Synchronization-based Parameter Estimation of Neuronal Networks

We study automated parameter searches on single neurons and two cell networks. In order to get round the effects of unknown initial conditions we focus on methods that are based on synchronization of the dynamical system to observed time series. The parameters are estimated with a slow dynamic equation that converges to the best value of the parameter. As this implementation does not require restarts parameters can be estimated real-time. For single cells it is possible to identify conductances of different channels, even when the observed series have a lower resolution than the integration step. Synchronization becomes problematic in two cell networks with a single unidirectional connection, because the sending neuron cannot not be synchronized to a desired state. A new method is developed that is, contrary to other synchronization-based methods, able to estimate network parameters. This method temporarily slows down or speeds up a neuron in order to get the spike timing correct. We show that convergence will not occur because this new method because it has chaotic dynamics. However, we are still able to identify proper values of the parameters as the chaotic attractor has basins of attraction around the optimal parameter values.