Download Integrate-and

LECTURE 4
Single Neuron Models (2)
I. Overview
II. Single-Compartment Models
− Integrate-and-Fire Models
− Firing rate models
− The Hodgkin-Huxley Model
− Synaptic conductance description
− The Runge-Kutta method
III. Multi-Compartment Models
− Two-Compartment Models
What is missing in single-compartment
models ?
• Membrane is assumed to be equipotential
(at the same potential everywhere). Actually
there is attenuation and delay within a
neuron
• It is not possible to study propagation
through axon
Presynaptic origins are different between the
apical tuft and more proximal apical dendrites
or basal dendrites
(Spruston 2008)
Multi-compartment models
For simplicity, we begin by computing the coupling between two compartment
that have the same length L and radius a.
The total current flowing from compartment μ + 1 to compartment μ is:
The surface area is:
Thus, we find that
Realistic Neuron (and Network) Simulators
The Runge-Kutta method, which is a standard
numerical integration, is poorly suited for solving
this multi-compartment models, because it is too
slow
Two freely available modeling packages for
detailed neural models are in wide use, Neuron
and Genesis
NEURON
(http://www.neuron.yale.edu/neuron/)
A flexible and powerful simulator of neurons and
networks by Michael Hines, John W. Moore, and
Ted Carnevale
Neuron 7.0 / 16 January 2009;
Spike initiation and propagation in an
anatomically detailed model of a pyramidal cell
Enhancements for modeling networks
Although NEURON began in the domain of single-cell
models, since the early 1990s it has been applied to
network models that contain large numbers of cells and
connections
Carnevale, N.T. and Hines, M.L. The NEURON Book.
Cambridge, UK: Cambridge University Press, 2006
Migliore, M., Cannia, C., Lytton, W.W., Markram, H. and
Hines, M.L. Parallel network simulations with NEURON.
Journal of Computational Neuroscience 21:110-119, 2006
GENESIS －The GEneral NEural Simulation
System
(http://www.genesis-sim.org/GENESIS)
A general purpose software platform that was developed to
support the biologically realistic simulation of neural
systems, ranging from subcellular components and
biochemical reactions to complex models of single
neurons, simulations of large networks, and systemslevel models
First released to the public in 1988
Repeating sequences from the view widget that
represents the membrane potentials for each of
the cells in the network
I. Overview
II. Single-Compartment Models
− Integrate-and-Fire Models
− Firing rate models
− The Hodgkin-Huxley Model
− Synaptic conductance description
− The Runge-Kutta method
III. Multi-Compartment Models
− Two-Compartment Models
There are many types of two-compartment
models depending on the specific problems.
The following is an example.
A
a fast-activating,
persistent
current
a slowly activating
current
6 ms
225 ms
A brief current injection to the dendritic compartment induces a burst that outlasts
the stimulus ( a form of fast positive feedback). Burst firing terminates even for a
sustained current injection (a negative feedback process)
(Kepecs, Wang, and Lisman, 2002)
dVS
gc
cm
  I Leak  I Na  I K  (Vd  Vs )  I s
dt
p
dVd
gc
cm
  I Leak  I NaP  I KS 
(Vs  Vd )  I d
dt
1 p
p = somatic area/total area
Two-Compartment models are very useful!
For instance ……
Distinct firing patterns in model neurons with identical
channel distributions but different dendritic morphology
250 pm
25 mV
100 ms
(Mainen and Sejnowski 1996, Nature)
Figure legend
Digital reconstructions of dendritic arborizations of
neurons from rat somatosensory cortex (a) and cat visual
cortex (b-d). a, Layer 3 aspiny stellate. b, Layer 4 spiny
stellate. c, Layer 3 pyramid. d, Layer 5 pyramid
METHODS. Standard compartmental modelling
techniques were used to simulate spatially extended
neurons. All currents were calculated using conventional
Hodgkin-Huxley-style kinetics
4 voltage-dependent currents: fast Na+, fast K+, slow
non-inactwating K+, and high-voltage activated Ca2+;
1 Ca2+-dependent current K+
(Mainen and Sejnowski 1996, Nature)
Effects of electrical structure on firing pattem
in a reduced two-compartment model
(Mainen and Sejnowski 1996, Nature)
(Mainen and Sejnowski 1996, Nature)
burst
(Mainen and Sejnowski 1996, Nature)
The essential behaviour of the model depends
on partial electrical coupling of fast active
conductances localized to the soma and axon
and slow active currents located throughout
the dendrites
Backpropagation
A backpropagating action
potential recorded
simultaneously from the
soma and dendrite of a layer
II/III pyramidal neuron in a
slice from rat somatosensory
cortex.
(Spruston 2008)
Reduced two-compartment model
1. Including the minimal biophysical mechanisms
necessary to reproduce bursting in a pyramidal cell
2. Involving in effects of electrical structure on firing
pattem
3. Involving in backpropagating-related properties
Overview of the single neural models
Biological Reality
Numerical Simulation
• Detailed conductance based and multicompartment models
• Two-compartment models
• Conductance based models (H-H)
• Integrate-and-fire models
• Firing rate neurons
Artificial
Analytical Solution
作业及思考题
1. 如何构造Multi-Compartment 神经元模型？求解 MultiCompartment 模型的常用软件有哪些？
2. 简化的Two-Compartment 神经元模型可以揭示神经元
的什么特性？