COS514: Computational Neuroscience (CS, Foundations)

The thematic unit COS514 will provide tools and methods for characterizing what nervous systems do, determine how they function, and understand why they operate in particular ways. In the introduction, the main biophysical aspects of neurons will be covered and the mechanism behind the creation of the action potential will be described. Also, the biophysics of excitatory and inhibitory synapses will be covered. In the next part of the course two simple mathematical models for neurons will be covered: the passive membrane model and the leaky integrate-and-fire model. The equivalent electrical circuits for these models are presented, the corresponding equations are derived, and their solutions are found analytically. Subsequently, the Hodgkin-Huxley neuron model is addressed, along with the equivalent electrical circuit and the full model equations for the membrane potential and the gating variables are derived.  Taking into consideration the spatial extension of neurons, we will study the topic of dendritic function and how dendrites can be modeled as cables. The cable equation for the passive dendrite is derived and corresponding stationary solutions are calculated analytically. Dendritic theory is completed by presenting the famous Rall cable theory and compartmental models. The topic of neuron plasticity will be addressed next, and the differences between structural and functional plasticity, in particular. The Hebb’s postulate will be formulated and the biophysical mechanism behind plasticity is explained. Spike Timing-Dependent Plasticity is described mathematically. Three rules and their corresponding models are presented: Hebb’s rule, covariance rule and Oja’s rule. Comparisons between these rules are made. Finally, the course  will deal with the subject of neural encoding, that is, how stimuli are reflected on the neural responses. Various techniques for neural recordings are presented and the neural code is explained through an example experiment. Concepts such as neural response function, firing rate, tuning curves, reverse correlation function, and spike-train statistics are addressed.