this paper we propose that the irregular ISI arises as a consequence of a specific problem that cortical neurons must solve: the problem of dynamic range or gain control. Cortical neurons receive 3000--10,000 synaptic contacts, 85% of which are asymmetric and hence presumably excitatory (Peters, 1987; Braitenberg and Schuz, 1991). More than half of these contacts are thought to arise from neurons within a 100--200 #m radius of the target cell, reflecting the stereotypical columnar organization of neocortex. Because neurons within a cortical column typically share similar physiological properties, the conditions that excite one neuron are likely to excite a considerable fraction of its afferent input as well (Mountcastle, 1978; Peters and Sethares, 1991), creating a scenario in which saturation of the neuron's firing rate could easily occur. This problem is exacerbated by the fact that EPSPs from individual axons appear to exert substantial impact on the membrane potential (Mason et al., 1991; Otmakhov Received Sept. 15, 1997; revised Feb. 25, 1998; accepted March 3, 1998.

To understand the interspike interval (ISI) variability displayed by visual cortical neurons (Softky and Koch, 1993), it is critical to examine the dynamics of their neuronal integration as well as the variability in their synaptic input current. Most previous models have focused on the latter factor. We match a simple integrate-and-fire model to the experimentally measured integrative properties of cortical regular spiking cells (McCormick et al., 1985). After setting RC parameters, the post-spike voltage reset is set to match experimental measurements of neuronal gain (obtained from in vitro plots of firing frequency vs. injected current). Examination of the resulting model leads to an intuitive picture of neuronal integration that unifies the seemingly contradictory "1= p N " and "random walk" pictures that have previously been proposed. When ISI's are dominated by post-spike recovery, 1= p N arguments hold and spiking is regular; after the "memory" of the last spike becomes ne...

this technical difficulty by considering for example in a simplified setting only correlation variables

mutal Slovin, and Moshe Abeles. Spatiotemporal structure of millisecond time scale. cortical activity: properties and behavioral relevance. J. Neuro- The single neuron time-dependent rate function was taken physiol. 79: 2857–2874, 1998. The study was designed to reveal by many as the coding parameter (e.g., Barlow 1972, 1992, occurrences of precise firing sequences (PFSs) in cortical activity and to test their behavioral relevance. Two monkeys were trained 1994; Newsome et al. 1989; Rolls 1991). Others suggested to perform a delayed-response paradigm and to open puzzle boxes. a population coding, based on either the summed activity of Extracellular activity was recorded from neurons in premotor and neurons (Georgopoulos et al. 1986; Schwartz 1994), or the prefrontal areas with an array of six microelectrodes. An algorithm coherency in firing among cells (Eckhorn et al. 1988; Engel was developed to detect PFSs, defined as a set of three spikes and et al. 1991a–c; Gray and Singer 1992; Gray et al. 1989, two intervals with a precision of {1 ms repeating significantly 1992). Both views ignored the detailed temporal structure more than expected by chance. The expected level of repetition of cortical activity, assuming that precision is not compatible was computed based on the firing rate and the pairwise correlation with a noisy cortical environment. Despite this notion, sevof

We analyze the effect of noise in integrate-and-fire neurons driven by timedependent input, and compare the diffusion approximation for the membrane potential to escape noise. It is shown that for time-dependent sub-threshold input, diffusive noise can be replaced by escape noise with a hazard function that has a Gaussian dependence upon the distance between the (noise-free) membrane voltage and threshold. The approximation is improved if we add to the hazard function a probability current proportional to the derivative of the voltage. Stochastic resonance in response to periodic input occurs in both noise models and exhibits similar characteristics.

In the primate primary visual cortex (V1), the significance of individual action potentials has been difficult to determine, particularly in light of the considerable trial-to-trial variability of responses to visual stimuli. We show here that the information conveyed by an action potential depends on the duration of the immediately preceding interspike interval (ISI). The interspike intervals can be grouped into several different classes on the basis of reproducible features in the interspike interval histograms. Spikes in different classes bear different relationships to the visual stimulus, both qualitatively (in terms of the average stimulus preceding each spike) and quantitatively (in terms of the amount of information encoded per spike and per second). Spikes preceded by very short intervals (3 msec or less) convey information most efficiently and contribute disproportionately to the overall receptive-field properties of the neuron. Overall, V1

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Cortical neurons are typically driven by thousands of synaptic inputs. The arrival of a spike from one input may or may not be correlated with the arrival of other spikes from different inputs. How does this interdependence alter the probability that the postsynaptic neuron will fire? We constructed a simple random walk model in which the membrane potential of a target neuron fluctuates stochastically, driven by excitatory and inhibitory spikes arriving at random times. An analytic expression was derived for the mean output firing rate as a function of the firing rates and pairwise correlations of the inputs. This stochastic model made three quantitative predictions. (1) Correlations between pairs of excitatory or inhibitory inputs increase the fluctuations in synaptic drive, whereas correlations between excitatory–inhibitory pairs decrease them. (2) When excitation and inhibition are fully balanced (the mean net synaptic drive is zero),

We show that spike timing adds to the information content of spike trains for transiently presented stimuli but not for comparable steady-state stimuli, even if the latter elicit transient responses. Contrast responses of 22 single neurons in macaque V1 to periodic presentation of steady-state stimuli (drifting sinusoidal gratings) and transient stimuli (drifting edges) of optimal spatiotemporal parameters were recorded extracellularly. The responses were analyzed for contrast-dependent clustering in spaces determined by metrics sensitive to the temporal structure of spike trains. Two types of metrics, costbased spike time metrics and metrics based on Fourier harmonics of the response, were used. With both families of metrics, temporal coding of contrast is lacking in responses to drifting sinusoidal gratings of most (simple and complex) V1 A prevailing view of neural coding is that the meaningful signal

How does a neuron vary its mean output firing rate if the input changes from random to coherent activity? What are the critical parameters of the neuronal dynamics and input statistics? To answer these questions, we investigate the coincidence detection properties of an integrate-and-fire neuron. We derive an expression indicating how coincidence detection depends on neuronal parameters. Specifically, (i) we show how coincidence detection depends on the shape of the postsynaptic response function, the number of synapses, and the input statistics, and (ii) we demonstrate that there is an optimal threshold. Our considerations can be used to predict from neuronal parameters whether and to what extent a neuron can act as a coincidence detector and thus can convert a temporal code into a rate code. Physik-Department der TU Munchen (T35), D-85747 Garching bei Munchen, Germany y Swiss Federal Institute of Technology, Center of Neuromimetic Systems, EPFL-DI, CH-1015 Lausanne, Switz...