The Bernstein Center for Computational Neuroscience Freiburg

Announcement for the next
Informal Seminar
Johannes Friedrich
Theoretical Physics; TP III
Faculty of Physics
University of Würzburg

Leaky Integrate-and fire Networks with Unreliable Synapses

Monday, May 26th, 2008
13:00 h TIME
Bernstein Center
Hansastr. 9a
There is experimental evidence that synapses transmit an incoming spike not deterministically but with some probability which may be as low as a few percent. In my thesis I investigated the properties of a network of identical integrate-and-fire neurons with unreliable synapses which transmit with a delay time. Separately inhibitory and excitatory coupling was considered. The postsynaptic current was modeled with $alpha$-functions and $delta$-functions which incorporate a relative and an absolute delay respectively. First I considered two coupled neurons and studied the properties of the spike trains in dependence of the parameters. The statistical measures used are the ISI-distributions, the coefficient of variation and the Fano factor. Then I focused on fully connected networks of $N$ neurons. The numerical simulation for various parameter combinations gave rise to equilibrium states which are synchronous, asynchronous or display clustering. With inhibitory coupling the network relaxes into a state with clusters, or synfire chains. The formation of clusters, with number and size dependent on initial conditions, has already been known to occur for reliable transmission. With unreliable transmission the network looses its dependence on the initial state and the whole network consists of clusters of identical size which are stable, instead of the probabilistic nature of the synapses. Due to the unreliability the neurons of one cluster do not fire at exactly the same time, but are distributed around the mean of the cluster. Synchronization occurs not perfectly but only partially. Modeling the PSC with a delayed $delta$-function, I calculated the emph{pdf} of the neurons' phases analytically for the synchronous state. This result is general since it only requires mean and variance of the summed up input into a neuron. I was able to compute the number of emerging clusters for the first time analytically. It does not depend on the probability $p$ of synaptic transmission, but only on the effective coupling strength which is the product $gcdot p$, where $g$ is the coupling strength. Clusters could be used to encode information in their composition. The number of possible configurations scales exponentially with $N$ and algebraically with $n_c$. Synfire chains exchange neurons, but excitation is stable for some time. The survival time of a certain configuration decreases with decreasing $p$. While it has to diverge for $p=1$ at smaller probabilities the dependence is approximately exponential. Using an appropriate topology - oriented at the brain's columnar design - cluster states can propagate through a network conserving the configuration. The propagation time increases nearly linear with $1-p$. The columns in the brain are connected via excitatory synapses. As a first step I considered two excitatory coupled columns, each modeled as inhibitory population that displays clustering. In the weak coupling regime the results obtained for two neurons transfer and the populations synchronize with phase lag equal to the delay between the populations. For stronger coupling numerical simulations show regions of out-of-phase synchronization, antisynchrony, non-synchronous behavior and doublets. Doublets may play a part in the synchronization process for the $gamma$ frequency rhythm, found during states of sensory stimulation. I derived the boundaries of these regions analytically confirming the numerical results.
The talk is open to the public. Guests are cordially invited!