Training sensory–motor behavior in the connectome of an artificial C. elegans

Biophysical modeling and experimental analysis of the dynamics of C. elegans body-wall muscle cells

This study combines experimental techniques and mathematical modeling to investigate the dynamics of C. elegans body-wall muscle cells. Specifically, by conducting voltage clamp and mutant experiments, we identify key ion channels, particularly the L-type voltage-gated calcium channel (EGL-19) and potassium channels (SHK-1, SLO-2), which are crucial for generating action potentials. We develop Hodgkin-Huxley-based models for these channels and integrate them to capture the cells' electrical activity. To ensure the model accurately reflects cellular responses under depolarizing currents, we develop a parallel simulation-based inference method for determining the model's free parameters. This method performs rapid parallel sampling across high-dimensional parameter spaces, fitting the model to the responses of muscle cells to specific stimuli and yielding accurate parameter estimates. We validate our model by comparing its predictions against cellular responses to various current stimuli in experiments and show that our approach effectively determines suitable parameters for accurately modeling the dynamics in mutant cases. Additionally, we discover an optimal response frequency in body-wall muscle cells, which corresponds to a burst firing mode rather than regular firing mode. Our work provides the first experimentally constrained and biophysically detailed muscle cell model of C. elegans, and our analytical framework combined with robust and efficient parametric estimation method can be extended to model construction in other species.

Systematic generation of biophysically detailed models with generalization capability for non-spiking neurons

Unlike spiking neurons which compress continuous inputs into digital signals for transmitting information via action potentials, non-spiking neurons modulate analog signals through graded potential responses. Such neurons have been found in a large variety of nervous tissues in both vertebrate and invertebrate species, and have been proven to play a central role in neuronal information processing. If general and vast efforts have been made for many years to model spiking neurons using conductance-based models (CBMs), very few methods have been developed for non-spiking neurons. When a CBM is built to characterize the neuron behavior, it should be endowed with generalization capabilities (i.e. the ability to predict acceptable neuronal responses to different novel stimuli not used during the model’s building). Yet, since CBMs contain a large number of parameters, they may typically suffer from a lack of such a capability. In this paper, we propose a new systematic approach based on multi-objective optimization which builds general non-spiking models with generalization capabilities. The proposed approach only requires macroscopic experimental data from which all the model parameters are simultaneously determined without compromise. Such an approach is applied on three non-spiking neurons of the nematode Caenorhabditis elegans (C. elegans), a well-known model organism in neuroscience that predominantly transmits information through non-spiking signals. These three neurons, arbitrarily labeled by convention as RIM, AIY and AFD, represent, to date, the three possible forms of non-spiking neuronal responses of C. elegans.

The control structure of the nematode Caenorhabditis elegans: Neuro-sensory integration and proprioceptive feedback

We develop a biophysically realistic model of the nematode C. elegans that includes: (i) its muscle structure and activation, (ii) key connectomic activation circuitry, and (iii) a weighted and time-dynamic proprioception. In combination, we show that these model components can reproduce the complex waveforms exhibited in C. elegans locomotive behaviors, chiefly omega turns. This is achieved via weighted, time-dependent suppression of the proprioceptive signal. Though speculative, such dynamics are biologically plausible due to the presence of neuromodulators which have recently been experimentally implicated in the escape response, which includes an omega turn. This is the first integrated neuromechanical model to reveal a mechanism capable of generating the complex waveforms observed in the behavior of C. elegans, thus contributing to a mathematical framework for understanding how control decisions can be executed at the connectome level in order to produce the full repertoire of observed behaviors.

The Si elegans project at the interface of experimental and computational Caenorhabditis elegans neurobiology and behavior

OBJECTIVE

In light of recent progress in mapping neural function to behavior, we briefly and selectively review past and present endeavors to reveal and reconstruct nervous system function in Caenorhabditis elegans through simulation.

APPROACH

Rather than presenting an all-encompassing review on the mathematical modeling of C. elegans, this contribution collects snapshots of pathfinding key works and emerging technologies that recent single- and multi-center simulation initiatives are building on. We thereby point out a few general limitations and problems that these undertakings are faced with and discuss how these may be addressed and overcome.

MAIN RESULTS

Lessons learned from past and current computational approaches to deciphering and reconstructing information flow in the C. elegans nervous system corroborate the need of refining neural response models and linking them to intra- and extra-environmental interactions to better reflect and understand the actual biological, biochemical and biophysical events that lead to behavior. Together with single-center research efforts, the Si elegans and OpenWorm projects aim at providing the required, in some cases complementary tools for different hardware architectures to support advancement into this direction.

SIGNIFICANCE

Despite its seeming simplicity, the nervous system of the hermaphroditic nematode C. elegans with just 302 neurons gives rise to a rich behavioral repertoire. Besides controlling vital functions (feeding, defecation, reproduction), it encodes different stimuli-induced as well as autonomous locomotion modalities (crawling, swimming and jumping). For this dichotomy between system simplicity and behavioral complexity, C. elegans has challenged neurobiologists and computational scientists alike. Understanding the underlying mechanisms that lead to a context-modulated functionality of individual neurons would not only advance our knowledge on nervous system function and its failure in pathological states, but have directly exploitable benefits for robotics and the engineering of brain-mimetic computational architectures that are orthogonal to current von-Neumann-type machines.

The whole worm: brain-body-environment models of C. elegans

Brain, body and environment are in continuous dynamical interaction, and it is becoming increasingly clear that an animal's behavior must be understood as a product not only of its nervous system, but also of the ongoing feedback of this neural activity through the biomechanics of its body and the ecology of its environment. Modeling has an essential integrative role to play in such an understanding. But successful whole-animal modeling requires an animal for which detailed behavioral, biomechanical and neural information is available and a modeling methodology which can gracefully cope with the constantly changing balance of known and unknown biological constraints. Here we review recent progress on both optogenetic techniques for imaging and manipulating neural activity and neuromechanical modeling in the nematode worm Caenorhabditis elegans. This work demonstrates both the feasibility and challenges of whole-animal modeling.