Computational Neurophysiology

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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(!)

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Single Neuron Computation SNC
Simulate a neuron (cellular neurophysiology)

• Whats to be simulated?
• Structure Morphology / Topology
• Function
• Molecular
• Biophysical
• Synaptic
• Network element

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Inter-relations-I
GENESIS
Slide courtesy M. Rudolph
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Inter-relations-II
GENESIS
Slide courtesy M. Rudolph
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Cable Theory - I
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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
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Cable equation solution Exercise ?
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Overview I Complexity example SNC
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Dendrites Synapses in Real Life
Action potential Output
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Analytic Solutions The Small Difficulty
ra?
?
ra1?1
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Overview I Complexity example SNC
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Overview II Networks
Slide courtesy M. Rudolph
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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

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The Compartmental Approach - I
Slide courtesy M. Rudolph
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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
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The Compartmental Approach - III
Slide courtesy M. Rudolph
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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
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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

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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.
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(Roughly speaking!)
Cable equation for an isopotential compartment
reduces to a simple RC circuit
Slide courtesy R. Narayanan
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Compartmentalization The Procedure
Bower and Beeman, The Book of Genesis
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H-H Parallel Conductance Model
Slide courtesy R. Narayanan
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Single Compartment With Passive Active
Components
Only passive components
Passive and active components
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Ion Channel Modelling
Slide courtesy R. Narayanan
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Diversity of ion channels
Slide courtesy R. Narayanan
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Incorporating ion channels
Slide courtesy R. Narayanan
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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
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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
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 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

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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.
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