系统神经生物学模拟 - pku · 3. 数学模拟:神经元网络模型 蝗虫的嗅觉系统---...
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Systems Neuroscience ModelingSystems Neuroscience Modeling系统神经生物学模拟
陶乐天 北京大学生命科学学院 生物信息中心陶乐天 北京大学生命科学学院 生物信息中心Louis Tao, Center for Bioinformatics, College of Life Sciences, PKU
© Copyright 2010 Center for Bioinformatics, Peking University
Beijing, 29 March 2011
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Neuronal Networks Are Complex
~1011 neurons & 1015 connections
104 cells & 1,000 m wiring in 1 mm3 of cortex
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Neurons 神经元
• Information processing units 信息处理/加工单元
哺乳动物大脑 1010 1013 i li b i• 哺乳动物大脑:1010-1013 neurons in mammalian brains
• 104 cell bodies and roughly 103 m of ‘wiring’ per mm3
• Different shapes, sizes, functions, … 不同形状、大小、功能
• Spiking vs Analog neurons 锋电位(动作电位)vsSpiking vs. Analog neurons 锋电位(动作电位)vs. e.g., bipolar and amacrine cells in retina, sensory-motor neurons of invertebrates, …视网膜里的双极细胞与无长突细胞,无脊椎动物的感觉-运动神经元,等…
• Many other cells (e.g., glia cells 胶质细胞) in cortex: to supply energy, to provide structural stability, …, and not directly i l d i i f ti i
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involved in information processing
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系统神经生物学的研究系统神经生物学的研究
1 数据分析:神经元活性 与 刺激/行为 的 相关性1. 数据分析:神经元活性 与 刺激/行为 的 相关性
2 编码机制:动作电位频率(rate coding)2. 编码机制:动作电位频率(rate coding)动作电位时间(temporal coding)神经元群(P l ti di )神经元群(Population coding)吸引子 / 瞬变动态 (attractor/transient coding)
3. 数学模拟:以神经元模型为单元的网络动力系统
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Cortical Map of Orientation Preference朝向/方向选择
-----
Blasde
朝向/方向选择
0.5mm
el (1992)
-----
right eyeTypical experimental setup for optical imaging
left eye(above figure taken from Tsodyks et al 1999)
Show Larry’s Movie
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Show Larry s Movie
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2. 编码机制
朝向柱Orientation hypercolumn
初级视觉皮层的朝向选择性
视觉刺激:光栅
0( ) 1 sin( )x t I t k xI
朝向选择性
0( , ) 1 sin( )x t I t k xI cos , sin , k k k k k
对比
高对比中对比 刺激中对比 刺激低对比
Anderson et al, Science 2000
Blasdel 1992光成像数据分析结果
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,
Rate coding, population & ‘space’ coding
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蝗虫天线叶 (antenna lobe)Transient dynamics 瞬变动态
2. 编码机制Transient dynamics 瞬变动态
Spike times of 110 ne ronsSpike times of 110 neurons(nonlinearly) projected to 3 dimensional subspace
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Stopfer et al, Neuron 2003(Gilles Laurent 实验室)
3 dimensional subspaceLocally Linear Embedding (Roweis & Saul, Science 2000)
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局部线形嵌入 Locally Linear Embedding局部线形嵌入 Locally Linear Embedding
• Roweis & Saul, Science 2000• Modern Problem: How to find low dimensional subspace
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in high dimensional data?
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3. 数学模拟:神经元网络模型
蝗虫的嗅觉系统 --- 天线叶 (antenna lobe) 90 PN j ti (兴奋性)~ 90 PN projection neuron (兴奋性)
~ 30 LN local neuron (抑制性)稀疏的网络连接性 (sparse connectivity)
数学模型数值仿真数值仿真
1)系统分析
解2)了解机制
(左
© Copyright 2010 Center for Bioinformatics, Peking UniversityBazhenov et al, Neuron 2001
(左:Patel, Rangan & Cai, J.Comput. Neurosci., ’09)
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What is “cognitive function” at the neural level?如何研究认知功能?如何研究认知功能?
© Copyright 2010 Center for Bioinformatics, Peking Universitytenyearsofmylife.com/images/20060826.jpg
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fMRI: Functional Magnetic Resonance Imaging
© Copyright 2010 Center for Bioinformatics, Peking UniversityCourtney et al, Science, 1999
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Neuro-/Electro-physiology
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Romo & Salinas Nat Rev Neurosci 2003Machens et al Science 2005
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A Zebrafish RoadmapA Zebrafish Roadmap
Genes to Cells to Networks to Behavior• Cortical regions and behavior• Attractors?
C ll d t kCells and networks• High resolution imaging, data analysis, and
mathematical modeling• Dynamical / Functional Analog of Brainbow
© Copyright 2009 Center for Bioinformatics, Peking University
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A Zebrafish RoadmapA Zebrafish Roadmap
从 基 到 细胞 到 络 到 行为从 基因 到 细胞 到 网络 到 行为
• 大脑区域与行为大脑区域与行为• 吸引子 / Attractor
从 神经元 到 网络
• 高分辨率的光学成像 数据分析 数学模型• 高分辨率的光学成像、数据分析、数学模型• 有‘功能’、动态的Brainbow
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引吸引子 / Attractor
• 点• Point 点
• Line 线Line 线
• Circle or Ellipse 圆圈/椭圆 (limit cycle, planetary orbits, …)
• Higher & non-integer (fractal) dimensional geometric objects / chaotic dynamical systemgeometric objects / chaotic dynamical system 混沌动力学 dx y x
dt
dy x z ydtdz xy z
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Wikipedia, Lorenz_attractor_yb.svg
xy zdt
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‘吸引子’神经网络吸引子 神经网络
An attractor for the network exists ifAn attractor for the network exists if from any initial configuration of network states the network evolves in time until:
• A given configuration of network states repeats itself (point attractor).• A given sequence of network states repeats itself (limit cycle attractor).• The network states evolve non-
i di llperiodically
D J Amit. Modelling Brain Function: The
© Copyright 2010 Center for Bioinformatics, Peking University
World of Attractor Neural Nets. Cambridge University Press, New York, 1989.
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吸引子与记忆
Basic tenants of attractor network theory as applied to memory:theory as applied to memory:1. Memories reside in specialized recurrent neural networks as specific
tt f l ti itpatterns of neuronal activity.2. Memory states are imprinted in the network by modifications of recurrent synaptic connections.3. As a result of synaptic modifications, memory states can be retrieved through
D J Amit. Modelling Brain Function: The World of Attractor Neural Nets. Cambridge University
memory states can be retrieved through input of partial cues and persist due to recurrent self-excitation (turn into attractor states of the network).Attractor Neural Nets. Cambridge University
Press, New York, 1989. )
John J. Hopfield. PNAS, 1982Misha Tsodyks. Neuron, 2005
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吸引子与癫痫seizure / epilepsy
W J Freeman IEEE Transactions onW. J. Freeman. IEEE Transactions on Circuits and Systems 35 (7), 1988
© Copyright 2010 Center for Bioinformatics, Peking UniversityKeogh et al Epilepsy Research 66:75-90, 2005
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利用光学成像技术来研究认知功能
虾虾
© Copyright 2010 Center for Bioinformatics, Peking UniversityTg(HuC:cameleon)
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斑马鱼 发育生物学的模式动物
3 months
3 days10 min
2 days45 min
1 day~ 1 hour
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13 hours~ 3.5 hours
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钙浓度代表神经元活跃性resting active
K+Na+ Ca2+
K+
Na+ Ca2+
Ion Concentration outside (in mM)
Concentration inside (in mM)
RatioOut : In
Eion(at 37°C)) ) ( )
K+ 5 100 1:20 -80 mV
N + 150 15 10 1 62 VNa+ 150 15 10:1 62 mV
Ca2+ 2 0.002 10,000:1 123 mV
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Cl- 150 13 11.5:1 -65 mV
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FRET指示钙离子浓度的原理FRET指示钙离子浓度的原理
CFP YFPCFP YFP
Miyawaki et al., Nature 388:882-887, 1997
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Multi-photon/Confocal Fluorescence Imaging
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Detection of the FRET response of cameleon-expressing neurons to stimulationexpressing neurons to stimulation
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Fan et al., J Biomed Optics 12(3), 030417 (2007)
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PTZ induces epileptiform-like electrographic activity in zebrafish larvae
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Baraban et al. Neuroscience 131: 759-768, 2005
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PTZ induces characteristic behaviors in zebrafish larvaein zebrafish larvae
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PTZ与神经元内钙浓度的变化
7 dpf
© Copyright 2009 Center for Bioinformatics, Peking University
Srinivasamoorthy et al.
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PTZ与神经元内钙浓度的变化
Spatial Characteristics of Seizure
Evolution of Calcium Activity as a Function of CompartmentPhase-Intensity Plot
© Copyright 2009 Center for Bioinformatics, Peking UniversitySrinivasamoorthy et al. in revision
TeO: optic tectum; Th: thalamus; CeP: cerebellar plate;MO: medulla oblongata
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吸引子?
© Copyright 2009 Center for Bioinformatics, Peking UniversitySrinivasamoorthy et al. in revision
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Relating Calcium Activity and Behavior
© Copyright 2009 Center for Bioinformatics, Peking UniversitySrinivasamoorthy et al. in revision
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Next on Our Zebrafish RoadmapNext on Our Zebrafish Roadmap
Genes to Cells to Networks to Behavior• Cortical regions and behavior• Attractors?
C ll d t kCells and networks• High resolution imaging, data analysis, and
th ti l d limathematical modeling• Dynamical / Functional Analog of Brainbow• Some Preliminary Results• Some Preliminary Results
© Copyright 2009 Center for Bioinformatics, Peking UniversityBackground Image --- A. Pan (Harvard) “Brainbow”
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电生理与神经功能网络分析电生理与神经功能网络分析
荧光钙离子指示剂
神经元动作电位时间/频率神经元动作电位时间/频率神经元动作电位时间/频率神经元细胞内钙浓度
神经元功能网络与模型神经元功能网络与模型神经元功能网络与模型
神经元细胞内钙浓度
神经元动作电位时间/频率神经元功能网络与模型神经元功能网络与模型神经元功能网络与模型
神经元动作电位时间/频率
神经元功能网络与模型
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FRET指示钙离子浓度的原理指示钙离子浓度的原理
YFPCFP
BB
© Copyright 2010 Center for Bioinformatics, Peking UniversityMiyawaki et al., PNAS 96:2135-2140, 1999
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钙浓度与神经元动作电位时间/频率动作电位时间/频率
动作电位时间或频率
动作电位时间或频率时间序列
卷积
去卷积
钙浓度钙浓度钙浓度
© Copyright 2010 Center for Bioinformatics, Peking UniversityYaksi & Friedrich, Nature Methods 2006
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Ca2+ Concentration & Neuronal Activity
© Copyright 2010 Center for Bioinformatics, Peking University
Yaksi & Friedrich, Nature Methods 2006
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荧光钙离子指示剂 钙浓度神经元动作电位频率神经元动作电位频率
神经元功能网络神经元功能网络
Y/CFP FRET SVD-Based Signal Calcium NeuronalRatio
钙离子指示剂(荧光亮度)
Multivariate DataAnalysis
基于主成分分析的多元数据分析
g(BackgroundSubtracted)
信号(除背景)
CalciumConcentration钙离子浓度
Activity神经元动作电位
频率多元数据分析 (除背景)
Sornborger & Lauderdale (U Georgia)
© Copyright 2010 Center for Bioinformatics, Peking University
斑马鱼荧光成像数据 (unpublished)Tao et al 分析方法 (in revision)
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利用数学模型寻找合理的神经元群动力系统
(Tao et al, in revisn.)
© Copyright 2010 Center for Bioinformatics, Peking University(Tao et al, in preparation)
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非负矩阵分析结果:神经元群的分布
(Tao et al, in revision)
© Copyright 2010 Center for Bioinformatics, Peking University
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© Copyright 2010 Center for Bioinformatics, Peking University
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非负矩阵分析结果:神经元群的动态
伪色图:伪色图:神经元群空间分布
神经元群的动态/活性
© Copyright 2010 Center for Bioinformatics, Peking University
神经元群的动态/活性(Tao et al, in revision)
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Acknowledgments
D rerio seizure modelCBI @ PKU
Wei Liping 魏丽萍D. rerio seizure model @ U Georgia
James Lauderdale
p g 魏丽萍Gao Ge 高歌Bian Yang 边洋
Wang Cong 王聪Andrew SornborgerCharles Keith (USC Beaufort)
Wang Cong 王聪
Math @ PKU姜Lauderdale Lab Members
A. Majumder, X. Fan, G. Srinivasamoorthy,J. Broder, E. Porter,
S R i J Ki
Jiang Ming 姜明
C elegans & D rerio @ PKUS. Reagin, J. Kim C. elegans & D. rerio @ PKULiu Dong 刘东
Vi l b h i iVisual behavior inD. melanogastor @ IBP ?
Zhu Yan 朱岩
© Copyright 2010 Center for Bioinformatics, Peking University
Funding: 北大985/211,US NIH, UGa Engineering Grant, UGa Research Foundation
Zhu Yan 朱岩
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© Copyright 2010 Center for Bioinformatics, Peking University
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Questions?Questions?