Connecting a connectome to behavior: an ensemble of neuroanatomical models of C. elegans klinotaxis

Simple olfactory navigation in air and water

Two simple algorithms based on combining odor concentration differences across time and space along with information on the flow direction are tested for their ability to locate an odor source in four different odor landscapes. Image data taken from air plumes in three different regimes and a water plume are used as test environments for a bilateral ("stereo sampling") algorithm using concentration differences across two sensors and a "casting" algorithm that uses successive samples to decide orientation. Agents are started at random locations and orientations in the landscape and allowed to move until they reach the source of the odor (success) or leave the imaged area (failure). Parameters for the algorithm are chosen to optimize success and to minimize path length to the source. Success rates over 90% are consistently obtained with path lengths that can be as low as twice the starting distance from the source in air and four times the distance in the highly turbulent water plumes. We find that parameters that optimize success often lead to more exploratory pathways to the source. Information about the direction from which the odor is coming is necessary for successful navigation in the water plume and reduces the path length in the three tested air plumes.

Milking a spherical cow: Toy models in neuroscience

There are many different kinds of models, and they play many different roles in the scientific endeavour. Neuroscience, and biology more generally, has understandably tended to emphasise empirical models that are grounded in data and make specific, experimentally testable predictions. Meanwhile, strongly idealised or 'toy' models have played a central role in the theoretical development of other sciences such as physics. In this paper, we examine the nature of toy models and their prospects in neuroscience.

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.

Innate Orientating Behavior of a Multi-Legged Robot Driven by the Neural Circuits of C. elegans

The objective of this research is to achieve biologically autonomous control by utilizing a whole-brain network model, drawing inspiration from biological neural networks to enhance the development of bionic intelligence. Here, we constructed a whole-brain neural network model of Caenorhabditis elegans (C. elegans), which characterizes the electrochemical processes at the level of the cellular synapses. The neural network simulation integrates computational programming and the visualization of the neurons and synapse connections of C. elegans, containing the specific controllable circuits and their dynamic characteristics. To illustrate the biological neural network (BNN)'s particular intelligent control capability, we introduced an innovative methodology for applying the BNN model to a 12-legged robot's movement control. Two methods were designed, one involving orientation control and the other involving locomotion generation, to demonstrate the intelligent control performance of the BNN. Both the simulation and experimental results indicate that the robot exhibits more autonomy and a more intelligent movement performance under BNN control. The systematic approach of employing the whole-brain BNN for robot control provides biomimetic research with a framework that has been substantiated by innovative methodologies and validated through the observed positive outcomes. This method is established as follows: (1) two integrated dynamic models of the C. elegans' whole-brain network and the robot moving dynamics are built, and all of the controllable circuits are discovered and verified; (2) real-time communication is achieved between the BNN model and the robot's dynamical model, both in the simulation and the experiments, including applicable encoding and decoding algorithms, facilitating their collaborative operation; (3) the designed mechanisms using the BNN model to control the robot are shown to be effective through numerical and experimental tests, focusing on 'foraging' behavior control and locomotion control.

Biophysical modeling of the whole-cell dynamics of C. elegans motor and interneurons families

The nematode Caenorhabditis elegans is a widely used model organism for neuroscience. Although its nervous system has been fully reconstructed, the physiological bases of single-neuron functioning are still poorly explored. Recently, many efforts have been dedicated to measuring signals from C. elegans neurons, revealing a rich repertoire of dynamics, including bistable responses, graded responses, and action potentials. Still, biophysical models able to reproduce such a broad range of electrical responses lack. Realistic electrophysiological descriptions started to be developed only recently, merging gene expression data with electrophysiological recordings, but with a large variety of cells yet to be modeled. In this work, we contribute to filling this gap by providing biophysically accurate models of six classes of C. elegans neurons, the AIY, RIM, and AVA interneurons, and the VA, VB, and VD motor neurons. We test our models by comparing computational and experimental time series and simulate knockout neurons, to identify the biophysical mechanisms at the basis of inter and motor neuron functioning. Our models represent a step forward toward the modeling of C. elegans neuronal networks and virtual experiments on the nematode nervous system.

Emergent dynamics in a robotic model based on the Caenorhabditis elegans connectome

We analyze the neural dynamics and their relation with the emergent actions of a robotic vehicle that is controlled by a neural network numerical simulation based on the nervous system of the nematode Caenorhabditis elegans. The robot interacts with the environment through a sensor that transmits the information to sensory neurons, while motor neurons outputs are connected to wheels. This is enough to allow emergent robot actions in complex environments, such as avoiding collisions with obstacles. Working with robotic models makes it possible to simultaneously keep track of the dynamics of all the neurons and also register the actions of the robot in the environment in real time, while avoiding the complex technicalities of simulating a real environment. This allowed us to identify several relevant features of the neural dynamics associated with the emergent actions of the robot, some of which have already been observed in biological worms. These results suggest that some basic aspects of behaviors observed in living beings are determined by the underlying structure of the associated neural network.

Neural Network-Based Autonomous Search Model with Undulatory Locomotion Inspired by Caenorhabditis Elegans

Caenorhabditis elegans (C. elegans) exhibits sophisticated chemotaxis behavior with a unique locomotion pattern using a simple nervous system only and is, therefore, well suited to inspire simple, cost-effective robotic navigation schemes. Chemotaxis in C. elegans involves two complementary strategies: klinokinesis, which allows reorientation by sharp turns when moving away from targets; and klinotaxis, which gradually adjusts the direction of motion toward the preferred side throughout the movement. In this study, we developed an autonomous search model with undulatory locomotion that combines these two C. elegans chemotaxis strategies with its body undulatory locomotion. To search for peaks in environmental variables such as chemical concentrations and radiation in directions close to the steepest gradients, only one sensor is needed. To develop our model, we first evolved a central pattern generator and designed a minimal network unit with proprioceptive feedback to encode and propagate rhythmic signals; hence, we realized realistic undulatory locomotion. We then constructed adaptive sensory neuron models following real electrophysiological characteristics and incorporated a state-dependent gating mechanism, enabling the model to execute the two orientation strategies simultaneously according to information from a single sensor. Simulation results verified the effectiveness, superiority, and realness of the model. Our simply structured model exploits multiple biological mechanisms to search for the shortest-path concentration peak over a wide range of gradients and can serve as a theoretical prototype for worm-like navigation robots.

Discovering sparse control strategies in neural activity

Biological circuits such as neural or gene regulation networks use internal states to map sensory input to an adaptive repertoire of behavior. Characterizing this mapping is a major challenge for systems biology. Though experiments that probe internal states are developing rapidly, organismal complexity presents a fundamental obstacle given the many possible ways internal states could map to behavior. Using C. elegans as an example, we propose a protocol for systematic perturbation of neural states that limits experimental complexity and could eventually help characterize collective aspects of the neural-behavioral map. We consider experimentally motivated small perturbations—ones that are most likely to preserve natural dynamics and are closer to internal control mechanisms—to neural states and their impact on collective neural activity. Then, we connect such perturbations to the local information geometry of collective statistics, which can be fully characterized using pairwise perturbations. Applying the protocol to a minimal model of C. elegans neural activity, we find that collective neural statistics are most sensitive to a few principal perturbative modes. Dominant eigenvalues decay initially as a power law, unveiling a hierarchy that arises from variation in individual neural activity and pairwise interactions. Highest-ranking modes tend to be dominated by a few, “pivotal” neurons that account for most of the system’s sensitivity, suggesting a sparse mechanism of collective control.

Fixed Point Attractor Theory Bridges Structure and Function in C. elegans Neuronal Network

Understanding the structure–function relationship in a neuronal network is one of the major challenges in neuroscience research. Despite increasing researches at circuit connectivity and neural network structure, their structure-based biological interpretability remains unclear. Based on the attractor theory, here we develop an analytical framework that links neural circuit structures and their functions together through fixed point attractor in Caenorhabditis elegans. In this framework, we successfully established the structural condition for the emergence of multiple fixed points in C. elegans connectome. Then we construct a finite state machine to explain how functions related to bistable phenomena at the neural activity and behavioral levels are encoded. By applying the proposed framework to the command circuit in C. elegans, we provide a circuit level interpretation for the forward-reverse switching behaviors. Interestingly, network properties of the command circuit and first layer amphid interneuron circuit can also be inferred from their functions in this framework. Our research indicates the reliability of the fixed point attractor bridging circuit structure and functions, suggesting its potential applicability to more complex neuronal circuits in other species.

Synaptic counts approximate synaptic contact area in Drosophila

The pattern of synaptic connections among neurons defines the circuit structure, which constrains the computations that a circuit can perform. The strength of synaptic connections is costly to measure yet important for accurate circuit modeling. Synaptic surface area has been shown to correlate with synaptic strength, yet in the emerging field of connectomics, most studies rely instead on the counts of synaptic contacts between two neurons. Here we quantified the relationship between synaptic count and synaptic area as measured from volume electron microscopy of the larval Drosophila central nervous system. We found that the total synaptic surface area, summed across all synaptic contacts from one presynaptic neuron to a postsynaptic one, can be accurately predicted solely from the number of synaptic contacts, for a variety of neurotransmitters. Our findings support the use of synaptic counts for approximating synaptic strength when modeling neural circuits.

Neural model generating klinotaxis behavior accompanied by a random walk based on C. elegans connectome

Klinotaxis is a strategy of chemotaxis behavior in Caenorhabditis elegans (C. elegans), and random walking is evident during its locomotion. As yet, the understanding of the neural mechanisms underlying these behaviors has remained limited. In this study, we present a connectome-based simulation model of C. elegans to concurrently realize realistic klinotaxis and random walk behaviors and explore their neural mechanisms. First, input to the model is derived from an ASE sensory neuron model in which the all-or-none depolarization characteristic of ASEL neuron is incorporated for the first time. Then, the neural network is evolved by an evolutionary algorithm; klinotaxis emerged spontaneously. We identify a plausible mechanism of klinotaxis in this model. Next, we propose the liquid synapse according to the stochastic nature of biological synapses and introduce it into the model. Adopting this, the random walk is generated autonomously by the neural network, providing a new hypothesis as to the neural mechanism underlying the random walk. Finally, simulated ablation results are fairly consistent with the biological conclusion, suggesting the similarity between our model and the biological network. Our study is a useful step forward in behavioral simulation and understanding the neural mechanisms of behaviors in C. elegans.

Towards the Idea of Molecular Brains

How can single cells without nervous systems perform complex behaviours such as habituation, associative learning and decision making, which are considered the hallmark of animals with a brain? Are there molecular systems that underlie cognitive properties equivalent to those of the brain? This review follows the development of the idea of molecular brains from Darwin’s “root brain hypothesis”, through bacterial chemotaxis, to the recent discovery of neuron-like r-protein networks in the ribosome. By combining a structural biology view with a Bayesian brain approach, this review explores the evolutionary labyrinth of information processing systems across scales. Ribosomal protein networks open a window into what were probably the earliest signalling systems to emerge before the radiation of the three kingdoms. While ribosomal networks are characterised by long-lasting interactions between their protein nodes, cell signalling networks are essentially based on transient interactions. As a corollary, while signals propagated in persistent networks may be ephemeral, networks whose interactions are transient constrain signals diffusing into the cytoplasm to be durable in time, such as post-translational modifications of proteins or second messenger synthesis. The duration and nature of the signals, in turn, implies different mechanisms for the integration of multiple signals and decision making. Evolution then reinvented networks with persistent interactions with the development of nervous systems in metazoans. Ribosomal protein networks and simple nervous systems display architectural and functional analogies whose comparison could suggest scale invariance in information processing. At the molecular level, the significant complexification of eukaryotic ribosomal protein networks is associated with a burst in the acquisition of new conserved aromatic amino acids. Knowing that aromatic residues play a critical role in allosteric receptors and channels, this observation suggests a general role of π systems and their interactions with charged amino acids in multiple signal integration and information processing. We think that these findings may provide the molecular basis for designing future computers with organic processors.

Conditions for the emergence of circumnutations in plant roots

The plant root system shows remarkably complex behaviors driven by environmental cues and internal dynamics, whose interplay remains largely unknown. A notable example is circumnutation growth movements, which are growth oscillations from side to side of the root apex. Here we describe a model capable of replicating root growth behaviors, which we used to analyze the role of circumnuntations, revealing their emergence I) under gravitropic stress, as a combination of signal propagation and sensitivity to the signal carriers; II) as a result of the interplay between gravitropic and thigmotropic responses; and III) as a behavioral strategy to detect and react to resource gradients. The latter function requires the presence of a hypothetical internal oscillator whose parameters are regulated by the perception of environmental resources.

Dynamical consequences of sensory feedback in a half-center oscillator coupled to a simple motor system

We investigate a simple model for motor pattern generation that combines central pattern generator (CPG) dynamics with a sensory feedback (FB) mechanism. Our CPG comprises a half-center oscillator with conductance-based Morris-Lecar model neurons. Output from the CPG drives a push-pull motor system with biomechanics based on experimental data. A sensory feedback conductance from the muscles allows modulation of the CPG activity. We consider parameters under which the isolated CPG system has either "escape" or "release" dynamics, and we study both inhibitory and excitatory feedback conductances. We find that increasing the FB conductance relative to the CPG conductance makes the system more robust against external perturbations, but more susceptible to internal noise. Conversely, increasing the CPG conductance relative to the FB conductance has the opposite effects. We find that the "closed-loop" system, with sensory feedback in place, exhibits a richer repertoire of behaviors than the "open-loop" system, with motion determined entirely by the CPG dynamics. Moreover, we find that purely feedback-driven motor patterns, analogous to a chain reflex, occur only in the inhibition-mediated system. Finally, for pattern generation systems with inhibition-mediated sensory feedback, we find that the distinction between escape- and release-mediated CPG mechanisms is diminished in the presence of internal noise. Our observations support an anti-reductionist view of neuromotor physiology: Understanding mechanisms of robust motor control requires studying not only the central pattern generator circuit in isolation, but the intact closed-loop system as a whole.

A Neuromechanical Model of Multiple Network Rhythmic Pattern Generators for Forward Locomotion in C. elegans

Multiple mechanisms contribute to the generation, propagation, and coordination of the rhythmic patterns necessary for locomotion in Caenorhabditis elegans. Current experiments have focused on two possibilities: pacemaker neurons and stretch-receptor feedback. Here, we focus on whether it is possible that a chain of multiple network rhythmic pattern generators in the ventral nerve cord also contribute to locomotion. We use a simulation model to search for parameters of the anatomically constrained ventral nerve cord circuit that, when embodied and situated, can drive forward locomotion on agar, in the absence of pacemaker neurons or stretch-receptor feedback. Systematic exploration of the space of possible solutions reveals that there are multiple configurations that result in locomotion that is consistent with certain aspects of the kinematics of worm locomotion on agar. Analysis of the best solutions reveals that gap junctions between different classes of motorneurons in the ventral nerve cord can play key roles in coordinating the multiple rhythmic pattern generators.

Persistent thermal input controls steering behavior in Caenorhabditis elegans

Motile organisms actively detect environmental signals and migrate to a preferable environment. Especially, small animals convert subtle spatial difference in sensory input into orientation behavioral output for directly steering toward a destination, but the neural mechanisms underlying steering behavior remain elusive. Here, we analyze a C. elegans thermotactic behavior in which a small number of neurons are shown to mediate steering toward a destination temperature. We construct a neuroanatomical model and use an evolutionary algorithm to find configurations of the model that reproduce empirical thermotactic behavior. We find that, in all the evolved models, steering curvature are modulated by temporally persistent thermal signals sensed beyond the time scale of sinusoidal locomotion of C. elegans. Persistent rise in temperature decreases steering curvature resulting in straight movement of model worms, whereas fall in temperature increases curvature resulting in crooked movement. This relation between temperature change and steering curvature reproduces the empirical thermotactic migration up thermal gradients and steering bias toward higher temperature. Further, spectrum decomposition of neural activities in model worms show that thermal signals are transmitted from a sensory neuron to motor neurons on the longer time scale than sinusoidal locomotion of C. elegans. Our results suggest that employments of temporally persistent sensory signals enable small animals to steer toward a destination in natural environment with variable, noisy, and subtle cues.

A free-living nematode Caenorhabditis elegans memorizes an environmental temperature and steers toward the remembered temperature on a thermal gradient. How does the C. elegans nervous system, consisting of 302 neurons, achieve the thermotactic steering behavior? Here, we address this question through neuroanatomical modeling and simulation analyses. We find that persistent thermal input modulates steering curvature of model worms; worms run straight when they move up to a destination temperature, whereas run crookedly when move away from the destination. As a result, worms steer toward the destination temperature as observed in experiments. Our analysis also shows that persistent thermal signals are transmitted from a thermosensory neuron to dorsal and ventral neck motor neurons, regulating the balance of dorsoventral muscle contractions of model worms and generating steering behavior. This study indicates that C. elegans can steer toward a destination temperature without processing acute thermal input that informs to which direction it should steer. Such indirect mechanism of steering behavior is potentially employed in other motile organisms.

Synaptic polarity and sign-balance prediction using gene expression data in the Caenorhabditis elegans chemical synapse neuronal connectome network

Graph theoretical analyses of nervous systems usually omit the aspect of connection polarity, due to data insufficiency. The chemical synapse network of Caenorhabditis elegans is a well-reconstructed directed network, but the signs of its connections are yet to be elucidated. Here, we present the gene expression-based sign prediction of the ionotropic chemical synapse connectome of C. elegans (3,638 connections and 20,589 synapses total), incorporating available presynaptic neurotransmitter and postsynaptic receptor gene expression data for three major neurotransmitter systems. We made predictions for more than two-thirds of these chemical synapses and observed an excitatory-inhibitory (E:I) ratio close to 4:1 which was found similar to that observed in many real-world networks. Our open source tool (http://EleganSign.linkgroup.hu) is simple but efficient in predicting polarities by integrating neuronal connectome and gene expression data.

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.

Sequence Alterations of Cortical Genes Linked to Individual Connectivity of the Human Brain

Individual differences in humans are driven by unique brain structural and functional profiles, presumably mediated in part through differential cortical gene expression. However, the relationships between cortical gene expression profiles and individual differences in large-scale neural network organization remain poorly understood. In this study, we aimed to investigate whether the magnitude of sequence alterations in regional cortical genes mapped onto brain areas with high degree of functional connectivity variability across individuals. First, human genetic expression data from the Allen Brain Atlas was used to identify protein-coding genes associated with cortical areas, which delineated the regional genetic signature of specific cortical areas based on sequence alteration profiles. Thereafter, we identified brain regions that manifested high degrees of individual variability by using test-retest functional connectivity magnetic resonance imaging and graph-theory analyses in healthy subjects. We found that rates of genetic sequence alterations shared a distinct spatial topography with cortical regions exhibiting individualized (highly-variable) connectivity profiles. Interestingly, gene expression profiles of brain regions with highly individualized connectivity patterns and elevated number of sequence alterations are devoted to neuropeptide-signaling-pathways and chemical-synaptic-transmission. Our findings support that genetic sequence alterations may underlie important aspects of brain connectome individualities in humans. Significance Statement: The neurobiological underpinnings of our individuality as humans are still an unsolved question. Although the notion that genetic variation drives an individual's brain organization has been previously postulated, specific links between neural connectivity and gene expression profiles have remained elusive. In this study, we identified the magnitude of population-based sequence alterations in discrete cortical regions and compared them to the brain topological distribution of functional connectivity variability across an independent human sample. We discovered that brain regions with high degree of connectional individuality are defined by increased rates of genetic sequence alterations; these findings specifically implicated genes involved in neuropeptide-signaling pathways and chemical-synaptic transmission. These observations support that genetic sequence alterations may underlie important aspects of the emergence of the brain individuality across humans.

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.

A multilayer circuit architecture for the generation of distinct locomotor behaviors in Drosophila

Animals generate diverse motor behaviors, yet how the same motor neurons (MNs) generate two distinct or antagonistic behaviors remains an open question. Here, we characterize Drosophila larval muscle activity patterns and premotor/motor circuits to understand how they generate forward and backward locomotion. We show that all body wall MNs are activated during both behaviors, but a subset of MNs change recruitment timing for each behavior. We used TEM to reconstruct a full segment of all 60 MNs and 236 premotor neurons (PMNs), including differentially-recruited MNs. Analysis of this comprehensive connectome identified PMN-MN 'labeled line' connectivity; PMN-MN combinatorial connectivity; asymmetric neuronal morphology; and PMN-MN circuit motifs that could all contribute to generating distinct behaviors. We generated a recurrent network model that reproduced the observed behaviors, and used functional optogenetics to validate selected model predictions. This PMN-MN connectome will provide a foundation for analyzing the full suite of larval behaviors.

A quantitative model of conserved macroscopic dynamics predicts future motor commands

In simple organisms such as Caenorhabditis elegans, whole brain imaging has been performed. Here, we use such recordings to model the nervous system. Our model uses neuronal activity to predict expected time of future motor commands up to 30 s prior to the event. These motor commands control locomotion. Predictions are valid for individuals not used in model construction. The model predicts dwell time statistics, sequences of motor commands and individual neuron activation. To develop this model, we extracted loops spanned by neuronal activity in phase space using novel methodology. The model uses only two variables: the identity of the loop and the phase along it. Current values of these macroscopic variables predict future neuronal activity. Remarkably, our model based on macroscopic variables succeeds despite consistent inter-individual differences in neuronal activation. Thus, our analytical framework reconciles consistent individual differences in neuronal activation with macroscopic dynamics that operate universally across individuals.

How can we go about trying to understand an object as complex as the brain? The traditional approach is to begin by studying its component parts, cells called neurons. Once we understand how individual neurons work, we can use computers to simulate the activity of networks of neurons. The result is a computer model of the brain. By comparing this model to data from real brains, we can try to make the model as similar to a real brain as possible.

But whose brain should we try to reproduce? The roundworm C. elegans, for example, has just 302 neurons in total. Advances in brain imaging mean it is now possible to identify each of these neurons and compare its activity across worms. But doing so reveals that the activity of any given neuron varies greatly between individuals. This is true even among genetically identical worms performing the same behavior.

Researchers trying to model the roundworm brain have attempted to model the average activity of each neuron across many worms. They hoped they could use these averages to predict the behavior of other worms from their neuronal activity. But this approach did not to work. Even in roundworms, the coordinated activity of many neurons is required to generate even simple behaviors. Averaging the activity of neurons across worms thus scrambles the information that encodes each behavior.

Brennan and Proekt have now overcome this problem by developing a more abstract model that treats the nervous system as a whole. The model takes into account changes in the activity of neurons, and in the worms’ behavior, over time. A model of this type built using one set of worms can predict the behavior of another set of worms. This approach may work because in evolution natural selection acts at the level of behaviors, and not at the level of individual neurons. The activity of individual neurons can thus vary between animals, even when those neurons encode the same behavior. This means it may also be possible to model the human brain without knowing the activity of each of its billions of neurons.

A computational model of internal representations of chemical gradients in environments for chemotaxis of Caenorhabditis elegans

The small roundworm Caenorhabditis elegans employs two strategies, termed pirouette and weathervane, which are closely related to the internal representation of chemical gradients parallel and perpendicular to the travelling direction, respectively, to perform chemotaxis. These gradients must be calculated from the chemical information obtained at a single point, because the sensory neurons are located close to each other at the nose tip. To formulate the relationship between this sensory input and internal representations of the chemical gradient, this study proposes a simple computational model derived from the directional decomposition of the chemical concentration at the nose tip that can generate internal representations of the chemical gradient. The ability of the computational model was verified by using a chemotaxis simulator that can simulate the body motions of pirouette and weathervane, which confirmed that the computational model enables the conversion of the sensory input and head-bending angles into both types of gradients with high correlations of approximately r > 0.90 (p < 0.01) with the true gradients. In addition, the chemotaxis index of the model was 0.64, which is slightly higher than that in the actual animal (0.57). In addition, simulation using a connectome-based neural network model confirmed that the proposed computational model is implementable in the actual network structure.

From head to tail: a neuromechanical model of forward locomotion in Caenorhabditis elegans

With 302 neurons and a near-complete reconstruction of the neural and muscle anatomy at the cellular level, Caenorhabditis elegans is an ideal candidate organism to study the neuromechanical basis of behaviour. Yet despite the breadth of knowledge about the neurobiology, anatomy and physics of C. elegans, there are still a number of unanswered questions about one of its most basic and fundamental behaviours: forward locomotion. How the rhythmic pattern is generated and propagated along the body is not yet well understood. We report on the development and analysis of a model of forward locomotion that integrates the neuroanatomy, neurophysiology and body mechanics of the worm. Our model is motivated by experimental analysis of the structure of the ventral cord circuitry and the effect of local body curvature on nearby motoneurons. We developed a neuroanatomically grounded model of the head motoneuron circuit and the ventral nerve cord circuit. We integrated the neural model with an existing biomechanical model of the worm's body, with updated musculature and stretch receptors. Unknown parameters were evolved using an evolutionary algorithm to match the speed of the worm on agar. We performed 100 evolutionary runs and consistently found electrophysiological configurations that reproduced realistic control of forward movement. The ensemble of successful solutions reproduced key experimental observations that they were not designed to fit, including the wavelength and frequency of the propagating wave. Analysis of the ensemble revealed that head motoneurons SMD and RMD are sufficient to drive dorsoventral undulations in the head and neck and that short-range posteriorly directed proprioceptive feedback is sufficient to propagate the wave along the rest of the body.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

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'.

Connectome to behaviour: modelling Caenorhabditis elegans at cellular resolution

It has been 30 years since the 'mind of the worm' was published in Philosophical Transactions B (White et al 1986 Phil. Trans. R. Soc. Lond. B314, 1-340). Predicting Caenorhabditis elegans' behaviour from its wiring diagram has been an enduring challenge since then. This special theme issue of Philosophical Transactions B combines research from neuroscientists, physicists, mathematicians and engineers to discuss advances in neural activity imaging, behaviour quantification and multiscale simulations, and how they are bringing the goal of whole-animal modelling at cellular resolution within reach.This article is part of a discussion meeting issue 'Connectome to behaviour: modelling C. elegans at cellular resolution'.

Potential role of a ventral nerve cord central pattern generator in forward and backward locomotion in Caenorhabditis elegans

C. elegans locomotes in an undulatory fashion, generating thrust by propagating dorsoventral bends along its body. Although central pattern generators (CPGs) are typically involved in animal locomotion, their presence in C. elegans has been questioned, mainly because there has been no evident circuit that supports intrinsic network oscillations. With a fully reconstructed connectome, the question of whether it is possible to have a CPG in the ventral nerve cord (VNC) of C. elegans can be answered through computational models. We modeled a repeating neural unit based on segmentation analysis of the connectome. We then used an evolutionary algorithm to determine the unknown physiological parameters of each neuron so as to match the features of the neural traces of the worm during forward and backward locomotion. We performed 1,000 evolutionary runs and consistently found configurations of the neural circuit that produced oscillations matching the main characteristic observed in experimental recordings. In addition to providing an existence proof for the possibility of a CPG in the VNC, we suggest a series of testable hypotheses about its operation. More generally, we show the feasibility and fruitfulness of a methodology to study behavior based on a connectome, in the absence of complete neurophysiological details.

Optimal synaptic signaling connectome for locomotory behavior in Caenorhabditis elegans: Design minimizing energy cost

The detailed knowledge of C. elegans connectome for 3 decades has not contributed dramatically to our understanding of worm's behavior. One of main reasons for this situation has been the lack of data on the type of synaptic signaling between particular neurons in the worm's connectome. The aim of this study was to determine synaptic polarities for each connection in a small pre-motor circuit controlling locomotion. Even in this compact network of just 7 neurons the space of all possible patterns of connection types (excitation vs. inhibition) is huge. To deal effectively with this combinatorial problem we devised a novel and relatively fast technique based on genetic algorithms and large-scale parallel computations, which we combined with detailed neurophysiological modeling of interneuron dynamics and compared the theory to the available behavioral data. As a result of these massive computations, we found that the optimal connectivity pattern that matches the best locomotory data is the one in which all interneuron connections are inhibitory, even those terminating on motor neurons. This finding is consistent with recent experimental data on cholinergic signaling in C. elegans, and it suggests that the system controlling locomotion is designed to save metabolic energy. Moreover, this result provides a solid basis for a more realistic modeling of neural control in these worms, and our novel powerful computational technique can in principle be applied (possibly with some modifications) to other small-scale functional circuits in C. elegans.

A Functional Subnetwork Approach to Designing Synthetic Nervous Systems That Control Legged Robot Locomotion

A dynamical model of an animal's nervous system, or synthetic nervous system (SNS), is a potentially transformational control method. Due to increasingly detailed data on the connectivity and dynamics of both mammalian and insect nervous systems, controlling a legged robot with an SNS is largely a problem of parameter tuning. Our approach to this problem is to design functional subnetworks that perform specific operations, and then assemble them into larger models of the nervous system. In this paper, we present networks that perform addition, subtraction, multiplication, division, differentiation, and integration of incoming signals. Parameters are set within each subnetwork to produce the desired output by utilizing the operating range of neural activity, R, the gain of the operation, k, and bounds based on biological values. The assembly of large networks from functional subnetworks underpins our recent results with MantisBot.

Template for the neural control of directed stepping generalized to all legs of MantisBot

We previously developed a neural controller for one leg of our six-legged robot, MantisBot, that could direct locomotion toward a goal by modulating leg-local reflexes with simple descending commands from a head sensor. In this work, we successfully apply an automated method to tune the control network for all three pairs of legs of our hexapod robot MantisBot in only 90 s with a desktop computer. Each foot's motion changes appropriately as the body's intended direction of travel changes. In addition, several results from studies of walking insects are captured by this model. This paper both demonstrates the broad applicability of this control method for robots, and suggests neural mechanisms underlying observations from walking insects.

Generating Executable Models of the Drosophila Central Complex

The central complex (CX) is a set of neuropils in the center of the fly brain that have been implicated as playing an important role in vision-mediated behavior and integration of spatial information with locomotor control. In contrast to currently available data regarding the neural circuitry of neuropils in the fly's vision and olfactory systems, comparable data for the CX neuropils is relatively incomplete; many categories of neurons remain only partly characterized, and the synaptic connectivity between CX neurons has yet to be fully determined. Successful modeling of the information processing functions of the CX neuropils therefore requires a means of easily constructing and testing a range of hypotheses regarding both the high-level structure of their neural circuitry and the properties of their constituent neurons and synapses. To this end, we have created a web application that enables simultaneous graphical querying and construction of executable models of the CX neural circuitry based upon currently available information regarding the geometry and polarity of the arborizations of identified local and projection neurons in the CX. The application's novel functionality is made possible by the Fruit Fly Brain Observatory, a platform for collaborative study and development of fruit fly brain models.

Network neuroscience

Despite substantial recent progress, our understanding of the principles and mechanisms underlying complex brain function and cognition remains incomplete. Network neuroscience proposes to tackle these enduring challenges. Approaching brain structure and function from an explicitly integrative perspective, network neuroscience pursues new ways to map, record, analyze and model the elements and interactions of neurobiological systems. Two parallel trends drive the approach: the availability of new empirical tools to create comprehensive maps and record dynamic patterns among molecules, neurons, brain areas and social systems; and the theoretical framework and computational tools of modern network science. The convergence of empirical and computational advances opens new frontiers of scientific inquiry, including network dynamics, manipulation and control of brain networks, and integration of network processes across spatiotemporal domains. We review emerging trends in network neuroscience and attempt to chart a path toward a better understanding of the brain as a multiscale networked system.

Estimating Sensorimotor Mapping From Stimuli to Behaviors to Infer C. elegans Movements by Neural Transmission Ability Through Connectome Databases

One of the ultimate goals of computational neuroscience is to quantitatively connect between complex neural circuits and behaviors. In the past decades, the touch response circuit in Caenorhabditis elegans (C. elegans) has extensively been investigated in studies using genetically modified or laser-ablated worms. Synaptic connections, including chemical and electrical synapses, have been identified for most neurons in the C. elegans. However, we still do not know whether the empirically observed touch responses can be derived from connectome reconstructed from databases. To address this issue, we defined the transmission abilities (or levels) of neurons in a rate model in order to infer the behaviors of wild-type and ablated worms in response to posterior/nose/anterior touch stimuli. Our analysis showed that transmission abilities can be used to identify sensorimotor mapping from stimuli to movements and then to infer the C. elegans behaviors under simulations based on the perspective of decision-making, and provide useful information about how chemical and electronic synapses should be combined in the neural network movement analysis. This paper reveals an efficient tool that provided insights into the functions of complex neural circuits.

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.

Suppression of phase synchronisation in network based on cat's brain

We have studied the effects of perturbations on the cat's cerebral cortex. According to the literature, this cortex structure can be described by a clustered network. This way, we construct a clustered network with the same number of areas as in the cat matrix, where each area is described as a sub-network with a small-world property. We focus on the suppression of neuronal phase synchronisation considering different kinds of perturbations. Among the various controlling interventions, we choose three methods: delayed feedback control, external time-periodic driving, and activation of selected neurons. We simulate these interventions to provide a procedure to suppress undesired and pathological abnormal rhythms that can be associated with many forms of synchronisation. In our simulations, we have verified that the efficiency of synchronisation suppression by delayed feedback control is higher than external time-periodic driving and activation of selected neurons of the cat's cerebral cortex with the same coupling strengths.

Rich-Club Organization in Effective Connectivity among Cortical Neurons

The performance of complex networks, like the brain, depends on how effectively their elements communicate. Despite the importance of communication, it is virtually unknown how information is transferred in local cortical networks, consisting of hundreds of closely spaced neurons. To address this, it is important to record simultaneously from hundreds of neurons at a spacing that matches typical axonal connection distances, and at a temporal resolution that matches synaptic delays. We used a 512-electrode array (60 μm spacing) to record spontaneous activity at 20 kHz from up to 500 neurons simultaneously in slice cultures of mouse somatosensory cortex for 1 h at a time. We applied a previously validated version of transfer entropy to quantify information transfer. Similar to in vivo reports, we found an approximately lognormal distribution of firing rates. Pairwise information transfer strengths also were nearly lognormally distributed, similar to reports of synaptic strengths. Some neurons transferred and received much more information than others, which is consistent with previous predictions. Neurons with the highest outgoing and incoming information transfer were more strongly connected to each other than chance, thus forming a "rich club." We found similar results in networks recorded in vivo from rodent cortex, suggesting the generality of these findings. A rich-club structure has been found previously in large-scale human brain networks and is thought to facilitate communication between cortical regions. The discovery of a small, but information-rich, subset of neurons within cortical regions suggests that this population will play a vital role in communication, learning, and memory. Significance statement: Many studies have focused on communication networks between cortical brain regions. In contrast, very few studies have examined communication networks within a cortical region. This is the first study to combine such a large number of neurons (several hundred at a time) with such high temporal resolution (so we can know the direction of communication between neurons) for mapping networks within cortex. We found that information was not transferred equally through all neurons. Instead, ∼70% of the information passed through only 20% of the neurons. Network models suggest that this highly concentrated pattern of information transfer would be both efficient and robust to damage. Therefore, this work may help in understanding how the cortex processes information and responds to neurodegenerative diseases.

Fluctuation-Driven Neural Dynamics Reproduce Drosophila Locomotor Patterns

The neural mechanisms determining the timing of even simple actions, such as when to walk or rest, are largely mysterious. One intriguing, but untested, hypothesis posits a role for ongoing activity fluctuations in neurons of central action selection circuits that drive animal behavior from moment to moment. To examine how fluctuating activity can contribute to action timing, we paired high-resolution measurements of freely walking Drosophila melanogaster with data-driven neural network modeling and dynamical systems analysis. We generated fluctuation-driven network models whose outputs-locomotor bouts-matched those measured from sensory-deprived Drosophila. From these models, we identified those that could also reproduce a second, unrelated dataset: the complex time-course of odor-evoked walking for genetically diverse Drosophila strains. Dynamical models that best reproduced both Drosophila basal and odor-evoked locomotor patterns exhibited specific characteristics. First, ongoing fluctuations were required. In a stochastic resonance-like manner, these fluctuations allowed neural activity to escape stable equilibria and to exceed a threshold for locomotion. Second, odor-induced shifts of equilibria in these models caused a depression in locomotor frequency following olfactory stimulation. Our models predict that activity fluctuations in action selection circuits cause behavioral output to more closely match sensory drive and may therefore enhance navigation in complex sensory environments. Together these data reveal how simple neural dynamics, when coupled with activity fluctuations, can give rise to complex patterns of animal behavior.

Information Flow through a Model of the C. elegans Klinotaxis Circuit

Understanding how information about external stimuli is transformed into behavior is one of the central goals of neuroscience. Here we characterize the information flow through a complete sensorimotor circuit: from stimulus, to sensory neurons, to interneurons, to motor neurons, to muscles, to motion. Specifically, we apply a recently developed framework for quantifying information flow to a previously published ensemble of models of salt klinotaxis in the nematode worm Caenorhabditis elegans. Despite large variations in the neural parameters of individual circuits, we found that the overall information flow architecture circuit is remarkably consistent across the ensemble. This suggests structural connectivity is not necessarily predictive of effective connectivity. It also suggests information flow analysis captures general principles of operation for the klinotaxis circuit. In addition, information flow analysis reveals several key principles underlying how the models operate: (1) Interneuron class AIY is responsible for integrating information about positive and negative changes in concentration, and exhibits a strong left/right information asymmetry. (2) Gap junctions play a crucial role in the transfer of information responsible for the information symmetry observed in interneuron class AIZ. (3) Neck motor neuron class SMB implements an information gating mechanism that underlies the circuit’s state-dependent response. (4) The neck carries more information about small changes in concentration than about large ones, and more information about positive changes in concentration than about negative ones. Thus, not all directions of movement are equally informative for the worm. Each of these findings corresponds to hypotheses that could potentially be tested in the worm. Knowing the results of these experiments would greatly refine our understanding of the neural circuit underlying klinotaxis.

Controlling legs for locomotion-insights from robotics and neurobiology

Walking is the most common terrestrial form of locomotion in animals. Its great versatility and flexibility has led to many attempts at building walking machines with similar capabilities. The control of walking is an active research area both in neurobiology and robotics, with a large and growing body of work. This paper gives an overview of the current knowledge on the control of legged locomotion in animals and machines and attempts to give walking control researchers from biology and robotics an overview of the current knowledge in both fields. We try to summarize the knowledge on the neurobiological basis of walking control in animals, emphasizing common principles seen in different species. In a section on walking robots, we review common approaches to walking controller design with a slight emphasis on biped walking control. We show where parallels between robotic and neurobiological walking controllers exist and how robotics and biology may benefit from each other. Finally, we discuss where research in the two fields diverges and suggest ways to bridge these gaps.

Robotics and neuroscience

In the attempt to build adaptive and intelligent machines, roboticists have looked at neuroscience for more than half a century as a source of inspiration for perception and control. More recently, neuroscientists have resorted to robots for testing hypotheses and validating models of biological nervous systems. Here, we give an overview of the work at the intersection of robotics and neuroscience and highlight the most promising approaches and areas where interactions between the two fields have generated significant new insights. We articulate the work in three sections, invertebrate, vertebrate and primate neuroscience. We argue that robots generate valuable insight into the function of nervous systems, which is intimately linked to behaviour and embodiment, and that brain-inspired algorithms and devices give robots life-like capabilities.

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.

Multiplex networks of cortical and hippocampal neurons revealed at different timescales

Recent studies have emphasized the importance of multiplex networks--interdependent networks with shared nodes and different types of connections--in systems primarily outside of neuroscience. Though the multiplex properties of networks are frequently not considered, most networks are actually multiplex networks and the multiplex specific features of networks can greatly affect network behavior (e.g. fault tolerance). Thus, the study of networks of neurons could potentially be greatly enhanced using a multiplex perspective. Given the wide range of temporally dependent rhythms and phenomena present in neural systems, we chose to examine multiplex networks of individual neurons with time scale dependent connections. To study these networks, we used transfer entropy--an information theoretic quantity that can be used to measure linear and nonlinear interactions--to systematically measure the connectivity between individual neurons at different time scales in cortical and hippocampal slice cultures. We recorded the spiking activity of almost 12,000 neurons across 60 tissue samples using a 512-electrode array with 60 micrometer inter-electrode spacing and 50 microsecond temporal resolution. To the best of our knowledge, this preparation and recording method represents a superior combination of number of recorded neurons and temporal and spatial recording resolutions to any currently available in vivo system. We found that highly connected neurons ("hubs") were localized to certain time scales, which, we hypothesize, increases the fault tolerance of the network. Conversely, a large proportion of non-hub neurons were not localized to certain time scales. In addition, we found that long and short time scale connectivity was uncorrelated. Finally, we found that long time scale networks were significantly less modular and more disassortative than short time scale networks in both tissue types. As far as we are aware, this analysis represents the first systematic study of temporally dependent multiplex networks among individual neurons.

Spinal circuits can accommodate interaction torques during multijoint limb movements

The dynamic interaction of limb segments during movements that involve multiple joints creates torques in one joint due to motion about another. Evidence shows that such interaction torques are taken into account during the planning or control of movement in humans. Two alternative hypotheses could explain the compensation of these dynamic torques. One involves the use of internal models to centrally compute predicted interaction torques and their explicit compensation through anticipatory adjustment of descending motor commands. The alternative, based on the equilibrium-point hypothesis, claims that descending signals can be simple and related to the desired movement kinematics only, while spinal feedback mechanisms are responsible for the appropriate creation and coordination of dynamic muscle forces. Partial supporting evidence exists in each case. However, until now no model has explicitly shown, in the case of the second hypothesis, whether peripheral feedback is really sufficient on its own for coordinating the motion of several joints while at the same time accommodating intersegmental interaction torques. Here we propose a minimal computational model to examine this question. Using a biomechanics simulation of a two-joint arm controlled by spinal neural circuitry, we show for the first time that it is indeed possible for the neuromusculoskeletal system to transform simple descending control signals into muscle activation patterns that accommodate interaction forces depending on their direction and magnitude. This is achieved without the aid of any central predictive signal. Even though the model makes various simplifications and abstractions compared to the complexities involved in the control of human arm movements, the finding lends plausibility to the hypothesis that some multijoint movements can in principle be controlled even in the absence of internal models of intersegmental dynamics or learned compensatory motor signals.

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.