Hansel D, Sompolinsky H
Centre de Physique Théorique, UPR014-CNRS, Ecole Polytechnique, Palaiseau, France.
J Comput Neurosci. 1996 Mar;3(1):7-34. doi: 10.1007/BF00158335.
Neurons in cortical slices emit spikes or bursts of spikes regularly in response to a suprathreshold current injection. This behavior is in marked contrast to the behavior of cortical neurons in vivo, whose response to electrical or sensory input displays a strong degree of irregularity. Correlation measurements show a significant degree of synchrony in the temporal fluctuations of neuronal activities in cortex. We explore the hypothesis that these phenomena are the result of the synchronized chaos generated by the deterministic dynamics of local cortical networks. A model of a "hypercolumn" in the visual cortex is studied. It consists of two populations of neurons, one inhibitory and one excitatory. The dynamics of the neurons is based on a Hodgkin-Huxley type model of excitable voltage-clamped cells with several cellular and synaptic conductances. A slow potassium current is included in the dynamics of the excitatory population to reproduce the observed adaptation of the spike trains emitted by these neurons. The pattern of connectivity has a spatial structure which is correlated with the internal organization of hypercolumns in orientation columns. Numerical simulations of the model show that in an appropriate parameter range, the network settles in a synchronous chaotic state, characterized by a strong temporal variability of the neural activity which is correlated across the hypercolumn. Strong inhibitory feedback is essential for the stabilization of this state. These results show that the cooperative dynamics of large neuronal networks are capable of generating variability and synchrony similar to those observed in cortex. Auto-correlation and cross-correlation functions of neuronal spike trains are computed, and their temporal and spatial features are analyzed. In other parameter regimes, the network exhibits two additional states: synchronized oscillations and an asynchronous state. We use our model to study cortical mechanisms for orientation selectivity. It is shown that in a suitable parameter regime, when the input is not oriented, the network has a continuum of states, each representing an inhomogeneous population activity which is peaked at one of the orientation columns. As a result, when a weakly oriented input stimulates the network, it yields a sharp orientation tuning. The properties of the network in this regime, including the appearance of virtual rotations and broad stimulus-dependent cross-correlations, are investigated. The results agree with the predictions of the mean field theory which was previously derived for a simplified model of stochastic, two-state neurons. The relation between the results of the model and experiments in visual cortex are discussed.
皮层切片中的神经元在响应阈上电流注入时会定期发放单个尖峰或尖峰簇。这种行为与皮层神经元在体内的行为形成鲜明对比，后者对电刺激或感觉输入的反应表现出很强的不规则性。相关性测量表明，皮层中神经元活动的时间波动存在显著程度的同步性。我们探讨了这样一种假设，即这些现象是由局部皮层网络的确定性动力学产生的同步混沌的结果。研究了视觉皮层中一个“超柱”的模型。它由两类神经元组成，一类是抑制性的，另一类是兴奋性的。神经元的动力学基于具有多种细胞和突触电导的霍奇金 - 赫胥黎型可兴奋电压钳制细胞模型。在兴奋性神经元群体的动力学中包含了一个缓慢的钾电流，以重现观察到的这些神经元发放的尖峰序列的适应性。连接模式具有一种空间结构，该结构与定向柱中超柱的内部组织相关。模型的数值模拟表明，在适当的参数范围内，网络会进入一种同步混沌状态，其特征是神经活动具有强烈的时间变异性，且这种变异性在整个超柱中是相关的。强大的抑制性反馈对于这种状态的稳定至关重要。这些结果表明，大型神经元网络的协同动力学能够产生与在皮层中观察到的类似的变异性和同步性。计算了神经元尖峰序列的自相关和互相关函数，并分析了它们的时间和空间特征。在其他参数范围内，网络表现出另外两种状态：同步振荡和异步状态。我们使用我们的模型来研究皮层的方向选择性机制。结果表明，在合适的参数范围内，当输入没有方向时，网络具有一系列连续的状态，每个状态代表一种不均匀的群体活动，该活动在其中一个定向柱处达到峰值。因此，当一个弱定向的输入刺激网络时，它会产生尖锐的方向调谐。研究了该范围内网络的特性，包括虚拟旋转的出现和广泛的依赖刺激的互相关。结果与先前为随机二态神经元的简化模型推导的平均场理论的预测一致。讨论了模型结果与视觉皮层实验之间的关系。
