1. From LIF to HH Equivalent circuit for passive membrane The Hodgkin-Huxley model for active membrane Analysis of excitability and refractoriness using the membrane model

2. Compartmental Models Anatomical description of whole cell Currents between compartments (dendrite soma hillock) Single compartment model (space clamped LIF: fixed point, limit cycle) Two compartment model (dendrite-soma, 2 coupled LIFs, 2 compartment HH) Summary of phenomena

3. Synaptic Dynamics Synapses determine transmitter release Synapses have an active life! Depressing, facilitating Adaptation, gain control Differential equation models (Tsodyks, Varela) Markov models Extension of neural networks to include dynamic synapses (Maass and Markram).

4. Response to Stimuli and Reliability Response of a neuron to a single current pulse (exp.) (graded and all or none responses) Response of a neuron to two successive pulses (refractory period) Periodic stimulation (phase locking, quasiperiodicity and chaos) Aperiodic stimulation (synchronization) Theoretical analysis (dynamical system approach)

5. Information-theoretic approaches Encoding versus processing Rate code, long time constant, integrator Time code, small time constant, coincidence detector (reliability) Interspike interval code (ISI reconstruction) I=int rho log(rho) Linear correlation coefficient Coherence Coding fraction Mutual information Where from here? Biophysics of coding, Biophysics of information processing.

6. Stochastic Resonance What is SR? Examples from physiology Response of a neuron to subthreshold periodic input and noise Response of a neuron to suprathreshold periodic input and noise Applications of SR

7. Recurrent Excitation with Delay Functional role (amplification, Central Pattern Generation) Experimental data (description, interpretation) Construction of the model of the recurrent circuit Analysis of the behavior of the model using a dynamical system approach

8. SYNCHRONY IN NETWORKS Definition of synchrony Functional role of synchrony Modeling a network of integrate and fire units Analysis of a 2-neuron network Generalization to larger networks and influence of other parameters

9. MODELING THE ACTIVITY OF ELECTRORECEPTORS Stochastic phase locking Similar to subthreshold Is noise helping? Study with LIF: sub: No, but supra: yes to get ISIH like non-brusty P-units. Interval correlation: LIF not enough? LIF with dynamical threshold Tuning curves: Effect of noise

10. MODELING A PATHOLOGY Description of the pathology Construction of the model Bifurcation analysis Reduction of the model Discussion of mechanisms