the loss is defined as a linear combination of costs and benefits of pathway activity so as to balance opposing design goals commonly found in applications. Since both components of the loss function have different magnitudes, for each model we first swept the weights α1 and α2 across many model simulations, and chose values that led to similar values for both components; this prevents the optimizer from biasing the search towards low loss values caused by the scaling effects alone. For the fatty acid model in Figure 3 we also optimized the circuit rise time and overshoot % defined in eq 5. Details on all objective functions can found in the Supporting Information.

Data Availability

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The Python code for this paper is available on Zenodo at https://doi.org/10.5281/zenodo.7926205.

Supporting Information

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The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acssynbio.3c00120.

  • Details of model construction for toy, glucaric acid, fatty acid, and p-aminostyrene models, including parameter values and model equations; Additional supporting figures related to hyperparameter tuning (PDF)

Terms & Conditions

Most electronic Supporting Information files are available without a subscription to ACS Web Editions. Such files may be downloaded by article for research use (if there is a public use license linked to the relevant article, that license may permit other uses). Permission may be obtained from ACS for other uses through requests via the RightsLink permission system: http://pubs.acs.org/page/copyright/permissions.html.

Author Information

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  • Corresponding Author
    • Diego A. Oyarzún - School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, U.K.;  The Alan Turing Institute, London NW1 2DB, U.K.;  School of Biological Sciences, University of Edinburgh, Edinburgh EH9 3JH, U.K.;  Orcidhttps://orcid.org/0000-0002-0381-5278;  Email: [email protected]
  • Authors
    • Charlotte Merzbacher - School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, U.K.;  Orcidhttps://orcid.org/0009-0000-2853-1864
    • Oisin Mac Aodha - School of Informatics, University of Edinburgh, Edinburgh EH8 9AB, U.K.;  The Alan Turing Institute, London NW1 2DB, U.K.
  • Author Contributions

    CM built the optimization pipeline, ran simulations, and produced figures. CM and DAO analyzed results. DAO and OMA supervised the research.

  • Funding

    CM and DAO were supported by the United Kingdom Research and Innovation (grant EP/S02431X/1, UKRI Centre for Doctoral Training in Biomedical AI).

  • Notes
    The authors declare no competing financial interest.

References

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    Robustness, and the ability to function and thrive amid changing and unfavorable environments, is a fundamental requirement for living systems. Until now it has been an open question how large and complex biological networks can exhibit robust behaviors, such as perfect adaptation to a variable stimulus, since complexity is generally associated with fragility. Here we report that all networks that exhibit robust perfect adaptation (RPA) to a persistent change in stimulus are decomposable into well-defined modules, of which there exist two distinct classes. These two modular classes represent a topological basis for all RPA-capable networks, and generate the full set of topological realizations of the internal model principle for RPA in complex, self-organizing, evolvable bionetworks. This unexpected result supports the notion that evolutionary processes are empowered by simple and scalable modular design principles that promote robust performance no matter how large or complex the underlying networks become.
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    Drengstig, T.; Ueda, H. R.; Ruoff, P. Predicting perfect adaptation motifs in reaction kinetic networks. J. Phys. Chem. B 2008, 112, 16752– 16758,  DOI: 10.1021/jp806818c
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    Predicting Perfect Adaptation Motifs in Reaction Kinetic Networks
    Drengstig, Tormod; Ueda, Hiroki R.; Ruoff, Peter
    Journal of Physical Chemistry B (2008), 112 (51), 16752-16758CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
    A review. Adaptation and compensation mechanisms are important to keep organisms fit in a changing environment. "Perfect adaptation" describes an organism's response to an external stepwise perturbation by resetting some of its variables precisely to their original preperturbation values. Examples of perfect adaptation are found in bacterial chemotaxis, photoreceptor responses, or MAP kinase activities. Two concepts have evolved for how perfect adaptation may be understood. In one approach, so-called "robust perfect adaptation", the adaptation is a network property (due to integral feedback control), which is independent of rate const. values. In the other approach, which we have termed "nonrobust perfect adaptation", a fine-tuning of rate const. values is needed to show perfect adaptation. Although integral feedback describes robust perfect adaptation in general terms, it does not directly show where in a network perfect adaptation may be obsd. Using control theoretic methods, we are able to predict robust perfect adaptation sites within reaction kinetic networks and show that a prerequisite for robust perfect adaptation is that the network is open and irreversible. We applied the method on various reaction schemes and found that new (robust) perfect adaptation motifs emerge when considering suggested models of bacterial and eukaryotic chemotaxis.
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    Woods, M. L.; Leon, M.; Perez-Carrasco, R.; Barnes, C. P. A statistical approach reveals designs for the most robust stochastic gene oscillators. ACS Synth. Biol. 2016, 5, 459– 470,  DOI: 10.1021/acssynbio.5b00179
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    A Statistical Approach Reveals Designs for the Most Robust Stochastic Gene Oscillators
    Woods, Mae L.; Leon, Miriam; Perez-Carrasco, Ruben; Barnes, Chris P.
    ACS Synthetic Biology (2016), 5 (6), 459-470CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
    The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed. Can we make genetic oscillators arbitrarily robust. These questions are tech. challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and conc. on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the no. of interactions, the presence of autoregulation, and degrdn. of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding addnl. feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biol.
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    Gonzalez, J.; Longworth, J.; James, D. C.; Lawrence, N. D. Bayesian optimization for synthetic gene design. arXiv , May 7, 2015.  DOI: 10.48550/arXiv.1505.01627 .
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    Shen, J.; Liu, F.; Tu, Y.; Tang, C. Finding gene network topologies for given biological function with recurrent neural network. Nat. Commun. 2021, 12, 1– 10,  DOI: 10.1038/s41467-021-23420-5
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    Zhang, F.; Carothers, J. M.; Keasling, J. D. Design of a dynamic sensor-regulator system for production of chemicals and fuels derived from fatty acids. Nat. Biotechnol. 2012, 30, 354– 359,  DOI: 10.1038/nbt.2149
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    Design of a dynamic sensor-regulator system for production of chemicals and fuels derived from fatty acids
    Zhang, Fuzhong; Carothers, James M.; Keasling, Jay D.
    Nature Biotechnology (2012), 30 (4), 354-359CODEN: NABIF9; ISSN:1087-0156. (Nature Publishing Group)
    Microbial prodn. of chems. is now an attractive alternative to chem. synthesis. Current efforts focus mainly on constructing pathways to produce different types of mols. However, there are few strategies for engineering regulatory components to improve product titers and conversion yields of heterologous pathways. Here we developed a dynamic sensor-regulator system (DSRS) to produce fatty acid-based products in Escherichia coli, and demonstrated its use for biodiesel prodn. The DSRS uses a transcription factor that senses a key intermediate and dynamically regulates the expression of genes involved in biodiesel prodn. This DSRS substantially improved the stability of biodiesel-producing strains and increased the titer to 1.5 g/l and the yield threefold to 28% of the theor. max. Given the large no. of natural sensors available, this DSRS strategy can be extended to many other biosynthetic pathways to balance metab., thereby increasing product titers and conversion yields and stabilizing prodn. hosts.
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    Oyarzún, D. A.; Stan, G.-B. V. Synthetic gene circuits for metabolic control: design trade-offs and constraints. J. R. Soc., Interface 2013, 10, 20120671,  DOI: 10.1098/rsif.2012.0671
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    Synthetic gene circuits for metabolic control: design trade-offs and constraints
    Oyarzun Diego A; Stan Guy-Bart V
    Journal of the Royal Society, Interface (2013), 10 (78), 20120671 ISSN:.
    A grand challenge in synthetic biology is to push the design of biomolecular circuits from purely genetic constructs towards systems that interface different levels of the cellular machinery, including signalling networks and metabolic pathways. In this paper, we focus on a genetic circuit for feedback regulation of unbranched metabolic pathways. The objective of this feedback system is to dampen the effect of flux perturbations caused by changes in cellular demands or by engineered pathways consuming metabolic intermediates. We consider a mathematical model for a control circuit with an operon architecture, whereby the expression of all pathway enzymes is transcriptionally repressed by the metabolic product. We address the existence and stability of the steady state, the dynamic response of the network under perturbations, and their dependence on common tuneable knobs such as the promoter characteristic and ribosome binding site (RBS) strengths. Our analysis reveals trade-offs between the steady state of the enzymes and the intermediates, together with a separation principle between promoter and RBS design. We show that enzymatic saturation imposes limits on the parameter design space, which must be satisfied to prevent metabolite accumulation and guarantee the stability of the network. The use of promoters with a broad dynamic range and a small leaky expression enlarges the design space. Simulation results with realistic parameter values also suggest that the control circuit can effectively upregulate enzyme production to compensate flux perturbations.
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    Xu, P.; Li, L.; Zhang, F.; Stephanopoulos, G.; Koffas, M. Improving fatty acids production by engineering dynamic pathway regulation and metabolic control. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 11299– 11304,  DOI: 10.1073/pnas.1406401111
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    Improving fatty acids production by engineering dynamic pathway regulation and metabolic control
    Xu, Peng; Li, Lingyun; Zhang, Fuming; Stephanopoulos, Gregory; Koffas, Mattheos
    Proceedings of the National Academy of Sciences of the United States of America (2014), 111 (31), 11299-11304CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Global energy demand and environmental concerns have stimulated increasing efforts to produce carbon-neutral fuels directly from renewable resources. Microbially derived aliph. hydrocarbons, the petroleum-replica fuels, have emerged as promising alternatives to meet this goal. However, engineering metabolic pathways with high productivity and yield requires dynamic redistribution of cellular resources and optimal control of pathway expression. Here we report a genetically encoded metabolic switch that enables dynamic regulation of fatty acids (FA) biosynthesis in Escherichia coli. The engineered strains were able to dynamically compensate the crit. enzymes involved in the supply and consumption of malonyl-CoA and efficiently redirect carbon flux toward FA biosynthesis. Implementation of this metabolic control resulted in an oscillatory malonyl-CoA pattern and a balanced metab. between cell growth and product formation, yielding 15.7- and 2.1-fold improvement in FA titer compared with the wild-type strain and the strain carrying the uncontrolled metabolic pathway. This study provides a new paradigm in metabolic engineering to control and optimize metabolic pathways facilitating the high-yield prodn. of other malonyl-CoA-derived compds.
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    Dunlop, M. J.; Keasling, J. D.; Mukhopadhyay, A. A model for improving microbial biofuel production using a synthetic feedback loop. Systems and Synthetic Biology 2010, 4, 95– 104,  DOI: 10.1007/s11693-010-9052-5
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    A model for improving microbial biofuel production using a synthetic feedback loop
    Dunlop Mary J; Keasling Jay D; Mukhopadhyay Aindrila
    Systems and synthetic biology (2010), 4 (2), 95-104 ISSN:.
    Cells use feedback to implement a diverse range of regulatory functions. Building synthetic feedback control systems may yield insight into the roles that feedback can play in regulation since it can be introduced independently of native regulation, and alternative control architectures can be compared. We propose a model for microbial biofuel production where a synthetic control system is used to increase cell viability and biofuel yields. Although microbes can be engineered to produce biofuels, the fuels are often toxic to cell growth, creating a negative feedback loop that limits biofuel production. These toxic effects may be mitigated by expressing efflux pumps that export biofuel from the cell. We developed a model for cell growth and biofuel production and used it to compare several genetic control strategies for their ability to improve biofuel yields. We show that controlling efflux pump expression directly with a biofuel-responsive promoter is a straightforward way of improving biofuel production. In addition, a feed forward loop controller is shown to be versatile at dealing with uncertainty in biofuel production rates.
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    Doong, S. J.; Gupta, A.; Prather, K. L. Layered dynamic regulation for improving metabolic pathway productivity in Escherichia coli. Proc. Natl. Acad. Sci. U. S. A. 2018, 115, 2964– 2969,  DOI: 10.1073/pnas.1716920115
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    Layered dynamic regulation for improving metabolic pathway productivity in Escherichia coli
    Doong, Stephanie J.; Gupta, Apoorv; Prather, Kristala L. J.
    Proceedings of the National Academy of Sciences of the United States of America (2018), 115 (12), 2964-2969CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
    Microbial prodn. of value-added chems. from biomass is a sustainable alternative to chem. synthesis. To improve product titer, yield, and selectivity, the pathways engineered into microbes must be optimized. One strategy for optimization is dynamic pathway regulation, which modulates expression of pathwayrelevant enzymes over the course of fermn. Metabolic engineers have used dynamic regulation to redirect endogenous flux toward product formation, balance the prodn. and consumption rates of key intermediates, and suppress prodn. of toxic intermediates until later in the fermn. Most cases, however, have utilized a single strategy for dynamically regulating pathway fluxes. Here we layer two orthogonal, autonomous, and tunable dynamic regulation strategies to independently modulate expression of two different enzymes to improve prodn. of D-glucaric acid from a heterologous pathway. The first strategy uses a previously described pathway-independent quorum sensing system to dynamically knock down glycolytic flux and redirect carbon into prodn. of glucaric acid, thereby switching cells from "growth" to "prodn." mode. The second strategy, developed in this work, uses a biosensor for myo-inositol (MI), an intermediate in the glucaric acid prodn. pathway, to induce expression of a downstream enzyme upon sufficient buildup of MI. The latter, pathway-dependent strategy leads to a 2.5-fold increase in titer when used in isolation and a fourfold increase when added to a strain employing the former, pathway-independent regulatory system. The dual-regulation strain produces nearly 2 g/L glucaric acid, representing the highest glucaric acid titer reported to date in Escherichia coli K-12 strains.
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    Ni, C.; Dinh, C. V.; Prather, K. L. Dynamic Control of Metabolism. Annu. Rev. Chem. Biomol. Eng. 2021, 12, 519,  DOI: 10.1146/annurev-chembioeng-091720-125738
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    Dynamic Control of Metabolism
    Ni, Cynthia; Dinh, Christina V.; Prather, Kristala L. J.
    Annual Review of Chemical and Biomolecular Engineering (2021), 12 (), 519-541CODEN: ARCBCY; ISSN:1947-5438. (Annual Reviews)
    A review. Metabolic engineering reprograms cells to synthesize value-added products. In doing so, endogenous genes are altered and heterologous genes can be introduced to achieve the necessary enzymic reactions. Dynamic regulation of metabolic flux is a powerful control scheme to alleviate and overcome the competing cellular objectives that arise from the introduction of these prodn. pathways. This review explores dynamic regulation strategies that have demonstrated significant prodn. benefits by targeting the metabolic node corresponding to a specific challenge. We summarize the stimulus-responsive control circuits employed in these strategies that det. the criterion for actuating a dynamic response and then examine the points of control that couple the stimulus-responsive circuit to a shift in metabolic flux.
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    Hartline, C. J.; Schmitz, A. C.; Han, Y.; Zhang, F. Dynamic control in metabolic engineering: Theories, tools, and applications. Metabolic Engineering 2021, 63, 126– 140,  DOI: 10.1016/j.ymben.2020.08.015
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    Dynamic control in metabolic engineering: Theories, tools, and applications
    Hartline, Christopher J.; Schmitz, Alexander C.; Han, Yichao; Zhang, Fuzhong
    Metabolic Engineering (2021), 63 (), 126-140CODEN: MEENFM; ISSN:1096-7176. (Elsevier B.V.)
    A review. Metabolic engineering has allowed the prodn. of a diverse no. of valuable chems. using microbial organisms. Many biol. challenges for improving bio-prodn. exist which limit performance and slow the commercialization of metabolically engineered systems. Dynamic metabolic engineering is a rapidly developing field that seeks to address these challenges through the design of genetically encoded metabolic control systems which allow cells to autonomously adjust their flux in response to their external and internal metabolic state. This review first discusses theor. works which provide mechanistic insights and design choices for dynamic control systems including two-stage, continuous, and population behavior control strategies. Next, we summarize mol. mechanisms for various sensors and actuators which enable dynamic metabolic control in microbial systems. Finally, important applications of dynamic control to the prodn. of several metabolite products are highlighted, including fatty acids, aroms., and terpene compds. Altogether, this review provides a comprehensive overview of the progress, advances, and prospects in the design of dynamic control systems for improved titer, rate, and yield metrics in metabolic engineering.
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    Tonn, M. K.; Thomas, P.; Barahona, M.; Oyarzún, D. A. Stochastic modelling reveals mechanisms of metabolic heterogeneity. Commun. Biol. 2019, 2, 108,  DOI: 10.1038/s42003-019-0347-0
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    Stochastic modelling reveals mechanisms of metabolic heterogeneity
    Tonn Mona K; Thomas Philipp; Barahona Mauricio; Oyarzun Diego A; Oyarzun Diego A; Oyarzun Diego A
    Communications biology (2019), 2 (), 108 ISSN:.
    Phenotypic variation is a hallmark of cellular physiology. Metabolic heterogeneity, in particular, underpins single-cell phenomena such as microbial drug tolerance and growth variability. Much research has focussed on transcriptomic and proteomic heterogeneity, yet it remains unclear if such variation permeates to the metabolic state of a cell. Here we propose a stochastic model to show that complex forms of metabolic heterogeneity emerge from fluctuations in enzyme expression and catalysis. The analysis predicts clonal populations to split into two or more metabolically distinct subpopulations. We reveal mechanisms not seen in deterministic models, in which enzymes with unimodal expression distributions lead to metabolites with a bimodal or multimodal distribution across the population. Based on published data, the results suggest that metabolite heterogeneity may be more pervasive than previously thought. Our work casts light on links between gene expression and metabolism, and provides a theory to probe the sources of metabolite heterogeneity.
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    Mannan, A. A.; Liu, D.; Zhang, F.; Oyarzún, D. A. Fundamental Design Principles for Transcription-Factor-Based Metabolite Biosensors. ACS Synth. Biol. 2017, 6, 1851– 1859,  DOI: 10.1021/acssynbio.7b00172
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    Fundamental Design Principles for Transcription-Factor-Based Metabolite Biosensors
    Mannan, Ahmad A.; Liu, Di; Zhang, Fuzhong; Oyarzun, Diego A.
    ACS Synthetic Biology (2017), 6 (10), 1851-1859CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
    Metabolite biosensors are central to current efforts toward precision engineering of metab. Although most research has focused on building new biosensors, their tunability remains poorly understood and is fundamental for their broad applicability. Here we asked how genetic modifications shape the dose-response curve of biosensors based on metabolite-responsive transcription factors. Using the lac system in Escherichia coli as a model system, we built promoter libraries with variable operator sites that reveal interdependencies between biosensor dynamic range and response threshold. We developed a phenomenol. theory to quantify such design constraints in biosensors with various architectures and tunable parameters. Our theory reveals a maximal achievable dynamic range and exposes tunable parameters for orthogonal control of dynamic range and response threshold. Our work sheds light on fundamental limits of synthetic biol. designs and provides quant. guidelines for biosensor design in applications such as dynamic pathway control, strain optimization, and real-time monitoring of metab.
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    Zhou, L.-B.; Zeng, A.-P. Exploring Lysine Riboswitch for Metabolic Flux Control and Improvement of L-Lysine Synthesis in Corynebacterium glutamicum. ACS Synth. Biol. 2015, 4, 729– 734,  DOI: 10.1021/sb500332c
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    Exploring Lysine Riboswitch for Metabolic Flux Control and Improvement of L-Lysine Synthesis in Corynebacterium glutamicum
    Zhou, Li-Bang; Zeng, An-Ping
    ACS Synthetic Biology (2015), 4 (6), 729-734CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
    Riboswitch, a regulatory part of an mRNA mol. that can specifically bind a metabolite and regulate gene expression, is attractive for engineering biol. systems, esp. for the control of metabolic fluxes in industrial microorganisms. Here, we demonstrate the use of lysine riboswitch and intracellular L-lysine as a signal to control the competing but essential metabolic by-pathways of lysine biosynthesis. To this end, we first examd. the natural lysine riboswitches of Eschericia coli (ECRS) and Bacillus subtilis (BSRS) to control the expression of citrate synthase (gltA) and thus the metabolic flux in the tricarboxylic acid (TCA) cycle in E. coli. ECRS and BSRS were then successfully used to control the gltA gene and TCA cycle activity in a lysine producing strain Corynebacterium glutamicum LP917, resp. Compared with the strain LP917, the growth of both lysine riboswitch-gltA mutants was slower, suggesting a reduced TCA cycle activity. The lysine prodn. was 63% higher in the mutant ECRS-gltA and 38% higher in the mutant BSRS-gltA, indicating a higher metabolic flux into the lysine synthesis pathway. This is the first report on using an amino acid riboswitch for improvement of lysine biosynthesis. The lysine riboswitches can be easily adapted to dynamically control other essential but competing metabolic pathways or even be engineered as an "on-switch" to enhance the metabolic fluxes of desired metabolic pathways.
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    Chaves, M.; Oyarzún, D. A. Dynamics of complex feedback architectures in metabolic pathways. Automatica 2019, 99, 323– 332,  DOI: 10.1016/j.automatica.2018.10.046
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    Liu, D.; Zhang, F. Metabolic feedback circuits provide rapid control of metabolite dynamics. ACS Synth. Biol. 2018, 7, 347– 356,  DOI: 10.1021/acssynbio.7b00342
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    Metabolic Feedback Circuits Provide Rapid Control of Metabolite Dynamics
    Liu, Di; Zhang, Fuzhong
    ACS Synthetic Biology (2018), 7 (2), 347-356CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
    Metab. constitutes the basis of life, and the dynamics of metab. dictate various cellular processes. However, exactly how metabolite dynamics are controlled remains poorly understood. By studying an engineered fatty acid-producing pathway as a model, we found that upon transcription activation a metabolic product from an unregulated pathway required seven cell cycles to reach to its steady state level, with the speed mostly limited by enzyme expression dynamics. To overcome this limit, we designed metabolic feedback circuits (MeFCs) with three different architectures, and exptl. measured and modeled their metabolite dynamics. Our engineered MeFCs could dramatically shorten the rise-time of metabolites, decreasing it by as much as 12-fold. The findings of this study provide a systematic understanding of metabolite dynamics in different architectures of MeFCs and have potentially immense applications in designing synthetic circuits to improve the productivities of engineered metabolic pathways.
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    Stevens, J. T.; Carothers, J. M. Designing RNA-based genetic control systems for efficient production from engineered metabolic pathways. ACS Synth. Biol. 2015, 4, 107– 115,  DOI: 10.1021/sb400201u
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    Designing RNA-Based Genetic Control Systems for Efficient Production from Engineered Metabolic Pathways
    Stevens, Jason T.; Carothers, James M.
    ACS Synthetic Biology (2015), 4 (2), 107-115CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
    Engineered metabolic pathways can be augmented with dynamic regulatory controllers to increase prodn. titers by minimizing toxicity and helping cells maintain homeostasis. We investigated the potential for dynamic RNA-based genetic control systems to increase prodn. through simulation anal. of an engineered p-aminostyrene (p-AS) pathway in E. coli. To map the entire design space, we formulated 729 unique mechanistic models corresponding to all of the possible control topologies and mechanistic implementations in the system under study. Two thousand sampled simulations were performed for each of the 729 system designs to relate the potential effects of dynamic control to increases in p-AS prodn. (total of 3 × 106 simulations). Our anal. indicates that dynamic control strategies employing aptazyme-regulated expression devices (aREDs) can yield >10-fold improvements over static control. We uncovered generalizable trends in successful control architectures and found that highly performing RNA-based control systems are exptl. tractable. Analyzing the metabolic control state space to predict optimal genetic control strategies promises to enhance the design of metabolic pathways.
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    Frazier, P. I. A tutorial on Bayesian optimization. arXiv , July 8, 2018.  DOI: 10.48550/arXiv.1807.02811 .
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    Moon, T. S.; Yoon, S.-H.; Lanza, A. M.; Roy-Mayhew, J. D.; Prather, K. L. J. Production of glucaric acid from a synthetic pathway in recombinant Escherichia coli. Applied and Environmental Microbiology 2009, 75, 589– 595,  DOI: 10.1128/AEM.00973-08
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    Production of glucaric acid from a synthetic pathway in recombinant Escherichia coli
    Moon, Tae Seok; Yoon, Sang-Hwal; Lanza, Amanda M.; Roy-Mayhew, Joseph D.; Jones-Prather, Kristala L.
    Applied and Environmental Microbiology (2009), 75 (3), 589-595CODEN: AEMIDF; ISSN:0099-2240. (American Society for Microbiology)
    A synthetic pathway has been constructed for the prodn. of glucuronic and glucaric acids from glucose in Escherichia coli. Coexpression of the genes encoding myo-inositol-1-phosphate synthase (Ino1) from Saccharomyces cerevisiae and myo-inositol oxygenase (MIOX) from mice led to prodn. of glucuronic acid through the intermediate myo-inositol. Glucuronic acid concns. up to 0.3 g/L were measured in the culture broth. The activity of MIOX was rate limiting, resulting in the accumulation of both myo-inositol and glucuronic acid as final products, in approx. equal concns. Inclusion of a third enzyme, uronate dehydrogenase (Udh) from Pseudomonas syringae, facilitated the conversion of glucuronic acid to glucaric acid. The activity of this recombinant enzyme was more than 2 orders of magnitude higher than that of Ino1 and MIOX and increased overall flux through the pathway such that glucaric acid concns. in excess of 1 g/L were obsd. This represents a novel microbial system for the biol. prodn. of glucaric acid, a "top value-added chem." from biomass.
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    Bergstra, J.; Yamins, D.; Cox, D. Making a science of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures. In International Conference on Machine Learning; ICML, 2013; pp 115– 123.
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    Snoek, J.; Larochelle, H.; Adams, R. P. Practical bayesian optimization of machine learning algorithms. In Advances in Neural Information Processing Systems; NeurIPS, 2012; Vol. 25.
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    Enzymes, representing the largest and by far most complex group of proteins, play an essential role in all processes of life, including metab., gene expression, cell division, the immune system, and others. Their function, also connected to most diseases or stress control makes them interesting targets for research and applications in biotechnol., medical treatments, or diagnosis. Their functional parameters and other properties are collected, integrated, and made available to the scientific community in the BRaunschweig ENzyme DAtabase (BRENDA). In the last 30 years BRENDA has developed into one of the most highly used biol. databases worldwide. The data contents, the process of data acquisition, data integration and control, the ways to access the data, and visualizations provided by the website are described and discussed.
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  1. Shanna Gu, Fuzhou Zhu, Lin Zhang, Jianping Wen. Mid–Long Chain Dicarboxylic Acid Production via Systems Metabolic Engineering: Progress and Prospects. Journal of Agricultural and Food Chemistry 2024, 72 (11) , 5555-5573. https://doi.org/10.1021/acs.jafc.4c00002
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  • Abstract

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    Figure 1

    Figure 1. Bayesian optimization for the design of circuit architectures and parameters. (A) Previous optimization methods have focused on genetic circuits in isolation from other cellular processes. For multiscale circuits, optimization approaches become infeasible due to the difficulty of simulating stiff dynamical systems in many locations of the design space; a common example of such multiscale systems are gene circuits that control metabolic production. (3) We propose the use of Bayesian optimization (BayesOpt) for efficient optimization of architectures and parameters in multiscale circuits. (B) Schematic of a mixed-integer Bayesian optimization loop; the objective function is regarded a random variable to be optimized over an input space comprised of continuous parameters and a set of discrete circuit architectures. At each iteration, the algorithm computes the value of the objective function from the solution of an ordinary differential equation (ODE) model at a single location in the input space. The algorithm learns the shape of the objective landscape using a nonparametric statistical model, (37) which is employed to propose a new location in the input space through an acquisition function designed to balance exploration and exploitation of the input space; more details in the Methods. The algorithm iteratively learns the shape of the performance landscape until convergence to a global optimum. (C) Example metabolic pathway under gene regulation. We consider three negative feedback architectures plus open loop control; the architectures are named based on the net effect of the metabolite on gene expression. The intermediate X1 binds a transcription factor (TF) that controls the expression of pathway enzymes, either as an activator or repressor. Vin is the constant influx to the engineered pathway from native metabolism. The TF dose-response curve (at right) is described by three parameters, ki, θi, and ni, where i = 1, 2. The aim is to find designs with optimal architecture and dose-response parameters (ki, θi); for simplicity the Hill coefficient was fixed to ni = 2. (D) Performance landscapes of the four feasible circuit architectures. We exclude architectures with positive feedback loops as these are prone to multistability. (47) The shape of the performance landscape defined in eq 3 shows substantial variation across the four architectures. This leads to a highly nonconvex mixed-integer optimization problem. Heatmaps show the value of the objective J computed on a regular grid of the indicated parameters. (E) Comparison of BayesOpt against other strategies using the toy model as a benchmark; lower objective function values are better. Shown are the results for random sampling (N = 1,000 samples), grid search (N = 40,000), a genetic algorithm (55) (N = 100 individuals, N = 1,000 generations), and a gradient-based optimizer to find optimal continuous parameter values for each architecture. (48)

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    Figure 2. Robustness of optimal circuits to parameter uncertainty. (A) Schematic of a dynamic pathway for production of glucaric acid in Escherichia coli. (26) The pathway includes allosteric inhibition and export of an intermediate to the extracellular space. The core pathway components myoinositol (MI) and glucaric acid (GA) are modeled explicitly, as are the enzymes Ino1 and MIOX. The enzyme SuhB is not rate-limiting and is not modeled explicitly. Vin is the constant influx to the engineered pathway from native metabolism. As in Figure 1C, the architectures are named based on the net effect of the metabolite on gene expression. (B) Sample run of the BayesOpt algorithm for 1,000 iterations of the loop in Figure 1B. Black line shows the descent on the value of the objective function. Dots show all samples colored by architecture; pie charts show the fraction of architectures explored by the algorithm, and the fraction of samples taken from the majority architecture (dual control). The first quarter of the run had the most exploration of architectures other than dual control, with 38.6% of samples coming from nonmajority architectures. This percentage steadily decreased over the iterations but did not drop below 20%, illustrating the global nature of the optimization routine. (C) To examine the robustness of the optimal solutions to parameter uncertainty, we computed optimal solutions for many perturbed parameters of the allosteric activation of MIOX by its substrate myoinositol (MI). Strip plot shows the best objective function values achieved for background and perturbed kinetic parameters (Vm,MIOX, aMIOX, ka,MIOX) in eq 4. Kinetic parameters were perturbed using Latin Hypercube sampling (56) in the range (−100%, +100%) of the nominal values (Supporting Information). We observed little difference between background and perturbed values; dashed line denotes the mean value of the objective function. Only one of the N = 100 runs for perturbed parameters failed to converge the optimum. (D) Optimal architectures across runs with background and perturbed parameter values. Both background and perturbed systems resulted in over 80% of runs selecting dual control as the optimal architecture. (E) Average dose-response curves and distribution of optimal parameters for the dual control architecture with perturbed allosteric parameters. The repressive and activatory loops have substantially different dose-response curves on average. The distributions of the dose-response parameters (right) show important variations in their mean and dispersion. The parameter ki and θi determine the maximal enzyme expression rate and regulatory threshold, respectively.

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    Figure 3

    Figure 3. Optimization of metabolite dynamics in a fatty acid synthesis pathway. (A) Pathway diagrams with various control architectures implemented in Escherichia coli. (33) The metabolic loop employs a metabolite-responsive transcription factor, whereas the gene loop includes only a repressor expressed on the same promoter as the enzyme. (B) Representative run of BayesOpt with cost-benefit objective showing the best objective function value (black line). All samples are colored by their architecture. Pie charts of each quarter of the run show continued exploration of all architectures despite clear stratification in losses. (C) Optimal trade-off curve between overshoot and rise time. The objective weight α was swept from α = 0.01 to α = 10,000 and BayesOpt was run for 100 iterations at each α value. The optimal parameter values were used to compute the rise time and overshoot for visualization. The inset shows three sample trajectories illustrating how different optimal architectures navigate the trade-off between overshoot and rise time.

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    Figure 4. Bayesian optimization in a complex pathway. (A) Schematic of pathway for production of p-aminostyrene. (34) Two intermediates can act as ligands for metabolite-dependent riboregulators, and three promoter sites of control. The optimization problem has 16 continuous decision variables and 27 circuit architectures. The substrate S is converted by enzymes A, B, and C to X1, which is then converted by E to X2. The toxic substrate X2 is then pumped out of the cell via an efflux pump to form the product P. Both X1 and X2 can act on the transcription factors TF1 and TF2. Vin is the constant influx to the engineered pathway from native metabolism. (B) Representative run of the BayesOpt algorithm; the method samples many architectures before settling on the optimal one. Pie charts show continued exploration of a large number of architectures. The winning architecture is shown in the inset. (C) The p-aminostyrene pathway has several forms of substrate, protein, and enzyme toxicity expressed via a toxicity factor τ (see eq 6). To explore the effects of protein and metabolite toxicity, we perturbed the toxicity factor. Metabolite-induced toxicity was perturbed on the nominal range (1 × 10–3, 1 × 10–4) and protein-induced toxicity on the range (1 × 10–4, 1 × 101) respectively. Both ranges were selected to match the ranges provided in the literature. (34) Latin Hypercube sampling was used to generate N = 100 perturbed parameter values, and the optimal solutions were compared to an equal number of background solutions using the nominal parameter values. (D) Visualization of the optimal solutions; scatter plot of principal components of the optimal parameter values for the model with perturbed toxicity parameters (N = 100). Contour plots show the background distribution of parameter values.

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      Brophy, Jennifer A. N.; Voigt, Christopher A.
      Nature Methods (2014), 11 (5), 508-520CODEN: NMAEA3; ISSN:1548-7091. (Nature Publishing Group)
      A review. Cells navigate environments, communicate and build complex patterns by initiating gene expression in response to specific signals. Engineers seek to harness this capability to program cells to perform tasks or create chems. and materials that match the complexity seen in nature. This review describes new tools that aid the construction of genetic circuits. Circuit dynamics can be influenced by the choice of regulators and changed with expression 'tuning knobs'. We collate the failure modes encountered when assembling circuits, quantify their impact on performance and review mitigation efforts. Finally, we discuss the constraints that arise from circuits having to operate within a living cell. Collectively, better tools, well-characterized parts and a comprehensive understanding of how to compose circuits are leading to a breakthrough in the ability to program living cells for advanced applications, from living therapeutics to the at. manufg. of functional materials.
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    2. 2
      Shaw, W. M.; Yamauchi, H.; Mead, J.; Gowers, G. O. F.; Bell, D. J.; Öling, D.; Larsson, N.; Wigglesworth, M.; Ladds, G.; Ellis, T. Engineering a Model Cell for Rational Tuning of GPCR Signaling. Cell 2019, 177, 782– 796,  DOI: 10.1016/j.cell.2019.02.023
      2
      Engineering a Model Cell for Rational Tuning of GPCR Signaling
      Shaw, William M.; Yamauchi, Hitoshi; Mead, Jack; Gowers, Glen-Oliver F.; Bell, David J.; Oling, David; Larsson, Niklas; Wigglesworth, Mark; Ladds, Graham; Ellis, Tom
      Cell (Cambridge, MA, United States) (2019), 177 (3), 782-796.e27CODEN: CELLB5; ISSN:0092-8674. (Cell Press)
      G protein-coupled receptor (GPCR) signaling is the primary method eukaryotes use to respond to specific cues in their environment. However, the relation between stimulus and response for each GPCR is difficult to predict due to diversity in natural signal transduction architecture and expression. Using genome engineering in yeast, the authors constructed an insulated, modular GPCR signal transduction system to study how the response to stimuli can be predictably tuned using synthetic tools. The authors delineated the contributions of a minimal set of key components via computational and exptl. refactoring, identifying simple design principles for rationally tuning the dose response. Using five different GPCRs, this enables cells and consortia to be engineered to respond to desired concns. of peptides, metabolites, and hormones relevant to human health. This work enables rational tuning of cell sensing while providing a framework to guide reprogramming of GPCR-based signaling in other systems.
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    3. 3
      Zhang, F.; Carothers, J. M.; Keasling, J. D. Design of a dynamic sensor-regulator system for production of chemicals and fuels derived from fatty acids. Nat. Biotechnol. 2012, 30, 354– 9,  DOI: 10.1038/nbt.2149
      3
      Design of a dynamic sensor-regulator system for production of chemicals and fuels derived from fatty acids
      Zhang, Fuzhong; Carothers, James M.; Keasling, Jay D.
      Nature Biotechnology (2012), 30 (4), 354-359CODEN: NABIF9; ISSN:1087-0156. (Nature Publishing Group)
      Microbial prodn. of chems. is now an attractive alternative to chem. synthesis. Current efforts focus mainly on constructing pathways to produce different types of mols. However, there are few strategies for engineering regulatory components to improve product titers and conversion yields of heterologous pathways. Here we developed a dynamic sensor-regulator system (DSRS) to produce fatty acid-based products in Escherichia coli, and demonstrated its use for biodiesel prodn. The DSRS uses a transcription factor that senses a key intermediate and dynamically regulates the expression of genes involved in biodiesel prodn. This DSRS substantially improved the stability of biodiesel-producing strains and increased the titer to 1.5 g/l and the yield threefold to 28% of the theor. max. Given the large no. of natural sensors available, this DSRS strategy can be extended to many other biosynthetic pathways to balance metab., thereby increasing product titers and conversion yields and stabilizing prodn. hosts.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC38XksVegt7Y%253D&md5=2f65b42ed0cba0c179950c5fc252057a
    4. 4
      Ma, W.; Trusina, A.; El-Samad, H.; Lim, W. A.; Tang, C. Defining network topologies that can achieve biochemical adaptation. Cell 2009, 138, 760– 773,  DOI: 10.1016/j.cell.2009.06.013
      4
      Defining network topologies that can achieve biochemical adaptation
      Ma, Wenzhe; Trusina, Ala; El-Samad, Hana; Lim, Wendell A.; Tang, Chao
      Cell (Cambridge, MA, United States) (2009), 138 (4), 760-773CODEN: CELLB5; ISSN:0092-8674. (Cell Press)
      Many signaling systems show adaptation-the ability to reset themselves after responding to a stimulus. We computationally searched all possible three-node enzyme network topologies to identify those that could perform adaptation. Only two major core topologies emerge as robust solns.: a neg. feedback loop with a buffering node and an incoherent feedforward loop with a proportioner node. Minimal circuits contg. these topologies are, within proper regions of parameter space, sufficient to achieve adaptation. More complex circuits that robustly perform adaptation all contain at least one of these topologies at their core. This anal. yields a design table highlighting a finite set of adaptive circuits. Despite the diversity of possible biochem. networks, it may be common to find that only a finite set of core topologies can execute a particular function. These design rules provide a framework for functionally classifying complex natural networks and a manual for engineering networks. For a video summary of this article, see the PaperFlick file with the Supplemental Data available online.
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    5. 5
      Li, Z.; Liu, S.; Yang, Q. Incoherent inputs enhance the robustness of biological oscillators. Cell Systems 2017, 5, 72– 81,  DOI: 10.1016/j.cels.2017.06.013
      5
      Incoherent Inputs Enhance the Robustness of Biological Oscillators
      Li, Zhengda; Liu, Shixuan; Yang, Qiong
      Cell Systems (2017), 5 (1), 72-81.e4CODEN: CSEYA4; ISSN:2405-4712. (Cell Press)
      Robust biol. oscillators retain the crit. ability to function in the presence of environmental perturbations. Although central architectures that support robust oscillations have been extensively studied, networks contg. the same core vary drastically in their potential to oscillate, and it remains elusive what peripheral modifications to the core contribute to this functional variation. Here, we have generated a complete atlas of two- and three-node oscillators computationally, then systematically analyzed the assocn. between network structure and robustness. We found that, while certain core topologies are essential for producing a robust oscillator, local structures can substantially modulate the robustness of oscillations. Notably, local nodes receiving incoherent or coherent inputs resp. promote or attenuate the overall network robustness in an additive manner. We validated these relationships in larger-scale networks reflective of real biol. oscillators. Our findings provide an explanation for why auxiliary structures not required for oscillation are evolutionarily conserved and suggest simple ways to evolve or design robust oscillators.
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    6. 6
      Qiao, L.; Zhao, W.; Tang, C.; Nie, Q.; Zhang, L. Network topologies that can achieve dual function of adaptation and noise attenuation. Cell Systems 2019, 9, 271– 285,  DOI: 10.1016/j.cels.2019.08.006
      6
      Network Topologies That Can Achieve Dual Function of Adaptation and Noise Attenuation
      Qiao, Lingxia; Zhao, Wei; Tang, Chao; Nie, Qing; Zhang, Lei
      Cell Systems (2019), 9 (3), 271-285.e7CODEN: CSEYA4; ISSN:2405-4712. (Cell Press)
      Many signaling systems execute adaptation under circumstances that require noise attenuation. Here, we identify an intrinsic trade-off existing between sensitivity and noise attenuation in the three-node networks. We demonstrate that although fine-tuning timescales in three-node adaptive networks can partially mediate this trade-off in this context, it prolongs adaptation time and imposes unrealistic parameter constraints. By contrast, four-node networks can effectively decouple adaptation and noise attenuation to achieve dual function without a trade-off, provided that these functions are executed sequentially. We illustrate ideas in seven biol. examples, including Dictyostelium discoideum chemotaxis and the p53 signaling network and find that adaptive networks are often assocd. with a noise attenuation module. Our approach may be applicable to finding network design principles for other dual and multiple functions.
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    7. 7
      Dasika, M. S.; Maranas, C. D. OptCircuit: An optimization based method for computational design of genetic circuits. BMC Syst. Biol. 2008, 2, 1– 19,  DOI: 10.1186/1752-0509-2-24
      There is no corresponding record for this reference.
    8. 8
      Otero-Muras, I.; Banga, J. R. Automated Design Framework for Synthetic Biology Exploiting Pareto Optimality. ACS Synth. Biol. 2017, 6, 1180– 1193,  DOI: 10.1021/acssynbio.6b00306
      8
      Automated Design Framework for Synthetic Biology Exploiting Pareto Optimality
      Otero-Muras, Irene; Banga, Julio R.
      ACS Synthetic Biology (2017), 6 (7), 1180-1193CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
      In this work the authors consider Pareto optimality for automated design in synthetic biol. The authors present a generalized framework based on a mixed-integer dynamic optimization formulation that, given design specifications, allows the computation of Pareto optimal sets of designs, i.e. the set of best trade-offs for the metrics of interest. The authors show how this framework can be used for (i) forward design, i.e., finding the Pareto optimal set of synthetic designs for implementation, and (ii) reverse design i.e. analyzing and inferring motifs and/or design principles of gene regulatory networks from the Pareto set of optimal circuits. Finally, the authors illustrate the capabilities and performance of this framework considering four case studies. In the first problem the authors consider the forward design of an oscillator. In the remaining problems, the authors illustrate how to apply the reverse design approach to find motifs for stripe formation, rapid adaptation, and fold-change detection, resp.
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    9. 9
      Hiscock, T. W. Adapting machine-learning algorithms to design gene circuits. BMC Bioinformatics 2019, 20, 1– 13,  DOI: 10.1186/s12859-019-2788-3
      There is no corresponding record for this reference.
    10. 10
      Verma, B. K.; Mannan, A. A.; Zhang, F.; Oyarzún, D. A. Trade-offs in biosensor optimization for dynamic pathway engineering. ACS Synth. Biol. 2022, 11, 228– 240,  DOI: 10.1021/acssynbio.1c00391
      10
      Trade-Offs in Biosensor Optimization for Dynamic Pathway Engineering
      Verma, Babita K.; Mannan, Ahmad A.; Zhang, Fuzhong; Oyarzun, Diego A.
      ACS Synthetic Biology (2022), 11 (1), 228-240CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
      Recent progress in synthetic biol. allows the construction of dynamic control circuits for metabolic engineering. This technol. promises to overcome many challenges encountered in traditional pathway engineering, thanks to its ability to self-regulate gene expression in response to bioreactor perturbations. The central components in these control circuits are metabolite biosensors that read out pathway signals and actuate enzyme expression. However, the construction of metabolite biosensors is a major bottleneck for strain design, and a key challenge is to understand the relation between biosensor dose-response curves and pathway performance. Here we employ multiobjective optimization to quantify performance trade-offs that arise in the design of metabolite biosensors. Our approach reveals strategies for tuning dose-response curves along an optimal trade-off between prodn. flux and the cost of an increased expression burden on the host. We explore properties of control architectures built in the literature and identify their advantages and caveats in terms of performance and robustness to growth conditions and leaky promoters. We demonstrate the optimality of a control circuit for glucaric acid prodn. in Escherichia coli, which has been shown to increase the titer by 2.5-fold as compared to static designs. Our results lay the groundwork for the automated design of control circuits for pathway engineering, with applications in the food, energy, and pharmaceutical sectors.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB3MXivVCmtLvN&md5=1bbe5adb7e2b47694952cd54d33d7d69
    11. 11
      Banga, J. Optimization in computational systems biology. BMC Syst. Biol. 2008, 2, 47,  DOI: 10.1186/1752-0509-2-47
      11
      Optimization in computational systems biology
      Banga Julio R
      BMC systems biology (2008), 2 (), 47 ISSN:.
      Optimization aims to make a system or design as effective or functional as possible. Mathematical optimization methods are widely used in engineering, economics and science. This commentary is focused on applications of mathematical optimization in computational systems biology. Examples are given where optimization methods are used for topics ranging from model building and optimal experimental design to metabolic engineering and synthetic biology. Finally, several perspectives for future research are outlined.
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    12. 12
      Hairer, E.; Wanner, G. Solving Ordinary Differential Equations II: Stiff and Differential-Algebraic Problems; Springer-Verlag, 1996.
      There is no corresponding record for this reference.
    13. 13
      Blanchini, F.; Franco, E.; Giordano, G. A structural classification of candidate oscillatory and multistationary biochemical systems. Bulletin of Mathematical Biology 2014, 76, 2542– 69,  DOI: 10.1007/s11538-014-0023-y
      13
      A Structural Classification of Candidate Oscillatory and Multistationary Biochemical Systems
      Blanchini, Franco; Franco, Elisa; Giordano, Giulia
      Bulletin of Mathematical Biology (2014), 76 (10), 2542-2569CODEN: BMTBAP; ISSN:0092-8240. (Springer)
      Mol. systems are uncertain: The variability of reaction parameters and the presence of unknown interactions can weaken the predictive capacity of solid math. models. However, strong conclusions on the admissible dynamic behaviors of a model can often be achieved without detailed knowledge of its specific parameters. In systems with a sign-definite Jacobian, for instance, cycle-based criteria related to the famous Thomas' conjectures have been largely used to characterize oscillatory and multistationary dynamic outcomes. We build on the rich literature focused on the identification of potential oscillatory and multistationary behaviors using parameter-free criteria. We propose a classification for sign-definite non-autocatalytic biochem. networks, which summarizes several existing results in the literature. We call weak (strong) candidate oscillators systems which can possibly (exclusively) transition to instability due to the presence of a complex pair of eigenvalues, while we call weak (strong) candidate multistationary systems those which can possibly (exclusively) transition to instability due to the presence of a real eigenvalue. For each category, we provide a characterization based on the exclusive or simultaneous presence of pos. and neg. cycles in the assocd. sign graph. Most realistic examples of biochem. networks fall in the gray area of systems in which both pos. and neg. cycles are present: Therefore, both oscillatory and bistable behaviors are in principle possible. However, many canonical example circuits exhibiting oscillations or bistability fall in the categories of strong candidate oscillators/multistationary systems, in agreement with our results.
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    14. 14
      Briat, C.; Gupta, A.; Khammash, M. Antithetic proportional-integral feedback for reduced variance and improved control performance of stochastic reaction networks. J. R. Soc., Interface 2018, 15, 20180079,  DOI: 10.1098/rsif.2018.0079
      14
      Antithetic proportional-integral feedback for reduced variance and improved control performance of stochastic reaction networks
      Briat, Corentin; Gupta, Ankit; Khammash, Mustafa
      Journal of the Royal Society, Interface (2018), 15 (143), 20180079/1-20180079/13CODEN: JRSICU; ISSN:1742-5662. (Royal Society)
      The ability of a cell to regulate and adapt its internal state in response to unpredictable environmental changes is called homeostasis and this ability is crucial for the cell's survival and proper functioning. Understanding how cells can achieve homeostasis, despite the intrinsic noise or randomness in their dynamics, is fundamentally important for both systems and synthetic biol. In this context, a significant development is the proposed antithetic integral feedback (AIF) motif, which is found in natural systems, and is known to ensure robust perfect adaptation for the mean dynamics of a given mol. species involved in a complex stochastic biomol. reaction network. From the standpoint of applications, one drawback of this motif is that it often leads to an increased cell-to-cell heterogeneity or variance when compared to a constitutive (i.e. open-loop) control strategy. Our goal in this paper is to show that this performance deterioration can be countered by combining the AIF motif and a neg. feedback strategy. Using a tailored moment closure method, we derive approx. expressions for the stationary variance for the controlled network that demonstrate that increasing the strength of the neg. feedback can indeed decrease the variance, sometimes even below its constitutive level. Numerical results verify the accuracy of these results and we illustrate them by considering three biomol. networks with two types of neg. feedback strategies. Our computational anal. indicates that there is a trade-off between the speed of the settling-time of the mean trajectories and the stationary variance of the controlled species; i.e. smaller variance is assocd. with larger settling-time.
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    15. 15
      Briat, C.; Gupta, A.; Khammash, M. Antithetic integral feedback ensures robust perfect adaptation in noisy biomolecular networks. Cell Systems 2016, 2, 15– 26,  DOI: 10.1016/j.cels.2016.01.004
      15
      Antithetic Integral Feedback Ensures Robust Perfect Adaptation in Noisy Biomolecular Networks
      Briat, Corentin; Gupta, Ankit; Khammash, Mustafa
      Cell Systems (2016), 2 (1), 15-26CODEN: CSEYA4; ISSN:2405-4712. (Cell Press)
      The ability to adapt to stimuli is a defining feature of many biol. systems and crit. to maintaining homeostasis. While it is well appreciated that neg. feedback can be used to achieve homeostasis when networks behave deterministically, the effect of noise on their regulatory function is not understood. Here, we combine probability and control theory to develop a theory of biol. regulation that explicitly takes into account the noisy nature of biochem. reactions. We introduce tools for the anal. and design of robust homeostatic circuits and propose a new regulation motif, which we call antithetic integral feedback. This motif exploits stochastic noise, allowing it to achieve precise regulation in scenarios where similar deterministic regulation fails. Specifically, antithetic integral feedback preserves the stability of the overall network, steers the population of any regulated species to a desired set point, and adapts perfectly. We suggest that this motif may be prevalent in endogenous biol. circuits and useful when creating synthetic circuits.
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    16. 16
      Bhattacharya, P.; Raman, K.; Tangirala, A. K. Discovering adaptation-capable biological network structures using control-theoretic approaches. PLOS Computational Biology 2022, 18, e1009769  DOI: 10.1371/journal.pcbi.1009769
      16
      Discovering adaptation-capable biological network structures using control-theoretic approaches
      Bhattacharya, Priyan; Raman, Karthik; Tangirala, Arun K.
      PLoS Computational Biology (2022), 18 (1), e1009769CODEN: PCBLBG; ISSN:1553-7358. (Public Library of Science)
      Constructing biol. networks capable of performing specific biol. functionalities has been of sustained interest in synthetic biol. Adaptation is one such ubiquitous functional property, which enables every living organism to sense a change in its surroundings and return to its operating condition prior to the disturbance. In this paper, we present a generic systems theory-driven method for designing adaptive protein networks. First, we translate the necessary qual conditions for adaptation to math constraints using the language of systems theory, which we then map back as design requirements for the underlying networks. We go on to prove that a protein network with different input-output nodes (proteins) needs to be at least of third-order in order to provide adaptation. Next, we show that the necessary design principles obtained for a three-node network in adaptation consist of neg. feedback or a feed-forward realization. We argue that presence of a particular class of neg. feedback or feed-forward realization is necessary for a network of any size to provide adaptation. Further, we claim that the necessary structural conditions derived in this work are the strictest among the ones hitherto existed in the literature. Finally, we prove that the capability of producing adaptation is retained for the admissible motifs even when the output node is connected with a downstream system in a feedback fashion. This explains how complex biol. networks achieve robustness while keeping the core motifs unchanged in the context of a particular functionality. We corroborate our theory results with detailed and thorough numerical simulations. Overall, our results present a generic, systematic and robust framework for designing various kinds of biol. networks.
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    17. 17
      Araujo, R. P.; Liotta, L. A. The topological requirements for robust perfect adaptation in networks of any size. Nat. Commun. 2018, 9, 1757,  DOI: 10.1038/s41467-018-04151-6
      17
      The topological requirements for robust perfect adaptation in networks of any size
      Araujo Robyn P; Araujo Robyn P; Liotta Lance A
      Nature communications (2018), 9 (1), 1757 ISSN:.
      Robustness, and the ability to function and thrive amid changing and unfavorable environments, is a fundamental requirement for living systems. Until now it has been an open question how large and complex biological networks can exhibit robust behaviors, such as perfect adaptation to a variable stimulus, since complexity is generally associated with fragility. Here we report that all networks that exhibit robust perfect adaptation (RPA) to a persistent change in stimulus are decomposable into well-defined modules, of which there exist two distinct classes. These two modular classes represent a topological basis for all RPA-capable networks, and generate the full set of topological realizations of the internal model principle for RPA in complex, self-organizing, evolvable bionetworks. This unexpected result supports the notion that evolutionary processes are empowered by simple and scalable modular design principles that promote robust performance no matter how large or complex the underlying networks become.
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    18. 18
      Drengstig, T.; Ueda, H. R.; Ruoff, P. Predicting perfect adaptation motifs in reaction kinetic networks. J. Phys. Chem. B 2008, 112, 16752– 16758,  DOI: 10.1021/jp806818c
      18
      Predicting Perfect Adaptation Motifs in Reaction Kinetic Networks
      Drengstig, Tormod; Ueda, Hiroki R.; Ruoff, Peter
      Journal of Physical Chemistry B (2008), 112 (51), 16752-16758CODEN: JPCBFK; ISSN:1520-6106. (American Chemical Society)
      A review. Adaptation and compensation mechanisms are important to keep organisms fit in a changing environment. "Perfect adaptation" describes an organism's response to an external stepwise perturbation by resetting some of its variables precisely to their original preperturbation values. Examples of perfect adaptation are found in bacterial chemotaxis, photoreceptor responses, or MAP kinase activities. Two concepts have evolved for how perfect adaptation may be understood. In one approach, so-called "robust perfect adaptation", the adaptation is a network property (due to integral feedback control), which is independent of rate const. values. In the other approach, which we have termed "nonrobust perfect adaptation", a fine-tuning of rate const. values is needed to show perfect adaptation. Although integral feedback describes robust perfect adaptation in general terms, it does not directly show where in a network perfect adaptation may be obsd. Using control theoretic methods, we are able to predict robust perfect adaptation sites within reaction kinetic networks and show that a prerequisite for robust perfect adaptation is that the network is open and irreversible. We applied the method on various reaction schemes and found that new (robust) perfect adaptation motifs emerge when considering suggested models of bacterial and eukaryotic chemotaxis.
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    19. 19
      Woods, M. L.; Leon, M.; Perez-Carrasco, R.; Barnes, C. P. A statistical approach reveals designs for the most robust stochastic gene oscillators. ACS Synth. Biol. 2016, 5, 459– 470,  DOI: 10.1021/acssynbio.5b00179
      19
      A Statistical Approach Reveals Designs for the Most Robust Stochastic Gene Oscillators
      Woods, Mae L.; Leon, Miriam; Perez-Carrasco, Ruben; Barnes, Chris P.
      ACS Synthetic Biology (2016), 5 (6), 459-470CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
      The engineering of transcriptional networks presents many challenges due to the inherent uncertainty in the system structure, changing cellular context, and stochasticity in the governing dynamics. One approach to address these problems is to design and build systems that can function across a range of conditions; that is they are robust to uncertainty in their constituent components. Here we examine the parametric robustness landscape of transcriptional oscillators, which underlie many important processes such as circadian rhythms and the cell cycle, plus also serve as a model for the engineering of complex and emergent phenomena. The central questions that we address are: Can we build genetic oscillators that are more robust than those already constructed. Can we make genetic oscillators arbitrarily robust. These questions are tech. challenging due to the large model and parameter spaces that must be efficiently explored. Here we use a measure of robustness that coincides with the Bayesian model evidence, combined with an efficient Monte Carlo method to traverse model space and conc. on regions of high robustness, which enables the accurate evaluation of the relative robustness of gene network models governed by stochastic dynamics. We report the most robust two and three gene oscillator systems, plus examine how the no. of interactions, the presence of autoregulation, and degrdn. of mRNA and protein affects the frequency, amplitude, and robustness of transcriptional oscillators. We also find that there is a limit to parametric robustness, beyond which there is nothing to be gained by adding addnl. feedback. Importantly, we provide predictions on new oscillator systems that can be constructed to verify the theory and advance design and modeling approaches to systems and synthetic biol.
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    20. 20
      Gonzalez, J.; Longworth, J.; James, D. C.; Lawrence, N. D. Bayesian optimization for synthetic gene design. arXiv , May 7, 2015.  DOI: 10.48550/arXiv.1505.01627 .
      There is no corresponding record for this reference.
    21. 21
      Shen, J.; Liu, F.; Tu, Y.; Tang, C. Finding gene network topologies for given biological function with recurrent neural network. Nat. Commun. 2021, 12, 1– 10,  DOI: 10.1038/s41467-021-23420-5
      There is no corresponding record for this reference.
    22. 22
      Zhang, F.; Carothers, J. M.; Keasling, J. D. Design of a dynamic sensor-regulator system for production of chemicals and fuels derived from fatty acids. Nat. Biotechnol. 2012, 30, 354– 359,  DOI: 10.1038/nbt.2149
      22
      Design of a dynamic sensor-regulator system for production of chemicals and fuels derived from fatty acids
      Zhang, Fuzhong; Carothers, James M.; Keasling, Jay D.
      Nature Biotechnology (2012), 30 (4), 354-359CODEN: NABIF9; ISSN:1087-0156. (Nature Publishing Group)
      Microbial prodn. of chems. is now an attractive alternative to chem. synthesis. Current efforts focus mainly on constructing pathways to produce different types of mols. However, there are few strategies for engineering regulatory components to improve product titers and conversion yields of heterologous pathways. Here we developed a dynamic sensor-regulator system (DSRS) to produce fatty acid-based products in Escherichia coli, and demonstrated its use for biodiesel prodn. The DSRS uses a transcription factor that senses a key intermediate and dynamically regulates the expression of genes involved in biodiesel prodn. This DSRS substantially improved the stability of biodiesel-producing strains and increased the titer to 1.5 g/l and the yield threefold to 28% of the theor. max. Given the large no. of natural sensors available, this DSRS strategy can be extended to many other biosynthetic pathways to balance metab., thereby increasing product titers and conversion yields and stabilizing prodn. hosts.
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    23. 23
      Oyarzún, D. A.; Stan, G.-B. V. Synthetic gene circuits for metabolic control: design trade-offs and constraints. J. R. Soc., Interface 2013, 10, 20120671,  DOI: 10.1098/rsif.2012.0671
      23
      Synthetic gene circuits for metabolic control: design trade-offs and constraints
      Oyarzun Diego A; Stan Guy-Bart V
      Journal of the Royal Society, Interface (2013), 10 (78), 20120671 ISSN:.
      A grand challenge in synthetic biology is to push the design of biomolecular circuits from purely genetic constructs towards systems that interface different levels of the cellular machinery, including signalling networks and metabolic pathways. In this paper, we focus on a genetic circuit for feedback regulation of unbranched metabolic pathways. The objective of this feedback system is to dampen the effect of flux perturbations caused by changes in cellular demands or by engineered pathways consuming metabolic intermediates. We consider a mathematical model for a control circuit with an operon architecture, whereby the expression of all pathway enzymes is transcriptionally repressed by the metabolic product. We address the existence and stability of the steady state, the dynamic response of the network under perturbations, and their dependence on common tuneable knobs such as the promoter characteristic and ribosome binding site (RBS) strengths. Our analysis reveals trade-offs between the steady state of the enzymes and the intermediates, together with a separation principle between promoter and RBS design. We show that enzymatic saturation imposes limits on the parameter design space, which must be satisfied to prevent metabolite accumulation and guarantee the stability of the network. The use of promoters with a broad dynamic range and a small leaky expression enlarges the design space. Simulation results with realistic parameter values also suggest that the control circuit can effectively upregulate enzyme production to compensate flux perturbations.
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    24. 24
      Xu, P.; Li, L.; Zhang, F.; Stephanopoulos, G.; Koffas, M. Improving fatty acids production by engineering dynamic pathway regulation and metabolic control. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 11299– 11304,  DOI: 10.1073/pnas.1406401111
      24
      Improving fatty acids production by engineering dynamic pathway regulation and metabolic control
      Xu, Peng; Li, Lingyun; Zhang, Fuming; Stephanopoulos, Gregory; Koffas, Mattheos
      Proceedings of the National Academy of Sciences of the United States of America (2014), 111 (31), 11299-11304CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Global energy demand and environmental concerns have stimulated increasing efforts to produce carbon-neutral fuels directly from renewable resources. Microbially derived aliph. hydrocarbons, the petroleum-replica fuels, have emerged as promising alternatives to meet this goal. However, engineering metabolic pathways with high productivity and yield requires dynamic redistribution of cellular resources and optimal control of pathway expression. Here we report a genetically encoded metabolic switch that enables dynamic regulation of fatty acids (FA) biosynthesis in Escherichia coli. The engineered strains were able to dynamically compensate the crit. enzymes involved in the supply and consumption of malonyl-CoA and efficiently redirect carbon flux toward FA biosynthesis. Implementation of this metabolic control resulted in an oscillatory malonyl-CoA pattern and a balanced metab. between cell growth and product formation, yielding 15.7- and 2.1-fold improvement in FA titer compared with the wild-type strain and the strain carrying the uncontrolled metabolic pathway. This study provides a new paradigm in metabolic engineering to control and optimize metabolic pathways facilitating the high-yield prodn. of other malonyl-CoA-derived compds.
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    25. 25
      Dunlop, M. J.; Keasling, J. D.; Mukhopadhyay, A. A model for improving microbial biofuel production using a synthetic feedback loop. Systems and Synthetic Biology 2010, 4, 95– 104,  DOI: 10.1007/s11693-010-9052-5
      25
      A model for improving microbial biofuel production using a synthetic feedback loop
      Dunlop Mary J; Keasling Jay D; Mukhopadhyay Aindrila
      Systems and synthetic biology (2010), 4 (2), 95-104 ISSN:.
      Cells use feedback to implement a diverse range of regulatory functions. Building synthetic feedback control systems may yield insight into the roles that feedback can play in regulation since it can be introduced independently of native regulation, and alternative control architectures can be compared. We propose a model for microbial biofuel production where a synthetic control system is used to increase cell viability and biofuel yields. Although microbes can be engineered to produce biofuels, the fuels are often toxic to cell growth, creating a negative feedback loop that limits biofuel production. These toxic effects may be mitigated by expressing efflux pumps that export biofuel from the cell. We developed a model for cell growth and biofuel production and used it to compare several genetic control strategies for their ability to improve biofuel yields. We show that controlling efflux pump expression directly with a biofuel-responsive promoter is a straightforward way of improving biofuel production. In addition, a feed forward loop controller is shown to be versatile at dealing with uncertainty in biofuel production rates.
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    26. 26
      Doong, S. J.; Gupta, A.; Prather, K. L. Layered dynamic regulation for improving metabolic pathway productivity in Escherichia coli. Proc. Natl. Acad. Sci. U. S. A. 2018, 115, 2964– 2969,  DOI: 10.1073/pnas.1716920115
      26
      Layered dynamic regulation for improving metabolic pathway productivity in Escherichia coli
      Doong, Stephanie J.; Gupta, Apoorv; Prather, Kristala L. J.
      Proceedings of the National Academy of Sciences of the United States of America (2018), 115 (12), 2964-2969CODEN: PNASA6; ISSN:0027-8424. (National Academy of Sciences)
      Microbial prodn. of value-added chems. from biomass is a sustainable alternative to chem. synthesis. To improve product titer, yield, and selectivity, the pathways engineered into microbes must be optimized. One strategy for optimization is dynamic pathway regulation, which modulates expression of pathwayrelevant enzymes over the course of fermn. Metabolic engineers have used dynamic regulation to redirect endogenous flux toward product formation, balance the prodn. and consumption rates of key intermediates, and suppress prodn. of toxic intermediates until later in the fermn. Most cases, however, have utilized a single strategy for dynamically regulating pathway fluxes. Here we layer two orthogonal, autonomous, and tunable dynamic regulation strategies to independently modulate expression of two different enzymes to improve prodn. of D-glucaric acid from a heterologous pathway. The first strategy uses a previously described pathway-independent quorum sensing system to dynamically knock down glycolytic flux and redirect carbon into prodn. of glucaric acid, thereby switching cells from "growth" to "prodn." mode. The second strategy, developed in this work, uses a biosensor for myo-inositol (MI), an intermediate in the glucaric acid prodn. pathway, to induce expression of a downstream enzyme upon sufficient buildup of MI. The latter, pathway-dependent strategy leads to a 2.5-fold increase in titer when used in isolation and a fourfold increase when added to a strain employing the former, pathway-independent regulatory system. The dual-regulation strain produces nearly 2 g/L glucaric acid, representing the highest glucaric acid titer reported to date in Escherichia coli K-12 strains.
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    27. 27
      Ni, C.; Dinh, C. V.; Prather, K. L. Dynamic Control of Metabolism. Annu. Rev. Chem. Biomol. Eng. 2021, 12, 519,  DOI: 10.1146/annurev-chembioeng-091720-125738
      27
      Dynamic Control of Metabolism
      Ni, Cynthia; Dinh, Christina V.; Prather, Kristala L. J.
      Annual Review of Chemical and Biomolecular Engineering (2021), 12 (), 519-541CODEN: ARCBCY; ISSN:1947-5438. (Annual Reviews)
      A review. Metabolic engineering reprograms cells to synthesize value-added products. In doing so, endogenous genes are altered and heterologous genes can be introduced to achieve the necessary enzymic reactions. Dynamic regulation of metabolic flux is a powerful control scheme to alleviate and overcome the competing cellular objectives that arise from the introduction of these prodn. pathways. This review explores dynamic regulation strategies that have demonstrated significant prodn. benefits by targeting the metabolic node corresponding to a specific challenge. We summarize the stimulus-responsive control circuits employed in these strategies that det. the criterion for actuating a dynamic response and then examine the points of control that couple the stimulus-responsive circuit to a shift in metabolic flux.
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    28. 28
      Hartline, C. J.; Schmitz, A. C.; Han, Y.; Zhang, F. Dynamic control in metabolic engineering: Theories, tools, and applications. Metabolic Engineering 2021, 63, 126– 140,  DOI: 10.1016/j.ymben.2020.08.015
      28
      Dynamic control in metabolic engineering: Theories, tools, and applications
      Hartline, Christopher J.; Schmitz, Alexander C.; Han, Yichao; Zhang, Fuzhong
      Metabolic Engineering (2021), 63 (), 126-140CODEN: MEENFM; ISSN:1096-7176. (Elsevier B.V.)
      A review. Metabolic engineering has allowed the prodn. of a diverse no. of valuable chems. using microbial organisms. Many biol. challenges for improving bio-prodn. exist which limit performance and slow the commercialization of metabolically engineered systems. Dynamic metabolic engineering is a rapidly developing field that seeks to address these challenges through the design of genetically encoded metabolic control systems which allow cells to autonomously adjust their flux in response to their external and internal metabolic state. This review first discusses theor. works which provide mechanistic insights and design choices for dynamic control systems including two-stage, continuous, and population behavior control strategies. Next, we summarize mol. mechanisms for various sensors and actuators which enable dynamic metabolic control in microbial systems. Finally, important applications of dynamic control to the prodn. of several metabolite products are highlighted, including fatty acids, aroms., and terpene compds. Altogether, this review provides a comprehensive overview of the progress, advances, and prospects in the design of dynamic control systems for improved titer, rate, and yield metrics in metabolic engineering.
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    29. 29
      Tonn, M. K.; Thomas, P.; Barahona, M.; Oyarzún, D. A. Stochastic modelling reveals mechanisms of metabolic heterogeneity. Commun. Biol. 2019, 2, 108,  DOI: 10.1038/s42003-019-0347-0
      29
      Stochastic modelling reveals mechanisms of metabolic heterogeneity
      Tonn Mona K; Thomas Philipp; Barahona Mauricio; Oyarzun Diego A; Oyarzun Diego A; Oyarzun Diego A
      Communications biology (2019), 2 (), 108 ISSN:.
      Phenotypic variation is a hallmark of cellular physiology. Metabolic heterogeneity, in particular, underpins single-cell phenomena such as microbial drug tolerance and growth variability. Much research has focussed on transcriptomic and proteomic heterogeneity, yet it remains unclear if such variation permeates to the metabolic state of a cell. Here we propose a stochastic model to show that complex forms of metabolic heterogeneity emerge from fluctuations in enzyme expression and catalysis. The analysis predicts clonal populations to split into two or more metabolically distinct subpopulations. We reveal mechanisms not seen in deterministic models, in which enzymes with unimodal expression distributions lead to metabolites with a bimodal or multimodal distribution across the population. Based on published data, the results suggest that metabolite heterogeneity may be more pervasive than previously thought. Our work casts light on links between gene expression and metabolism, and provides a theory to probe the sources of metabolite heterogeneity.
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    30. 30
      Mannan, A. A.; Liu, D.; Zhang, F.; Oyarzún, D. A. Fundamental Design Principles for Transcription-Factor-Based Metabolite Biosensors. ACS Synth. Biol. 2017, 6, 1851– 1859,  DOI: 10.1021/acssynbio.7b00172
      30
      Fundamental Design Principles for Transcription-Factor-Based Metabolite Biosensors
      Mannan, Ahmad A.; Liu, Di; Zhang, Fuzhong; Oyarzun, Diego A.
      ACS Synthetic Biology (2017), 6 (10), 1851-1859CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
      Metabolite biosensors are central to current efforts toward precision engineering of metab. Although most research has focused on building new biosensors, their tunability remains poorly understood and is fundamental for their broad applicability. Here we asked how genetic modifications shape the dose-response curve of biosensors based on metabolite-responsive transcription factors. Using the lac system in Escherichia coli as a model system, we built promoter libraries with variable operator sites that reveal interdependencies between biosensor dynamic range and response threshold. We developed a phenomenol. theory to quantify such design constraints in biosensors with various architectures and tunable parameters. Our theory reveals a maximal achievable dynamic range and exposes tunable parameters for orthogonal control of dynamic range and response threshold. Our work sheds light on fundamental limits of synthetic biol. designs and provides quant. guidelines for biosensor design in applications such as dynamic pathway control, strain optimization, and real-time monitoring of metab.
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    31. 31
      Zhou, L.-B.; Zeng, A.-P. Exploring Lysine Riboswitch for Metabolic Flux Control and Improvement of L-Lysine Synthesis in Corynebacterium glutamicum. ACS Synth. Biol. 2015, 4, 729– 734,  DOI: 10.1021/sb500332c
      31
      Exploring Lysine Riboswitch for Metabolic Flux Control and Improvement of L-Lysine Synthesis in Corynebacterium glutamicum
      Zhou, Li-Bang; Zeng, An-Ping
      ACS Synthetic Biology (2015), 4 (6), 729-734CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
      Riboswitch, a regulatory part of an mRNA mol. that can specifically bind a metabolite and regulate gene expression, is attractive for engineering biol. systems, esp. for the control of metabolic fluxes in industrial microorganisms. Here, we demonstrate the use of lysine riboswitch and intracellular L-lysine as a signal to control the competing but essential metabolic by-pathways of lysine biosynthesis. To this end, we first examd. the natural lysine riboswitches of Eschericia coli (ECRS) and Bacillus subtilis (BSRS) to control the expression of citrate synthase (gltA) and thus the metabolic flux in the tricarboxylic acid (TCA) cycle in E. coli. ECRS and BSRS were then successfully used to control the gltA gene and TCA cycle activity in a lysine producing strain Corynebacterium glutamicum LP917, resp. Compared with the strain LP917, the growth of both lysine riboswitch-gltA mutants was slower, suggesting a reduced TCA cycle activity. The lysine prodn. was 63% higher in the mutant ECRS-gltA and 38% higher in the mutant BSRS-gltA, indicating a higher metabolic flux into the lysine synthesis pathway. This is the first report on using an amino acid riboswitch for improvement of lysine biosynthesis. The lysine riboswitches can be easily adapted to dynamically control other essential but competing metabolic pathways or even be engineered as an "on-switch" to enhance the metabolic fluxes of desired metabolic pathways.
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    32. 32
      Chaves, M.; Oyarzún, D. A. Dynamics of complex feedback architectures in metabolic pathways. Automatica 2019, 99, 323– 332,  DOI: 10.1016/j.automatica.2018.10.046
      There is no corresponding record for this reference.
    33. 33
      Liu, D.; Zhang, F. Metabolic feedback circuits provide rapid control of metabolite dynamics. ACS Synth. Biol. 2018, 7, 347– 356,  DOI: 10.1021/acssynbio.7b00342
      33
      Metabolic Feedback Circuits Provide Rapid Control of Metabolite Dynamics
      Liu, Di; Zhang, Fuzhong
      ACS Synthetic Biology (2018), 7 (2), 347-356CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
      Metab. constitutes the basis of life, and the dynamics of metab. dictate various cellular processes. However, exactly how metabolite dynamics are controlled remains poorly understood. By studying an engineered fatty acid-producing pathway as a model, we found that upon transcription activation a metabolic product from an unregulated pathway required seven cell cycles to reach to its steady state level, with the speed mostly limited by enzyme expression dynamics. To overcome this limit, we designed metabolic feedback circuits (MeFCs) with three different architectures, and exptl. measured and modeled their metabolite dynamics. Our engineered MeFCs could dramatically shorten the rise-time of metabolites, decreasing it by as much as 12-fold. The findings of this study provide a systematic understanding of metabolite dynamics in different architectures of MeFCs and have potentially immense applications in designing synthetic circuits to improve the productivities of engineered metabolic pathways.
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    34. 34
      Stevens, J. T.; Carothers, J. M. Designing RNA-based genetic control systems for efficient production from engineered metabolic pathways. ACS Synth. Biol. 2015, 4, 107– 115,  DOI: 10.1021/sb400201u
      34
      Designing RNA-Based Genetic Control Systems for Efficient Production from Engineered Metabolic Pathways
      Stevens, Jason T.; Carothers, James M.
      ACS Synthetic Biology (2015), 4 (2), 107-115CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
      Engineered metabolic pathways can be augmented with dynamic regulatory controllers to increase prodn. titers by minimizing toxicity and helping cells maintain homeostasis. We investigated the potential for dynamic RNA-based genetic control systems to increase prodn. through simulation anal. of an engineered p-aminostyrene (p-AS) pathway in E. coli. To map the entire design space, we formulated 729 unique mechanistic models corresponding to all of the possible control topologies and mechanistic implementations in the system under study. Two thousand sampled simulations were performed for each of the 729 system designs to relate the potential effects of dynamic control to increases in p-AS prodn. (total of 3 × 106 simulations). Our anal. indicates that dynamic control strategies employing aptazyme-regulated expression devices (aREDs) can yield >10-fold improvements over static control. We uncovered generalizable trends in successful control architectures and found that highly performing RNA-based control systems are exptl. tractable. Analyzing the metabolic control state space to predict optimal genetic control strategies promises to enhance the design of metabolic pathways.
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    35. 35
      Frazier, P. I. A tutorial on Bayesian optimization. arXiv , July 8, 2018.  DOI: 10.48550/arXiv.1807.02811 .
      There is no corresponding record for this reference.
    36. 36
      Moon, T. S.; Yoon, S.-H.; Lanza, A. M.; Roy-Mayhew, J. D.; Prather, K. L. J. Production of glucaric acid from a synthetic pathway in recombinant Escherichia coli. Applied and Environmental Microbiology 2009, 75, 589– 595,  DOI: 10.1128/AEM.00973-08
      36
      Production of glucaric acid from a synthetic pathway in recombinant Escherichia coli
      Moon, Tae Seok; Yoon, Sang-Hwal; Lanza, Amanda M.; Roy-Mayhew, Joseph D.; Jones-Prather, Kristala L.
      Applied and Environmental Microbiology (2009), 75 (3), 589-595CODEN: AEMIDF; ISSN:0099-2240. (American Society for Microbiology)
      A synthetic pathway has been constructed for the prodn. of glucuronic and glucaric acids from glucose in Escherichia coli. Coexpression of the genes encoding myo-inositol-1-phosphate synthase (Ino1) from Saccharomyces cerevisiae and myo-inositol oxygenase (MIOX) from mice led to prodn. of glucuronic acid through the intermediate myo-inositol. Glucuronic acid concns. up to 0.3 g/L were measured in the culture broth. The activity of MIOX was rate limiting, resulting in the accumulation of both myo-inositol and glucuronic acid as final products, in approx. equal concns. Inclusion of a third enzyme, uronate dehydrogenase (Udh) from Pseudomonas syringae, facilitated the conversion of glucuronic acid to glucaric acid. The activity of this recombinant enzyme was more than 2 orders of magnitude higher than that of Ino1 and MIOX and increased overall flux through the pathway such that glucaric acid concns. in excess of 1 g/L were obsd. This represents a novel microbial system for the biol. prodn. of glucaric acid, a "top value-added chem." from biomass.
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    37. 37
      Bergstra, J.; Yamins, D.; Cox, D. Making a science of model search: Hyperparameter optimization in hundreds of dimensions for vision architectures. In International Conference on Machine Learning; ICML, 2013; pp 115– 123.
      There is no corresponding record for this reference.
    38. 38
      Snoek, J.; Larochelle, H.; Adams, R. P. Practical bayesian optimization of machine learning algorithms. In Advances in Neural Information Processing Systems; NeurIPS, 2012; Vol. 25.
      There is no corresponding record for this reference.
    39. 39
      Bar-Even, A.; Noor, E.; Savir, Y.; Liebermeister, W.; Davidi, D.; Tawfik, D. S.; Milo, R. The moderately efficient enzyme: evolutionary and physicochemical trends shaping enzyme parameters. Biochemistry 2011, 50, 4402– 4410,  DOI: 10.1021/bi2002289
      39
      The Moderately Efficient Enzyme: Evolutionary and Physicochemical Trends Shaping Enzyme Parameters
      Bar-Even, Arren; Noor, Elad; Savir, Yonatan; Liebermeister, Wolfram; Davidi, Dan; Tawfik, Dan S.; Milo, Ron
      Biochemistry (2011), 50 (21), 4402-4410CODEN: BICHAW; ISSN:0006-2960. (American Chemical Society)
      The kinetic parameters of enzymes are key to understanding the rate and specificity of most biol. processes. Although specific trends are frequently studied for individual enzymes, global trends are rarely addressed. We performed an anal. of kcat and KM values of several thousand enzymes collected from the literature. We found that the "av. enzyme" exhibits a kcat of ∼10 s-1 and a kcat/KM of ∼ 105 s-1 M-1, much below the diffusion limit and the characteristic textbook portrayal of kinetically superior enzymes. Why do most enzymes exhibit moderate catalytic efficiencies Maximal rates may not evolve in cases where weaker selection pressures are expected. We find, for example, that enzymes operating in secondary metab. are, on av., ∼ 30-fold slower than those of central metab. We also find indications that the physicochem. properties of substrates affect the kinetic parameters. Specifically, low mol. mass and hydrophobicity appear to limit KM optimization. In accordance, substitution with phosphate, CoA, or other large modifiers considerably lowers the KM values of enzymes utilizing the substituted substrates. It therefore appears that both evolutionary selection pressures and physicochem. constraints shape the kinetic parameters of enzymes. It also seems likely that the catalytic efficiency of some enzymes toward their natural substrates could be increased in many cases by natural or lab. evolution.
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    40. 40
      Venayak, N.; Anesiadis, N.; Cluett, W. R.; Mahadevan, R. Engineering metabolism through dynamic control. Curr. Opin. Biotechnol. 2015, 34, 142– 152,  DOI: 10.1016/j.copbio.2014.12.022
      40
      Engineering metabolism through dynamic control
      Venayak, Naveen; Anesiadis, Nikolaos; Cluett, William R.; Mahadevan, Radhakrishnan
      Current Opinion in Biotechnology (2015), 34 (), 142-152CODEN: CUOBE3; ISSN:0958-1669. (Elsevier B.V.)
      A review. Metabolic engineering has proven crucial for the microbial prodn. of valuable chems. Due to the rapid development of tools in synthetic biol., there has been recent interest in the dynamic regulation of flux through metabolic pathways to overcome some of the issues arising from traditional strategies lacking dynamic control. There are many diverse implementations of dynamic control, with a range of metabolite sensors and inducers being used. Furthermore, control has been implemented at the transcriptional, translational and post-translational levels. Each of these levels have unique sets of engineering tools, and allow for control at different dynamic time-scales. In order to extend the applications of dynamic control, new tools are required to improve the dynamics of regulatory circuits. Further study and characterization of circuit robustness is also needed to improve their applicability to industry. The successful implementation of dynamic control, using technologies that are amenable to commercialization, will be a fundamental step in advancing metabolic engineering.
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    41. 41
      Hartline, C.; Mannan, A.; Liu, D.; Zhang, F.; Oyarzún, D. Metabolite sequestration enables rapid recovery from fatty acid depletion in Escherichia coli. mBio 2020, 11, 590943,  DOI: 10.1128/mBio.03112-19
      There is no corresponding record for this reference.
    42. 42
      Zhu, Y.; Li, Y.; Xu, Y.; Zhang, J.; Ma, L.; Qi, Q.; Wang, Q. Development of bifunctional biosensors for sensing and dynamic control of glycolysis flux in metabolic engineering. Metabolic Engineering 2021, 68, 142– 151,  DOI: 10.1016/j.ymben.2021.09.011
      42
      Development of bifunctional biosensors for sensing and dynamic control of glycolysis flux in metabolic engineering
      Zhu, Yuan; Li, Ying; Xu, Ya; Zhang, Jian; Ma, Linlin; Qi, Qingsheng; Wang, Qian
      Metabolic Engineering (2021), 68 (), 142-151CODEN: MEENFM; ISSN:1096-7176. (Elsevier B.V.)
      Glycolysis is the primary metabolic pathway in all living organisms. Maintaining the balance of glycolysis flux and biosynthetic pathways is the crucial matter involved in the microbial cell factory. Few regulation systems can address the issue of metabolic flux imbalance in glycolysis. Here, we designed and constructed a bifunctional glycolysis flux biosensor that can dynamically regulate glycolysis flux for overprodn. of desired biochems. A series of pos.-and neg.-response biosensors were created and modified for varied thresholds and dynamic ranges. These engineered glycolysis flux biosensors were verified to be able to characterize in vivo fructose-1,6-diphosphate concn. Subsequently, the biosensors were applied for fine-tuning glycolysis flux to effectively balance the biosynthesis of two chems.: mevalonate and N-acetylglucosamine. A glycolysis flux-dynamically controlled Escherichia coli strain achieved a 111.3 g/L mevalonate titer in a 1L fermenter.
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    43. 43
      Schomburg, I.; Jeske, L.; Ulbrich, M.; Placzek, S.; Chang, A.; Schomburg, D. The BRENDA enzyme information system–From a database to an expert system. Journal of biotechnology 2017, 261, 194– 206,  DOI: 10.1016/j.jbiotec.2017.04.020
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      The BRENDA enzyme information system-From a database to an expert system
      Schomburg, I.; Jeske, L.; Ulbrich, M.; Placzek, S.; Chang, A.; Schomburg, D.
      Journal of Biotechnology (2017), 261 (), 194-206CODEN: JBITD4; ISSN:0168-1656. (Elsevier B.V.)
      Enzymes, representing the largest and by far most complex group of proteins, play an essential role in all processes of life, including metab., gene expression, cell division, the immune system, and others. Their function, also connected to most diseases or stress control makes them interesting targets for research and applications in biotechnol., medical treatments, or diagnosis. Their functional parameters and other properties are collected, integrated, and made available to the scientific community in the BRaunschweig ENzyme DAtabase (BRENDA). In the last 30 years BRENDA has developed into one of the most highly used biol. databases worldwide. The data contents, the process of data acquisition, data integration and control, the ways to access the data, and visualizations provided by the website are described and discussed.
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    44. 44
      Zhang, Y.; Nielsen, J.; Liu, Z. Metabolic engineering of Saccharomyces cerevisiae for production of fatty acid–derived hydrocarbons. Biotechnology and Bioengineering 2018, 115, 2139– 2147,  DOI: 10.1002/bit.26738
      44
      Metabolic engineering of Saccharomyces cerevisiae for production of fatty acid-derived hydrocarbons
      Zhang, Yiming; Nielsen, Jens; Liu, Zihe
      Biotechnology and Bioengineering (2018), 115 (9), 2139-2147CODEN: BIBIAU; ISSN:0006-3592. (John Wiley & Sons, Inc.)
      A review. Fatty acid-derived hydrocarbons attract increasing attention as biofuels due to their immiscibility with water, high-energy content, low f.p., and high compatibility with existing refineries and end-user infrastructures. Yeast Saccharomyces cerevisiae has advantages for prodn. of fatty acid-derived hydrocarbons as its native routes toward fatty acid synthesis involve only a few reactions that allow more efficient conversion of carbon substrates. Here we describe major biosynthetic pathways of fatty acid-derived hydrocarbons in yeast, and summarize key metabolic engineering strategies, including enhancing precursor supply, eliminating competing pathways, and expressing heterologous pathways. With recent advances in yeast prodn. of fatty acid-derived hydrocarbons, our review identifies key research challenges and opportunities for future optimization, and concludes with perspectives and outlooks for further research directions.
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    45. 45
      Goikhman, M. Y.; Yevlampieva, N.; Kamanina, N.; Podeshvo, I.; Gofman, I.; Mil’tsov, S.; Khurchak, A.; Yakimanskii, A. New polyamides with main-chain cyanine chromophores. Polymer Science Series A 2011, 53, 457– 468,  DOI: 10.1134/S0965545X11060058
      45
      New polyamides with main-chain cyanine chromophores
      Goikhman, M. Ya.; Yevlampieva, N. P.; Kamanina, N. V.; Podeshvo, I. V.; Gofman, I. V.; Mil'tsov, S. A.; Khurchak, A. P.; Yakimanskii, A. V.
      Polymer Science, Series A (2011), 53 (6), 457-468CODEN: PSSAFE; ISSN:1555-6107. (MAIK Nauka/Interperiodica)
      Polyamides contg. main-chain cyanine chromophores are synthesized, and their mol., nonlinear optical, and mech. properties are studied. It is shown that the Kerr electro-optical effect in polymer solns. is detd. by the rigidity of polymer chains and that the nonlinear optical properties are dependent only on the chromophore content.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC3MXnsF2murw%253D&md5=6f513e841344b6a2f8bc341fbbaff899
    46. 46
      Ellington, A. D.; Szostak, J. W. In vitro selection of RNA molecules that bind specific ligands. Nature 1990, 346, 818– 822,  DOI: 10.1038/346818a0
      46
      In vitro selection of RNA molecules that bind specific ligands
      Ellington, Andrew D.; Szostak, Jack W.
      Nature (London, United Kingdom) (1990), 346 (6287), 818-22CODEN: NATUAS; ISSN:0028-0836.
      Subpopulations of RNA mols. that bind specifically to a variety of org. dyes have been isolated from a population of random sequence RNA mols. Roughly one in 1010 random sequence RNA mols. folds in such a way as to create a specific binding site for small ligands.
      >> More from SciFinder ®
      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADyaK3MXitVGgsw%253D%253D&md5=522ad1b4f0284ee88173b02035f9e9c5
    47. 47
      Oyarzún, D. A.; Chaves, M. Design of a bistable switch to control cellular uptake. Journal of The Royal Society Interface 2015, 12, 20150618,  DOI: 10.1098/rsif.2015.0618
      47
      Design of a bistable switch to control cellular uptake
      Oyarzun Diego A; Chaves Madalena
      Journal of the Royal Society, Interface (2015), 12 (113), 20150618 ISSN:.
      Bistable switches are widely used in synthetic biology to trigger cellular functions in response to environmental signals. All bistable switches developed so far, however, control the expression of target genes without access to other layers of the cellular machinery. Here, we propose a bistable switch to control the rate at which cells take up a metabolite from the environment. An uptake switch provides a new interface to command metabolic activity from the extracellular space and has great potential as a building block in more complex circuits that coordinate pathway activity across cell cultures, allocate metabolic tasks among different strains or require cell-to-cell communication with metabolic signals. Inspired by uptake systems found in nature, we propose to couple metabolite import and utilization with a genetic circuit under feedback regulation. Using mathematical models and analysis, we determined the circuit architectures that produce bistability and obtained their design space for bistability in terms of experimentally tuneable parameters. We found an activation-repression architecture to be the most robust switch because it displays bistability for the largest range of design parameters and requires little fine-tuning of the promoters' response curves. Our analytic results are based on on-off approximations of promoter activity and are in excellent qualitative agreement with simulations of more realistic models. With further analysis and simulation, we established conditions to maximize the parameter design space and to produce bimodal phenotypes via hysteresis and cell-to-cell variability. Our results highlight how mathematical analysis can drive the discovery of new circuits for synthetic biology, as the proposed circuit has all the hallmarks of a toggle switch and stands as a promising design to control metabolic phenotypes across cell cultures.
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      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A280%3ADC%252BC28risVWqsA%253D%253D&md5=b1206bb3c912b068b3c574eb3f50782c
    48. 48
      Virtanen, P.; Gommers, R.; Oliphant, T. E.; Haberland, M.; Reddy, T.; Cournapeau, D.; Burovski, E.; Peterson, P.; Weckesser, W.; Bright, J. SciPy 1.0: fundamental algorithms for scientific computing in Python. Nat. Methods 2020, 17, 261– 272,  DOI: 10.1038/s41592-019-0686-2
      48
      SciPy 1.0: fundamental algorithms for scientific computing in Python
      Virtanen, Pauli; Gommers, Ralf; Oliphant, Travis E.; Haberland, Matt; Reddy, Tyler; Cournapeau, David; Burovski, Evgeni; Peterson, Pearu; Weckesser, Warren; Bright, Jonathan; van der Walt, Stefan J.; Brett, Matthew; Wilson, Joshua; Millman, K. Jarrod; Mayorov, Nikolay; Nelson, Andrew R. J.; Jones, Eric; Kern, Robert; Larson, Eric; Carey, C. J.; Polat, Ilhan; Feng, Yu; Moore, Eric W.; Vander Plas, Jake; Laxalde, Denis; Perktold, Josef; Cimrman, Robert; Henriksen, Ian; Quintero, E. A.; Harris, Charles R.; Archibald, Anne M.; Ribeiro, Antonio H.; Pedregosa, Fabian; van Mulbregt, Paul
      Nature Methods (2020), 17 (3), 261-272CODEN: NMAEA3; ISSN:1548-7091. (Nature Research)
      Abstr.: SciPy is an open-source scientific computing library for the Python programming language. Since its initial release in 2001, SciPy has become a de facto std. for leveraging scientific algorithms in Python, with over 600 unique code contributors, thousands of dependent packages, over 100,000 dependent repositories and millions of downloads per yr. In this work, we provide an overview of the capabilities and development practices of SciPy 1.0 and highlight some recent tech. developments.
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    49. 49
      Abdi, H.; Williams, L. J. Principal component analysis. Wiley Interdisciplinary Reviews: Computational Statistics 2010, 2, 433– 459,  DOI: 10.1002/wics.101
      There is no corresponding record for this reference.
    50. 50
      Liu, D.; Mannan, A. A.; Han, Y.; Oyarzún, D. A.; Zhang, F. Dynamic metabolic control: towards precision engineering of metabolism. Journal of Industrial Microbiology and Biotechnology 2018, 45, 535– 543,  DOI: 10.1007/s10295-018-2013-9
      50
      Dynamic metabolic control: towards precision engineering of metabolism
      Liu, Di; Mannan, Ahmad A.; Han, Yichao; Oyarzun, Diego A.; Zhang, Fuzhong
      Journal of Industrial Microbiology & Biotechnology (2018), 45 (7), 535-543CODEN: JIMBFL; ISSN:1367-5435. (Springer)
      Advances in metabolic engineering have led to the synthesis of a wide variety of valuable chems. in microorganisms. The key to commercializing these processes is the improvement of titer, productivity, yield, and robustness. Traditional approaches to enhancing prodn. use the "push-pull-block" strategy that modulates enzyme expression under static control. However, strains are often optimized for specific lab. set-up and are sensitive to environmental fluctuations. Exposure to sub-optimal growth conditions during large-scale fermn. often reduces their prodn. capacity. Moreover, static control of engineered pathways may imbalance cofactors or cause the accumulation of toxic intermediates, which imposes burden on the host and results in decreased prodn. To overcome these problems, the last decade has witnessed the emergence of a new technol. that uses synthetic regulation to control heterologous pathways dynamically, in ways akin to regulatory networks found in nature. Here, we review natural metabolic control strategies and recent developments in how they inspire the engineering of dynamically regulated pathways. We further discuss the challenges of designing and engineering dynamic control and highlight how model-based design can provide a powerful formalism to engineer dynamic control circuits, which together with the tools of synthetic biol., can work to enhance microbial prodn.
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    51. 51
      Radivojević, T.; Costello, Z.; Workman, K.; García Martín, H. A machine learning Automated Recommendation Tool for synthetic biology. Nat. Commun. 2020, 11, 1– 14,  DOI: 10.1038/s41467-020-18008-4
      There is no corresponding record for this reference.
    52. 52
      Carbonell, P.; Radivojevic, T.; García Martín, H. Opportunities at the Intersection of Synthetic Biology, Machine Learning, and Automation. ACS Synth. Biol. 2019, 8, 1474– 1477,  DOI: 10.1021/acssynbio.8b00540
      52
      Opportunities at the Intersection of Synthetic Biology, Machine Learning, and Automation
      Carbonell, Pablo; Radivojevic, Tijana; Garcia Martin, Hector
      ACS Synthetic Biology (2019), 8 (7), 1474-1477CODEN: ASBCD6; ISSN:2161-5063. (American Chemical Society)
      A review. Our inability to predict the behavior of biol. systems severely hampers progress in bioengineering and biomedical applications. We cannot predict the effect of genotype changes on phenotype, nor extrapolate the large-scale behavior from small-scale expts. Machine learning techniques recently reached a new level of maturity, and are capable of providing the needed predictive power without a detailed mechanistic understanding. However, they require large amts. of data to be trained. The amt. and quality of data required can only be produced through a combination of synthetic biol. and automation, so as to generate a large diversity of biol. systems with high reproducibility. A sustained investment in the intersection of synthetic biol., machine learning, and automation will drive forward predictive biol., and produce improved machine learning algorithms.
      >> More from SciFinder ®
      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BC1MXhtlKlt77F&md5=71d8ef5175d99b332d7679340da63e4a
    53. 53
      Nikolados, E.-M.; Wongprommoon, A.; Aodha, O. M.; Cambray, G.; Oyarzún, D. A. Accuracy and data efficiency in deep learning models of protein expression. Nat. Commun. 2022, 13, 7755,  DOI: 10.1038/s41467-022-34902-5
      53
      Accuracy and data efficiency in deep learning models of protein expression
      Nikolados, Evangelos-Marios; Wongprommoon, Arin; Aodha, Oisin Mac; Cambray, Guillaume; Oyarzun, Diego A.
      Nature Communications (2022), 13 (1), 7755CODEN: NCAOBW; ISSN:2041-1723. (Nature Portfolio)
      Synthetic biol. often involves engineering microbial strains to express high-value proteins. Thanks to progress in rapid DNA synthesis and sequencing, deep learning has emerged as a promising approach to build sequence-to-expression models for strain optimization. But such models need large and costly training data that create steep entry barriers for many labs. Here we study the relation between accuracy and data efficiency in an atlas of machine learning models trained on datasets of varied size and sequence diversity. We show that deep learning can achieve good prediction accuracy with much smaller datasets than previously thought. We demonstrate that controlled sequence diversity leads to substantial gains in data efficiency and employed Explainable AI to show that convolutional neural networks can finely discriminate between input DNA sequences. Our results provide guidelines for designing genotype-phenotype screens that balance cost and quality of training data, thus helping promote the wider adoption of deep learning in the biotechnol. sector.
      >> More from SciFinder ®
      https://chemport.cas.org/services/resolver?origin=ACS&resolution=options&coi=1%3ACAS%3A528%3ADC%252BB38XjtFart7zI&md5=edb00255d2f8ea0804dd8697423d4c55
    54. 54
      Gardner, D. J.; Reynolds, D. R.; Woodward, C. S.; Balos, C. J. Enabling new flexibility in the SUNDIALS suite of nonlinear and differential/algebraic equation solvers. ACM Trans. Math. Softw. 2022, 48, 1,  DOI: 10.1145/3539801
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      Solgi, R. M. Geneticalgorithm Package ; 2020. https://pypi.org/project/geneticalgorithm/.
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      Loh, W.-L. On Latin hypercube sampling. Ann. Statist. 1996, 24, 2058– 2080,  DOI: 10.1214/aos/1069362310
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