to any of the stimuli learned have rates which gradually increase with the amplitude of synaptic potentiation. b. When the average LTP increases beyond a critical value, specific local attractors appear abruptly against the background of the global uniform spontaneous attractor. This happens with either gradual or discrete stochastic LTP. 4. The above findings predict that in the process of learning unfamiliar stimuli, there is a stage in which all neurons selective to any of the learned stimuli enhance their spontaneous activity relative to the rest. Then, abruptly, selective delay activity appear. Both facts could be observed in single unit recordings in delayed match to sample experiments. 5. Beyond this critical learning strength the local module has two types of collective activity. It either participates in the global spontaneous activity, or it maintains a stimulus selective elevated activity distribution. The particular mode of behavior depends on the stimulus: if it is unfa

Shunting inhibition---a conductance change with a reversal potential close to the resting potential of the cell---has been shown to have a divisive effect on subthreshold EPSP amplitudes. It has therefore been assumed to have the same divisive effect on firing rates. We show that shunting inhibition actually has a subtractive effect on the firing rate in most circumstances. Averaged over several interspike intervals, the spiking mechanism effectively clamps the somatic membrane potential to a value significantly above the resting potential, so that the current through the shunting conductance is approximately independent of the firing rate. This leads to a subtractive rather than a divisive effect. In addition, at distal synapses shunting inhibition will also have an approximately subtractive effect if the excitatory conductance is not small compared to the inhibitory conductance. Therefore regulating a cell's passive membrane conductance---for instance via massive feedback---is not an...

this article). Stochastic forcing also broadens the peak of the average subthreshold voltage versus input current curves as in Figure 5b (not shown). In view of this, we have set out to determine (1) whether a subtractive effect is also present with stochastic synaptic input and (2) whether stochastic input produces a divisive regime at lower firing frequencies, as in the compartmental model. For simplicity we considered only the voltage-independent case (# 0) of equation 4.1, since divisiveness was also seen for the S synapses in the compartmental simulations (see Figure 5a). There are a variety of ways in which a stochastic synaptic model with reversal potentials can be approximated by diffusion models (Lansk y & Sato, 1999). Here we let the conductance g in the LIF model be a stochastic quantity by setting g = +#(g)#(t) where g is the mean conductance and #(t) is a stochastic process of standard deviation #( g). To match the smoothness of the conductance fluctuations in the compartmental model, we model #(t) as an Ornstein-Uhlenbeck process (lowpass-filtered gaussian white noise) with correlation time # 75 ms; our results were not qualitatively sensitive to this correlation time. Equation 4.1 thus becomes a stochastic differential equation with multiplicative noise (since the noise term multiplies the state variable Vm ): #t + #( g)#(t) I (4.7 # ) ## #t =- # +#(4.7 ## ) where # is gaussian white noise with zero-mean and unit standard deviation. Numerical simulations produced sigmoidal curves of mean firing rate versus input current I (see Figure 7), as expected. Increases in inhibitory firing rate in the compartmental model were modeled here as increases in mean conductance g; these increases are linearly related, as discussed above...

We present a dynamical theory of integrate-and-fire neurons with strong synaptic coupling. We show how phase-locked states that are stable in the weak coupling regime can destabilize as the coupling is increased, leading to states characterized by spatiotemporal variations in the interspike intervals (ISIs). The dynamics is compared with that of a corresponding network of analog neurons in which the outputs of the neurons are taken to be mean firing rates. A fundamental result is that for slow interactions, there is good agreement between the two models (on an appropriately defined timescale). Various examples of desynchronization in the strong coupling regime are presented. First, a globally coupled network of identical neurons with strong inhibitory coupling is shown to exhibit oscillator death in which some of the neurons suppress the activity of others. However, the stability of the synchronous state persists for very large networks and fast synapses. Second, an asymmetric network with a mixture of excitation and inhibition is shown to exhibit periodic bursting patterns. Finally, a one-dimensional network of neurons with long-range interactions is shown to desynchronize to a state with a spatially periodic pattern of mean firing rates across the network. This is modulated by deterministic fluctuations of the instantaneous firing rate whose size is an increasing function of the speed of synaptic response. 1

The speed of processing in the visual cortical areas can be fast, with for example the latency of neuronal responses increasing by only approximately 10 ms per area in the ventral visual system sequence V1 to V2 to V4 to inferior temporal visual cortex. This has led to the suggestion that rapid visual processing can only be based on the feedforward connections between cortical areas. To test this idea, we investigated the dynamics of information retrieval in multiple layer networks using a four-stage feedforward network modelled with continuous dynamics with integrate-and-fire neurons, and associative synaptic connections between stages with a synaptic time constant of 10 ms. Through the implementation of continuous dynamics, we found latency differences in information retrieval of only 5 ms per layer when local excitation was absent and processing was purely feedforward. However, information latency differences increased significantly when non-associative local excitation was included. We also found that local recurrent excitation through associatively modified synapses can contribute significantly to processing in as little as 15 ms per layer, including the feedforward and local feedback processing. Moreover, and in contrast to purely feed-forward processing, the contribution of local recurrent feedback was useful and approximately this rapid even when retrieval was made difficult by noise. These findings suggest that cortical information processing can benefit from recurrent circuits when the allowed processing time per cortical area is at least 15 ms long.

A description of neuronal activity on the level of ion channels, as in the Hodgkin-Huxley model, leads to a set of coupled nonlinear differential equations which are difficult to analyze. In this paper, we present a conceptual framework for a reduction of the nonlinear spike dynamics to a threshold process. Spikes occur if the membrane potential u(t) reaches a threshold #. The voltage response to spike input is described by the postsynaptic potential ffl. Postsynaptic potentials of several input spikes are added linearly until u reaches #. The output pulse itself and the reset/refractory period which follow the pulse are described by a function j. Since ffl and j can be interpreted as response kernels, the resulting model is called the Spike Response Model (SRM). After a short review of the Hodgkin-Huxley model we show that (i) Hodgkin-Huxley dynamics with time-dependent input can be reproduced to a high degree of accuracy by the SRM; (ii) the simple integrate-and-fire neuron is a spe...

A neuron extensively receives both inhibitory and excitatory inputs. What is the ratio r between these two types of input so that the neuron could most accurately read out input information (rate)? We explore the issue in the present paper provided that the neuron is an ideal observer--decoding the input information with the attainment of the Cramer-Rao inequality bound. It is found that in general adding certain amounts of inhibitory inputs to a neuron improves its capability of accurately decoding the input information. By calculating the Fisher information of an integrate-and-fire neuron, we determine the optimal ratio r for decoding the input information from an observation of the e#erent interspike intervals. Surprisingly the Fisher information could be zero for certain values of the ratio, seemingly implying that it is impossible to read out the encoded information at these values. By analyzing the maximum likelihood estimate of the input information, it is then concluded that the input information is in fact most easily estimated at the points where the Fisher information vanishes. 1

The subthreshold membrane time constant ø governs how quickly the membrane potential approaches equilibrium, and has been used to estimate how quickly a neuron can respond to its inputs. However, spiking neurons do not have an equilibrium voltage; subthreshold dynamics do not apply to their firing rates. In fact, a spiking neuron can respond much faster than ø . For current step inputs, a non-adapting spiking neuron reaches its final firing after a single interspike interval, and an ensemble of such neurons can respond arbitrarily fast. Firing rate dynamics are controlled by postsynaptic conductances, adaptation, and other processes in the cell, rather than passive properties of the membrane. The spiking mechanism can speed up neuronal responses, so that information can be passed to successive stages of a feedforward network in considerably less time than ø . Introduction Computations in the nervous system can be considered on many different organizational scales, from the filtering p...

llular recordings in rat neocortex. Neurosci. 54:329--346. [12, 83] Torre, V., and Poggio, T. 1978. A synaptic mechanism possibly underlying directional selectivity to motion. Proc. R. Soc. Lond. B 202:409--416. [56] Towe, A. L. 1973. Sampling single neuron activity. In: Bioelectric Recording Techniques. Part A. Cellular Processes and Brain Potentials. Thompson, R. F., Patterson, M. M., eds., pp. 79-93. Academic Press. [20] Tranchina, D., and Nicholson, C. 1986. A model for the polarization of neurons by extrinsically applied electric fields. Biophys. J. 50:1139--1156. [30, 33, 34] Traub, R. D., Dudek, F. E., Snow, R. W., and Knowles, W. D. 1985a. Computer simulations indicate that electrical field effects contribute to the shape of the epileptiform field potential. Neurosci. 15:947--958. [27, 35] Traub, R. D., Dudek, F. E., Taylor, C. P., and Knowles, W. D. 1985b. Simulation of hippocampal afterdischa