Alexei A. Koulakov

Model for a robust neural integrator.

Integrator circuits in the brain show persistent firing that reflects the sum of previous excitatory and inhibitory inputs from external sources. Integrator circuits have been implicated in parametric working memory, decision making and motor control. Previous work has shown that stable integrator function can be achieved by an excitatory recurrent neural circuit, provided synaptic strengths are tuned with extreme precision (better than 1% accuracy). Here we show that integrator circuits can function without fine tuning if the neuronal units have bistable properties. Two specific mechanisms of bistability are analyzed, one based on local recurrent excitation, and the other on the voltage-dependence of the NMDA (N-methyl-D-aspartate) channel. Neither circuit requires fine tuning to perform robust integration, and the latter actually exploits the variability of neuronal conductances.

Precise olfactory responses tile the sniff cycle

In terrestrial vertebrates, sniffing controls odorant access to receptors, and therefore sets the timescale of olfactory stimuli. We found that odorants evoked precisely sniff-locked activity in mitral/tufted cells in the olfactory bulb of awake mouse. The trial-to-trial response jitter averaged 12 ms, a precision comparable to other sensory systems. Individual cells expressed odor-specific temporal patterns of activity and, across the population, onset times tiled the duration of the sniff cycle. Responses were more tightly time-locked to the sniff phase than to the time after inhalation onset. The spikes of single neurons carried sufficient information to discriminate odors. In addition, precise locking to sniff phase may facilitate ensemble coding by making synchrony relationships across neurons robust to variation in sniff rate. The temporal specificity of mitral/tufted cell output provides a potentially rich source of information for downstream olfactory areas.

Speed-accuracy tradeoff in olfaction.

The basic psychophysical principle of speed-accuracy tradeoff (SAT) has been used to understand key aspects of neuronal information processing in vision and audition, but the principle of SAT is still debated in olfaction. In this study we present the direct observation of SAT in olfaction. We developed a behavioral paradigm for mice in which both the duration of odorant sampling and the difficulty of the odor discrimination task were controlled by the experimenter. We observed that the accuracy of odor discrimination increases with the duration of imposed odorant sampling, and that the rate of this increase is slower for harder tasks. We also present a unifying picture of two previous, seemingly disparate experiments on timing of odorant sampling in odor discrimination tasks. The presence of SAT in olfaction provides strong evidence for temporal integration in olfaction and puts a constraint on models of olfactory processing.

Charge density wave in two-dimensional electron liquid in weak magnetic field.

We study the ground state of a clean two-dimensional electron liquid in a weak magnetic field where

Orientation preference patterns in mammalian visual cortex: a wire length minimization approach.

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Correlated Connectivity and the Distribution of Firing Rates in the Neocortex

lower Landau levels are completely filled and the upper level is partially filled. It is shown that the electrons at the upper Landau level form domains with filling factors equal to 1 and zero. The domains alternate with a spatial period of order of the cyclotron radius, which is much larger than the interparticle distance at the upper Landau level. The one-particle density of states, which can be probed by tunneling experiments, is shown to have a gap linearly dependent on the magnetic field in the limit of large

Orbitofrontal Cortex Is Required for Optimal Waiting Based on Decision Confidence

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Classical model for the negative dc conductivity of ac-driven two-dimensional electrons near the cyclotron resonance

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In Search of the Structure of Human Olfactory Space

In the visual cortex of many mammals, orientation preference changes smoothly along the cortical surface, with the exception of singularities such as pinwheels and fractures. The reason for the existence of these singularities has remained elusive, suggesting that they are developmental artifacts. We show that singularities reduce the length of intracortical neuronal connections for some connection rules. Therefore, pinwheels and fractures could be evolutionary adaptations keeping cortical volume to a minimum. Wire length minimization approach suggests that interspecies differences in orientation preference maps reflect differences in intracortical neuronal circuits, thus leading to experimentally testable predictions. We discuss application of our model to direction preference maps.

Competition is a driving force in topographic mapping

Two recent experimental observations pose a challenge to many cortical models. First, the activity in the auditory cortex is sparse, and firing rates can be described by a lognormal distribution. Second, the distribution of nonzero synaptic strengths between nearby cortical neurons can also be described by a lognormal distribution. Here we use a simple model of cortical activity to reconcile these observations. The model makes the experimentally testable prediction that synaptic efficacies onto a given cortical neuron are statistically correlated, i.e., it predicts that some neurons receive stronger synapses than other neurons. We propose a simple Hebb-like learning rule that gives rise to such correlations and yields both lognormal firing rates and synaptic efficacies. Our results represent a first step toward reconciling sparse activity and sparse connectivity in cortical networks.