# Nonlinear control in the nematode C. elegans

arXiv: https://arxiv.org/abs/2001.08332 · HTML: https://mlsanity.com/paper/2001.08332/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Jan 2020.

## Built on by (most cited first, 1 of 1)

- [Deep Generative Modeling for Identification of Noisy, Non-Stationary Dynamical Systems](https://mlsanity.com/paper/2410.02079/) (2024)

## Abstract (arXiv)

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.