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

A multiscale sensorimotor model of experience-dependent behavior in a minimal organism

To survive in ever-changing environments, living organisms need to continuously combine the ongoing external inputs they receive, representing present conditions, with their dynamical internal state, which includes influences of past experiences. It is still unclear in general, however 1) how this happens at the molecular and cellular levels and 2) how the corresponding molecular and cellular processes are integrated with the behavioral responses of the organism. Here, we address these issues by modeling mathematically a particular behavioral paradigm in a minimal model organism, namely chemotaxis in the nematode C. elegans. Specifically, we use a long-standing collection of elegant experiments on salt chemotaxis in this animal, in which the migration direction varies depending on its previous experience. Our model integrates the molecular, cellular, and organismal levels to reproduce the experimentally observed experience-dependent behavior. The model proposes specific molecular mechanisms for the encoding of current conditions and past experiences in key neurons associated with this response, predicting the behavior of various mutants associated with those molecular circuits.

Modelling learning in C. elegans chemosensory and locomotive circuitry for T-maze navigation

Recently, a new type of Caenorhabditis elegans associative learning was reported, where nematodes learn to reach a target arm in an empty T‐maze, after they have successfully located reward (food) in the same side arm of a similar, baited, training maze. Here, we present a simplified mathematical model of C. elegans chemosensory and locomotive circuitry that replicates C. elegans navigation in a T‐maze and predicts the underlying mechanisms generating maze learning. Based on known neural circuitry, the model circuit responds to food‐released chemical cues by modulating motor neuron activity that drives simulated locomotion. We show that, through modulation of interneuron activity, such a circuit can mediate maze learning by acquiring a turning bias, even after a single training session. Simulated nematode maze navigation during training conditions in food‐baited mazes and during testing conditions in empty mazes is validated by comparing simulated behaviour with new experimental video data, extracted through the implementation of a custom‐made maze tracking algorithm. Our work provides a mathematical framework for investigating the neural mechanisms underlying this novel learning behaviour in C. elegans. Model results predict neuronal components involved in maze and spatial learning and identify target neurons and potential neural mechanisms for future experimental investigations into this learning behaviour.

Integrative Neuroscience of Paramecium, a "Swimming Neuron"

Paramecium is a unicellular organism that swims in fresh water by beating thousands of cilia. When it is stimulated (mechanically, chemically, optically, thermally…), it often swims backward then turns and swims forward again. This "avoiding reaction" is triggered by a calcium-based action potential. For this reason, some authors have called Paramecium a "swimming neuron." This review summarizes current knowledge about the physiological basis of behavior of Paramecium.

Measuring and modeling whole-brain neural dynamics in Caenorhabditis elegans

The compact nervous system of the nematode Caenorhabditis elegans makes it a powerful playground to study how neural dynamics constrained by neuroanatomy generate neural function and behavior. The ability to record neural activity from the whole brain simultaneously in this worm has opened several research avenues and is providing insights into brain-wide neural coding of locomotion, sleep, and other behaviors. We review these findings and the development of new methods, including new microscopes, new genetic tools, and new modeling approaches. We conclude with a discussion of the role of theory in interpreting or driving new experiments in C. elegans and potential paths forward.

What would a synthetic connectome look like?

A major challenge of contemporary neuroscience is to unravel the structure of the connectome, the ensemble of neural connections that link between different functional units of the brain, and to reveal how this structure relates to brain function. This thriving area of research largely follows the general tradition in biology of reverse-engineering, which consists of first observing and characterizing a biological system or process, and then deconstructing it into its fundamental building blocks in order to infer its modes of operation. However, a complementary form of biology has emerged, synthetic biology, which emphasizes construction-based forward-engineering. The synthetic biology approach comprises the assembly of new biological systems out of elementary biological parts. The rationale is that the act of building a system can be a powerful method for gaining deep understanding of how that system works. As the fields of connectomics and synthetic biology are independently growing, I propose to consider the benefits of combining the two, to create synthetic connectomics, a new form of neuroscience and a new form of synthetic biology. The goal of synthetic connectomics would be to artificially design and construct the connectomes of live behaving organisms. Synthetic connectomics could serve as a unifying platform for unraveling the complexities of brain operation and perhaps also for generating new forms of artificial life, and, in general, could provide a valuable opportunity for empirically exploring theoretical predictions about network function. What would a synthetic connectome look like? What purposes would it serve? How could it be constructed? This review delineates the novel notion of a synthetic connectome and aims to lay out the initial steps towards its implementation, contemplating its impact on science and society.

The Cognitive Lens: a primer on conceptual tools for analysing information processing in developmental and regenerative morphogenesis

Brains exhibit plasticity, multi-scale integration of information, computation and memory, having evolved by specialization of non-neural cells that already possessed many of the same molecular components and functions. The emerging field of basal cognition provides many examples of decision-making throughout a wide range of non-neural systems. How can biological information processing across scales of size and complexity be quantitatively characterized and exploited in biomedical settings? We use pattern regulation as a context in which to introduce the Cognitive Lens-a strategy using well-established concepts from cognitive and computer science to complement mechanistic investigation in biology. To facilitate the assimilation and application of these approaches across biology, we review tools from various quantitative disciplines, including dynamical systems, information theory and least-action principles. We propose that these tools can be extended beyond neural settings to predict and control systems-level outcomes, and to understand biological patterning as a form of primitive cognition. We hypothesize that a cognitive-level information-processing view of the functions of living systems can complement reductive perspectives, improving efficient top-down control of organism-level outcomes. Exploration of the deep parallels across diverse quantitative paradigms will drive integrative advances in evolutionary biology, regenerative medicine, synthetic bioengineering, cognitive neuroscience and artificial intelligence. This article is part of the theme issue 'Liquid brains, solid brains: How distributed cognitive architectures process information'.

Novel Technological Advances in Functional Connectomics in C. elegans

The complete structure and connectivity of the Caenorhabditis elegans nervous system ("mind of a worm") was first published in 1986, representing a critical milestone in the field of connectomics. The reconstruction of the nervous system (connectome) at the level of synapses provided a unique perspective of understanding how behavior can be coded within the nervous system. The following decades have seen the development of technologies that help understand how neural activity patterns are connected to behavior and modulated by sensory input. Investigations on the developmental origins of the connectome highlight the importance of role of neuronal cell lineages in the final connectivity matrix of the nervous system. Computational modeling of neuronal dynamics not only helps reconstruct the biophysical properties of individual neurons but also allows for subsequent reconstruction of whole-organism neuronal network models. Hence, combining experimental datasets with theoretical modeling of neurons generates a better understanding of organismal behavior. This review discusses some recent technological advances used to analyze and perturb whole-organism neuronal function along with developments in computational modeling, which allows for interrogation of both local and global neural circuits, leading to different behaviors. Combining these approaches will shed light into how neural networks process sensory information to generate the appropriate behavioral output, providing a complete understanding of the worm nervous system.

A Single-Cell Level and Connectome-Derived Computational Model of the Drosophila Brain

Computer simulations play an important role in testing hypotheses, integrating knowledge, and providing predictions of neural circuit functions. While considerable effort has been dedicated into simulating primate or rodent brains, the fruit fly (Drosophila melanogaster) is becoming a promising model animal in computational neuroscience for its small brain size, complex cognitive behavior, and abundancy of data available from genes to circuits. Moreover, several Drosophila connectome projects have generated a large number of neuronal images that account for a significant portion of the brain, making a systematic investigation of the whole brain circuit possible. Supported by FlyCircuit (http://www.flycircuit.tw), one of the largest Drosophila neuron image databases, we began a long-term project with the goal to construct a whole-brain spiking network model of the Drosophila brain. In this paper, we report the outcome of the first phase of the project. We developed the Flysim platform, which (1) identifies the polarity of each neuron arbor, (2) predicts connections between neurons, (3) translates morphology data from the database into physiology parameters for computational modeling, (4) reconstructs a brain-wide network model, which consists of 20,089 neurons and 1,044,020 synapses, and (5) performs computer simulations of the resting state. We compared the reconstructed brain network with a randomized brain network by shuffling the connections of each neuron. We found that the reconstructed brain can be easily stabilized by implementing synaptic short-term depression, while the randomized one exhibited seizure-like firing activity under the same treatment. Furthermore, the reconstructed Drosophila brain was structurally and dynamically more diverse than the randomized one and exhibited both Poisson-like and patterned firing activities. Despite being at its early stage of development, this single-cell level brain model allows us to study some of the fundamental properties of neural networks including network balance, critical behavior, long-term stability, and plasticity.

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'.

Three-dimensional simulation of the Caenorhabditis elegans body and muscle cells in liquid and gel environments for behavioural analysis

To better understand how a nervous system controls the movements of an organism, we have created a three-dimensional computational biomechanical model of the Caenorhabditis elegans body based on real anatomical structure. The body model is created with a particle system-based simulation engine known as Sibernetic, which implements the smoothed particle-hydrodynamics algorithm. The model includes an elastic body-wall cuticle subject to hydrostatic pressure. This cuticle is then driven by body-wall muscle cells that contract and relax, whose positions and shape are mapped from C. elegans anatomy, and determined from light microscopy and electron micrograph data. We show that by using different muscle activation patterns, this model is capable of producing C. elegans-like behaviours, including crawling and swimming locomotion in environments with different viscosities, while fitting multiple additional known biomechanical properties of the animal. This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

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.

Development of a sensitive and quantitative UHPLC-MS/MS method to study the whole-body uptake of pharmaceuticals in zebrafish

An analytical procedure to measure the whole-body uptake of pharmaceuticals in zebrafish has been developed using state-of-the-art methodologies. A sample preparation procedure for 9 pharmaceuticals displaying a variety in physicochemical properties was developed using 10-day old zebrafish (TG898). For an efficient homogenization of the samples and subsequent recovery of the compounds of interest, different amounts of organic solvents in combination with acidic modifiers were added to zebrafish samples. Samples were subsequently processed using a powerful bath sonicator and centrifuged. Supernatant was then removed and evaporated in a vacuum oven before being reconstituted in a mobile phase-like solvent. Samples were analyzed using ultra-high performance liquid chromatography (UHPLC) on an Acquity BEH C₁₈ column (100 × 2.1mm, d_p=1.7µm) coupled to a Waters Xevo TQ-S mass spectrometer. For this purpose, a generic gradient was run, wherein the percentage of acetonitrile was varied from 3% to 82% in 10.5min at a flow rate of 0.41mL/min. Linearity of the method was demonstrated for all compounds (R² > 0.997) in a practically relevant concentration range. Matrix effects were between 81% and 106%, except for amitriptyline (51%). Using this method, it was demonstrated that a sample pretreatment using 1:2 (v/v) water:methanol in combination with 0.1% formic acid resulted in acceptable recoveries between 74% and 100% for all compounds. Together with the obtained lower limits of quantification of the analytical method (between 0.005 and 1.5ng/mL), this allowed the use of a single zebrafish to study the whole-body uptake of a particular drug, after incubating zebrafish at the maximum tolerated concentration for this drug.

Multistability and Long-Timescale Transients Encoded by Network Structure in a Model of C. elegans Connectome Dynamics

The neural dynamics of the nematode Caenorhabditis elegans are experimentally low-dimensional and may be understood as long-timescale transitions between multiple low-dimensional attractors. Previous modeling work has found that dynamic models of the worm's full neuronal network are capable of generating reasonable dynamic responses to certain inputs, even when all neurons are treated as identical save for their connectivity. This study investigates such a model of C. elegans neuronal dynamics, finding that a wide variety of multistable responses are generated in response to varied inputs. Specifically, we generate bifurcation diagrams for all possible single-neuron inputs, showing the existence of fixed points and limit cycles for different input regimes. The nature of the dynamical response is seen to vary according to the type of neuron receiving input; for example, input into sensory neurons is more likely to drive a bifurcation in the system than input into motor neurons. As a specific example we consider compound input into the neuron pairs PLM and ASK, discovering bistability of a limit cycle and a fixed point. The transient timescales in approaching each of these states are much longer than any intrinsic timescales of the system. This suggests consistency of our model with the characterization of dynamics in neural systems as long-timescale transitions between discrete, low-dimensional attractors corresponding to behavioral states.

Functionality and Robustness of Injured Connectomic Dynamics in C. elegans: Linking Behavioral Deficits to Neural Circuit Damage

Using a model for the dynamics of the full somatic nervous system of the nematode C. elegans, we address how biological network architectures and their functionality are degraded in the presence of focal axonal swellings (FAS) arising from neurodegenerative disease and/or traumatic brain injury. Using biophysically measured FAS distributions and swelling sizes, we are able to simulate the effects of injuries on the neural dynamics of C. elegans, showing how damaging the network degrades its low-dimensional dynamical responses. We visualize these injured neural dynamics by mapping them onto the worm's low-dimensional postures, i.e. eigenworm modes. We show that a diversity of functional deficits arise from the same level of injury on a connectomic network. Functional deficits are quantified using a statistical shape analysis, a procrustes analysis, for deformations of the limit cycles that characterize key behaviors such as forward crawling. This procrustes metric carries information on the functional outcome of injuries in the model. Furthermore, we apply classification trees to relate injury structure to the behavioral outcome. This makes testable predictions for the structure of an injury given a defined functional deficit. More critically, this study demonstrates the potential role of computational simulation studies in understanding how neuronal networks process biological signals, and how this processing is impacted by network injury.

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.

Vulnerability-Based Critical Neurons, Synapses, and Pathways in the Caenorhabditis elegans Connectome

Determining the fundamental architectural design of complex nervous systems will lead to significant medical and technological advances. Yet it remains unclear how nervous systems evolved highly efficient networks with near optimal sharing of pathways that yet produce multiple distinct behaviors to reach the organism’s goals. To determine this, the nematode roundworm Caenorhabditis elegans is an attractive model system. Progress has been made in delineating the behavioral circuits of the C. elegans, however, many details are unclear, including the specific functions of every neuron and synapse, as well as the extent the behavioral circuits are separate and parallel versus integrative and serial. Network analysis provides a normative approach to help specify the network design. We investigated the vulnerability of the Caenorhabditis elegans connectome by performing computational experiments that (a) “attacked” 279 individual neurons and 2,990 weighted synaptic connections (composed of 6,393 chemical synapses and 890 electrical junctions) and (b) quantified the effects of each removal on global network properties that influence information processing. The analysis identified 12 critical neurons and 29 critical synapses for establishing fundamental network properties. These critical constituents were found to be control elements—i.e., those with the most influence over multiple underlying pathways. Additionally, the critical synapses formed into circuit-level pathways. These emergent pathways provide evidence for (a) the importance of backward locomotion, avoidance behavior, and social feeding behavior to the organism; (b) the potential roles of specific neurons whose functions have been unclear; and (c) both parallel and serial design elements in the connectome—i.e., specific evidence for a mixed architectural design.

One of the most important scientific aims is to uncover the functional design principles of nervous systems. To reach this aim, it is useful to examine a complex nervous system that is both well specified and highly tractable, making the nematode roundworm Caenorhabditis elegans an attractive model system, especially since it is the only complete connectome currently available for analysis. In this computational study, we tested the effects of individual attacks on every neuron and synaptic connection in the C. elegans connectome to identify and characterize the most critical constituents of the network by quantifying the changes in key network properties of the connectome that influence information processing. Our analysis identified 12 neurons and 29 synapses critical to clustering, information integration and propagation. These critical constituents formed circuit-level structures that control network processing in the C. elegans connectome. We believe our study provides a significant advance in the understanding of the network topology of the C. elegans connectome, and provides insights into the fundamental architectural design of complex nervous systems.