arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2001.08332q-bio.NCmath.DSphysics.bio-ph
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非线性控制在线虫C. elegans

Nonlinear control in the nematode C. elegans

Megan Morrison, Charles Fieseler, J. Nathan Kutz

摘要:

最近的全脑钙成像记录线虫C。elegans已经证明,神经活动由低维流形上的动力学支配,所述低维流形可以根据行为状态来聚类。尽管在用线性或局部线性模型建模动态方面取得了进展,但仍然不清楚单个神经元网络如何产生所观察到的特征。特别是,在数据中观察到多个聚类或固定点,这些聚类或固定点不能用单个线性模型来表征。我们提出了一个非线性控制模型,这是全球性的,参数化只有四个自由参数,匹配的低维C显示的功能。线虫神经活动。除了再现数据的平均概率分布之外,过渡统计中的长和短时间尺度变化可以通过单个参数的变化来表征。这些宏观尺度的转变中的一些具有与似乎充当生物控制的单个神经调节剂的实验相关性,使得该模型能够生成关于这些神经调节剂对全局动态的影响的可检验的假设。该理论提供了一个优雅的表征神经元种群动力学在C。优雅此外,非线性控制框架的数学结构提供了一个范例,可以推广到具有任意数量的行为状态的更复杂的系统。

英文摘要:

Recent whole-brain calcium imaging recordings of the nematode C. elegans have demonstrated that neural activity is dominated by dynamics on a low-dimensional manifold that can be clustered according to behavioral states. Despite progress in modeling the dynamics with linear or locally linear models, it remains unclear how a single network of neurons can produce the observed features. In particular, there are multiple clusters, or fixed points, observed in the data which cannot be characterized by a single linear model. We propose a nonlinear control model which is global and parameterized by only four free parameters that match the features displayed by the low-dimensional C. elegans neural activity. In addition to reproducing the average probability distribution of the data, long and short time-scale changes in transition statistics can be characterized via changes in a single parameter. Some of these macro-scale transitions have experimental correlates to single neuro-modulators that seem to act as biological controls, allowing this model to generate testable hypotheses about the effect of these neuro-modulators on the global dynamics. The theory provides an elegant characterization of the neuron population dynamics in C. elegans. Moreover, the mathematical structure of the nonlinear control framework provides a paradigm that can be generalized to more complex systems with an arbitrary number of behavioral states.

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