Salve Meeting 2003
Computational modeling of the nervous system: where math, biology and philosophy meet

The basics


Gábor Szirtes
http://people.inf.elte.hu/gszirtes
ELTE Faculty of Informatics
Dept of Information Systems
NIPG group

 
 
- Personal introduction
- Some thoughts about what we are up to
- The logic behind
- The real intro: what ‘bottom-up’ computational neuroscience can and cannot offer
- What next?
 
Introduction
- Our group: Neural Information Processing Group (12 PhD and 5 MSc students)
- Our head : Dr. habil. András Lorincz
- Research interest: development of biologically motivated algorithms for chasing our ‘Holy Grail’, the intelligence.
- Projects spanning from brain modeling to face recognition, to effective information search, to RL...
 


Sources of confusion
- Multidisciplinary area
- The most ancient and puzzling questions still not answered
- Confronting scientific and everyday concepts
- Striking complexity

Where should we start?
 
 
The long term goal: to understand the nature of intelligence
Instead of giving a convincing definition, we can:
- sense intelligence
- define subparts (tasks)
- specify the neural bases of these tasks
- develop different (competing) approaches
 

Conceptual differences in research
- Descriptive, mechanistic or interpreting models (hypothesis sets) [Dayan and Abbot, 2001]
- Bottom-up or top-down methodology
 
 
Two goals of CNS
- Modeling to test hypotheses
- Simulations as experimenting tools to predict or explain (same caveats)
 

Basics I.
• Only electric properties count
• Influential cell parts can be substituted with equivalent electric circuit elements (ion channels – conductive components, membrane - capacitance)
• Systematic approximations and neglects are permitted

Dynamical systems (membrane potential changes in time and space and ion channels kinetics) with ODE description
 

Illustration I.
 
 
Basics II.
• Hodgkin-Huxley description (Nobel-prize 1963)
• Cable equation
• Inclusion of synaptic transmission
• Theory of dynamic and chaotic systems
• Extensions (Other ion channels, complex kinetics, Nagumo-FitzHugh model, phase plane analysis, network theory,…)
• Simulation environments: GENESIS, NEURON, MATLAB,…
 


Illustration III.
A detailed multicompartmental model of a Purkinje cell (De Schutter, E. and Bower, J. M. (1994). J. Neurophysiol. 71: 375-400. )
 
 

Abstract models

- MCP: the first abstract model (McCulloch and Pitts, 1943): binary input, binary state, threshold function. Used in ANN, too.
- Rate models: Abstract. Principal state variable is the firing frequency. Can be related to biologically relevant parameters
- Phase models: Abstract. Periodically firing neurons. Phase-coupled nets, oscillations, synchronicity

Conductance based models

I&F: explains only sub-threshold changes, APs are uniform. Many extensions exist
HH: The classical explanation of the AP generation with experimentally fitted kinetics. The core of the popular compartmental modeling
 

- Cable equation: describes the passive (no voltage-dependent channel) membrane of the dendrites. Input integration over space and time. Used in hybrid models (HH+cable)
 

…and the CONs

Mathematical problems: system of non-linear ODEs, arbitrary behavior can be simulated
Scientific problems: mindless data recording
Philosophical problems: Does not seem to provide a bridge over the gap between structure and (supposed) function
 
Info on the Web
- http://www.neuron.yale.edu
- http://www.genesis-sim.org/GENESIS/
- http://home.earthlink.net/~perlewitz/