Stochastic neural field model of stimulus-dependent variability in cortical neurons
Stochastic neural field model of stimulus-dependent variability in cortical neurons
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DOI：
10.1371/journal.pcbi.1006755
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发表时间：
2019-03-01
影响因子：
4.3
通讯作者：
Bressloff, Paul C.
中科院分区：
文献类型：
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作者：
Bressloff, Paul C.
我们使用随机神经场理论来分析环形吸引子网络中神经变异性的刺激依赖调谐。我们使用微扰方法来说明如何将神经场方程归结为描述自发形成的调谐曲线或凸起解的随机漂移的一对随机非线性相位方程。这些方程是使用在循环统计理论中广为人知的二元冯·米塞斯分布的修正版本来分析的。我们首先考虑单环网络，并推导出一个简单的数学表达式，它解释了实验观察到的神经变异性的双峰(或M形)调谐。然后，我们探讨了网络间耦合对环状网络中的刺激依赖变异性的影响。它们可能代表通过垂直突触连接连接的皮质超柱的两个不同层中的细胞群体，或者代表同一层中通过水平斑块连接连接的两个不同皮质超柱的细胞群体。我们发现，神经变异性可以被抑制或促进，这取决于网络间的耦合是兴奋的还是抑制的，以及外部刺激对这两个网络的相对强度和偏差。这些结果与一般的观察结果是一致的，即通过外部刺激或调制驱动来增加平均放电率往往会降低神经变异性。作者摘要当前感兴趣的一个主题是关于刺激开始后抑制皮质变异性的神经机制。由于逐次试验的可变性和噪声相关性已知会影响神经元的信息能力，这种抑制可以提高种群编码的准确性。主要的候选机制之一是抑制多个吸引子之间的噪声诱导的跃迁，环形吸引子网络就是一个例子。后者已被用来模拟实验测量的定向选择性中颞叶(MT)神经元的随机调谐曲线。在这篇文章中，我们展示了如何利用连续统神经场模型中自发形成的调谐曲线或凸起的随机漂移来分析环形吸引子网络中神经变异性的刺激相关调谐。神经场的优势在于，人们可以推导出神经活动的二阶统计量的显式数学表达式，并探索这如何依赖于重要的模型参数，如噪声水平、循环连接的强度和输入对比度。
We use stochastic neural field theory to analyze the stimulus-dependent tuning of neural variability in ring attractor networks. We apply perturbation methods to show how the neural field equations can be reduced to a pair of stochastic nonlinear phase equations describing the stochastic wandering of spontaneously formed tuning curves or bump solutions. These equations are analyzed using a modified version of the bivariate von Mises distribution, which is well-known in the theory of circular statistics. We first consider a single ring network and derive a simple mathematical expression that accounts for the experimentally observed bimodal (or M-shaped) tuning of neural variability. We then explore the effects of inter-network coupling on stimulus-dependent variability in a pair of ring networks. These could represent populations of cells in two different layers of a cortical hypercolumn linked via vertical synaptic connections, or two different cortical hypercolumns linked by horizontal patchy connections within the same layer. We find that neural variability can be suppressed or facilitated, depending on whether the inter-network coupling is excitatory or inhibitory, and on the relative strengths and biases of the external stimuli to the two networks. These results are consistent with the general observation that increasing the mean firing rate via external stimuli or modulating drives tends to reduce neural variability.Author summary A topic of considerable current interest concerns the neural mechanisms underlying the suppression of cortical variability following the onset of a stimulus. Since trial-by-trial variability and noise correlations are known to affect the information capacity of neurons, such suppression could improve the accuracy of population codes. One of the main candidate mechanisms is the suppression of noise-induced transitions between multiple attractors, as exemplified by ring attractor networks. The latter have been used to model experimentally measured stochastic tuning curves of directionally selective middle temporal (MT) neurons. In this paper we show how the stimulus-dependent tuning of neural variability in ring attractor networks can be analyzed in terms of the stochastic wandering of spontaneously formed tuning curves or bumps in a continuum neural field model. The advantage of neural fields is that one can derive explicit mathematical expressions for the second-order statistics of neural activity, and explore how this depends on important model parameters, such as the level of noise, the strength of recurrent connections, and the input contrast.