神经信息处理的简单模型研究
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摘要
计算神经科学是一门跨领域的交叉学科，把实验神经科学和理论研究科学联系在一起，运用物理，数学以及工程学的概念和分析工具来科学地研究大脑的工作原理。近年来，随着实验技术的发展，实验数据的不断累积，大脑的研究工作越来越需要计算模型的方法，从系统，跨层次的角度来探讨大脑的工作机制。然而，神经系统极其复杂，它是一个典型的高维，多尺度，非线性的动态系统。计算神经科学的一个目标就是发展简单的计算模型，一方面它能抓住生物系统的关键特征，另一方面使得定量的分析成为可能。本文根据在突触，环路层面发现的实验现象，建立了一些符合生物事实的简单的模型，从理论上分析这些模型的计算意义。我们着重回答以下几个计算问题：1）实验现象背后的生物物理机制；2）从神经网络角度的来看，这些现象的计算意义是怎样的。本文的工作主要在以下三个方面：
首先，基于实验上发现的兴奋性和抑制性输入在胞体上的整合计算公式，发展了一个简单的基于树突信息整合的单神经元模型，并详细的分析了分流抑制的生物物理机制。模型的分析结果在很多方面与实验现象一致。进一步的，基于简化的单神经元模型，我们分析了突触信息的整合公式在网络计算中的作用。特别地，我们探讨了分流抑制项的计算功能。通过计算模拟仿真，我们发现分流抑制可以介导神经元低水平的持续性放电活动。另外，分流抑制可以实现网络动力学的除法归一化操作。
其次，系统地分析了一个普遍存在于感觉系统初级通路的神经环路，如嗅觉系统和视觉系统。该环路存在突触短时程衰减和突触前抑制两个显著的机制。以嗅觉系统为例，我们首先通过模型模拟的方法考察了该环路处理空域信息的能力，仿真发现该环路可以实现实验上观察到的神经元输入输出函数的输入性增益控制。进一步地，我们发现该环路可以实现气味身份信息的不变性表达，而气味的浓度信息由神经元群的瞬态反应编码。然后，我们分析了该环路处理时序信息的特点，发现该环路可以等效为一个自适应的微分计算器，而且，对突变信号的瞬态反应幅值满足Weber-Fechner法则。神经环路的这些特性有利于神经信息的高效处理。
最后，系统地分析了果蝇嗅觉系统的稀疏编码网络。稀疏编码是神经系统普遍采用的信息编码机制，它可以有效的减小刺激模式之间的相关性。在果蝇的嗅觉系统中，蘑菇体中的Kenyon cell以稀疏表示的方式编码天线叶中小球的气味信息。然而，实验上发现天线叶的小球中平均有3个姊妹细胞。这些姊妹细胞接收的突触输入相同，相互之间以电突触的方式相互耦合，这样，姊妹细胞电活动反应在任何时刻都是高度相关的。嗅觉系统为什么需要这些信息冗余的姊妹细胞，目前还不清楚。为此，我们建立了一个前向传输网络模型来研究姊妹细胞对神经信息的处理的功用，特别是它们对于下级神经元Kenyoncell的稀疏码表示有什么影响。理论分析表明：1）姊妹细胞可以有效的提升Kenyon cell稀疏表示对噪声的鲁棒性，当姊妹细胞数为4-5个时，系统对噪声的鲁棒性趋于饱和；2）基于经济连接，能量最省，信息保真传输等原则，模型预测了Kenyon cell与投射神经元的平均连接数，约10个左右，这与实验数据高度吻合。
Computational neuroscience is an interdisciplinary science that applies concepts andanalytical tools from physics, mathematics, and engineering to explore the underlyingmechanisms of brain functions, with a strong emphasis on the interaction of experimentsand theories. In recent years, as the development of experimental neuroscience, a hugeamount of date has been accumulated. The brain research is in urgent need of computa-tional modeling method, to investigate the working mechanisms of brain in terms of anintegrated system. Nevertheless, nervous system is an extremely complicated system, itinvolves multiple nonlinear interactions in a high-dimensional dynamical system. A goalin theoretical neuroscience is to develop simple models which, on one hand, capture thefundamental features of the real biologic systems, and on the other hand, allow us to pur-sue analytical treatment unveiling the general principle of brain function. Based on theexperimental fndings in synapses and neural circuits, we build some biophysically realis-tic simple models to theoretically investigate their roles in neural information processing.In particular, we are concentrated on answering these computational problems:1)Thebiophysical mechanisms behind experimental fndings;2)The computational meanings ofthese experimental evidences, especially in terms of neural networks. The main works inthis thesis are listed as follows:
(1) The experimental study has found that the integration of excitatory and inhibito-ry currents at the soma of a neuron can be expressed as a simple arithmetic rule. Basedon this simple arithmetic rule, we carry out a biophysical motivated derivation of a singlecompartment model that integrates the nonlinear efects of shunting inhibition, wherean inhibitory input on the route of an excitatory input to the soma cancels or “shunts”the excitatory potential. Our results agree with the experimental fndings. Using ournew simplifed formulation, we devise a spiking network model where inhibitory neuronsact as global shunting gates, and show that the network exhibits persistent activity ina low fring regime. We further build a continuous attractor neural network model andshow that shunting inhibition could be well approximated as an operation of divisivenormalization in the network dynamics.
(2) Systematically analyze a canonical neural circuit which is widely existed in theearly pathway of sensory systems, e.g., visual system and olfactory system. The circuit is endowed with mechanisms, namely short term synaptic depression and presynapticinhibition. We frst investigate how spatial information is processed in this circuit. Simu-lation results reveal that it can input gain control of a single neuron’s IO function, whichis observed in experiment. Moreover, the circuit could achieve concentration invariantrepresentations to odorant stimuli, while the odor concentration information is encodedin the network transient dynamics. Second, we explore the power of the circuit to processtemporal information. We fnd that the circuit could be approximated as a adaptive dif-ferentiator, with its transient response obeying the Weber-Fechner law. These propertiesare of great importance for the circuit to efciently process neural information.
(3) Analyze the sparse coding network in the olfactory system of drosophila. Sparsecoding is a common coding mechanism in the brain to achieve efcient pattern separation.In the olfactory system of the fy drosopohila melangaster, projection neurons (PNs)in the antennal lobe (AL) convert a dense activation of glomeruli into a sparse fringpattern of Kenyon cells (KCs) in the mushroom body (MB). A sparse code of odorqualities has the advantage to achieve efcient decorrelation of the representation ofsimilar odors. While the sparseness of a code is directly related to its decorrelationproperties, too low fring probabilities might result in other disadvantages for the brain.We here investigate the structure of the sparse projection from the antennal lobe to themushroom body in regard to faithful information transmission and robustness to extrinsicand intrinsic noise. In particular, we emphasize on understanding the role of the highlycorrelated homotypic projection neurons found in the glomeruli of fies which receiveidentical information from their ORN input but target randomly diferent KCs. We fndthat a certain number of sister cells is crucial for the robustness of the sparse KC codeto noise. Our analysis predicts that4-5sister cells per glomerulus would be sufcient,which is in good anatomical agreement in fies. Moreover, we estimate how many PNsshould optimally connect to a single KC, and found that values around10would sufceto guarantee both, robust information transmission and a very sparse odor representationin MB.
首先，基于实验上发现的兴奋性和抑制性输入在胞体上的整合计算公式，发展了一个简单的基于树突信息整合的单神经元模型，并详细的分析了分流抑制的生物物理机制。模型的分析结果在很多方面与实验现象一致。进一步的，基于简化的单神经元模型，我们分析了突触信息的整合公式在网络计算中的作用。特别地，我们探讨了分流抑制项的计算功能。通过计算模拟仿真，我们发现分流抑制可以介导神经元低水平的持续性放电活动。另外，分流抑制可以实现网络动力学的除法归一化操作。
其次，系统地分析了一个普遍存在于感觉系统初级通路的神经环路，如嗅觉系统和视觉系统。该环路存在突触短时程衰减和突触前抑制两个显著的机制。以嗅觉系统为例，我们首先通过模型模拟的方法考察了该环路处理空域信息的能力，仿真发现该环路可以实现实验上观察到的神经元输入输出函数的输入性增益控制。进一步地，我们发现该环路可以实现气味身份信息的不变性表达，而气味的浓度信息由神经元群的瞬态反应编码。然后，我们分析了该环路处理时序信息的特点，发现该环路可以等效为一个自适应的微分计算器，而且，对突变信号的瞬态反应幅值满足Weber-Fechner法则。神经环路的这些特性有利于神经信息的高效处理。
最后，系统地分析了果蝇嗅觉系统的稀疏编码网络。稀疏编码是神经系统普遍采用的信息编码机制，它可以有效的减小刺激模式之间的相关性。在果蝇的嗅觉系统中，蘑菇体中的Kenyon cell以稀疏表示的方式编码天线叶中小球的气味信息。然而，实验上发现天线叶的小球中平均有3个姊妹细胞。这些姊妹细胞接收的突触输入相同，相互之间以电突触的方式相互耦合，这样，姊妹细胞电活动反应在任何时刻都是高度相关的。嗅觉系统为什么需要这些信息冗余的姊妹细胞，目前还不清楚。为此，我们建立了一个前向传输网络模型来研究姊妹细胞对神经信息的处理的功用，特别是它们对于下级神经元Kenyoncell的稀疏码表示有什么影响。理论分析表明：1）姊妹细胞可以有效的提升Kenyon cell稀疏表示对噪声的鲁棒性，当姊妹细胞数为4-5个时，系统对噪声的鲁棒性趋于饱和；2）基于经济连接，能量最省，信息保真传输等原则，模型预测了Kenyon cell与投射神经元的平均连接数，约10个左右，这与实验数据高度吻合。
Computational neuroscience is an interdisciplinary science that applies concepts andanalytical tools from physics, mathematics, and engineering to explore the underlyingmechanisms of brain functions, with a strong emphasis on the interaction of experimentsand theories. In recent years, as the development of experimental neuroscience, a hugeamount of date has been accumulated. The brain research is in urgent need of computa-tional modeling method, to investigate the working mechanisms of brain in terms of anintegrated system. Nevertheless, nervous system is an extremely complicated system, itinvolves multiple nonlinear interactions in a high-dimensional dynamical system. A goalin theoretical neuroscience is to develop simple models which, on one hand, capture thefundamental features of the real biologic systems, and on the other hand, allow us to pur-sue analytical treatment unveiling the general principle of brain function. Based on theexperimental fndings in synapses and neural circuits, we build some biophysically realis-tic simple models to theoretically investigate their roles in neural information processing.In particular, we are concentrated on answering these computational problems:1)Thebiophysical mechanisms behind experimental fndings;2)The computational meanings ofthese experimental evidences, especially in terms of neural networks. The main works inthis thesis are listed as follows:
(1) The experimental study has found that the integration of excitatory and inhibito-ry currents at the soma of a neuron can be expressed as a simple arithmetic rule. Basedon this simple arithmetic rule, we carry out a biophysical motivated derivation of a singlecompartment model that integrates the nonlinear efects of shunting inhibition, wherean inhibitory input on the route of an excitatory input to the soma cancels or “shunts”the excitatory potential. Our results agree with the experimental fndings. Using ournew simplifed formulation, we devise a spiking network model where inhibitory neuronsact as global shunting gates, and show that the network exhibits persistent activity ina low fring regime. We further build a continuous attractor neural network model andshow that shunting inhibition could be well approximated as an operation of divisivenormalization in the network dynamics.
(2) Systematically analyze a canonical neural circuit which is widely existed in theearly pathway of sensory systems, e.g., visual system and olfactory system. The circuit is endowed with mechanisms, namely short term synaptic depression and presynapticinhibition. We frst investigate how spatial information is processed in this circuit. Simu-lation results reveal that it can input gain control of a single neuron’s IO function, whichis observed in experiment. Moreover, the circuit could achieve concentration invariantrepresentations to odorant stimuli, while the odor concentration information is encodedin the network transient dynamics. Second, we explore the power of the circuit to processtemporal information. We fnd that the circuit could be approximated as a adaptive dif-ferentiator, with its transient response obeying the Weber-Fechner law. These propertiesare of great importance for the circuit to efciently process neural information.
(3) Analyze the sparse coding network in the olfactory system of drosophila. Sparsecoding is a common coding mechanism in the brain to achieve efcient pattern separation.In the olfactory system of the fy drosopohila melangaster, projection neurons (PNs)in the antennal lobe (AL) convert a dense activation of glomeruli into a sparse fringpattern of Kenyon cells (KCs) in the mushroom body (MB). A sparse code of odorqualities has the advantage to achieve efcient decorrelation of the representation ofsimilar odors. While the sparseness of a code is directly related to its decorrelationproperties, too low fring probabilities might result in other disadvantages for the brain.We here investigate the structure of the sparse projection from the antennal lobe to themushroom body in regard to faithful information transmission and robustness to extrinsicand intrinsic noise. In particular, we emphasize on understanding the role of the highlycorrelated homotypic projection neurons found in the glomeruli of fies which receiveidentical information from their ORN input but target randomly diferent KCs. We fndthat a certain number of sister cells is crucial for the robustness of the sparse KC codeto noise. Our analysis predicts that4-5sister cells per glomerulus would be sufcient,which is in good anatomical agreement in fies. Moreover, we estimate how many PNsshould optimally connect to a single KC, and found that values around10would sufceto guarantee both, robust information transmission and a very sparse odor representationin MB.
引文
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