While animal behavior is often quantified through discrete motifs, this is only an approximation to fundamentally continuous dynamics and ignores important variability within each motif. Here, we develop a behavioral phase space in which the instantaneous state is smoothly unfolded as a combination of postures and their short-time dynamics. We apply this approach to C. elegans and show that the dynamics lie on a 6D space, which is globally composed of three sets of cyclic trajectories that form the animal’s basic behavioral motifs: forward, backward and turning locomotion. In contrast to global stereotypy, variability is evident by the presence of locally-unstable dynamics for each set of cycles. Across the full phase space we show that the Lyapunov spectrum is symmetric with positive, chaotic exponents driving variability balanced by negative, dissipative exponents driving stereotypy. The symmetry of the spectrum holds for different environments and for human walking, suggesting a general condition of motor control. Finally, we use the reconstructed phase space to analyze the complexity of the dynamics along the worm’s body and find evidence for multiple, spatially-separate oscillators driving C. elegans locomotion.

Decision making is a central function of the brain and the focus of intensive study in neuroscience, psychology, and economics. Value-based decision making (e.g., ‘which fragrance do you prefer?’ not 'which smells more like roses?') guides significant, sometimes life-changing, choices yet its neuronal basis is poorly understood. Research into this question would be accelerated by the introduction of genetically tractable invertebrates with small nervous systems, like the Drosophila and C. elegans. We have recently shown that the nematode C. elegans makes value-based decisions. This was done using a formal economic method – the Generalized Axiom of Revealed Preference (GARP). The basis of the method is to establish that the subject's choices are internally consistent with respect to transitivity (A > B > C ⇒ A > C). In the wild, C. elegans feeds on a variety of bacteria and learns to prefer the more nutritious species. We tested worms on a set of decisions between a high quality species and a low quality species at a range of relative concentrations and found the worm’s choices to be 100% transitive, the necessary and sufficient condition for value-based decision making. Further, we found that the olfactory neuron AWC, known to be activated by the sudden absence of food, is required for intact food choice behavior. Surprisingly, however, we found that AWC is also activated by the switch from high quality food to low quality food, even when the two foods are at the same concentration. Thus, food value may be represented at the level of individual olfactory neurons. We are now investigating the neural mechanisms of choice transitivity. C. elegans selects food sources utilizing klinotaxis, a chemotaxis strategy during locomotion in which the worm’s head bends more deeply on the side of preferred food. The chemosensory neurons, interneurons, and motor neurons of a candidate circuit for klinotaxis have been identified. Extrapolating from our findings with respect to AWC, we have developed a model of the circuit in which distinct chemosensory neuron types encode food quality and quantity during particular phases of head bending. Activation of downstream interneurons in the model is the weighted sum of these inputs in accordance with phase information. The model proposes that the signs and strengths of synaptic weights in the biological circuit are adjusted to ensure that subjective value is a monotonic function of the relative quantity of high and low quality food, a property that guarantees transitivity under GARP. Work in progress tests the model using calcium imaging, optogenetic activation, and ablations of each neuron in the circuit.

Populations of neurons in the brains of many different animals, ranging from invertebrates to primates, typically coordinate their activities to generate low dimensional and transient activity dynamics, an operational principle serving many neuronal functions like sensory coding, decision making and motor control. However, the mechanism that bind individual neurons to global population states are not yet known. Are population dynamics driven by a smaller number of pacemaker neurons or are they an emergent property of neuronal networks? What are the features in global network architecture that support coordinated network wide dynamics? In order to address these problems, we study neuronal population dynamics in C. elegans. We recently developed a calcium imaging approach to record the activity of nearly all neuron in the worm brain in real time and at single cell resolution. We show that brain activity of C. elegans is dominated by brain wide coordinated population dynamics involving a large fraction of interneurons and motor neurons. The activity patterns of these neuronal ensembles recur in an orderly and cyclical fashion. In subsequent experiments, we characterized these brain dynamics functionally and found that they represent action commands and their assembly into a typical action sequence of these animals: forward crawling – backward crawling – turning. Deciphering the mechanisms underlying neuronal population dynamics is key to understanding the principal computations performed by neuronal networks in the brains of animals, and perhaps will inspire the design of novel machine learning algorithms for robotic control. In this talk, I will discuss three of our approaches to uncover these mechanisms: First, using graph theory, we aim to identify the key features of neuronal network architecture that support functional dynamics. We found that rich club neurons, i.e. highly interconnected network hubs contribute most to brain dynamics. However, simple measures of synaptic connectivity (e.g. connection strength) failed to predict functional interactions between these neurons; unlike higher order network statistics that measure the similarity in synaptic input patterns. We next performed systematic perturbations by interrogation of rich club neurons via transgenic neuronal inhibition tools. Using whole brain imaging in combination with computational analysis methods we found that upon inhibition of critical hubs, leading to a disintegration of the network, most other individual neurons remain vigorously active, however the global coordination across neurons was abolished. Based on these results we hypothesize that neuronal population dynamics are an emergent property of neuronal networks. Finally, we aim to recapitulate C. elegans brain dynamics in silico. Here, we generate neuronal network simulations based on deterministic and stochastic biophysical models of neurons and synapses, at multiscale levels of abstraction. We then adopt a genetic algorithm for neuronal circuit parameter optimization, to find the best matches between simulations and measured calcium dynamics. This approach enables us to test our hypotheses, and to predict unknown properties of neural circuits important for brain dynamics.

Effective spatial navigation is essential for the survival of animals. Navigation, or the search for favorable conditions, is fundamentally an adaptive behavior that can depend on the changing environment, the animal's past history of success and failure and its internal state. C. elegans implements combinations of systematic and stochastic navigational strategies that are modulated by plasticity across a range of time scales. Here, we combine experiments and computational modeling to characterise adaptation in gustatory and nociceptive salt sensing neurons and construct a simulation framework in which animals can navigate a virtual environment. Our model, and simulations on a variety of smooth, rugged or complex landscapes, suggest that these different forms of sensory adaptation combine to dynamically modulate navigational strategies, giving rise to effective exploration and navigation of the environment. Inspired by this compact and elegant sensory circuit, we present a robotic simulation framework, capable of robustly searching for landmarks in a toy simulation environment.

William R. Schafer1, Gang Yan2, 3, Petra E. Vértes4, Emma K. Towlson3, Yee Lian Chew1, Denise S. Walker1, & Albert-László Barabási3 1Division of Neurobiology, MRC Laboratory of Molecular Biology, Cambridge Biomedical Campus, Francis Crick Avenue, Cambridge CB2 0QH, UK. 2School of Physics Science and Engineering, Tongji University, Shanghai 200092, China. 3Center for Complex Network Research and Department of Physics, Northeastern University, Boston, Massachusetts 02115, USA. 4Department of Psychiatry, Behavioural and Clinical Neuroscience Institute, University of Cambridge, Cambridge CB2 0SZ, UK.

Large-scale efforts are underway to map the neuronal connectomes of many animals, from flies to humans. However, even for small connectomes, such as that of C. elegans, it has been difficult to relate the structure of neuronal wiring patterns to the function of neural circuits. Recent theoretical studies have suggested that control theory might provide a framework to understand structure-function relationships in complex biological networks, including neuronal connectomes. To test this hypothesis experimentally, we have used the complete neuronal connectome of C. elegans to identify neurons predicted to affect the controllability of the body muscles and assess the effect of ablating these neurons on locomotor behavior. We identified 12 neural classes whose removal from the connectome reduced the structural controllability of the body neuromusculature, one of which was the uncharacterized PDB motorneuron. Consistent with the control theory prediction, ablation of PDB had a specific effect on locomotion, altering the dorsoventral polarity of large turns. Control analysis also predicted that three members of the DD motorneuron class (DD4, DD5 and DD6) are individually required for body muscle controllability, while more anterior DDs (DD1, DD2 and DD3) are not. Indeed, we found that ablation of DD4 or DD5, but not DD2 or DD3, led to abnormalities in posterior body movements, again consistent with control theory predictions. We are currently using the control framework to probe other parts of the C. elegans connectome, and are developing more sophisticated approaches behavioral analysis in order to more precisely relate ablation phenotypes to specific muscle groups. We anticipate that the control framework validated by this work may have application in the analysis of larger neuronal connectomes and other complex networks.

The membrane potential of a biological neuron is considered to be one of the most importantproperties to understand its dynamic state. While the action potential or discrete “spike” featureof mammalian neurons has been emphasized as an information bearing signal, biologicalevidence exists that even without action potentials, neurons process information and give rise todifferent behavioral states. Nowhere is this more evident than in the nematode worm C.elegans , where its entire nervous system of 302 neurons, despite a lack of action potentials,organizes complex behaviors such as mating, predator avoidance, location of food sources, andmany others. For thirty years, the C. elegans nervous system has remained the only adult animal that has hadits nervous system connectivity mapped at the level of individual synapses and gap junctions.As part of the international open science collaboration known as OpenWorm, we have built a1simulation framework, known as c302, that enables us to assemble the known connectivity andother biological data of the C. elegans nervous system into a Hodgkin­Huxley­based simulationthat can be run in the NEURON simulation engine. Using a physical simulation of the C. elegans body, known as Sibernetic, we have injected simple sinusoidal activation patterns of the muscle cells of the C. elegans and produced simplecrawling and swimming behavior. With the goal of producing the same simple sinusoids in themuscle cells, we have used c302 to select a subnetwork from the full C. elegans nervoussystem and used machine learning techniques to fit dynamic parameters that are underspecifiedby the data. Our preliminary results still leave many important biological features out, butinitially demonstrate that it is possible to make motor neurons produce sinusoidal activitypatterns in the muscles as used in the physical simulation.

In this talk I will discuss these initial results and discuss future directions for a betterunderstanding of the information processing underlying the C. elegans’ nervous system.

One of the grand scientific challenges of this century is to understand how behavior is grounded in the interaction between an organism’s brain, its body, and its environment. Although a lot of attention and resources are focused on understanding the human brain, I will argue that the study of simpler organisms are an ideal place to begin to address this challenge. I will introduce the nematode worm Caernohabditis elegans, with just 302 neurons, the only fully-reconstructed connectome at the cellular level, and a rich behavioral repertoire that we are still discovering. I will describe a computational approach to address such grand challenge. I will lay out some of the advantages of expressing our understanding in equations and computational models rather than just words. I will describe our unique methodology for exploring the unknown biological parameters of the model through the use of evolutionary algorithms. We train the neural networks on what they should do, with little or no instructions on how to do it. The effort is then to analyze and understand the evolved solutions as a way to generate novel, often unexpected, hypotheses. As an example, I will focus on how the rhythmic pattern is both generated and propagated along the body during locomotion.