Izquierdo EJ et al. (2010) J Neurosci "Evolution and analysis of minimal neural circuits for klinotaxis in Caenorhabditis elegans."

Lockery SR, Izquierdo EJ

[J Neurosci, 2010]

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.

Izquierdo EJ et al. (2015) PLoS One "Information Flow through a Model of the C. elegans Klinotaxis Circuit."

Williams PL, Beer RD, Izquierdo EJ

[PLoS One, 2015]

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.

Izquierdo EJ et al. (2016) Curr Opin Neurobiol "The whole worm: brain-body-environment models of C. elegans."

Izquierdo EJ, Beer RD

[Curr Opin Neurobiol, 2016]

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.

Izquierdo EJ et al. (2013) PLoS Comput Biol "Connecting a connectome to behavior: an ensemble of neuroanatomical models of C. elegans klinotaxis."

Beer RD, Izquierdo EJ

[PLoS Comput Biol, 2013]

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.

Izquierdo EJ et al. (2018) Philos Trans R Soc Lond B Biol Sci "From head to tail: a neuromechanical model of forward locomotion in Caenorhabditiselegans."

Beer RD, Izquierdo EJ

[Philos Trans R Soc Lond B Biol Sci, 2018]

With 302 neurons and a near-complete reconstruction of the neural and muscle anatomy at the cellular level, <i>Caenorhabditis elegans</i> 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 <i>C. elegans</i>, 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 <i>C. elegans</i> at cellular resolution'.

Olivares, E.O. et al. (2017) International Worm Meeting "Connectome analysis shows the feasibility of ventral cord central pattern generators driving locomotion in C. elegans."

Izquierdo, E.J., Olivares, E.O., Beer, R.D.

[International Worm Meeting, 2017]

Since nearly its entire behavioral repertoire is expressed through movement, understanding the neural basis of locomotion is especially critical as a foundation upon which analyses of all other behaviors must build. C. elegans locomotes in an undulatory fashion, generating thrust by propagating dorso-ventral bends along its body. How the rhythmic patterns are generated is not yet understood. While central pattern generators are involved in animal locomotion from leech to humans, their presence in C. elegans has been questioned, mainly because there has been no evident neural motif that supports intrinsic oscillations. With a fully reconstructed connectome, the question of whether it is possible to have a CPG in the ventral cord of C. elegans can be answered through computational models. We modeled the ventral cord circuit based on the most up-to-date connectome data and segmentation analysis. In order to explore the possibility of intrinsic oscillations, we 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 1000 evolutionary runs and consistently found circuits that produced oscillations matching the main characteristic observed in experimental recordings. While most of the successful solutions shared common mechanisms, the polarity and weight of the synapses were not always the same. Each of the different solutions represents a configuration capable of generating locomotion-like intrinsic oscillations. This insight can be used to propose experiments on the living organism that test the hypotheses generated by the different solutions. Analysis of successful networks suggested roles for the known motorneurons that aligned well with experimental evidence. It also suggested a role for the AS-class, which has been almost entirely ignored in the study of C. elegans locomotion. In the majority of evolved circuits, motorneuron AS was fundamental to both the generation of oscillations and to the dorsoventral antiphase coordination. We also found that in most of the solutions the AS-class was bistable, while the B- and A-class were not. This is different from what previous models of locomotion had proposed thus far. In addition to providing an existence proof for the possibility of intrinsic oscillations in the ventral cord, we suggest a series of testable hypotheses about its operation. More generally, we show the feasibility and fruitfulness of a methodology to study behavior from a connectome, while neurophysiological properties are still missing.

Xu X et al. (2005) FEBS Lett "Linking integrin to IP(3) signaling is important for ovulation in Caenorhabditis elegans."

Lee M, Shih HY, Seo S, Xu X, Ahn J, Lee D

[FEBS Lett, 2005]

Signals from germ and myoepithelial sheath cells initiate ovulation in Caenorhabditis elegans. The coordinated dilation and contraction of spermatheca lead to subsequent fertilization of oocyte. Either the dominant negative mutant pat-3 beta integrin or disruption of talin expression block ovulation [Cram, E.J., Clark, S.G. and Schwarzbauer, J.E. (2003) Talin loss-of-function uncovers roles in cell contractility and migration in C. elegans. J. Cell. Sci. 116, 3871-3878; Lee, M., Cram, E.J., Shen, B. and Schwarzbauer, J.E. (2001) Role of beta pat-3 integrins in development and function of Caenorhabditis elegans muscles and gonads. J. Biol. Chem. 276, 36404-36410], suggesting that the interaction between the cell and the extracellular matrix (ECM) is also important for ovulation. Here, we report that integrin plays an essential role in fertility via IP(3) signaling. Sterility caused by RNAi of pat-3 and ECM molecules was suppressed by increased IP(3) signaling. Our data suggest that the cell-ECM interaction controls ovulation via IP(3) signaling.

Zhang SG et al. (2022) Nonlinear Dynamics Psychol Life Sci "Dynamic Markers for Chaotic Motion in C. elegans."

Singhvi A, Hastings HM, Susman KM, Zhang SG, Magnes J

[Nonlinear Dynamics Psychol Life Sci, 2022]

We describe the locomotion of Caenorhabditis elegans (C. elegans) using nonlinear dynamics. C. elegans is a commonly studied model organism based on ease of maintenance and simple neurological structure. In contrast to traditional microscopic techniques, which require constraining motion to a 2D microscope slide, dynamic diffraction allows the observation of locomotion in 3D as a time series of the intensity at a single point in the diffraction pattern. The electric field at any point in the far-field diffraction pattern is the result of a superposition of the electric fields bending around the worm. As a result, key features of the motion can be recovered by analyzing the intensity time series. One can now apply modern nonlinear techniques; embedding and recurrence plots, providing valuable insight for visualizing and comparing data sets. We found significant markers of low-dimensional chaos. Next, we implemented a minimal biomimetic simulation of the central pattern generator of C. elegans with FitzHugh-Nagumo neurons, which exhibits undulatory oscillations similar to those of the real C. elegans. Finally, we briefly describe the construction of a biomimetic version of the Izquierdo and Beer robotic worm using Keener's implementation of the Nagumo et al. circuit.

Alicea, Bradly et al. (2015) International Worm Meeting "An experimental evolution model of C. Elegans adaptability."

Schroeder, Nathan, Androwski, Rebecca, Alicea, Bradly

[International Worm Meeting, 2015]

While the genetic architecture of C. elegans is well-studied, the adaptability of various strains and their reproductive fitness is less understood. To address this, an experimental-based model will allow for characterization of C. elegans adaptability amongst strains which may exhibit low reproductive potential and/or survivability under selection. Two experimental approaches representing within- and between-generation survivability (preconditioning and experimental evolution, respectively) will allow survivability to be assessed. Preconditioning [1] assesses adaptability within a generation using environmental selection, while experimental evolution [2] assesses adaptability via cross-generational artificial selection. For a given strain, populations grown from single founder individuals are repeatedly subject to genetic drift and then selected for fecundity (largest brood size). These results demonstrate how specific genotypes exhibit robustness in the face of adaptive constraints.Biological adaptability involves both survivability and reproductive fitness. Survivability is the degree to which a single founder worm can survive and produce viable clones (e.g. the number of generations constituting a single genealogy). Reproductive fitness is the mean population size for a given genealogy. In strains with high survivability, founder populations with high reproductive fitness should also generate subsequent founder populations with a high degree of survivability. Strains with high reproductive fitness but low overall progeny sizes may also exhibit high adaptability if selection results enhances adaptation to varying environmental conditions. While this model does not control for stochastic effects and demographic constraints [3], it does allow for genealogies with consistently high survivability [4].1. Calabrese, E.J. et.al, Tox App Pharm, 222(1), 122-128 (2007).2. Kawecki, T.J. et.al, Trends Ecol Evol, 27(10), 547-560 (2012).3. Szendro, I.G. et.al, PNAS, 110(2), 571-576 (2012).4. Wahl, L.M., Krakauer, D.C., Genetics, 156(3), 1437-1448 (2000).

Mullen, Greg et al. (2011) International Worm Meeting "UNC-41/stonin functions with AP2 to recycle synaptic vesicles in C. elegans."

Gu, Mingyu, Mathews, Ellie, Mullen, Greg, McManus, John, Hobson, Robert, Jorgensen, Erik, Watanabe, Shigeki, Rand, Jim, Grundahl, Kiely

[International Worm Meeting, 2011]

The recycling of synaptic vesicles requires the recovery of vesicle proteins and membrane. Stonin 2 is a mammalian synaptic protein that is thought to act as an adaptor to recruit the synaptic vesicle protein synaptotagmin to sites of synaptic vesicle endocytosis (the Drosophila stonin ortholog is STNB). To characterize the role of stonins in synaptic vesicle endocytosis, we examined unc-41 mutants; the unc-41 locus encodes the stonin/STNB ortholog in C. elegans. The unc-41 gene encodes two protein isoforms that are differentially expressed in the C. elegans nervous system: UNC-41A is expressed in all neurons, while UNC-41B is expressed in a subset of neurons, including the GABAergic motorneurons in the ventral nerve cord. The UNC-41 proteins are localized to synapses, similar to the pattern seen with SNT-1. We examined the synaptic localization of GFP-tagged SNT-1 in unc-41 mutants. Consistent with studies in Drosophila, tagged synaptotagmin is dimmer and mislocalized in unc-41 mutants, and fluorescence is also observed in non-synaptic regions such as commissures. In contrast, GFP::UNC-41 is properly localized in snt-1 mutants, demonstrating a unidirectional relationship for localization. Ultrastructural analysis indicates that unc-41 mutants exhibit a defect in membrane retrieval: synaptic vesicle numbers are reduced by 50% compared to wild type. We conclude that UNC-41 is required to recruit synaptotagmin and recover membrane during synaptic vesicle endocytosis. apm-2 mutants (pka dpy-23), lacking the m2 subunit of AP2, exhibit a similar deficit in synaptic vesicle endocytosis. Because in mammals, both m2 and stonin 2 can bind synaptotagmin, we considered the possibility that these proteins carried out overlapping functions in C. elegans. However, nematodes lacking both UNC-41 and m2 (unc-41 apm-2 double mutants) exhibit a decrease in synaptic vesicle number comparable to either single mutant. Our data suggest that UNC-41 and m2 function in the same pathway for synaptic vesicle membrane recycling. (Supported by NIH grants NS034307 to E.J. and NS033187 and GM059642 to J.R.).