[Paper Review] Unsupervised learning of control signals and their encodings in $ extit{C. elegans}$ whole-brain recordings

Charles Fieseler, Manuel Zimmer+1 more|arXiv (Cornell University)|Jan 23, 2020

Neural dynamics and brain function5 references4 citations

TL;DR

This paper proposes a global, linear dynamical system with unsupervised learning of sparse control signals to model C. elegans whole-brain neural dynamics from calcium imaging data. Using Dynamic Mode Decomposition with Control (DMDc), it reconstructs nonlinear population dynamics as linear evolution driven by few key neurons, identifying control signals linked to behavioral transitions with predictive encoding across time delays.

ABSTRACT

Recent whole brain imaging experiments on $ extit{C. elegans}$ has revealed that the neural population dynamics encode motor commands and stereotyped transitions between behaviors on low dimensional manifolds. Efforts to characterize the dynamics on this manifold have used piecewise linear models to describe the entire state space, but it is unknown how a single, global dynamical model can generate the observed dynamics. Here, we propose a control framework to achieve such a global model of the dynamics, whereby underlying linear dynamics is actuated by sparse control signals. This method learns the control signals in an unsupervised way from data, then uses $ extit{ Dynamic Mode Decomposition with control}$ (DMDc) to create the first global, linear dynamical system that can reconstruct whole-brain imaging data. These control signals are shown to be implicated in transitions between behaviors. In addition, we analyze the time-delay encoding of these control signals, showing that these transitions can be predicted from neurons previously implicated in behavioral transitions, but also additional neurons previously unidentified. Moreover, our decomposition method allows one to understand the observed nonlinear global dynamics instead as linear dynamics with control. The proposed mathematical framework is generic and can be generalized to other neurosensory systems, potentially revealing transitions and their encodings in a completely unsupervised way.

Motivation & Objective

• To develop a global, linear dynamical model that captures nonlinear neural population dynamics in C. elegans without piecewise approximations.
• To identify sparse, biologically interpretable control signals that drive transitions between discrete behaviors like forward movement, reversal, and turning.
• To understand how these control signals are encoded in neural activity with time-delayed predictive power.
• To provide a data-driven, unsupervised framework applicable to other neurosensory systems for identifying transition mechanisms.

Proposed method

• Applies Dynamic Mode Decomposition with Control (DMDc) to whole-brain calcium imaging data to learn a global linear dynamical system with control inputs.
• Uses unsupervised sparse variable selection to identify minimal sets of neurons acting as control signals for behavioral transitions.
• Employs a novel elimination pathway in the encoding analysis to determine the timescales and neural substrates of control signal propagation.
• Models transitions as sparse, transient signals acting on a globally linear system, avoiding piecewise or hybrid dynamical models.
• Integrates time-delayed analysis to predict transitions from pre-activation patterns in identified neurons.
• Validates reconstruction quality by comparing predicted dynamics to observed whole-brain activity.

Experimental results

Research questions

• RQ1 Can a single, global linear dynamical system with control inputs reconstruct the complex, nonlinear neural dynamics observed in C. elegans whole-brain recordings?
• RQ2 Which neurons encode the control signals responsible for initiating transitions between discrete behaviors such as forward movement, reversal, and turning?
• RQ3 Can the timing and sequence of neural activity preceding transitions be predicted from the identified control signals with time-delayed encoding?
• RQ4 How does the proposed framework compare to piecewise linear or locally linear models in reconstructing behavioral dynamics?
• RQ5 What is the biological interpretability and generalizability of the identified control signals across different behavioral states?

Key findings

• The proposed DMDc-based model successfully reconstructs whole-brain calcium imaging data using a single global linear system with sparse control signals, achieving high reconstruction fidelity.
• Control signals were identified in a small subset of neurons, including previously implicated ones like AVB and AIY, as well as novel candidates not previously linked to transitions.
• Time-delayed encoding analysis revealed that behavioral transitions can be predicted from neural activity up to 1.5 seconds in advance, with predictive power extending across multiple neuron types.
• The method successfully captures dynamics during forward movement and transitions to reversal/turn, but reconstruction quality degrades during prolonged forward states, suggesting intrinsic complexity or nonlinearity in this regime.
• The framework reveals that nonlinear dynamics can be understood as linear dynamics with sparse, transient control inputs, offering a simpler and more interpretable model than piecewise or hybrid systems.
• The unsupervised learning approach identifies biologically plausible control signals without prior labeling of behavioral states, enabling hypothesis generation for future experimental validation.