The 2015 whole-body simulation of chemotaxis in the nematode Caenorhabditis elegans (Soh, Suzuki, Kurita and Tsuji) accounted for the animal's gradient-climbing behavior with interneurons that compute chemical gradients internally, from the head-bending angle and the second temporal derivative of concentration, but its network parameters were set manually and by numerical search rather than by any optimization grounded in the information the real worm has; in the companion neural-network paper of the same conference (Sakamoto, Soh, Suzuki, Kurita and Tsuji), and again in the authors' 2018 follow-up, the corresponding network was instead fitted by supervised backpropagation through time against gradient targets that the animal itself cannot measure. The open question is whether this account is biologically plausible: whether the interneuron network, when optimized automatically under naturalistic constraints — using only locally sensed concentration changes at the nose tip and body proprioceptive signals, with a behavioral objective such as maximizing the chemotaxis index — still produces faithful internal gradient estimates and a functional specialization among interneurons that arises from the optimization itself and can be attributed to identified neurons, and whether real neural computation is direct gradient calculation or richer distributed or internal-state dynamics, under locomotion generation and mechanotransduction that are biologically realistic rather than prescribed. The authors' 2018 follow-up resolved the computational feasibility of local-input gradient computation but still trained on teacher signals; behavior-level evolution has been demonstrated only for a sub-strategy (klinotaxis), leaving the full question open.

Background

The roundworm Caenorhabditis elegans performs chemotaxis — directed movement up or down a chemical concentration gradient — using two interleaved behavioral strategies: the pirouette (a reversal followed by a sharp reorientation, triggered by worsening conditions along the direction of travel) and the weathervane response (a gradual curving toward higher concentration during forward motion). Behavioral experiments (Pierce-Shimomura, Morse and Lockery 1999; Iino and Yoshida 2009) established that the pirouette rate tracks the gradient component parallel to the direction of travel while the curving rate of weathervane tracks the perpendicular component. Because the worm's main salt-sensing neurons, the left–right pair ASEL and ASER located together at the nose tip, sample concentration at essentially a single point, the nervous system cannot measure a spatial gradient directly by comparing two sensors; it must infer both gradient components from the temporal history of local concentration together with body configuration. The worm's connectome — the complete wiring diagram of its 302 neurons (White et al. 1986) — makes it the leading system for asking how such computation might be implemented, and optogenetic experiments (Kocabas et al. 2012) showed that symmetric activation of the interneuron pair AIY changes pirouette frequency while asymmetric activation changes curving, suggesting interneurons indeed carry gradient-related signals. A separate modeling tradition evolved small or connectome-based networks for klinotaxis (the weathervane component) with fitness-based evolutionary algorithms and purely local sensory input (Izquierdo and Lockery 2010; Izquierdo and Beer 2013), but these treated only gradual curving, not the pirouette, and did not couple the full body mechanics. Soh, Suzuki, Kurita and Tsuji (2015) built the first simulation combining a whole-body multibody model of the worm (a linked-segment rigid-body simulation whose motion follows the Newton–Euler equations of rigid-body dynamics) with an ASE-to-interneuron network — described independently as three layers of interneurons — that outputs the probabilities of selecting pirouette, weathervane or random-walk movements, and in which the gradient of the attractant is determined from the head-bending angle and the second temporal derivative of concentration. The locomotion literature the paper cites is the central-pattern-generator (CPG) and stretch-receptor account of nematode movement — a CPG being an oscillatory neural circuit producing rhythmic undulation and stretch receptors being proprioceptive neurons sensing body bending — but the published description of the model does not specify the waveform or the transduction characteristics actually used. The network's parameters were not obtained under the information constraints the animal faces: an independent review of the model states that 'their parameter tuning was done manually and thus may not represent the natural C. elegans features'. Supervised fitting of the same group's connectome-based network appears in the companion paper of the same conference (Sakamoto, Soh, Suzuki, Kurita and Tsuji 2015), where 'the parameters of the neural network model were adjusted using the backpropagation through time (BPTT) algorithm' and the network 'was verified for its ability to generate temporal and spatial gradients', with neuron-ablation simulations exhibiting 'the same trends as the biological experiment' — a route that presupposes gradient target signals instead of deriving them from the animal's own sensory input. In either case the resulting parameter set is only one of many possible solutions and its biological plausibility is uncertain; locomotion also remains simplified, since the 2018 follow-up prescribes body motion by a sinusoidal function of the joint angles and explicitly ignores the small random wriggling of the nose tip that modulates real sensory input, and nonlinear, time-delayed proprioceptive mechanotransduction has not been incorporated into the chemotaxis loop.

Problem Statement

Determine whether the gradient-computing account of C. elegans chemotaxis embodied in the whole-body simulation of Soh et al. (2015) is biologically plausible. Specifically: (1) when the interneuron network's parameters (connection weights and sigmoid parameters) are optimized automatically under naturalistic constraints — using only information available to the real worm, namely the locally sensed time course of concentration at the nose tip and body/proprioceptive signals, with a behavioral objective such as maximizing the chemotaxis index (the standard performance measure for gradient climbing, defined as (Tin−Tout)/Ttotal(T_{\mathrm{in}} - T_{\mathrm{out}})/T_{\mathrm{total}}, where TinT_{\mathrm{in}} and ToutT_{\mathrm{out}} are the times spent inside and outside a radius of 2/π\sqrt{2/\pi} cm around the attractant peak), rather than by manual tuning or by supervised fitting against gradient targets — does the network still generate accurate internal estimates of the chemical gradients parallel and perpendicular to the direction of travel, where accurate means matching the true gradients of the simulated environment? Global quantities such as the true gradient field and the peak location are available for evaluating the resulting network and for scoring the behavioral objective, but they are not available to the network as inputs or as fitting targets. And does a functional specialization among interneurons — a division of labour in which distinct interneurons come to represent the gradient components parallel and perpendicular to the direction of travel — arise under such optimization and admit attribution to identified interneurons, rather than being stipulated by the network architecture, given that in the 2018 network this assignment was imposed as an assumption and documented parameter redundancy limited per-neuron attribution? (2) Is the model's assumption that interneurons directly calculate the chemical gradients correct for the actual animal, or does the real neural computation involve more complex or distributed dynamics, such as the persistent internal states implicated by recent state-switching analyses? (3) Do these conclusions depend on the simplified locomotion and proprioception of this modeling line — for instance body motion prescribed by a sinusoidal function, which ignores the nose-tip wriggling that modulates the actual sensory input — and do they still hold when locomotion generation and mechanotransduction are made biologically realistic, including nonlinear and time-delayed proprioceptive feedback? Part (2) is about the actual animal rather than the model, so the simulation study cannot settle it; part (3) concerns whether the conclusions hold under biologically realistic locomotion and mechanotransduction. Note that a negative answer counts only as a bounded claim about the families the study enumerates and exhausts: the failure of one particular optimizer, objective or network instantiation to produce such representations does not by itself establish that they cannot arise under naturalistic optimization, and the general question remains open for the optimizers, objectives and network instantiations outside those families.

References

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