A spike-phase neural code has been proposed as a mechanism to encode stimuli based on the precise timing of spikes relative to the phase of membrane potential oscillations. This form of coding has been reported in both in vivo and in vitro experiments across several regions of the brain, yet there are concerns that such precise timing may be compromised by an effect referred to as variance accumulation, wherein spike timing variance increases over the phase of an oscillation. Here, we provide a straightforward explanation of this effect based on the theoretical spike time variance. The proposed theory is consistent with recordings of mitral neurons. It shows that spike time variance can increase in a nonlinear fashion with spike number, in a way that is dependent upon the frequency and amplitude of the oscillation. Further, non-monotonic accumulation of variance can arise from different combinations of oscillation parameters. Nonlinear accumulation sometimes leads to lower variance than that of a mean rate-matched homogeneous Poisson process, particularly for spikes that occur in later phases of oscillation. However, such an advantage is limited to a narrow range of oscillation amplitudes and frequencies. These results suggest fundamental constraints on spike-phase coding, and reveal how certain spikes in a sequence may exhibit increased firing time precision relative to their neighbors.

中文翻译：

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膜电位振荡过程中尖峰时间变化的非单调累积。

已经提出了尖峰相位神经代码作为一种基于尖峰相对于膜电位振荡相位的精确定时来编码刺激的机制。已经在大脑的多个区域进行的体内和体外实验中都报告了这种编码形式，但是人们担心这种精确的时序可能会受到称为方差累积的影响而受到损害，其中尖峰时序方差在整个阶段都增加振荡。在这里，我们基于理论上的尖峰时间方差提供了对此影响的简单解释。提出的理论与二尖瓣神经元的记录是一致的。结果表明，尖峰时间方差可以随尖峰数的增加而非线性增加，其方式取决于振荡的频率和幅度。进一步，振荡参数的不同组合会引起方差的非单调累积。非线性累积有时会导致比平均速率匹配的均匀Poisson过程更低的方差，特别是对于出现在振荡后期的尖峰。但是，这样的优点限于振荡幅度和频率的窄范围。这些结果表明了对尖峰相位编码的基本限制，并揭示了序列中的某些尖峰相对于其邻居而言可能表现出增加的触发时间精度。这样的优点限于振荡幅度和频率的狭窄范围。这些结果表明了对尖峰相位编码的基本限制，并揭示了序列中的某些尖峰相对于其邻居而言可能表现出增加的触发时间精度。这样的优点限于振荡幅度和频率的狭窄范围。这些结果表明了对尖峰相位编码的基本限制，并揭示了序列中的某些尖峰相对于其邻居而言可能表现出增加的触发时间精度。