Coding and Decoding with Adapting Neurons: A Population Approach to the Peri-Stimulus Time Histogram

The response of a neuron to a time-dependent stimulus, as measured in a Peri-Stimulus-Time-Histogram (PSTH), exhibits an intricate temporal structure that reflects potential temporal coding principles. Here we analyze the encoding and decoding of PSTHs for spiking neurons with arbitrary refractoriness and adaptation. As a modeling framework, we use the spike response model, also known as the generalized linear neuron model. Because of refractoriness, the effect of the most recent spike on the spiking probability a few milliseconds later is very strong. The influence of the last spike needs therefore to be described with high precision, while the rest of the neuronal spiking history merely introduces an average self-inhibition or adaptation that depends on the expected number of past spikes but not on the exact spike timings. Based on these insights, we derive a ‘quasi-renewal equation’ which is shown to yield an excellent description of the firing rate of adapting neurons. We explore the domain of validity of the quasi-renewal equation and compare it with other rate equations for populations of spiking neurons. The problem of decoding the stimulus from the population response (or PSTH) is addressed analogously. We find that for small levels of activity and weak adaptation, a simple accumulator of the past activity is sufficient to decode the original input, but when refractory effects become large decoding becomes a non-linear function of the past activity. The results presented here can be applied to the mean-field analysis of coupled neuron networks, but also to arbitrary point processes with negative self-interaction.

通过脉冲刺激时间直方图（Peri-Stimulus-Time-Histogram, PSTH）测得的神经元对时变刺激的响应，呈现出反映潜在时间编码原理的复杂时间结构。本文针对具有任意不应期与适应特性的锋电位神经元，分析了其脉冲刺激时间直方图的编码与解码过程。我们采用锋电位响应模型（spike response model，亦称广义线性神经元模型）作为建模框架。由于不应期的存在，末次锋电位在数毫秒内对锋电位发放概率的影响极为显著，因此需高精度地刻画末次锋电位的作用；而其余神经元锋电位历史仅会引入平均自抑制或适应效应，该效应仅取决于过去锋电位的预期数量，而非精确的锋电位发放时刻。基于上述认知，我们推导出了准更新方程，该方程可出色地描述具有适应特性的神经元的发放率。我们探究了准更新方程的有效域，并将其与锋电位神经元群体的其他发放率方程进行了对比。我们还以类似的思路解决了从群体响应（或脉冲刺激时间直方图）中解码刺激的问题。研究发现，在低活动水平与弱适应条件下，仅需对过往活动进行简单累积即可解码原始输入；但当不应期效应变强时，解码过程会变为过往活动的非线性函数。本文所提出的结果既可应用于耦合神经元网络的平均场分析（mean-field analysis），也可推广至任意具有负自相互作用的点过程（point processes）。