References

Abbott et al., 1997

Abbott, L., Varela, J., Sen, K., and S.B., N. (1997). Synaptic depression and cortical gain control. Science, 275:220-4.

Abeles et al., 1994

Abeles, M., Prut, Y., Bergman, H., and Vaadia, E. (1994). Synchronization in neuronal transmission and its importance for information processing. Progress in Brain Research, 102:395-404.

Allen and Stevens, 1994

Allen, C. and Stevens, C. (1994). An evaluation of causes for unreliability of synaptic transmission. PNAS, 91:10380-3.

Bair et al., 1997

Bair, W., Cavanaugh, J., and Movshon, J. (1997). Reconstructing stimulus velocity from neuronal responses in area MT. NIPS, 10:34-40.

Bekkers and Stevens, 1990

Bekkers, J. and Stevens, C. (1990). Origin of variability in quantal size in cultured hippocampal neurons and hippocampal slices. PNAS, 87:5359-5362.

Bialek et al., 1993

Bialek, W., DeWeese, F., Rieke, F., and Warland, D. (1993). Bits and brains: Information flow in the nervous system. Physica A, 200:581-593.

Bialek et al., 1991

Bialek, W., Rieke, F., de Ruyter van Steveninck, R., and Warland, D. (1991). Reading a neural code. Science, 252:1854-1857.

Britten et al., 1992

Britten, K., Shadlen, M., Newsome, W., and Movshon, J. (1992). The analysis of visual motion: a comparison of neuronal and psychophysical performance. Journal of Neuroscience, 12:4745-4765.

Bryant and Segundo, 1976

Bryant, H. and Segundo, J. (1976). Spike initiation by transmembrane current: a white-noise analysis. J. Physiol., 260:279-314.

Buracas et al., 1996

Buracas, G., Zador, A., Deweese, M., and Albright, T. (1996). Measurements of information rates in monkey MT neurons in response to time-varying stimuli. Soc. for Neurosci. Abst., 22:717.

Castro-Alamancos and Connors, 1997

Castro-Alamancos, M. and Connors, B. (1997). Distinct forms of short-term plasticity at excitatory synapses of hippocampus and neocortex. PNAS, 94:4161-4166.

Dan et al., 1996

Dan, Y., Atick, J., and Reid, R. (1996). Efficient coding of natural scenes in the lateral geniculate nucleus: experimental test of a computational theory. J. Neurosci., 15:3351-62.

de Ruyter van Steveninck and Bialek, 1988

de Ruyter van Steveninck, R. and Bialek, W. (1988). Real-time performance of a movement-senstivive neuron in the blowfly visual system: coding and information transmission in short spike sequences. Proc. R. Soc. Lond. B, 234:379-414.

de Ruyter van Steveninck et al., 1997

de Ruyter van Steveninck, R., Lewen, G. D., Strong, S. P., and Koberle, R. (1997). Reproducibility and variability in neural spike trains. Science, 275:1805-1807.

de Ruyter Van Steveninck and Laughlin, 1996

de Ruyter Van Steveninck, R. R. and Laughlin, S. B. (1996). The rate of information transfer at graded-potential synapses. Nature, 379:642-645.

DeWeese, 1995

DeWeese, M. (1995). Optimization principles for the neural code. PhD thesis, Dept of Physics, Princeton University.

DeWeese, 1996

DeWeese, M. (1996). Optimization principles for the neural code. NIPS, 8:281-287.

Dobrunz and Stevens, 1997

Dobrunz, L. and Stevens, C. (1997). Heterogeneity of release probability, facilitation and depletion at central synapses. Neuron, 18:995-1008.

Fano, 1947

Fano, U. (1947). Ionization yield of rations. II. the fluctuations of the number of ions. Phys. Rev., 72:26-29.

Feller, 1971

Feller, W. (1971). An introduction to probability theory and its applications, vol. 2, edition. Wiley.

Ferster and Spruston, 1995

Ferster, D. and Spruston, N. (1995). Cracking the neuronal code. Science, 270:756-757.

Fisher et al., 1997

Fisher, S., Fischer, T., and Carew, T. (1997). Multiple overlapping processes underlying short-term synaptic enhancement. T.I.N.S., 20:170-7.

Gabbiani and Koch, 1996

Gabbiani, F. and Koch, C. (1996). Coding of time-varying signals in spike trains. Neural Computation, 8:44-66.

Gabbiani et al., 1996

Gabbiani, F., Metzner, W., Wessel, R., and C., K. (1996). Coding of time-varying signals in spike trains. Nature, 384:564-7.

Golomb et al., 1997

Golomb, D., Hertz, J., Panzeri, S., Treves, A., and B., R. (1997). How well can we estimate the information carried in neuronal responses from limited samples? Neural Computation, 3:649-65.

Hessler et al., 1993

Hessler, N., Shirke, A., and R., M. (1993). The probability of transmitter release at a mammalian central synapse. Nature, 366:569-572.

Katz, 1966

Katz, B. (1966). Nerve, muscle, and synapse. New York, McGraw-Hill.

MacKay and McCulloch, 1952

MacKay, D. and McCulloch, W. (1952). The limiting information capacity of a neuronal link. Bull. Math. Biophys., 14:127-135.

Magleby, 1987

Magleby, K. (1987). Short term synaptic plasticity. In Edelman, G. M., Gall, W. E., and Cowan, W. M., editors, Synaptic function. Wiley, New York.

Mainen and Sejnowski, 1995

Mainen, Z. and Sejnowski, T. (1995). Reliability of spike timing in neocortical neurons. Science, 268:1503-1505.

Markram and Tsodyks, 1996

Markram, H. and Tsodyks, M. (1996). Redistribution of synaptic efficacy between neocortical pyramidal neurons. Nature, 382:807-10.

Optican and Richmond, 1987

Optican, L. and Richmond, B. (1987). Temporal encoding of two-dimensional patterns by single units in primate inferior temporal cortex. iii. information theoretic analysis. J. Neurophysiol., 57:162-178.

Richmond and Optican, 1990

Richmond, B. and Optican, L. (1990). Temporal encoding of two-dimensional patterns by single units in primate primary visual cortex. ii. information transmission. J. Neurophysiol., 64:370-380.

Rieke et al., 1997

Rieke, F., Warland, D., de Ruyter van Steveninck, R., and Bialek, W. (1997). Spikes: Exploring the neural code. MIT Press.

Rosenmund et al., 1993

Rosenmund, C., Clements, J., and Westbrook, G. (1993). Nonuniform probability of glutamate release at a hippocampal synapse. Science, 262:754-757.

Shadlen and Newsome, 1994

Shadlen, M. and Newsome, W. (1994). Noise, neural codes and cortical organization. Current Opinion in Neurobiology, 4:569-579.

Shadlen and Newsome, 1995

Shadlen, M. and Newsome, W. (1995). Is there a signal in the noise? [comment]. Current Opinion in Neurobiology, 5:248-250.

Shannon and Weaver, 1948

Shannon, C. and Weaver, W. (1948). A Mathematical theory of communication. Univ. of Illinois Press.

Shepherd, 1990

Shepherd, G. (1990). The Synaptic Organization of the Brain, edition. Oxford University Press.

Softky, 1995

Softky, W. (1995). Simple codes versus efficient codes. Current Opinion in Neurobiology, 5:239-247.

Sorra and Harris, 1993

Sorra, K. and Harris, K. (1993). Occurrence and three-dimensional structure of multiple synapses between individual radiatum axons and their target pyramidal cells in hippocampal area CA1. J. Neuroscience, 13:3736-48.

Stevens and Zador, 1995

Stevens, C. and Zador, A. (1995). Neural coding: the engima of the brain. Current Biology, 12:1370-1371.

Stevens and Zador, 1996

Stevens, C. and Zador, A. (1996). Information through a spiking neuron. NIPS, 8:75-81.

Stratford et al., 1996

Stratford, K., Tarczy-Hornoch, K., Martin, K., Bannister, N., and J.J., J. (1996). Excitatory synaptic inputs to spiny stellate cells in cat visual cortex. Nature, 382:258-61.

Tovee et al., 1993

Tovee, M., Rolls, E., Treves, A., and R.P., B. (1993). Information encoding and the responses of single neurons in the primate temporal visual cortex. J. Neurophysiol., 70:640-654.

Tsodyks and Markram, 1997

Tsodyks, M. and Markram, H. (1997). The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proc. Natl. Acad. Sci., 94:719-23.

Varela et al., 1997

Varela, J. A., Sen, K., Gibson, J., Fost, J., Abbott, L. F., and Nelson, S. B. (1997). A quantitative description of short-term plasticity at excitatory synapses in layer 2/3 of rat primary visual cortex. J. Neurosci, 17:?

Warland et al., 1997

Warland, D., Reinagel, P., and Meister, M. (1997). Decoding visual information from a population of retinal ganglion cells. J. Neurophysiol., 78:2336-2350.

Zador and Dobrunz, 1997

Zador, A. and Dobrunz, L. (1997). Dynamic synapses in the cortex. Neuron, 19:1-4.

Zador and Maass, 1997

Zador, A. and Maass, W. (1997). Computing with dynamics synapses. NIPS, in press.

Zador and Pearlmutter, 1996

Zador, A. M. and Pearlmutter, B. A. (1996). VC dimension of an integrate and fire neuron model. Neural Computation, 8(3). 611-624.

Zucker, 1989

Zucker, R. (1989). Short-term synaptic plasticity. Annual Review of Neuroscience, 12:13-31.

  
Figure 1: Synaptic variability is the dominant source of output variability. A, top The spike generator is reliable. The response of a neuron from layer II/III of a slice of rat neocortex to 20 consecutive even-numbered trials in which precisely the same synthetic synaptic current was injected through a somatic electrode (see Methods). Most of the spikes are aligned to a precision of about 1 msec, although a few ``stray'' or ``displaced'' spikes are also seen. This experiment places a lower bound on the precision with which spikes can be generated in response to identically repeated stimuli; the remaining variability is due to some combination of experimental noise and the intrinsic variability of the spike generator. B, bottom Noisy synapses introduce output variability. The response to 20 consecutive odd-numbered trials (interleaved with the even-numbered trials presented in A) is shown. In this experiment, synthetic currents were generated from the same ensemble as in A, using a fixed pattern of presynaptic spikes drawn from a Poisson ensemble, but assuming that, because of synaptic failures, 3/10 spikes failed to elicit an EPSC (). (The current repeated injected in the experiment in A is equivalent to the assumption that the same 3/10 spikes failed to elicit an EPSC on every trial). Under these conditions, the effective output reliability is markedly decreased, as seen by the poor alignment of the spikes giving a haphazard appearance to the raster. For this experiment, quantal fluctuations-which would tend to further decrease the output reliability--were suppressed (CV=0). Parameters for synthetic synaptic currents: Quantal size (mean): 30 pA; quantal size (coefficient of variation): 0; ; .

  
Figure 2: Dependence of entropy and information firing rate in a model neuron. A,left The entropy and information per spike are plotted as a function of the firing rate in a model integrate-and-fire neuron. The dashed curve represents the total entropy, which quantifies the total output variability of the spike train. The dotted line represent the conditional entropy, which quantifies the variability that remains when the signal is held constant. The solid line is the mutual information between the input and the output, and is the difference between these quantities. B, right The corresponding entropy and information rates in bits/millisecond are shown. Parameters: mV; M; msec; mV; mV; quantal size (mean): 30 pA; quantal size (coefficient of variation): 0.2; ; . The spike rate was varied by increasing the presynaptic Poisson input rate. The smooth curves shown represent the fit of a high-order polynomial to the values computed at a large number of firing rates. In this and all other simulations presented, a binsize of 1 millisecond was used.

  
Figure 3: Information depends on synaptic release probability. A, left The information rate is plotted as a function of the firing rate for four values of the release probability , 0.9, 0.6, 0.3 in a model integrate-and-fire neuron. (top to bottom). The top curve is the same as that shown in Fig. 2B. B, right The information rate is plotted as a function of the release probability at F=40 Hz. In each simulation, was the same at all synapses. In order to maintain the Poisson input rate constant, the Poisson rate at each synapse was increased to compensate for the decrease in the Poisson rate due to synaptic failures; thus for all curves, EPSCs arrived at a net rate of 2.4/msec (see Model of synaptic drive for details). Except as indicated, the parameters are the same as in Fig. 2B.

  
Figure 4: Information rate depends on number of functional contacts. A, left The information rate is plotted as a function of release probability for three values of the number of functional contacts , 5 and 20 (bottom to top) in a model integrate-and-fire neuron. The bottom curve is the same as that shown in Fig. 3B. B, right The information rate is plotted as a function of the number of functional contacts for , F=40 Hz. In order to maintain the Poisson input rate constant, the Poisson rate at each synapse was increased to compensate for the changes in the due to synaptic failures or the number of functional contacts; thus for all curves, EPSCs arrived at a net rate of 2.4/msec (see Model of synaptic drive for details). Except as indicated, the parameters are the same as in Fig. 2.

  
Figure 5: Information is inversely proportional to the number of functional contacts in a mean rate code. In these simulations, the input Poisson rate was held constant. The Fano factor (the variance divided by the mean of the spike count) during a 250 millisecond window is plotted as a function of the number of functional contacts. This measure can be thought of as an effective ``noise-to-signal'' ratio for a mean rate code, since it reflects how well the spike count can be estimated. A larger ratio indicates that the spike count is harder to estimate. The curve illustrates that an increase in the number of functional contacts leads to an increase in the variance of the synaptic current driving the neuron, and thereby an increase in the Fano factor. In order to maintain the rate of Poisson input constant, the Poisson rate at each synapse was increased to compensate for the changes in the due to synaptic failures or the number of functional contacts; thus for all curves, EPSCs arrived at a net rate of 2.4/msec (see Model of synaptic drive for details). Except as indicated, the parameters are the same as in Fig. 2.