Recent whole-brain calcium imaging recordings of the nematode C. elegans have demonstrated that the neural activity associated with behavior is dominated by dynamics on a low-dimensional manifold that can be clustered according to behavioral states. Previous models of C. elegans dynamics have either been linear models, which cannot support the existence of multiple fixed points in the system, or Markov-switching models, which do not describe how control signals in C. elegans neural dynamics can produce switches between stable states. It remains unclear how a network of neurons can produce fast and slow timescale dynamics that control transitions between stable states in a single model. We propose a global, nonlinear control model which is minimally parameterized and captures the state transitions described by Markov-switching models with a single dynamical system. The model is fit by reproducing the timeseries of the dominant PCA mode in the calcium imaging data. Long and short time-scale changes in transition statistics can be characterized via changes in a single parameter in the control model. 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 control in 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.

中文翻译：

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线虫的非线性控制 线虫


最近对线虫秀丽隐杆线虫的全脑钙成像记录表明，与行为相关的神经活动由低维流形上的动态主导，可以根据行为状态进行聚类。以前的线虫动力学模型要么是线性模型，它不能支持系统中多个固定点的存在，要么是马尔可夫切换模型，它没有描述线虫神经动力学中的控制信号如何在稳定之间产生切换州。目前尚不清楚神经元网络如何产生快速和慢速的时间尺度动态，以控制单个模型中稳定状态之间的转换。我们提出了一种全局非线性控制模型，该模型最小化参数化并捕获由单个动态系统的马尔可夫切换模型描述的状态转换。该模型通过再现钙成像数据中主要 PCA 模式的时间序列来拟合。转变统计中的长时标和短时标变化可以通过控制模型中单个参数的变化来表征。其中一些宏观尺度的转变与似乎充当生物控制的单个神经调节剂具有实验相关性，使得该模型能够生成关于这些神经调节剂对全局动力学影响的可检验的假设。该理论提供了秀丽隐杆线虫神经元群体动态控制的优雅特征。此外，非线性控制框架的数学结构提供了一种范式，可以推广到具有任意数量行为状态的更复杂系统。