Transcript 神经元发放的类型

神经计算的生理和动力学指标
华南理工大学理学院数学系
刘深泉教授
基于电导的
神经元模型
dV n ions n synapse
I stimulus  g L (V  VL )  C   I k   I t
dt k 1
t 1
I kions  Gmax m x n y (V  Vions ),
Itsynapse  Gsynapse (V  Vsynapse )
• 泄漏电流，电容电流
• 离子电流，突触电流
• 跨膜电流，轴向传递
神经元发放的类型
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激发峰发放（Tonic Spiking），
相图峰发放（Phasic Spiking），
激发簇发放（Tonic Bursting），
相图簇发放（Phasic Bursting），
混合模式（Mixed Model），
发放频率适应性（Spike Frequency Adaptation），
第一类兴奋性（Class 1 Excitability），
第二类兴奋性（Class 2 Excitability），
发放延迟（Spike Latency），
阈值振荡（Subthreshold Oscillations），
周期选择与共振（Frequency Preference and Resonance），
时间一致与整合（Integration and Coincidence Detection），
反弹峰发放（Rebound Spike），
反弹簇发放（Rebound Bursting），
阈值可变性（Threshold Variability），
静息与发放双稳态（Bi-stability of Resting and Spiking States），
去极化（Depolarizing After-Potentials），
适应性（Accommodation），
抑制性激发峰发放（Inhibition-Induced Spiking），
抑制性激发簇发放（Inhibition-Induced Bursting）等。
神经元电位活动-峰发放和簇发放
SPIKE AND BURSTING
Bursts as a Unit of Neuronal Information
神经元-计算
CA1锥体神经元-ISI分岔现象
b.
神经元-ISI,AMP分岔现象
神经元兴奋性
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f–I curves for simple
models of type 1 and
type 2 behavior.
A: 6-variable Connor
et al. model of
molluscan neuron,
incorporating A-type
K+conductance,
showing type 1
behavior (Connor et
al. 1977).
B: 4-variable
Hodgkin–Huxley
model of the squid
giant axon membrane
patch, showing type 2
behavior (Hodgkin
and Huxley 1952).
C: 2-variable Morris–
Lecar model with
type 1 parameters
(Morris and Lecar
1981).
D: Morris–Lecar
model with type 2
parameters.
相位响应曲线（PRC）
树突影响
CA3 Pyramidal Neuron
• 树突切割位置．
• (A) 中等多棘神经元的多房室模型，dend51指向的房室为
接受刺激的树突，黑色长方形中标有数字的红圈表示相应
的切割位置1，2，3，4和5；
• (B) 长方形局部放大．
LTP hippocampus - LTD cerebellum
Spike-Timing Dependent Plasticity-STDP
Neuron simulation environment
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Matlab and Mathematica
NEURON - http://www.neuron.yale.edu/
GENESIS - http://genesis-sim.org/
XPPAUT - http://www.math.pitt.edu/~bard/xpp/xpp.html
MATCONT-http://www.matcont.ugent.be/
• HHsim: http://www.cs.cmu.edu/~dst/HHsim/
• L-Measure - http://cng.gmu.edu:8080/Lm/help/index.htm
• NeuroML - http://www.neuroml.org/index.php
• Scholarpedia -http://www.scholarpedia.org/article/Main_Page
Matlab and Mathematica
• MATLAB-Neural Network Toolbox
• Hindmarsh-Rose Neuron Model
5 Neuron simulation environment
for empirically-based simulations of neurons and networks of neurons.
• Welcome to the community of NEURON users and developers!
• This is the home page of the NEURON simulation environment,
which is used in classrooms and laboratories around the world for
building and using computational models of neurons and networks
of neurons. Here you will find installers and source code,
documentation, tutorials, announcements of courses and
conferences, and discussion forums about NEURON in particular
and computational neuroscience in general. Users who have special
interests and expertise are invited to participate in the NEURON
project, e.g. by helping to organize future meetings of the NEURON
Users' Group, or by participating in collaborative development of
documentation, tutorials, and software. We also welcome
suggestions for ways to make NEURON a more useful tool for
research and teaching.
https://senselab.med.yale.edu/modeldb/
6 GENESIS (simulation environment)
• GENESIS (the GEneral NEural SImulation
System) is 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 systems-level
models. The object-oriented approach taken by
GENESIS and its high-level simulation language
allows modelers to easily extend the capabilities
of the simulator, and to exchange, modify, and
reuse models or model components.
http://genesis-sim.org/
7 XPPAUT 6.10
• XPPAUT is a general numerical tool for simulating, animating,
and analyzing dynamical systems. These can range from
• discrete finite state models (e.g., McCulloch-Pitts neurons) to
• stochastic Markov models, to
• discretization of partial differential equations and integrodifferential
equations.
• The program evolved from a DOS program that was originally
written so that John Rinzel and Bard Ermentrout could easily
illustrate the dynamics of a simple model for an excitable
membrane. The DOS program, PHASEPLANE, became a
commercial project and was used for many years by a number
of patient folks.
http://www.math.pitt.edu/~bard/xpp/xpp.html
8 MATCONT, CL_MATCONT and
CL_MATCONT_for_MAPS
• The study of differential equations requires good and powerful
mathematical software. Also, a flexible and extendible package is
important. A powerful and widely used environment for scientific
computing is Matlab. The aim of MatCont and Cl_MatCont is to
provide a continuation and bifurcation toolbox which is compatible
with the standard Matlab ODE representation of differential
equations.
• MatCont is a graphical Matlab package for the interactive numerical
study of dynamical systems. It is developed in parallel with the
command line continuation toolbox Cl_MatCont. The package
(Cl_)MatCont is freely available for non-commercial use on an as is
basis. It should never be sold as part of some other software
product. Also, in no circumstances can the authors be held liable for
any deficiency, fault or other mishappening with regard to the use or
performance of (Cl_)MatCont.
The following actions are supported by the present
version of MatCont and Cl_MatCont
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continuation of equilibrium and periodic solutions with respect to a control parameter;
computation of phase response curves and their derivatives for periodic solutions;
detection of fold, Hopf and branching points on curves of equilibria;
computation of normal form coefficients for fold and Hopf equilibrium bifurcations;
continuation of fold and Hopf equilibrium bifurcations in two control parameters;
detection of all codim 2 equilibrium bifurcations (cusp, Bogdanov-Takens, generalized Hopf, zeroHopf, and double Hopf) on fold and Hopf curves;
computation of normal form coefficients for all codim 2 equilibrium bifurcations;
detection of branch bifurcation points on fold curves;
continuation of branching equilibria in three control parameters;
detection of flip, fold, torus and branch bifurcations of periodic solutions;
computation of normal form coefficients for bifurcations of periodic solutions;
continuation of flip, fold and torus bifurcations of periodic solutions in two control parameters;
detection of several codim 2 bifurcations of periodic solutions on fold, flip and torus bifurcation
curves;
switching to the period doubled branch in a flip point;
branch switching at branch points of equilibria and limit cycles;
continuation of branching periodic solutions in three control parameters;
continuation of orbits homoclinic to a hyperbolic saddle;
continuation of orbits homoclinic to a saddle-node.
HHsim:
Graphical Hodgkin-Huxle Simulator
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HHsim is a graphical simulation of a section of excitable neuronal membrane using
the Hodgkin-Huxley equations. It provides full access to the Hodgkin-Huxley
parameters, membrane parameters, stimulus parameters, and ion concentrations. To
learn about the Hodgkin-Huxley equations, see:
Channeling with Bard, an online tutorial by G. Bard Ermentrout.
Biophysics of Computation: Information Processing in Single Neurons, by Christof
Koch. (See chapter 6.)
Theoretical Neuroscience, by Peter Dayan and Larry F. Abbott. (See chapter 5.)
A Simple Sodium - Potassium Gate Model, by James K. Peterson.
In contrast with NEURON or GENESIS, which are vastly more sophisticated research
tools, HHsim is simple educational software designed specifically for graduate or
undergraduate neurophysiology courses. The user interface can be mastered in a
couple of minutes and provides many ways for the student to experiment. HHsim is
free software distributed under the GNU General Public License. The official HHsim
web site is at http://www.cs.cmu.edu/~dst/HHsim. The online documentation,
including sample screen shots, is available on this web site, and also included with
the program when you download it. Also included are sample exercises that use the
simulator.
9 L-Measure
• a web-accessible tool for the
analysis, comparison and
search of digital reconstructions
of neuronal morphologies
Data represented in a SWC format
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structure file n400.swc
digitized with Neurolucida
creature rat F344
region Hippocampus
field/layer CA1
cell type CA1 Pyramidal Cell in vivo young
contributed byBuzsaki_G & Turner_DA
published in J. Comp. Neurol. 391: 335-352, 1998
raw dataN400.asc
additional notes turner_p_ca1.txt
soma area 0.41E3
shrinkage correction (x, y, z) 1.33 1.33 4.00
version no.2.0
dated 1998-03-27
appleid correction 1.33 1.33 4.0
red-green image n400
1 1 -0.426 4.549 10 4.52 -1
2 1 -0.638 2.82 10 0.907 1
3 1 -0.838 1.516 10 4.52 2
4 1 -0.638 0 10 4.52 3
5 1 -0.426 0 10 4.52 4
6 1 -0.213 -1.955 10 4.2 5
7 1 -0.213 -2.168 10 4.2 6
8 1 -0.213 -3.471 10 4.2 7
9 1 0.213 -4.761 10 3.73 8
10 1 0.838 -6.504 10 3.57 9
11 1 1.264 -7.368 10 3.41 10
L-Measure to carry out an extensive statistical analysis of
publicly available digitized CA3 and CA1 pyramidal neurons.
11 Model Descriptions for
Computational Neuroscience
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Computational models based on detailed neuroanatomical and electrophysiological data have
been used for many years as an aid for understanding the function of the nervous system.
NeuroML is an international, collaborative initiative to develop a language for describing detailed
models of neural systems.
The aims of the NeuroML initiative are:
To create specifications for a language in XML to describe the biophysics, anatomy and network
architecture of neuronal systems at multiple scales
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To facilitate the exchange of complex neuronal models between researchers, allowing for greater
transparency and accessibility of models
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To promote software tools which support NeuroML and support the development of new software
and databases
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To encourage researchers with models within the scope of NeuroML to exchange and publish their
models in this format.
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NeuroML is a free and open community effort developed with input from many contributors. We
need your help as the language and tools continue to evolve. NeuroML v1.8.1 is the latest stable
release of the specification, and has been described in detail in a recent publication.
NeuroML version 2.0 is in active development. See here for details on the ongoing work towards
this new version of the language.
12 PyNN-http://neuralensemble.org/trac/PyNN
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PyNN (pronounced 'pine' ) is a is a simulator-independent language for building neuronal network models.
In other words, you can write the code for a model once, using the PyNN API and the Python programming
language, and then run it without modification on any simulator that PyNN supports (currently NEURON, NEST,
PCSIM and Brian).
The PyNN API aims to support modelling at a high-level of abstraction (populations of neurons, layers, columns
and the connections between them) while still allowing access to the details of individual neurons and synapses
when required. PyNN provides a library of standard neuron, synapse and synaptic plasticity models, which have
been verified to work the same on the different supported simulators. PyNN also provides a set of commonly-used
connectivity algorithms (e.g. all-to-all, random, distance-dependent, small-world) but makes it easy to provide your
own connectivity in a simulator-independent way, either using the Connection Set Algebra ( Djurfeldt, 2010) or by
writing your own Python code.
The low-level API is good for small networks, and perhaps gives more flexibility. The high-level API is good for
hiding the details and the book-keeping, allowing you to concentrate on the overall structure of your model.
The other thing that is required to write a model once and run it on multiple simulators is standard cell models.
PyNN translates standard cell-model names and parameter names into simulator-specific names, e.g. standard
model IF_curr_alpha is iaf_neuron in NEST and StandardIF in NEURON, while SpikeSourcePoisson is a
poisson_generator in NEST and a NetStim in NEURON. Only a few cell models have been implemented so far.
Even if you don't wish to run simulations on multiple simulators, you may benefit from writing your simulation code
using PyNN's powerful, high-level interface. In this case, you can use any neuron or synapse model supported by
your simulator, and are not restricted to the standard models.
PyNN is a work in progress, but is already being used for several large-scale simulation projects.
Download the current stable release of the API (0.7), or get the development version from the Subversion
repository.
13 Blue Brain Project
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The Blue Brain Project is an attempt to create a
synthetic brain by reverse-engineering the
mammalian brain down to the molecular level.
The aim of the project, founded in May 2005 by
the Brain and Mind Institute of the École
Polytechnique Fédérale de Lausanne (Switzerland)
is to study the brain's architectural and functional
principles. The project is headed by the Institute's
director, Henry Markram. Using a Blue Gene
supercomputer running Michael Hines's NEURON
software, the simulation does not consist simply of
an artificial neural network, but involves a
biologically realistic model of neurons. It is hoped
that it will eventually shed light on the nature of
consciousness.
There are a number of sub-projects, including the
Cajal Blue Brain, coordinated by the
Supercomputing and Visualization Center of
Madrid (CeSViMa), and others run by universities
and independent laboratories in the UK, US, and
Israel.
Blue Brain Project
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Neocortical column modelling
The initial goal of the project, completed in December 2006, was the
simulation of a rat neocortical column, which can be considered the smallest
functional unit of the neocortex (the part of the brain thought to be
responsible for higher functions such as conscious thought). Such a column
is about 2 mm tall, has a diameter of 0.5 mm and contains about 60,000
neurons in humans; rat neocortical columns are very similar in structure but
contain only 10,000 neurons (and 108 synapses). Between 1995 and 2005,
Markram mapped the types of neurons and their connections in such a
column.
Whole brain simulation
A longer term goal is to build a detailed, functional simulation of the
physiological processes in the human brain: "It is not impossible to build a
human brain and we can do it in 10 years," Henry Markram, director of the
Blue Brain Project said in 2009 at the TED conference in Oxford.In a BBC
World Service interview he said: "If we build it correctly it should speak and
have an intelligence and behave very much as a human does."
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Computational neuroscience is a subfield of neuroscience
that uses mathematical methods to simulate and understand
the function of the nervous system.
Experimental Neuroscience
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Theoretical Neuroscience
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Models of Neurons (Editor: Frances K. Skinner)
Spiking Networks
Network Dynamics (Editor: Marc-Oliver Gewaltig)
Brain Models (Editor: Marc-Oliver Gewaltig)
Dynamical Systems
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Electrophysiology
Neuron
Synapse
Memory
Conditioning
Consciousness (Editor: Anil K. Seth)
Vision
Olfaction (Editor: Maxim Bazhenov)
Neuroimaging
Oscillators
Synchronization
Pattern Formation
Chaos
Bifurcations
Simulation Environment
Computational Intelligence
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Brain Theory
Recurrent Networks
Feedforward Networks
Graph Theory
Reinforcement Learning
Evolutionary Computation
Information Theory
Statistics
Signal Analysis
Pattern Recognition (Editor: Ke Chen)
Navigation and Control
Robotics (Editor: Jan Peters)
14 ScholarpediaEncyclopedia of
computational
neuroscience
15 Sloan-Swartz Centers for
Theoretical Neurobiology
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The Centers for Theoretical Neurobiology were established at five outstanding U.S.
research institutions (Brandeis University, California Institute of Technology, New York
University, Salk Institute, and University of California at San Francisco) in 1994 by the
Sloan Foundation. The Swartz Foundation joined Sloan as co-sponsor of SloanSwartz Program in Theoretical Neurobiology in 2000.
The aim of the Program is to establish an integral role for theory and quantitative
approaches in neuroscience research. Theory, a natural part of research programs in
many sciences, was substantially absent from neuroscience. Recognizing the value
of an integrated theoretical approach, this initiative places both experimentally- and
theoretically-trained scientists from physics, mathematics and computer sciences into
selected experimental brain research laboratories. In that environment, they become
conversant with neuroscience questions and experimental approaches in
neurobiology, enabling them to apply their unusual vantage and theoretical skills to
cooperative lines of inquiry.
Research Centers and Initiatives
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Brandeis University
California Institute of Technology
Cold Spring Harbor Laboratory
Columbia
Harvard
New York University
Princeton
Salk Institute
University of California at San Diego
University of California at San Francisco
Yale
Swartz Prize for Theoretical and
Computational Neuroscience
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2011: Haim Sompolinsky
2010: Larry Abbott
2009: Horace Barlow
2008: Wilfrid Rall
$25,000 Swartz Prize for Theoretical and
Computational Neuroscience
16 Institute for Nonlinear Science
• The goal of neural science is to understand the brain,
mind, how we perceive, move, think, and remember. All
those things are dynamical processes which are taking
place in a complex, changing and noisy environment.
That means that these dynamical processes at all levels
from small neural networks to behavior should be stable
against perturbation but flexible and adaptive. The goal
of neurodynamics is to formulate the main dynamical
principles which can be a basis for such behavior and to
predict the possible activities of neurons and neural
ensembles using the tools of nonlinear dynamics.
Neurodynamics group
• Stability and Flexibility of small neural
circuits (CPGs)
• The role of sensory systems for the
organization of motor activity
• Winnerless Competition and the olfactory
system of insects
• Electronic Neurons and hybrid circuits
• Reconstruction of input spaces
• Mechanisms of synaptic plasticity
• Electronic Nervous Systems for Biomimetic
Robots
17 University of Ottawa Center for
Neural Dynamics
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Research Groups
Sensory Systems
Motor Control
Autonomic Nervous System Control
Memory and Plasticity
Neuromuscular Systems
Modeling
COMPUTATIONAL
NEUROSCIENCE
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http://home.earthlink.net/~perlewitz/sftwr.html
MODELING
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Microphysiological
Compartmental
Realistic Network
Interoperability
MODELING SUPPORT
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Data Aquisition & Control
Data Analysis & Visualization
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Morphology
Time Series
Network
Database Management
Differential Equation Solvers
多谢！