神经元钙峰串的信息含量：基于经验概率的熵率估计
Information Content in Neuronal Calcium Spike Trains: Entropy Rate Estimation based on Empirical Probabilities
摘要：
定量的信息内容和它的时间变化在细胞内的钙锋电位列车在神经元中帮助一个理解功能，如记忆，学习和认知。这种量化还可以揭示病理信号扰动，其可能导致破坏性神经退行性疾病，包括帕金森病、阿尔茨海默病和亨廷顿病。因此，熵率的估计，信息含量的信息理论的措施，承担主要的意义。然而，这种估计在本上下文中是具有挑战性的，因为，虽然熵率传统上是渐近地定义为长块的假设下的平稳性，神经元是已知的编码信息在短的时间间隔和相关的尖峰序列往往表现出非平稳性。在此背景下，我们提出了一个熵率估计的经验概率的基础上，在窗口内操作，短到足以确保近似平稳。具体来说，我们的估计，参数化的长度编码上下文，试图模拟神经元尖峰序列的底层记忆结构。在一个例子马尔可夫过程中，我们比较了所提出的方法的性能与版本的Lempel-Ziv算法，以及与一定的平稳分布的方法，发现前者表现出更高的精度水平和更快的收敛。此外，在实验记录的四个海马神经元的钙反应，所提出的方法表现出更快的收敛。值得注意的是，我们的技术在上述神经元的反应中检测到了底层过程记忆的结构异质性。我们相信，所提出的方法有利于这种异质性的大规模研究，这反过来又可以确定各种疾病的熵率估计的签名。
英文摘要：
Quantification of information content and its temporal variation in intracellular calcium spike trains in neurons helps one understand functions such as memory, learning, and cognition. Such quantification could also reveal pathological signaling perturbation that potentially leads to devastating neurodegenerative conditions including Parkinson's, Alzheimer's, and Huntington's diseases. Accordingly, estimation of entropy rate, an information-theoretic measure of information content, assumes primary significance. However, such estimation in the present context is challenging because, while entropy rate is traditionally defined asymptotically for long blocks under the assumption of stationarity, neurons are known to encode information in short intervals and the associated spike trains often exhibit nonstationarity. Against this backdrop, we propose an entropy rate estimator based on empirical probabilities that operates within windows, short enough to ensure approximate stationarity. Specifically, our estimator, parameterized by the length of encoding contexts, attempts to model the underlying memory structures in neuronal spike trains. In an example Markov process, we compared the performance of the proposed method with that of versions of the Lempel-Ziv algorithm as well as with that of a certain stationary distribution method and found the former to exhibit higher accuracy levels and faster convergence. Also, in experimentally recorded calcium responses of four hippocampal neurons, the proposed method showed faster convergence. Significantly, our technique detected structural heterogeneity in the underlying process memory in the responses of the aforementioned neurons. We believe that the proposed method facilitates large-scale studies of such heterogeneity, which could in turn identify signatures of various diseases in terms of entropy rate estimates.
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