Melanson Alexandre, Longtin André
Department of Physics, University of Ottawa, Ottawa, Canada.
Département de physique et d'astronomie, Université de Moncton, Moncton, Canada.
J Math Neurosci. 2019 Jul 26;9(1):6. doi: 10.1186/s13408-019-0074-3.
The emergent activity of biological systems can often be represented as low-dimensional, Langevin-type stochastic differential equations. In certain systems, however, large and abrupt events occur and violate the assumptions of this approach. We address this situation here by providing a novel method that reconstructs a jump-diffusion stochastic process based solely on the statistics of the original data. Our method assumes that these data are stationary, that diffusive noise is additive, and that jumps are Poisson. We use threshold-crossing of the increments to detect jumps in the time series. This is followed by an iterative scheme that compensates for the presence of diffusive fluctuations that are falsely detected as jumps. Our approach is based on probabilistic calculations associated with these fluctuations and on the use of the Fokker-Planck and the differential Chapman-Kolmogorov equations. After some validation cases, we apply this method to recordings of membrane noise in pyramidal neurons of the electrosensory lateral line lobe of weakly electric fish. These recordings display large, jump-like depolarization events that occur at random times, the biophysics of which is unknown. We find that some pyramidal cells increase their jump rate and noise intensity as the membrane potential approaches spike threshold, while their drift function and jump amplitude distribution remain unchanged. As our method is fully data-driven, it provides a valuable means to further investigate the functional role of these jump-like events without relying on unconstrained biophysical models.
生物系统的突发活动通常可以用低维的朗之万型随机微分方程来表示。然而，在某些系统中，会发生大的突发事件，这违背了这种方法的假设。我们在此通过提供一种仅基于原始数据的统计信息来重构跳跃扩散随机过程的新方法来解决这种情况。我们的方法假设这些数据是平稳的，扩散噪声是加性的，并且跳跃是泊松分布的。我们使用增量的阈值穿越来检测时间序列中的跳跃。接下来是一个迭代方案，用于补偿被错误检测为跳跃的扩散波动的存在。我们的方法基于与这些波动相关的概率计算以及福克 - 普朗克方程和微分查普曼 - 柯尔莫哥洛夫方程的使用。经过一些验证案例后，我们将此方法应用于弱电鱼电感受侧线叶锥体细胞的膜噪声记录。这些记录显示出在随机时间发生的大的、类似跳跃的去极化事件，其生物物理学尚不清楚。我们发现一些锥体细胞在膜电位接近动作电位阈值时会增加其跳跃率和噪声强度，而它们的漂移函数和跳跃幅度分布保持不变。由于我们的方法完全由数据驱动，它提供了一种有价值的手段，无需依赖无约束的生物物理模型即可进一步研究这些类似跳跃事件的功能作用。
