The influence of depolarization block on seizure-like activity in networks of excitatory and inhibitory neurons.

The inhibitory restraint necessary to suppress aberrant activity can fail when inhibitory neurons cease to generate action potentials as they enter depolarization block. We investigate possible bifurcation structures that arise at the onset of seizure-like activity resulting from depolarization block in inhibitory neurons. Networks of conductance-based excitatory and inhibitory neurons are simulated to characterize different types of transitions to the seizure state, and a mean field model is developed to verify the generality of the observed phenomena of excitatory-inhibitory dynamics.

Mean-field equations for neuronal networks with arbitrary degree distributions.

The emergent dynamics in networks of recurrently coupled spiking neurons depends on the interplay between single-cell dynamics and network topology. Most theoretical studies on network dynamics have assumed simple topologies, such as connections that are made randomly and independently with a fixed probability (Erdös-Rényi network) (ER) or all-to-all connected networks. However, recent findings from slice experiments suggest that the actual patterns of connectivity between cortical neurons are more structured than in the ER random network.

Bump attractor dynamics in prefrontal cortex explains behavioral precision in spatial working memory.

Prefrontal persistent activity during the delay of spatial working memory tasks is thought to maintain spatial location in memory. A 'bump attractor' computational model can account for this physiology and its relationship to behavior. However, direct experimental evidence linking parameters of prefrontal firing to the memory report in individual trials is lacking, and, to date, no demonstration exists that bump attractor dynamics underlies spatial working memory.

Directed functional connectivity matures with motor learning in a cortical pattern generator.

Sequential motor skills may be encoded by feedforward networks that consist of groups of neurons that fire in sequence (Abeles 1991; Long et al. 2010). However, there has been no evidence of an anatomic map of activation sequence in motor control circuits, which would be potentially detectable as directed functional connectivity of coactive neuron groups.

Searching for optimal stimuli: ascending a neuron's response function.

Many methods used to analyze neuronal response assume that neuronal activity has a fundamentally linear relationship to the stimulus. However, some neurons are strongly sensitive to multiple directions in stimulus space and have a highly nonlinear response. It can be difficult to find optimal stimuli for these neurons.

Synchronization from second order network connectivity statistics.

We investigate how network structure can influence the tendency for a neuronal network to synchronize, or its synchronizability, independent of the dynamical model for each neuron. The synchrony analysis takes advantage of the framework of second order networks, which defines four second order connectivity statistics based on the relative frequency of two-connection network motifs. The analysis identifies two of these statistics, convergent connections, and chain connections, as highly influencing the synchrony.

Computing linear approximations to nonlinear neuronal response.

We present an approach to obtain nonlinear information about neuronal response by computing multiple linear approximations. By calculating local linear approximations centered around particular stimuli, one can obtain insight into stimulus features that drive the response of highly nonlinear neurons, such as neurons highly selective to a small set of stimuli. We implement this approach based on stimulus-spike correlation (i.

A kinetic theory approach to capturing interneuronal correlation: the feed-forward case.

We present an approach for using kinetic theory to capture first and second order statistics of neuronal activity. We coarse grain neuronal networks into populations of neurons and calculate the population average firing rate and output cross-correlation in response to time varying correlated input. We derive coupling equations for the populations based on first and second order statistics of the network connectivity.

Pinpointing connectivity despite hidden nodes within stimulus-driven networks.

The effects of hidden nodes can lead to erroneous identification of connections among measured nodes in a network. For example, common input from a hidden node may cause correlations among a pair of measured nodes that could be misinterpreted as arising from a direct connection between the measured nodes. We present an approach to control for effects of hidden nodes in networks driven by a repeated stimulus.

A stimulus-dependent connectivity analysis of neuronal networks.

We present an analysis of interactions among neurons in stimulus-driven networks that is designed to control for effects from unmeasured neurons. This work builds on previous connectivity analyses that assumed connectivity strength to be constant with respect to the stimulus. Since unmeasured neuron activity can modulate with the stimulus, the effective strength of common input connections from such hidden neurons can also modulate with the stimulus.

A mathematical framework for inferring connectivity in probabilistic neuronal networks.

We describe an approach for determining causal connections among nodes of a probabilistic network even when many nodes remain unobservable. The unobservable nodes introduce ambiguity into the estimate of the causal structure. However, in some experimental contexts, such as those commonly used in neuroscience, this ambiguity is present even without unobservable nodes.

Persistent sodium currents in mesencephalic v neurons participate in burst generation and control of membrane excitability.

The functional and biophysical properties of a persistent sodium current (I(NaP)) previously proposed to participate in the generation of subthreshold oscillations and burst discharge in mesencephalic trigeminal sensory neurons (Mes V) were investigated in brain stem slices (rats, p7-p12) using whole cell patch-clamp methods. I(NaP) activated around -76 mV and peaked at -48 mV, with V1/2 of -58.7 mV.

Measuring linear and quadratic contributions to neuronal response.

We present a method to dissociate the sign-dependent (linear or odd-order) response from the sign-independent (quadratic or even-order) response of a neuron to sequences of random orthonormal stimulus elements. The method is based on a modification of the classical linear-nonlinear model of neural response. The analysis produces estimates of the stimulus features to which the neuron responds in a sign-dependent manner, the stimulus features to which the neuron responds in a sign-independent manner and the relative weight of the sign-independent response.

Full identification of a linear-nonlinear system via cross-correlation analysis.

A statistical model used extensively in vision research consists of a cascade of a linear operator followed by a static (memoryless) nonlinearity. Common applications include the measurement of simple-cell receptive fields in primary visual cortex and the modeling of human performance in various psychophysical tasks. It is well known that the front-end linear filter of the model can readily be recovered, up to a multiplicative constant, using reverse-correlation techniques.

Spike correlation measures that eliminate stimulus effects in response to white noise.

When measured in response to non-repeating white noise, standard covariance measures of two neuronal spike trains contain components due simply to a shared stimulus. We argue that, without stimulus repeats, model-free measures cannot in general remove these stimulus-induced components. We present spike correlation measures that eliminate them when the neural response can be approximated by a linear-nonlinear system.