3.1 Brown and Henri

At the beginning of the 20th century the nature of enzyme catalysis and kinetics was of widespread interest and was studied by several different authors, most notably Brown [1] and Henri [2, 3]. Of these, Brown [1] was probably the first to realize that a mechanism that required passage through an enzyme–substrate complex implied an upper limit on the rate of an enzyme-catalysed reaction, and he can be credited with introducing the first model of enzyme saturation. However, his interpretation was qualitative, unsupported by any algebra. Henri [2, 3] criticized it for its completely unrealistic assumption that the enzyme–substrate complex had a fixed lifetime, and derived an equation for the instantaneous rate of a reaction subject to product inhibition:

((4))

in which a is the total amount of sucrose, x is the amount of product at time

is a constant proportional to the amount of enzyme, and m and n are also constants. In his thesis [3], but not in his paper [2], he went on to note that if

when

then this can be simplified to

((5))

which is just the Michaelis–Menten equation in unfamiliar symbols, other than the fact that it expresses the rate at which the amount (not the concentration) of product changes, i.e. the rate of conversion [22], whereas today a kinetic equation usually expresses the rate at which the concentration changes. However, apart from noting that this gave a good account of the experimental observations with invertase, Henri took the matter no further: he did not point out that this simpler equation could form the basis of an experimental approach that would allow a far easier analysis than the attempts to use the time course that had long dominated efforts to understand the kinetics of enzyme-catalysed reactions.

Most of the early discussion of the enzyme–substrate complex incorporated two assumptions: that it must necessarily participate as an intermediate in the reaction mechanism; and that it was maintained at equilibrium with the free enzyme and substrate. Although Henri [2, 3] thought that its participation as an intermediate was the most likely interpretation, he also considered an alternative possibility, and found that if the complex existed only as a “nuisance complex” in a side reaction the kinetic behaviour would be indistinguishable from that given by assuming it to be an intermediate. That is true so far as the steady state is concerned, but transient-state measurements allow the two possibilities to be distinguished [23, 24]. Non-productive complexes can certainly exist, and can complicate the interpretation of data for enzymes that act in nature on large polymers when studied with small synthetic substrates [25], but no examples are known for which Henri's alternative mechanism is the whole explanation of enzyme saturation.

3.2 Van Slyke and Cullen

Van Slyke and Cullen [26], who were studying urease at about the same time as Michaelis and Menten's work, did not assume that the enzyme–substrate complex was at equilibrium with the free components; instead they assumed that it would be formed in an irreversible reaction and broken down in a second irreversible reaction to regenerate the free enzyme. They treated the time required for a complete catalytic cycle as the sum of the times required for the two steps, and the steady-state assumption was implicit in their treatment. Processes occurring in series can always be analysed in terms of additive times, but Van Slyke and Cullen's approach has not often been used explicitly in later work. However, it can be very useful, for example, for considering the steps in metabolic processes [27]. Assigning rate constants

and

to Van Slyke and Cullen's two processes allowed the rate equation to be written as follows:

((6))

This would be experimentally indistinguishable by steady-state experiments from Eq. (2), though the interpretation of the constant in the denominator is different. In a companion paper Van Slyke and Zacharias [28] extended this analysis to take account of the effects of reaction products and protons on the rate of reaction.

Van Slyke and co-workers did not mention Michaelis and Menten's paper, and were almost certainly unaware of it. Much later in his life Van Slyke made an indirect but important contribution to enzymology when he sponsored publication of the theory of induced fit [29]. In 1911, at the beginning of his career, he had worked with Emil Fischer in Berlin, but that did not inhibit him from facilitating the first dent in the long established lock-and-key model of enzyme specificity.

3.3 Reassessing Henri's contribution

Segal's classic review [30] provides a more detailed account of the development of understanding of the kinetics of enzyme-catalysed reactions than I have given here, and Mazat [31] makes a somewhat different (though not incompatible) assessment of the relative importance of the contributions of Henri on the one hand and Michaelis and Menten on the other. He points out that although attributing Eq. (2) to Michaelis and Menten alone is too deeply entrenched to be dislodged, it is not too late to give Henri due credit for his considerable contribution, and that Eq. (4) could very properly be called the “Henri equation”, the first equation for competitive product inhibition to be proposed, and conceptually important for understanding the effects of products on the invertase-catalysed reaction. In modern symbols the Henri equation would be written as follows:

((7))

in which

is the inhibition constant for product, and the other symbols are as in Eq. (2).

4.1 Control of pH

Although the term and definition of pH are rightly associated with Sørensen [20], Michaelis already had a clear grasp of the importance of the concept, and his work on the effect of hydrogen ions on invertase [32] appeared only a short time after publication of Sørensen's analysis. In the previous work on invertase, Henri [2, 3] ignored the question altogether, and Brown [1] reported that control of acidity was not necessary. O'Sullivan and Tompson [13] had carried out many experiments (they referred to “hundreds”) to determine how much acid needed to be added if reproducible results were to be obtained, but they did not attempt a theoretical analysis and simply made a vague statement that “the acidity was in the most favourable proportion”. Presumably Henri and Brown were able to evade the question by using preparations that contained enough natural buffering agents to maintain the pH constant, but it is clear that the reforms introduced by Sørensen [20] and Michaelis [32] are essential for any biochemical experiment today. Michaelis had a long-term interest in hydrogen-ion concentration, and his book [33] became the standard work on the subject. In particular, he introduced the “Michaelis functions” that allow interpretation of bell-shaped pH profiles. As noted already, Van Slyke and Zacharias [28] were also quick to recognize the importance of the hydrogen-ion concentration.

Michaelis's work on hydrogen ions was, in fact, well advanced when Sørensen's paper appeared. He discussed this in his autobiographical notes [34]:

The method of the hydrogen electrode was developed in order to measure the hydrogen ion concentration. It was shown that the effect of an enzyme such as invertase, trypsin, etc. depends on the concentration of the hydrogen ions, and not on the titration acidity. Just when this work was coming to a conclusion, the paper by Sorensen on the same subject was published. However, being familiar with the method, Michaelis, although deprived of the priority, extended these studies by showing that the dependence of enzyme activity on pH was of the same nature as the dependence of the dissociation of a weak acid on pH. The theory of buffers (under the name of “hydrogen ion regulators”) was developed.

4.2 Characterization of inhibitors

As noted already in 5, the Henri equation ((4), 2) takes account of product inhibition, and other predecessors of Michaelis and Menten were also aware that the products of a reaction could have an inhibitory effect on its rate. However, it was Michaelis and his collaborators Rona [35] and Pechstein [36] who first made a systematic study of inhibitors. They classified them as competitive if they increased the apparent value of

with no effect on V, as they observed for the effect of fructose on invertase, and non-competitive if they decreased the apparent value of V with no effect on

On that basis they reported that glucose was a non-competitive inhibitor of invertase, but in reality its effect is more complicated than that. Moreover, their classification is unfortunate for a different reason, as we now realize (probably first emphasized by Cleland [37]) that the rational classification is in terms of effects on the apparent values of

(competitive) and of V (uncompetitive): thus the opposite extreme from competitive inhibition is uncompetitive inhibition, and Michaelis's non-competitive inhibition is just a particular case of mixed inhibition, in which there are effects on both parameters.

4.3 Initial rates

Most of these points are still valid today, though the justification for ignoring the reverse reaction is often given incorrectly, not only by students in answers to examination questions, but sometimes even in textbooks [38] and recommendations of an international union [39]: the reverse reaction cannot occur if no products are present; there is no assumption about the magnitudes of the reverse rate constants;

if

regardless of the magnitude of

Even mutarotation is still important if it is regarded as a specific instance of a general problem, that the products of a reaction may undergo spontaneous reactions that affect the validity of the assay. Today mutarotation, and indeed the whole inversion process, can be much more conveniently followed by nuclear magnetic resonance spectroscopy [40], which allows all of the species in the reaction to be separately monitored, but, polarimetry was an advanced technique for its day, and offers an early example of the use of a physical method for following a chemical reaction.

It is perhaps less true that time courses are too complicated to use. It has long been known how to integrate the Michaelis–Menten equation itself, but methods for integrating steady-state equations for other cases were introduced in an ad hoc way, each mechanism being treated as a special case [41], and Boeker's general method [42, 43] appeared surprisingly recently. In modern practice the use of integrated equations for deducing kinetic parameters from time courses remains unusual. On the one hand even quite small effects of products can lead to large errors in the parameters [44], so the analysis is less straightforward than the initial-rate method introduced by Michaelis and Menten [4]. In addition, although it is easy to integrate Eq. (2), the resulting equation expresses the time t in terms of the concentration of product p and the initial concentration of substrate

:

((8))

whereas one would usually prefer to express p in terms of t. Goudar et al. [45] have shown how this can be achieved.

4.4 The foundation of steady-state kinetics

The importance of Michaelis and Menten's experimental approach lies in the fact that it was a general procedure, readily applicable to other cases, and easily extensible to take advantage of improvements in techniques and knowledge: if it were no more a method for studying invertase it would be forgotten by now. As already mentioned, Michaelis himself played a large part in developing methods for studying pH dependence [32, 33], as well as methods for characterizing enzyme inhibitors [35, 36].

The apparent conflict over the interpretation of the constant in the denominator of the rate equation (

in Eq. (2),

in Eq. (5),

in Eq. (6)), was resolved by recognizing that it was more realistic to regard it as function of three or more rate constants [7], so it defines the concentration of the enzyme–substrate complex in a steady state, not necessarily at equilibrium. This reinterpretation required no fundamental change in Michaelis and Menten's methodology.

The basic theory of steady-state enzyme kinetics could then be regarded as complete, and provided a firm foundation for the later development of methods for studying reactions with multiple substrates, reversibility and specificity. Although Haldane mentioned multiple substrates in his book [8], they were first studied in depth in the 1950s [46-48], but this work had comparatively little impact until it was brought into wide use by a set of landmark papers by Cleland [37, 49, 50]. These appeared just at the midpoint between Michaelis and Menten and the present, and thus have their 50th anniversary this year. Sad to report, Mo Cleland had a fatal accident only a few days after he had agreed to contribute to this Special Issue of FEBS Letters.

Haldane's analysis of reversibility [8] had come earlier: it later opened the door to analysis of the relationships between the thermodynamics and kinetics of enzyme catalysis [51-53]; see also the article by Noor et al. [54] in this issue. Just two important other components remained to be added to the basic theory to allow such development. The first was a convenient method for deriving non-trivial rate equations, which was provided by King and Altman's graphical method [55]; this is readily converted to algorithmic for computer implementation [56] and usable with modern packages such as Mathematica™ [57]. The second was the introduction of statistically satisfactory methods of data analysis, which were supplied by Wilkinson [58] and Johansen and Lumry [59] and brought into wide use with Cleland's computer programs [60].

A topic that took a surprisingly long time to be well understood was enzyme specificity, which was often discussed in vague terms related to the kinetic parameters measured for pure substrates in vitro, until Fersht [61] pointed out that the only useful physiological meaning would be one that defined the capacity of an enzyme to discriminate between substrates that are simultaneously available. In terms of the parameters of Eq. (2), this means that specificity is determined by

not by either V or

alone.