Connectome to behaviour: modelling C. elegans at cellular resolution

Connectomes of organisms, such as the nematode Caenorhabditis elegans (C. elegans), have been mapped on various scales: from macro to single neuron level. In addition, decades of research in describing biophysical processes have provided foundations for modeling single neuron dynamics as well as synaptic and electric processes between neurons. Thereby, models which incorporate biophysical dynamical system acting on top of the static connectome, called dynomes, become more detailed and realizable. Availability of near-complete connectome data along with experimental quantification of responses and interactions allowed us to develop a detailed dynome model for C. elegans’ somatic nervous system. Employing an interactive visualization platform to simulate the dynome we apply various stimuli regimes and show robust low-dimensional bifurcation structures which drive a variety of multistable neural voltage modes, such as fixed points, limit cycles, multi-oscillatory dynamics. Comparison of these modes with experimental studies allows us to link behavioral states with network responses in the form of low-dimensional attractors and transitions between them.

Computational models of the nervous system are developed at multiple scales to answer questions about how low level interactions between biological entities lead to higher level functions. Models of the nematode C. elegans have also been created at levels from individual neurons and muscles, subcircuits responsible for processing specific sensory inputs, body wide processes including locomotion, and detailed nervous system/musculature models. These models usually select a subset of anatomical and physiological properties of the worm and can address a specific set of questions relevant to that level of detail. The OpenWorm project has developed c302, a framework in Python which aims to facilitate creation of models of the nervous system and musculature of C. elegans, comprising all known cells or subsets thereof, and incorporating varying levels of detail for neurons, muscles and synapses. Information on the numbers, types, and polarity of synaptic connections are included in the models from the structured information on these gathered by the project. The models generated can be used with a variety of tools for model visualisation, simulation and analysis. Dr Padraig Gleeson will present c302 and show how these nervous system models are being incorporated into detailed 3D worm body models in OpenWorm.

The ultimate proof of our understanding of biological or technological systems is reflected in our ability to control them. While control theory offers mathematical tools to steer engineered and natural systems towards a desired state, we lack a framework to control complex self-organized systems. Here Albert-László will explore the controllability of an arbitrary complex network, identifying the set of driver nodes whose time-dependent control can guide the system’s entire dynamics. Virtually all technological and biological networks must be able to control their internal processes. Given that, issues related to control deeply shape the topology and the vulnerability of real systems. Consequently, unveiling the control principles of real networks, the goal of our research, forces us to address series of fundamental questions pertaining to our understanding of complex systems. Finally, Albert-László will discuss how control principles inform our ability to predict neurons involved in specific processes in the brain, offering an avenue to experimentally falsify and test the predictions of network control. 

Geppetto (geppetto.org) is an open-source web-based platform to explore and simulate neuroscience data and models. The platform, originally designed to support the simulation of a cell-level model of C. elegans as part of the OpenWorm project, has grown into a generic framework suitable for various neuroscience applications, offering out of the box solutions for data visualisation, integration and simulation. Geppetto is today used by Open Source Brain (opensourcebrain.org), to explore and simulate computational neuroscience models described in NeuroML version 2 with a variety of simulators and by the Virtual Fly Brain (virtualflybrain.org) to explore and visualise anatomy (including neuropil, segmented neurons and gene expression pattern data) and ontology knowledge base of Drosophila melanogaster. Geppetto is also being used to build a new experimental UI for the NEURON simulation environment based on Python and Jupyter. WormSim (wormsim.org) embeds Geppetto to let users explore dynamic mechanical and electrophysiological models of C. elegans produced by the OpenWorm project. Geppetto is capable of reading and visualising experimental data in the NWB format (nwb.org) to allow experimental and computational neuroscientists to share and compare data and models using a common platform.

Computational models provide a framework for integrating data across spatial scales and for exploring hypotheses about the mechanisms underlying neuronal and network dynamics. We have contributed to a successful system of interoperable, open source tools to address issues around creating, exchanging, and re-using models in neuroscience. In spite of this promising movement toward model sharing and reproducibility in the neuroscience community, it is extremely rare to see a specific, rigorous statement of the criteria used for evaluating models against experimental data. Another collaborative project from our group is providing a flexible infrastructure for assessing the scope and quality of models. The goal is to integrate experimental data with modeling efforts for more efficiency, better transparency, and greater impact of computational models in neuroscience research. We highlight examples of model validation from the C. elegans nervous system and also propose how hierarchical model validation, proceeding from the testing of small model components all the way to entire systems, can be used to systematically build a biologically-inspired model of an entire organism.

The brain organizes behaviours spanning several timescales, embedding individual movements into longer motor programs and action sequences that together serve to achieve behavioural goals. How this multi-timescale organization is implemented by neural circuits remains a fundamental unanswered question. Here, Dr Manuel Zimmer uncovers the functional relationships between three neuronal oscillators, each acting on different timescales to drive distinct behaviours. On the longest timescale, a network-wide oscillator commands the forward and reverse locomotion states. Whole nervous system imaging identified candidates for two shorter-timescale oscillators that are phase coupled to the long timescale brain oscillation and are nested within the forward locomotor program.  Using Ca2+-imaging in freely behaving worms and selective neuronal inhibition tools, the Zimmer group shows that one oscillator drives body movements for locomotion, while the other drives head-casting behaviours superimposed on to these body movements. These head casting behaviours can occur spontaneously or can be evoked by sensory stimulation. Our results establish so-termed ‘phase-nested’ oscillations as a repeated dynamical motif of the C. elegans nervous system and suggest a circuit mechanism for orchestrating motor commands spanning multiple timescales. Manuel will discuss our findings in the context of the meeting’s major objective to model the C. elegans nervous system.

The synaptic connectome of C. elegans has been mapped completely, and efforts are ongoing to map the connectomes of other animals. However, chemical synapses represent only one of several types of signaling interactions upon which the nervous system depends. In particular, neuromodulatory interactions involving monoamines, neuropeptides, or classical neurotransmitters are widespread in all nervous systems, and these interactions largely occur extrasynaptically between neurons unconnected by wired synapses. In C. elegans it is feasible to map these extrasynaptic networks comprehensively and at a single-cell level. We have compiled a draft extrasynaptic connectome for monoamine signaling, and in collaboration with others have begun mapping the extensive neuropeptide connectome. We are exploring the topologies of the neuromodulatory connectomes and their relationships with the wired synaptic and gap junction networks, as well as their functional roles in the control of behavioural states such as arousal. We are also developing approaches for behavioural analysis that can be used to probe the structure and function of both the synaptic and extrasynaptic networks. Further analysis of the C. elegans multilayer connectome should provide insight into how wired and wireless signaling interact in the brains of more complex animals.

The past 30 years of the connectome of C. elegans has both shown its necessity while also demonstrating its insufficiency for a complete explanation of how it functions. Formalization methods from computational neuroscience, neuroinformatics, and computational biophysics have demonstrated great potential to integrate what has been measured and understood about the structure and function of nervous systems in general and enable powerful predictions of its function. At the OpenWorm Foundation, the group has built an open science organization to perform this formalization and unlock these predictions, while placing all of the digital resources that are produced into the public domain immediately. Their current results represent a strong step towards building a working simulation of the C. elegans nervous system in the context of a simulated embodied digital worm, drawing from a multitude of data sources, observations, and existing simulations. In this talk, Dr Stephen Larson will review the progress that the research group has made in this endeavour and paint the picture for where the project is headed next.

Wave propagation during locomotory movements of C. elegans is constrained to a single dorso/ventral plane. In contrast, the tip of the head (snout) can make rapid exploratory movements in all directions relative to the body axis. These extra degrees of freedom are probably important for animals to seek and identify desirable passages in the interstices of the three dimensional matrix of soil particles, their usual habitat. The differences in degrees of freedom of movement between snout and body are reflected in the innervation of the musculature. Along the length of the body the two quadrants of dorsal muscle receive common innervation as do the two quadrants of ventral muscle. In contrast, muscles in the snout have an octagonal arrangement of innervation. It is likely that the foraging behaviour of the snout is mediated by octant-specific motor and sensory neurons, together with their associated interneurons. The well-defined structure and neural circuitry of the snout together with behavioural observations made with or without experimental interventions should facilitate the implementation of models of snout foraging which could lead to an understanding of the neural basis of this relatively complex behaviour, a behaviour that has similarities to the foraging behaviour of some vertebrates.