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Computational Neurophysiology

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Ion channels stochastic & biophysic models. Cellular membrane ... Voltage (mV) Overview I: Complexity example [SNC] Dendrites & Synapses in Real Life ... – PowerPoint PPT presentation

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Title: Computational Neurophysiology


1
Computational Neurophysiology
  • CompNeuro comes in many flavours
  • Molecular
  • Biochemical pathways
  • Ion channels stochastic biophysic models
  • Cellular membrane biophysics
  • Cell-cell signalling electrical chemical
    synaptic transmission
  • Emergent properties in the nervous system
  • Cognition
  • Consciousness(!)

2
Single Neuron Computation SNC
Simulate a neuron (cellular neurophysiology)
  • Whats to be simulated?
  • Structure Morphology / Topology
  • Function
  • Molecular
  • Biophysical
  • Synaptic
  • Network element

3
Inter-relations-I
GENESIS
Slide courtesy M. Rudolph
4
Inter-relations-II
GENESIS
Slide courtesy M. Rudolph
5
Cable Theory - I
6
Cable Theory - II
  • Cylindrical neural elements like axons and
    dendrites may be likened to thin, long cables
  • The cable is modeled as an infinite series of
    resistors and capacitors in parallel (as shown
    above)

Cable equation
7
Cable equation solution Exercise ?
8
Overview I Complexity example SNC
9
Dendrites Synapses in Real Life
Action potential Output
10
Analytic Solutions The Small Difficulty
ra?
?
ra1?1
11
Overview I Complexity example SNC
12
Overview II Networks
Slide courtesy M. Rudolph
13
Possible Solution
Compartmental Modelling
  • Whats needed?
  • The Parallel-Conductance (GHK) membrane
  • The Hodgkin-Huxley Model
  • Voltage clamp experiments
  • Ionic Conductance Kinetic Models
  • Action Potential model
  • Cable Theory

14
The Compartmental Approach - I
Slide courtesy M. Rudolph
15
The Compartmental Approach - II
The basic computational task to numerically
solve the cable equation which describes the
relationship between current and voltage in an
one- D cable
Slide courtesy M. Rudolph
16
The Compartmental Approach - III
Slide courtesy M. Rudolph
17
The Compartmental Approach - IV
reduction of cable equation to a set of ordinary
differential equations with first order
derivatives in time ? algebraic difference
equations with temporal discretization can be
solved numerically
Slide courtesy M. Rudolph
18
The Compartmental Approach - V
  • ? is the space constant, defined as the distance
    at which a potential decays to 1/e (0.37) of the
    potential at x0.
  • tmRmCm is the membrane time constant

19
Isopotential assumption
Isopotential assumption Split the cable into
smaller sections so that the amount of
attenuation for signals passing through that
section is negligible. In other words, the
potential across the compartment is constant
hence the isopotential nomenclature.
0
(Roughly speaking!)
Cable equation for an isopotential compartment
reduces to a simple RC circuit
Slide courtesy R. Narayanan
20
Compartmentalization The Procedure
Bower and Beeman, The Book of Genesis
21
H-H Parallel Conductance Model
Slide courtesy R. Narayanan
22
Single Compartment With Passive Active
Components
Only passive components
Passive and active components
23
Ion Channel Modelling
Slide courtesy R. Narayanan
24
Diversity of ion channels
Slide courtesy R. Narayanan
25
Incorporating ion channels
Slide courtesy R. Narayanan
26
Methods of numerical integration
  • Forward Euler method
  •   (simple, unstable, inaccurate)
  • Backward Euler method
  • (inaccurate, stable)
  • Crank-Nicholson method
  • (stable, more accurate)

Selection of a method of numerical integration is
guided by concerns of stability, accuracy and
efficiency
27
What can NEURON / GENESIS do?
GenerallyProvide tools for constructing,
exercising, and managing simplified up to
biologically realistic models of electrical and
chemical signaling in neurons and networks of
neurons.
Specifically Simulate biophysical and
biochemical dynamics of active membrane
properties (transmembrane currents,transmembrane
channels) electrotonic and active signalling
along dendritic and axonal cables, as well as in
cable structures with complex branching
morphology
28
 Why use NEURON / GENESIS?
  • easy to use
  • computational models on many levels(subcellular,
    cellular, network)
  • well suited for computational models that are
    closely linked to experimental data
  • computationally efficient and accurate while at
    the same time minimizing the required user effort
  • optimized for handling tree-shaped cable
    structures
  • optimized network simulations utilizing the
    event-based approach
  • user is not required to translate the problem
    into another domain,
  • Instead, is able to deal directly with concepts
    that are familiar at the neuroscience level

29
NEURON resources
http//www.neuron.yale.edu/ http//neuron.duke.edu
/
Hines, M.L. and Carnevale, N.T. Expanding
NEURON's repertoire of mechanisms with NMODL.
Neural Computation 12 (2000), 839-851.Hines,
M.L. and Carnevale, N.T. The NEURON Simulation
Environment.Neural Computation 9 (1997),
1179-1209. Hines, M.L. and Carnevale, N.T.
NEURON a tool for neuroscientists. The
Neuroscientist 7 (2001), 123-135.
30
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