Lapicque's introduction of the integrate-and-fire model neuron (1907)
Lapicque's introduction of the integrate-and-fire model neuron (1907)
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DOI：
10.1016/s0361-9230(99)00161-6
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发表时间：
1999-11-01
影响因子：
3.8
通讯作者：
Abbott, LF
中科院分区：
文献类型：
--
作者：
Abbott, LF
1907年，早在神经元动作电位产生机制被发现之前，Lapicque就开发了一种神经元模型，至今仍被广泛使用[3，7]。这一非凡的成就强调，在神经建模中，功能研究不一定需要了解机制。如果一种现象得到充分描述，即使其生物物理基础无法建立模型，也有可能取得重大进展。Lapicque使用由并联电容器和电阻器组成的电路对神经元进行建模（图1A）。它们代表细胞膜的电容和漏电阻。当然，这样简单的电路无法产生动作电位，但拉皮克假设，当膜电容器充电到一定的阈值电位时，就会产生动作电位，电容器就会放电，重置膜电位（图1B）。Lapicque使用该模型计算了神经纤维的放电频率，该神经纤维与固定电压下的刺激电极耦合。图1C呈现了示出模型对随时间变化的注入电流的响应的模拟仿真。由于Hodgkin和Huxley [2]的工作，我们现在可以构建包括负责动作电位产生的电压依赖性膜电导动力学的模型。尽管如此，对于许多建模目的，Lapicque的简单模型是足够的，非常有用的。正如今天所解释的，积分和点火模型并不局限于简单的电容器电阻器电路的线性膜特性。在这样的模型中可以包括精确建模的突触和亚阈值电导（例如，参见[8]）。整合激发模型的效用在于分离影响突触整合、爆发和适应的极快动作电位和较慢过程之间的时间尺度。虽然Lapicque，因为他那个时代的知识有限，别无选择，只能以简单的方式建模动作电位，但动作电位的刻板特征允许我们，即使在今天，使用相同的近似值来避免计算动作电位期间的电压轨迹。这使我们能够将智力和计算资源集中在可能与神经计算最相关的问题上，而无需花费时间和精力对已经很好理解的现象进行建模，即动作电位的产生。整合-激发模型已被广泛用于各种研究，从单个神经元的突触整合研究到包含数十万个神经元的网络模拟。整合-激发模型已被证明在阐明大型神经网络的性质以及此类网络中大量突触连接的含义方面特别有用。例如，集成并激发模型
In 1907, long before the mechanisms responsible for the generation of neuronal action potentials were known, Lapicque developed a neuron model that is still widely used today [3, 7]. This remarkable achievement stresses that, in neural modeling, studies of function do not necessarily require an understanding of mechanism. Significant progress is possible if a phenomenon is adequately described, even if its biophysical basis cannot be modeled. Lapicque modeled the neuron using an electric circuit consisting of a parallel capacitor and resistor (Fig. 1A). These represent the capacitance and leakage resistance of the cell membrane. Of course, such a simple circuit cannot generate action potentials, but Lapicque postulated that when the membrane capacitor was charged to certain threshold potential, an action potential would be generated and the capacitor would discharge, resetting the membrane potential (Fig. 1B). Lapicque used the model to compute the firing frequency of a nerve fiber resistively coupled to a stimulating electrode held at fixed voltage. Fig. 1C presents an analogous simulation showing the response of the model to a time-varying injected current. Due to the work of Hodgkin and Huxley [2], we can now construct models that include the dynamics of the voltage-dependent membrane conductances responsible for action potential generation. Nevertheless, for many modeling purposes, the simple model of Lapicque is adequate and extremely useful.As interpreted today, integrate-and-fire models are not restricted to the linear membrane properties of a simple capacitorresistor circuit. It is possible to include accurately modeled synaptic and subthreshold conductances in such a model (eg, see [8]). The utility of the integrate-and-fire model lies in the separation of time scales between the extremely rapid action potential and slower process that affect synaptic integration, bursting, and adaptation. While Lapicque, because of the limited knowledge of his time, had no choice but to model the action potential in a simple manner, the stereotypical character of action potentials allows us, even today, to use the same approximation to avoid computation of the voltage trajectory during an action potential. This allows us to focus both intellectual and computation resources on the issues likely to be most relevant in neural computation, without expending time and energy on modeling a phenomenon, the generation of action potentials, that is already well understood. Integrate-and-fire models have been used in a wide variety of studies ranging from investigations of synaptic integration by single neurons to simulations of networks containing hundreds of thousands of neurons. The integrate-and-fire model has proven particularly useful in elucidating the properties of large neural networks and the implications of large numbers of synaptic connections in such networks. For example, integrate-and-fire models