Theory of neural dynamics - Tchumatchenko Group

Theory of neural dynamics
Our research focuses on the computational modeling and mathematical analysis of single neurons, neuronal populations and recurrent networks. We employ analytic tools and computer simulations to investigate how single neurons and populations respond to their synaptic inputs, and how they interact to give rise to functioning neuronal circuits. Areas of particular interest include the role of synaptic adaptation, information representation, response time scales and the temporal and cross neuronal correlations.

Methods
We employ a combination of analytical techniques that include linear and non-linear differential equations and their solutions via linear perturbation theory, stochastic integrals (e.g correlated Gaussian ensemble), Fokker Planck formalism, interacting stochastic processes. On the computational side we use numerical simulations and modern programming languages.
Whenever possible we aim to verify the theoretical results in collaboration with experimental colleagues. We have therefore close ties to physiology laboratories and seek out new collaborations that provide intracellular recordings, multi-unit spiking activity with maximal simultaneous stimulus control.

Recent results
In a recurrent neuronal network, neurons receive a barrage of excitatory and inhibitory synaptic inputs. In such a situation a signal arriving at a neuronal subpopulation could modulate either the mean or the variance of the somatic current at each neuron. We therefore set out to investigate how these two encoding strategies are playing out in a population of neurons and whether one of them has a distinct computational advantage over the other. Using a threshold based model framework where spikes are modeled as positive threshold crossings of a continuous Gaussian process, we have calculated the linear and non-linear current-to-spikes response function. In the variance and mean channel, we provided explicit expressions for the linear and non-linear frequency response functions in the presence of correlated noise and use them to derive the population rate response to step-like stimuli. For mean-encoded signals, we found that the complete response function depends only on the temporal width of the input correlation function, but not on other functional specifics. Furthermore, we show that both mean- and variance-encoded signals can relay high-frequency inputs, and in both schemes step-like changes can be detected instantaneously. Finally, we obtained the pairwise spike correlation function and the spike triggered average from the linear mean-evoked response function. These results can be found here.

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