LEARNING OUTCOMES

Neurons: advanced biophysical modeling and computer simulation techniques. Synapses: Phenomenological models vs biophysical models; Exponential synapses at one and two time constants; Synaptic plasticity; Neuron networks: simplified models; Role of connectivity in network dynamics

AIMS AND LEARNING OUTCOMES

Goal of the teaching is to provide the theoretical contents for modeling neuronal structures at different scale, from single neuron up to large-scale complex networks. For this reason, the course will be focused on how to model and simulate the electrophysiological activity of neuronal structures. Based on the tools offered, the objectives of the course are:

- model neuronal networks with particular patterns of electrophysiological activity
- choose the correct neuron models based on experimental needs
- solve advanced theoretical problems of neuronal computation
- choose the best computational strategy based on the required problem

PREREQUISITES

Advanced knowledge of mathematics, mathematical analysis; analysis of electrophysiological signals; neurophysiology

TEACHING METHODS

Combination of traditional lectures, classroom discussion, and lab activities.

SYLLABUS/CONTENT

• Biophysical Model of Neurons
  • Brief introduction on equivalent membrane circuit and membrane electric properties
  • Passive models and propagation equation
  • Hodgkin and Huxley (HH) model and dynamics
  • From HH to multichannel neuron models
  • Role of neuron morphology and dendritic tree in the electrophysiological patterns
  • Reduced models: from multi-compartments to 2-3 compartments neurons
  • Calcium dynamics
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• Neuronal dynamics, excitability threshold, oscillations
  • Mathematical background of non-linear systems and portrait analysis
  • Hodgkin and Huxley model
  • Morris-Lecar model
  • Fitzhug-Nagumo model
     
• From bio-inspired to abstracted point neurons
  • The family of integrate-and-fire (IF) neurons
  • Leaky-Integrate-and-Fire (LIF)
  • Exponential-Integrate-and-Fire (EIF)
  • Quadratic-Integrate-and-Fire (QIF)
  • Advantages and limitations of IF models
  • The Izhikevich model
  • Stochastic models
  • Poissonian process
  • Renewal process
     
• The synaptic transmission and plasticity
  • Exponential synapse
  • Alpha function synapse
  • Dynamical models
  • Desthexhe model
  • Markovian models
  • Modeling the synaptic plasticity
  • Hebbian rule
  • Depression, Facilitation, Augmentation (short-term plasticity)
  • Long Term Potentiation/Depression
  • Spike Timing Dependent Plasticity (STDP)
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• Network Models
  • Firing Rate Model
  • Spiking Model
  • Point vs. multicompartmental networks
  • Balanced networks
  • Network architecture
  • Networks dynamics
  • Interplay between dynamics and connectivity
  • Different kind of connectivities
  • Building a graph
  • Properties of a graph
  • Functional, Structural, Effective connectivity

RECOMMENDED READING/BIBLIOGRAPHY

Slides available on Aulaweb.

• Methods in Neuronal Modeling, Koch and Segev, MIT press, 1999.
• Spiking Neuron Models, Gerstner and Kistler, Cambridge press, 2002.
• Dynamical systems in neuroscience,. Izhikevich, MIT press, 2007.
• Computational Modeling Methods for Neuroscientists, De Schutter, MIT press, 2010.
• Theoretical Neuroscience, Dayan and Abbott, MIT press, 2001.