Synaptic Depression and Cortical Gain Control

Deisz R., Prince D., J. Physiol. (London) 412 513 (1989);

Nelson S. B. and, Smetters D., Soc. Neurosci. Abstr. 19, 629 (1993);

Thomson A. M. and, Deuchars J., Trends Neurosci. 17, 119 (1994);

Stratford K. J., Tarczy-Hornoch K., Martin K. A. C., Bannister N. J., Jack J. J. B., Nature 382, 258 (1996).

Markram H., Tsodyks M., Nature 382, 807 (1996).

Nelson S. B., Varela J. A., Gibson J., Sen K., Abbott L. F., Soc. Neurosci. Abstr. 22 952 (1996);

Nelson S. B., Varela J. A., Sen K., Abbott L. F., in Proceedings of Computational Neuroscience-96, Bower J., Ed., July 96, in press.

Slices of rat primary visual cortex (400 μm thickness) were prepared from Long Evans rats (age 17 days to adult) by use of standard methods. Experiments were performed at 35°C. Transillumination was used to visualize the boundaries of primary visual cortex and the border between layers 2/3 and 4. Field potentials (n = 50 slices) were recorded with saline-filled pipettes, amplified by 10,000, filtered at 1 to 1000 Hz, and digitized with Pulse Control software [J. Herrington, K. R. Norton, R. J. Bookman (Univ. of Miami Press, Miami, FL, 1994)]. Trains of electrical stimuli (10 to 150 μA, biphasic, 80 μs) were applied via a monopolar stimulating electrode placed in layer 4 immediately below the recording site in layer 2/3. Stimulus artifacts and antidromic and synaptic responses were differentiated on the basis of latency and effects of tetrodotoxin, which blocks antidromic and synaptic responses, and 6-cyano-7-nitroquinoxaline-2,3-dione (CNQX), which blocks synaptic but not antidromic responses. Synaptic amplitudes were measured from the peak of the initial response, because slopes were often contaminated by antidromic responses. In several experiments in which antidromic responses were clearly separated from initial slopes, we confirmed that analysis of initial slopes and peaks yielded nearly identical measures of short-term plasticity [see V. Aroniadou and T. Teyler, Brain Res. 562, 136 (1991); G. Hess, C. D. Aizenman, J. P. Donoghue, J. Neurophysiol. 75, 1765 (1996). Changes in synaptic responses were not due to reduced polysynaptic contributions, because 50 to 90% reduction in response amplitude with 0.2 to 0.5 mM CNQX, which greatly decreases polysynaptic activation, produced no change in synaptic depression (n = 5). Synaptic responses recorded intracellularly in layer 2/3 in response to layer 4 stimulation (n = 14 cells) matched the latencies, time courses, and short-term plasticity observed in field-potential recordings (3).

This model is related to the analysis of K. L. Magleby and J. E. Zengel, J. Gen. Physiol. 80, 613 (1982); We have modeled all the forms of short-term plasticity seen at these synapses (3), but use a simpler one-component model here.

The specific parameter values used for the examples in this paper are f = 0.75 and τ = 300 ms, obtained from the fit of Fig. 1B. The results we present do not depend critically on the precise values of these parameters; any values within the observed ranges produce qualitatively similar results.

A(r) is computed by noting that, at steady state, the amplitude takes the same value at every spike. Immediately before a spike, the synaptic amplitude is A. This is multiplied by f, and by the time of the next spike, recovers exponentially to 1 + (fA − 1)exp (−1/rτ). Setting these two expressions equal to each other gives A(r) = [1 − exp(−1/rτ)]/[1 − f exp(−1/rτ)]. For large rates and f ≠ 1, we use the approximation exp(−1/rτ) ≈ 1 − 1/rτ to obtain A(r) ≈ 1/(1 − f)rτ.

Tsodyks and Markram have independently reached this conclusion and have considered its functional implications. [M. V. Tsodyks and H. Markram, in Lecture Notes in Computer Science, C. von der Malsburg, W. von Seelen, J. C. Vorbrüggen, B. Sendhoff, Eds. (Springer, Berlin, 1996), pp. 445–450; Proc. Natl. Acad. Sci. U.S.A., in press].

Fechner G. J., Elemente der Psychophysik (Breitkopf and Härtel, Leipzig, Germany, 1880); S. S. Stevens, in Handbook of Perception, E. C. Carterett and M. P. Friedman, Eds. (Academic Press, New York, 1974), vol. 2, pp. 361–389. This relation holds for a variety of sensory modalities and presumably arises from multiple neuronal mechanisms at both peripheral and central levels. The similar behavior of synaptic and perceptual responses need not imply a causal relationship. Rather, these may represent similar solutions to the problem of processing inputs with wide dynamic ranges. If responses proportional to ΔI/I are established at the periphery, transient responses of central neurons driven through depressing synapses will be proportional to ΔI/I divided by the firing rate of their afferents. Because the peripheral firing rate depends only logarithmically on I, the presence of depressing central synapses will have minimal impact on a Weber-Fechner relation established at the periphery.

All simulations use a single compartment integrate-and-fire neuron with a resting potential of −70 mV and a membrane time constant of 30 ms. Synapses are represented as conductance changes with a reversal potential of 0 mV. Upon arrival of a presynaptic spike, the conductance rises instantaneously to a value gα, where g is a constant (the same for all synapses) and α describes the depression at the synapses receiving the spike. The synaptic conductance decays back to zero with a time constant of 2 ms. Presynaptic spike trains were generated from a Poisson distribution. The factor α obeys the differential equation τdα/dt = 1 − α and is multiplied by f whenever a presynaptic spike occurs. When the membrane potential reaches −55 mV, the model neuron fires a spike and is reset to −58 mV. For Fig. 2, the model neuron had 200 synapses with g = 0.075 when depression was included and g = 0.0125 without depression. For Fig. 3, C through E, we used g = 0.027 with depression and g = 0.013 without depression. These adjustments were made to keep the firing rates in roughly the same range for all cases. All synaptic conductances are given in units of the resting membrane conductance.

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In the model, the firing rate of 500 afferents determines the firing rate of a single postsynaptic neuron. The firing rate of afferent i responding to the value x is given by r_i = (100 Hz)exp[−(x − x_i)²/2]. The values of the afferent tuning curve peaks, x_i, are spread uniformly in the range from −10 to 10. The firing rate of the postsynaptic neuron is given by R = Σ_iW_iA(r_i)r_i where A(r) is the steady-state amplitude in (7). The synaptic weight factor is W_i = exp(−x_i²/2).

Gawne T. J., Richmond B. J., J. Neurosci. 13 2758 (1993);

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We used an exponential distribution with a mean of 10 Hz for all inputs, but similar results can be obtained with any reasonable distribution.

To keep the average synaptic conductance constant as the number of synapses, n, was varied, the synaptic weight factor g was set proportional to 1/n. Other scalings of g are possible [see for example M. N. Shadlen and W. T. Newsome, Curr. Opin. Neurobiol. 4, 569 (1994); M. Tsodyks and T. J. Sejnowski, Network 6, 1 (1995); T. W. Troyer and K. D. Miller, Neural Comp., in press] but these do not alter the amplitude of the responses to synchronous uncorrelated rate changes relative to those evoked by asynchronous uncorrelated changes (noise).

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___ T., Kaushal P., Mitchison G. J., ibid., p. 412.

Abbott L. F., Sen K., Varela J. A., Gibson J., Nelson S. B., Soc. Neurosci. Abstr. 22, 952 (1996).

Such manipulations change the value of the parameter f in the model. The steady-state amplitude is proportional to 1/(1 − f)r for large r (7). The factor f can be considered to be the fraction of releasable transmitter remaining after a spike, so 1 − f is the fraction of transmitter released. The steady-state synaptic strength is gA with g proportional to the amount of transmitter released, and thus to 1 − f. As a result, the effective synaptic strength for sustained high rates is proportional to (1 − f)/(1 − f)r = 1/r and is independent of f.

See for example R. C. deCharms and M. M. Merzenich, Nature 381, 610 (1996).

Care and use of animals were in accordance with the guidelines of the Brandeis University animal care committee. We thank P. Dayan, E. Marder, K. Miller, and G. Turrigiano for helpful comments and advice. Supported by the Sloan Center for Theoretical Neurobiology at Brandeis University; NSF grants IBN-9421388, DMS-9503261, and IBN-9511094; a Sloan Research Fellowship; and the W. M. Keck Foundation.