A connectivity model for the locomotor network of Caenorhabditis elegans

Synthetic ablations in the C. elegans nervous system

Synthetic lethality, the finding that the simultaneous knockout of two or more individually nonessential genes leads to cell or organism death, has offered a systematic framework to explore cellular function, and also offered therapeutic applications. Yet the concept lacks its parallel in neuroscience—a systematic knowledge base on the role of double or higher order ablations in the functioning of a neural system. Here, we use the framework of network control to systematically predict the effects of ablating neuron pairs and triplets on the gentle touch response. We find that surprisingly small sets of 58 pairs and 46 triplets can reduce muscle controllability in this context, and that these sets are localized in the nervous system in distinct groups. Further, they lead to highly specific experimentally testable predictions about mechanisms of loss of control, and which muscle cells are expected to experience this loss.

“Synthetic lethality” in cell biology is an extreme example of the effects of higher order genetic interactions: The simultaneous knockout of two or more individually nonessential genes leads to cell death. We define a neural analog to this concept in relation to the locomotor response to gentle touch in C. elegans. Two or more neurons are synthetic essential if individually they are not required for this behavior, yet their combination is. We employ a network control approach to systematically assess all pairs and triplets of neurons by their effect on body wall muscle controllability, and find that only surprisingly small sets of neurons are synthetic essential. They are highly localized in the nervous system and predicted to affect control over specific sets of muscles.

Caenorhabditis elegans and the network control framework-FAQs

Control is essential to the functioning of any neural system. Indeed, under healthy conditions the brain must be able to continuously maintain a tight functional control between the system's inputs and outputs. One may therefore hypothesize that the brain's wiring is predetermined by the need to maintain control across multiple scales, maintaining the stability of key internal variables, and producing behaviour in response to environmental cues. Recent advances in network control have offered a powerful mathematical framework to explore the structure-function relationship in complex biological, social and technological networks, and are beginning to yield important and precise insights on neuronal systems. The network control paradigm promises a predictive, quantitative framework to unite the distinct datasets necessary to fully describe a nervous system, and provide mechanistic explanations for the observed structure and function relationships. Here, we provide a thorough review of the network control framework as applied to Caenorhabditis elegans (Yan et al. 2017 Nature550, 519-523. (doi:10.1038/nature24056)), in the style of Frequently Asked Questions. We present the theoretical, computational and experimental aspects of network control, and discuss its current capabilities and limitations, together with the next likely advances and improvements. We further present the Python code to enable exploration of control principles in a manner specific to this prototypical organism.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Functional connectomics from neural dynamics: probabilistic graphical models for neuronal network of Caenorhabditis elegans

We propose an approach to represent neuronal network dynamics as a probabilistic graphical model (PGM). To construct the PGM, we collect time series of neuronal responses produced by the neuronal network and use singular value decomposition to obtain a low-dimensional projection of the time-series data. We then extract dominant patterns from the projections to get pairwise dependency information and create a graphical model for the full network. The outcome model is a functional connectome that captures how stimuli propagate through the network and thus represents causal dependencies between neurons and stimuli. We apply our methodology to a model of the Caenorhabditis elegans somatic nervous system to validate and show an example of our approach. The structure and dynamics of the C. elegans nervous system are well studied and a model that generates neuronal responses is available. The resulting PGM enables us to obtain and verify underlying neuronal pathways for known behavioural scenarios and detect possible pathways for novel scenarios.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

C. elegans locomotion: small circuits, complex functions

With 302 neurons in the adult Caenorhabditis elegans nervous system, it should be possible to build models of complex behaviors spanning sensory input to motor output. The logic of the motor circuit is an essential component of such models. Advances in physiological, anatomical, and neurogenetic analysis are revealing a surprisingly complex signaling network in the worm's small motor circuit. We are progressing towards a systems level dissection of the network of premotor interneurons, motor neurons, and muscle cells that move the animal forward and backward in its environment.

Neurobiology of Caenorhabditis elegans Locomotion: Where Do We Stand?

Animals use a nervous system for locomotion in some stage of their life cycle. The nematode Caenorhabditis elegans, a major animal model for almost all fields of experimental biology, has long been used for detailed studies of genetic and physiological locomotion mechanisms. Of its 959 somatic cells, 302 are neurons that are identifiable by lineage, location, morphology, and neurochemistry in every adult hermaphrodite. Of those, 75 motoneurons innervate body wall muscles that provide the thrust during locomotion. In this Overview, we concentrate on the generation of either forward- or backward-directed motion during crawling and swimming. We describe locomotion behavior, the parts constituting the locomotion system, and the relevant neuronal connectivity. Because it is not yet fully understood how these components combine to generate locomotion, we discuss competing hypotheses and models.

Nematode locomotion: dissecting the neuronal-environmental loop

With a fully reconstructed and extensively characterized neural circuit, the nematode Caenorhabditis elegans is a promising model system for integrating our understanding of neuronal, circuit and whole-animal dynamics. Fundamental to addressing this challenge is the need to consider the tight neuronal-environmental coupling that allows the animal to survive and adapt to changing conditions. Locomotion behaviors are affected by environmental variables both at the biomechanical level and via adaptive sensory responses that drive and modulate premotor and motor circuits. Here we review significant advances in our understanding of proprioceptive control of locomotion, and more abstract models of spatial orientation and navigation. The growing evidence of the complexity of the underlying circuits suggests that the intuition gained is but the first step in elucidating the secrets of neural computation in this relatively simple system.