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