We explore a computationally efficient method of simulating realistic networks of neurons introduced by Knight, Manin, and Sirovich (1996) in which integrate-and-fire neurons are grouped into large populations of similar neurons. For each population, we form a probability density which represents the distribution of neurons over all possible states. The populations are coupled via stochastic synapses in which the conductance of a neuron is modulated according to the firing rates of its presynaptic populations. The evolution equation for each of these probability densities is a partial differential-integral equation which we solve numerically. Results obtained for several example networks are tested against conventional computations for groups of individual neurons. We apply this approach to modeling orientation tuning in the visual cortex. Our population density model is based on the recurrent feedback model of a hypercolumn in cat visual cortex of Somers et al. (1995). We simulate the response to oriented flashed bars. As in the Somers model, a weak orientation bias provided by feed-forward lateral geniculate input is transformed by intracortical circuitry into sharper orientation tuning which is independent of stimulus contrast. The population density approach appears to be a viable method for simulating large neural networks. Its computational efficiency overcomes some of the restrictions imposed by computation time in individual

We describe a new, computationally simple method for analyzing the dynamics of neuronal spike trains driven by external stimuli. The goal of our method is to test the predictions of simple spike-generating models against extracellularly recorded neuronal responses. Through a new statistic called the power ratio, we distinguish between two broad classes of responses: (1) responses that can be completely characterized by a variable firing rate, (for example, modulated Poisson and gamma spike trains); and (2) responses for which firing rate variations alone are not sufficient to characterize response dynamics (for example, leaky integrate-and-fire spike trains as well as Poisson spike trains with long absolute refractory periods). We show that the responses of many visual neurons in the cat retinal ganglion, cat lateral geniculate nucleus, and macaque primary visual cortex fall into the second class, which

Abstract. Recent studies have shown that local cortical feedback can have an important effect on the response of neurons in primary visual cortex to the orientation of visual stimuli. In this work, we study the role of the cortical feedback in shaping the spatiotemporal patterns of activity in cortex. Two questions are addressed: one, what are the limitations on the ability of cortical neurons to lock their activity to rotating oriented stimuli within a single receptive field? Two, can the local architecture of visual cortex lead to the generation of spontaneous traveling pulses of activity? We study these issues analytically by a population-dynamic model of a hypercolumn in visual cortex. The order parameter that describes the macroscopic behavior of the network is the time-dependent population vector of the network. We first study the network dynamics under the influence of a weakly tuned input that slowly rotates within the receptive field. We show that if the cortical interactions have strong spatial modulation, the network generates a sharply tuned activity profile that propagates across the hypercolumn in a path that is completely locked to the stimulus rotation. The resultant rotating population vector maintains a constant angular lag relative to the stimulus, the magnitude of which grows with the stimulus rotation frequency. Beyond a critical frequency the population vector does not lock to the stimulus but executes a quasi-periodic motion with an average frequency that is smaller than that of the stimulus. In the second part we consider the stable intrinsic state of the cortex under the influence of isotropic stimulation. We show that if the local inhibitory feedback is sufficiently strong, the network does not settle into a

Rate models are often used to study the behavior of large networks of spiking neurons. Here we propose a procedure to derive rate models which take into account the fluctuations of the input current and firing rate adaptation, two ubiquitous features in the central nervous system which have been previously overlooked in constructing rate models. The procedure is general and applies to any model of firing unit. As examples, we apply it to the leaky integrate-and-fire (IF) neuron, the leaky IF neuron with reversal potentials, and to the quadratic IF neuron. Two mechanisms of adaptation are considered, one due to an afterhyperpolarization current, the other to an adapting threshold for spike emission. The parameters of these simple models can be tuned to match experimental data obtained from neocortical pyramidal neurons. Finally, we show how the stationary model can be used to predict the time-varying activity of a large population of adapting neurons.

Linear regression of eye velocity on eye position and head velocity suggests a common oculomotor neural integrator. J Neurophysiol 88: 659–665, 2002; 10.1152/jn.00993.2001. The oculomotor system produces eye-position signals during fixations and head movements by integrating velocity-coded saccadic and vestibular inputs. A previous analysis of nucleus prepositus hypoglossi (nph) lesions in monkeys found that the integration time constant for maintaining fixations decreased, while that for the vestibuloocular reflex (VOR) did not. On this basis, it was concluded that saccadic inputs are integrated by the nph, but that the vestibular inputs are integrated elsewhere. We re-analyze the data from which this conclusion was drawn by performing a linear regression of eye velocity on eye position and head velocity to derive the time constant and velocity bias of an imperfect oculomotor neural integrator. The velocity-position regression procedure reveals that the integration

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Abstract. The result of computational operations performed at the single cell level are coded into sequences of action potentials (APs). In the cerebral cortex, due to its columnar organization, large number of neurons are involved in any individual processing task. It is therefore important to understand how the properties of coding at the level of neuronal populations are determined by the dynamics of single neuron AP generation. Here, we analyze how the AP generating mechanism determines the speed with which an ensemble of neurons can represent transient stochastic input signals. We analyze a generalization of the θ-neuron, the normal form of the dynamics of Type-I excitable membranes. Using a novel sparse matrix representation of the Fokker-Planck equation, which describes the ensemble dynamics, we calculate the transmission functions for small modulations of the mean current and noise noise amplitude. In the high-frequency limit the transmission function decays as ω −γ, where γ surprisingly depends on the phase θs at which APs are emitted. If at θs the dynamics is insensitive to external inputs, the transmission function decays as (i) ω −3 for the case of a modulation of a white noise input and as (ii) ω −2 for a modulation of the mean input current in the presence of a correlated and uncorrelated noise as well as (iii) in the case of a modulated amplitude of a correlated noise input. If the insensitivity condition is lifted, the transmission function always decays as ω −1,asinconductance based neuron models. In a physiologically plausible regime up to 1 kHz the typical response speed is, however, independent of the high-frequency limit and is set by the rapidness of the

ng various types of collective dynamics. And systems in between, which mix more complex ionic, neuro-transmitter and neural structure with large scale features[7]. Clearly, any such simulation implies a model. One could "run" the simulation and observe the behaviour of the system under consideration. But this is more like an experimental situation than like a theoretical one. If the simulated system is complex enough, generic statements about its product dynamics would be almost as gratifying and surprising as about an experiment. Moreover, to monitor the system's progress one would have to define and sharpen tools, much like in the experimental situation, since the system generates an enormous amount of noisy data. Thus it appears that the simulation hangs somewhere between the theoretical and the experimental. The matter may be sharpened further: One may be given the design of a part of the brain, consisting of operational features of the elements: neurons, synapses etc., as well as<

The role of the lateral geniculate nucleus (LGN) of the thalamus in visual encoding remains an open question. Here, we characterize the function of tonic and burst spikes in cat LGN X-cells in signaling features of natural stimuli. A significant increase in bursting was observed during natural stimulation (relative to white noise stimulation) and was linked to the strong correlation structure of the natural scene movies. Burst responses were triggered by specific stimulus events consisting of a prolonged inhibitory stimulus, followed by an excitatory stimulus, such as the movement of an object into the receptive field. LGN responses to natural scene movies were predicted using an integrate-and-fire (IF) framework and compared with experimentally observed responses. The standard IF model successfully predicted LGN responses to natural scene movies during tonic firing, indicating a linear relationship between stimulus and response. However, the IF model typically underpredicted the LGN response during periods of bursting, indicating a nonlinear amplification of the stimulus in the actual response. The addition of a burst mechanism to the IF model was necessary to accurately predict the entire LGN response. These results suggest that LGN bursts are an important part of the neural code, providing a nonlinear amplification of stimulus features that are typical of the natural environment. Key words: LGN; bursts; tonic; natural scenes; neural coding; integrate and fire

Introduction The quality of the visual signal transmitted to the brain is important for perception because it sets the minimum detectable stimulus. As a daylight visual signal is processed by the retina, each layer adds noise (Ashmore and Copenhagen, 1983; Freed et al., 2003) so that the signal quality of a ganglion cell is limited by retinal noise sources (Schellart and Spekreijse, 1973; Reich et al., 1977; Levine and Zimmerman, 1991; Troy and Robson, 1992; Croner et al., 1993; Freed, 2000), implying information loss (Geisler, 1989). The loss is thought to originate partly in selective processing of the signal and partly from noise sources such as stochastic vesicle release and channel gating (Barrett and Stevens, 1972; Schneidman et al., 1998; White et al., 2000; van Rossum et al., 2003). To understand how efficiently information is transferred and how neural mechanisms preserve signal quality, one could measure information loss at each retinal stage. One way is to compare the contr