From LIF to HH

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)
• Iint 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