Adaptive functional modeling of neural activity: a reservoir computing approach to neuronal cultures

Biological neural networks (BNN) are very rich and complex in terms of structure and spatiotemporal activity patterns. This complexity does not allow to directly relate their anatomical and biophysical properties to the dynamics of their electrical activity. Functional relevance of their structure and dynamics is also difficult to track analytically. The focus of this thesis is the development of adaptive computing tools, i.e. learning algorithms, for functional modeling of BNNs. Mammalian cortical cells can be dissociated from the brain and regrown outside of the body. They form in vitro closed system networks. To study functional modeling of BNNs, we utilize dissociated cultures of cortical neurons as reference BNNs. The anatomy in the brain is not anymore conserved in cultured networks, hence their connectivity does not reflect the structure in the brain. Neuronal cultures also do not have natural functions. Thus, we approach to functional modeling in neuronal cultures by investigating two problem settings: 1) We first regard the input-output relation of a BNN as a very detailed characterization of its function and model its response streams to input streams. We describe this approach as functional identification of a BNN, i.e. building an artificial system that is functionally equivalent to the reference BNN. 2) We regard the self-organized temporal activity patterns in cultures, i.e. dynamic attractors, as characteristics of their functions, as it has been argued that spatiotemporal patterns and dynamic attractors in in vivo brains reflect functionally relevant brain states. Here, we model the temporal activity patterns in the cultures based on a single cue signal that reflects the initial onset of the temporal pattern. Based on a cue signal, the model simulates the temporal pattern that the neuronal culture undergoes. We employ reservoir computing as a framework, which is argued to be a generic network model for cortical information processing. More specifically, we use Echo State Networks (ESN) of leaky integrator neurons. There have been efficient learning algorithms for ESNs that work on continuous valued time varying signals. For task 1, we take a point process framework rather than a continuous valued signal approach. Using feed-forward and recurrent reservoirs, we adapt the existing ESNs algorithms for point process data and develop their extensions for reservoir adaptation. The proposed algorithm learns predictive models of input-output relations. Receiver Operating Characteristic (ROC) curve and cross correlation analyses indicate that our ESN models can imitate the response signal of a reference biological network for random pulse train inputs. Moreover, point process based reservoir adaptation improves the performance of an ESN over readout-only training methods in many cases. This also holds for adaptive feed-forward reservoirs, which have no recurrent dynamics. Indeed, we show that feed-forward reservoirs perform significantly better than recurrent reservoirs for some of the subtasks. For task 2, we employ an Echo State Network (ESN) with leaky integrator neurons