Eduardo J. Izquierdo

Evolution and Analysis of Minimal Neural Circuits for Klinotaxis in Caenorhabditis elegans

Chemotaxis during sinusoidal locomotion in nematodes captures in simplified form the general problem of how dynamical interactions between the nervous system, body, and environment are exploited in the generation of adaptive behavior. We used an evolutionary algorithm to generate neural networks that exhibit klinotaxis, a common form of chemotaxis in which the direction of locomotion in a chemical gradient closely follows the line of steepest ascent. Sensory inputs and motor outputs of the model networks were constrained to match the inputs and outputs of the Caenorhabditis elegans klinotaxis network. We found that a minimalistic neural network, comprised of an ON-OFF pair of chemosensory neurons and a pair of neck muscle motor neurons, is sufficient to generate realistic klinotaxis behavior. Importantly, emergent properties of model networks reproduced two key experimental observations that they were not designed to fit, suggesting that the model may be operating according to principles similar to those of the biological network. A dynamical systems analysis of 77 evolved networks revealed a novel neural mechanism for spatial orientation behavior. This mechanism provides a testable hypothesis that is likely to accelerate the discovery and analysis of the biological circuitry for chemotaxis in C. elegans.

Connecting a Connectome to Behavior: An Ensemble of Neuroanatomical Models of C. elegans Klinotaxis

Increased efforts in the assembly and analysis of connectome data are providing new insights into the principles underlying the connectivity of neural circuits. However, despite these considerable advances in connectomics, neuroanatomical data must be integrated with neurophysiological and behavioral data in order to obtain a complete picture of neural function. Due to its nearly complete wiring diagram and large behavioral repertoire, the nematode worm Caenorhaditis elegans is an ideal organism in which to explore in detail this link between neural connectivity and behavior. In this paper, we develop a neuroanatomically-grounded model of salt klinotaxis, a form of chemotaxis in which changes in orientation are directed towards the source through gradual continual adjustments. We identify a minimal klinotaxis circuit by systematically searching the C. elegans connectome for pathways linking chemosensory neurons to neck motor neurons, and prune the resulting network based on both experimental considerations and several simplifying assumptions. We then use an evolutionary algorithm to find possible values for the unknown electrophsyiological parameters in the network such that the behavioral performance of the entire model is optimized to match that of the animal. Multiple runs of the evolutionary algorithm produce an ensemble of such models. We analyze in some detail the mechanisms by which one of the best evolved circuits operates and characterize the similarities and differences between this mechanism and other solutions in the ensemble. Finally, we propose a series of experiments to determine which of these alternatives the worm may be using.

A stochastic neuronal model predicts random search behaviors at multiple spatial scales in C. elegans

Random search is a behavioral strategy used by organisms from bacteria to humans to locate food that is randomly distributed and undetectable at a distance. We investigated this behavior in the nematode Caenorhabditis elegans, an organism with a small, well-described nervous system. Here we formulate a mathematical model of random search abstracted from the C. elegans connectome and fit to a large-scale kinematic analysis of C. elegans behavior at submicron resolution. The model predicts behavioral effects of neuronal ablations and genetic perturbations, as well as unexpected aspects of wild type behavior. The predictive success of the model indicates that random search in C. elegans can be understood in terms of a neuronal flip-flop circuit involving reciprocal inhibition between two populations of stochastic neurons. Our findings establish a unified theoretical framework for understanding C. elegans locomotion and a testable neuronal model of random search that can be applied to other organisms.

Associative Learning on a Continuum in Evolved Dynamical Neural Networks

This article extends previous work on evolving learning without synaptic plasticity from discrete tasks to continuous tasks. Continuous-time recurrent neural networks without synaptic plasticity are artificially evolved on an associative learning task. The task consists in associating paired stimuli: temperature and food. The temperature to be associated can be either drawn from a discrete set or allowed to range over a continuum of values. We address two questions: Can the learning without synaptic plasticity approach be extended to continuous tasks? And if so, how does learning without synaptic plasticity work in the evolved circuits? Analysis of the most successful circuits to learn discrete stimuli reveal finite state machine (FSM) like internal dynamics. However, when the task is modified to require learning stimuli on the full continuum range, it is not possible to extract a FSM from the internal dynamics. In this case, a continuous state machine is extracted instead.

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 animals 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.

An Integrated Neuromechanical Model of Steering in C. elegans .

In this paper, we extend our previous model circuit for steering in C. elegans to control a more realistic biomechanical model of forward locomotion. We show that the identified steering circuit is sufficient to steer the full body during forward locomotion while only innervating a few of the anterior most neck muscles. Analysis of the sensorimotor transformation and phasic stimulation experiments provides evidence that the principles of operation for steering discussed in the model are relevant for steering in the worm. Finally, the integration of the steering circuit in a physical model of the full body allows us to compare more closely the properties of the evolved solutions with those of the worm.

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.

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.Author SummaryDespite the relative simplicity of C. elegans, its locomotion machinery is not yet well understood. We focus on the generation of dorsoventral body bends. Although network central pattern generators are commonly involved in animal locomotion, their presence in C. elegans has been questioned due to a lack of an evident neural circuit to support it. We developed a computational model grounded in the available neuroanatomy and neurophysiology, and we used an evolutionary algorithm to explore the space of possible configurations of the circuit that matched the neural traces observed during forward and backward locomotion in the worm. Our results demonstrate that it is possible for the rhythmic contraction to be produced by a circuit present in the ventral nerve cord.

Analysis of Ultrastability in Small Dynamical Recurrent Neural Networks.

This paper reconsiders Ashby’s framework of adaptation within the context of dynamical neural networks. Agents are evolved to behave as an ultrastable dynamical system, without imposing a priori the nature of the behavior-changing mechanisms, or the strategy to explore the space of possible dynamics in the system. We analyze the resulting networks using dynamical systems theory for some of the simplest conditions. The picture that emerges from our analysis generalizes the idea of ultrastable mechanisms.

The dynamics of associative learning in an evolved situated agent

Artificial agents controlled by dynamic recurrent node networks with fixed weights are evolved to search for food and associate it with one of two different temperatures depending on experience. The task requires either instrumental or classical conditioned responses to be learned. The paper extends previous work in this area by requiring that a situated agent be capable of re-learning during its lifetime. We analyse the best-evolved agents behaviour and explain in some depth how it arises from the dynamics of the coupled agent-environment system.