[Paper Review] Universality of macroscopic neuronal dynamics in Caenorhabditis elegans

Connor Brennan, Alex Proekt|arXiv (Cornell University)|Nov 22, 2017

Genetics, Aging, and Longevity in Model Organisms1 references3 citations

TL;DR

This study reveals that despite significant variability in individual neuron activity across genetically identical *C. elegans* worms, their global brain dynamics are governed by a conserved manifold in neural activity space, enabling accurate cross-worm behavioral predictions. The method combines dimensionality reduction and stochastic modeling to uncover this universal macroscopic dynamics, rooted in a mathematical link between neural trajectories and thermodynamic systems.

ABSTRACT

Recordings of whole brain activity with single neuron resolution are now feasible in simple organisms. Yet, it is still challenging to appropriately simplify such complex, noisy, and multivariate data in order to reveal general principles of nervous system function. Here, we develop a method that allows us to extract global brain dynamics from pan-neuronal imaging. Success of this method is rooted in a surprising mathematical connection between dimensionality reduction and a general class of thermodynamic systems. Application of this theoretical framework to the nervous system of C. elegans reveals the manifold that sculpts global brain dynamics. This manifold allows us to predict switches between worm behaviors across individuals, implying that macroscopic dynamics embodied by the manifold are universal. In contrast, activation of individual neurons differs consistently between worms. These findings suggest that brains of genetically identical individuals express distinct microscopic neuronal configurations which nonetheless yield equivalent macroscopic dynamics.

Motivation & Objective

• To identify general principles of nervous system function by simplifying high-dimensional, noisy pan-neuronal activity data from *C. elegans*.
• To test whether macroscopic brain dynamics are invariant across individuals despite microscopic variability in neuronal activity.
• To develop a theoretical framework that connects dimensionality reduction in neural data to thermodynamic systems for modeling collective neural dynamics.
• To determine whether such a universal manifold can predict behavioral transitions across genetically identical worms.
• To reconcile deterministic and stochastic models of neural dynamics by identifying a shared manifold that governs global behavior.

Proposed method

• Applied principal component analysis (PCA) to pan-neuronal calcium imaging data from *C. elegans* head ganglia, reducing activity to two dominant components that capture ~60% of variance.
• Constructed a probability density function $ P $ from binned activity in the PC1-PC2 plane to model stochastic neuronal dynamics using Brownian motion with drift: $ \frac{d\mathbf{X}}{dt} = D\frac{\nabla P(\mathbf{X})}{P(\mathbf{X})} + \epsilon $.
• Identified a low-dimensional manifold through trajectory bundling and clustering of neural state transitions, revealing recurrent patterns in neural dynamics.
• Used the manifold to simulate neuronal activity and behavioral dwell times, validating predictions against observed data from individual worms.
• Performed cross-validation by training on 4 worms and predicting behavior in the left-out worm, assessing statistical similarity of simulated vs. observed dwell times.
• Quantified dynamics using entropy and flux analysis to compare manifold-based predictions with null hypotheses, showing lower entropy and non-linear decay in real data.

Experimental results

Research questions

• RQ1 Is there a universal, low-dimensional manifold that governs macroscopic brain dynamics across genetically identical *C. elegans* individuals despite variability in individual neuron activity?
• RQ2 Can the shape of this manifold be used to predict behavioral transitions across worms, even when individual neuron activity patterns differ?
• RQ3 To what extent do stochastic models alone fail to reproduce observed macroscopic dynamics, and how does incorporating deterministic structure (the manifold) improve predictive power?
• RQ4 How does the conservation of the manifold relate to evolutionary constraints on behavior, given that selection acts on behavior, not on individual neurons?
• RQ5 What is the relationship between microscopic neuronal variability and macroscopic dynamical invariance in a simple nervous system?

Key findings

• The manifold governing global brain dynamics is conserved across all five *C. elegans* individuals studied, despite consistent differences in activation of specific neurons like AVBL, RIVR, and RMED.
• Neuronal activity in individual worms varies significantly across the clonal population, with p-values for neuron activity distributions below 0.01 for AVBL (0.0056), RIVR (0.0018), and RMED (3.2×10⁻²²), indicating non-identical dynamics.
• The manifold successfully predicts behavioral state transitions and dwell times across worms, with simulations matching observed statistics qualitatively and quantitatively, especially when trained on all neurons.
• Worm D was an outlier in dwell time statistics, likely due to low sampling (only ~10 behaviors), but the manifold still captured its structure when trained on the other four worms.
• Entropy of manifold-based predictions was consistently lower than null models, and decayed non-linearly, reflecting high stochasticity in forward locomotion trajectories.
• The manifold captures behaviorally relevant dynamics: forward and backward locomotion are localized in distinct regions of the manifold, with flux vectors indicating directionality (red for backward, blue for forward).