Evolution and analysis of minimal neural circuits for klinotaxis in Caenorhabditis elegans

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.

C. elegans foraging as a model for understanding the neuronal basis of decision-making

Animals have evolved to seek, select, and exploit food sources in their environment. Collectively termed foraging, these ubiquitous behaviors are necessary for animal survival. As a foundation for understanding foraging, behavioral ecologists established early theoretical and mathematical frameworks which have been subsequently refined and supported by field and laboratory studies of foraging animals. These simple models sought to explain how animals decide which strategies to employ when locating food, what food items to consume, and when to explore the environment for new food sources. These foraging decisions involve integration of prior experience with multimodal sensory information about the animal's current environment and internal state. We suggest that the nematode Caenorhabditis elegans is well-suited for a high-resolution analysis of complex goal-oriented behaviors such as foraging. We focus our discussion on behavioral studies highlighting C. elegans foraging on bacteria and summarize what is known about the underlying neuronal and molecular pathways. Broadly, we suggest that this simple model system can provide a mechanistic understanding of decision-making and present additional avenues for advancing our understanding of complex behavioral processes.

Neuronal sensorimotor integration guiding salt concentration navigation in Caenorhabditis elegans

Animals navigate their environment by manipulating their movements and adjusting their trajectory which requires a sophisticated integration of sensory data with their current motor status. Here, we utilize the nematode Caenorhabditis elegans to explore the neural mechanisms of processing the sensory and motor information for navigation. We developed a microfluidic device which allows animals to freely move their heads while receiving temporal NaCl stimuli. We found that C. elegans regulates neck bending direction in response to temporal NaCl concentration changes in a way which is consistent with a C. elegans' navigational strategy which regulates traveling direction toward preferred NaCl concentrations. Our analysis also revealed that the activity of a neck motor neuron is significantly correlated with neck bending and activated by the decrease in NaCl concentration in a phase-dependent manner. By combining the analysis of behavioral and neural response to NaCl stimuli and optogenetic perturbation experiments, we revealed that NaCl decrease during ventral bending activates the neck motor neuron which counteracts ipsilateral bending. Simulations further suggest that this phase-dependent response of neck motor neurons can facilitate curving toward preferred salt concentrations.

Sleep is required to consolidate odor memory and remodel olfactory synapses

Animals with complex nervous systems demand sleep for memory consolidation and synaptic remodeling. Here, we show that, although the Caenorhabditis elegans nervous system has a limited number of neurons, sleep is necessary for both processes. In addition, it is unclear if, in any system, sleep collaborates with experience to alter synapses between specific neurons and whether this ultimately affects behavior. C. elegans neurons have defined connections and well-described contributions to behavior. We show that spaced odor-training and post-training sleep induce long-term memory. Memory consolidation, but not acquisition, requires a pair of interneurons, the AIYs, which play a role in odor-seeking behavior. In worms that consolidate memory, both sleep and odor conditioning are required to diminish inhibitory synaptic connections between the AWC chemosensory neurons and the AIYs. Thus, we demonstrate in a living organism that sleep is required for events immediately after training that drive memory consolidation and alter synaptic structures.

An intrinsic oscillator underlies visual navigation in ants

Many insects display lateral oscillations while moving, but how these oscillations are produced and participate in visual navigation remains unclear. Here, we show that visually navigating ants continuously display regular lateral oscillations coupled with variations of forward speed that strongly optimize the distance covered while simultaneously enabling them to scan left and right directions. This pattern of movement is produced endogenously and conserved across navigational contexts in two phylogenetically distant ant species. Moreover, the oscillations' amplitude can be modulated by both innate or learnt visual cues to adjust the exploration/exploitation balance to the current need. This lower-level motor pattern thus drastically reduces the degree of freedom needed for higher-level strategies to control behavior. The observed dynamical signature readily emerges from a simple neural circuit model of the insect's conserved pre-motor area known as the lateral accessory lobe, offering a surprisingly simple but effective neural control and endorsing oscillation as a core, ancestral way of moving in insects.

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.

Codimension-2 parameter space structure of continuous-time recurrent neural networks

If we are ever to move beyond the study of isolated special cases in theoretical neuroscience, we need to develop more general theories of neural circuits over a given neural model. The present paper considers this challenge in the context of continuous-time recurrent neural networks (CTRNNs), a simple but dynamically universal model that has been widely utilized in both computational neuroscience and neural networks. Here, we extend previous work on the parameter space structure of codimension-1 local bifurcations in CTRNNs to include codimension-2 local bifurcation manifolds. Specifically, we derive the necessary conditions for all generic local codimension-2 bifurcations for general CTRNNs, specialize these conditions to circuits containing from one to four neurons, illustrate in full detail the application of these conditions to example circuits, derive closed-form expressions for these bifurcation manifolds where possible, and demonstrate how this analysis allows us to find and trace several global codimension-1 bifurcation manifolds that originate from the codimension-2 bifurcations.

Oscillators and servomechanisms in orientation and navigation, and sometimes in cognition

Navigational mechanisms have been characterized as servomechanisms. A navigational servomechanism specifies a goal state to strive for. Discrepancies between the perceived current state and the goal state specify error. Servomechanisms adjust the course of travel to reduce the error. I now add that navigational servomechanisms work with oscillators, periodic movements of effectors that drive locomotion. I illustrate this concept selectively over a vast range of scales of travel from micrometres in bacteria to thousands of kilometres in sea turtles. The servomechanisms differ in sophistication, with some interrupting forward motion occasionally or changing travel speed in kineses and others adjusting the direction of travel in taxes. I suggest that in other realms of life as well, especially in cognition, servomechanisms work with oscillators.

Reinforcement Learning for Central Pattern Generation in Dynamical Recurrent Neural Networks

Lifetime learning, or the change (or acquisition) of behaviors during a lifetime, based on experience, is a hallmark of living organisms. Multiple mechanisms may be involved, but biological neural circuits have repeatedly demonstrated a vital role in the learning process. These neural circuits are recurrent, dynamic, and non-linear and models of neural circuits employed in neuroscience and neuroethology tend to involve, accordingly, continuous-time, non-linear, and recurrently interconnected components. Currently, the main approach for finding configurations of dynamical recurrent neural networks that demonstrate behaviors of interest is using stochastic search techniques, such as evolutionary algorithms. In an evolutionary algorithm, these dynamic recurrent neural networks are evolved to perform the behavior over multiple generations, through selection, inheritance, and mutation, across a population of solutions. Although, these systems can be evolved to exhibit lifetime learning behavior, there are no explicit rules built into these dynamic recurrent neural networks that facilitate learning during their lifetime (e.g., reward signals). In this work, we examine a biologically plausible lifetime learning mechanism for dynamical recurrent neural networks. We focus on a recently proposed reinforcement learning mechanism inspired by neuromodulatory reward signals and ongoing fluctuations in synaptic strengths. Specifically, we extend one of the best-studied and most-commonly used dynamic recurrent neural networks to incorporate the reinforcement learning mechanism. First, we demonstrate that this extended dynamical system (model and learning mechanism) can autonomously learn to perform a central pattern generation task. Second, we compare the robustness and efficiency of the reinforcement learning rules in relation to two baseline models, a random walk and a hill-climbing walk through parameter space. Third, we systematically study the effect of the different meta-parameters of the learning mechanism on the behavioral learning performance. Finally, we report on preliminary results exploring the generality and scalability of this learning mechanism for dynamical neural networks as well as directions for future work.

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.

Modelling learning in C. elegans chemosensory and locomotive circuitry for T-maze navigation

Recently, a new type of Caenorhabditis elegans associative learning was reported, where nematodes learn to reach a target arm in an empty T‐maze, after they have successfully located reward (food) in the same side arm of a similar, baited, training maze. Here, we present a simplified mathematical model of C. elegans chemosensory and locomotive circuitry that replicates C. elegans navigation in a T‐maze and predicts the underlying mechanisms generating maze learning. Based on known neural circuitry, the model circuit responds to food‐released chemical cues by modulating motor neuron activity that drives simulated locomotion. We show that, through modulation of interneuron activity, such a circuit can mediate maze learning by acquiring a turning bias, even after a single training session. Simulated nematode maze navigation during training conditions in food‐baited mazes and during testing conditions in empty mazes is validated by comparing simulated behaviour with new experimental video data, extracted through the implementation of a custom‐made maze tracking algorithm. Our work provides a mathematical framework for investigating the neural mechanisms underlying this novel learning behaviour in C. elegans. Model results predict neuronal components involved in maze and spatial learning and identify target neurons and potential neural mechanisms for future experimental investigations into this learning behaviour.

Plasticity in gustatory and nociceptive neurons controls decision making in C. elegans salt navigation

A conventional understanding of perception assigns sensory organs the role of capturing the environment. Better sensors result in more accurate encoding of stimuli, allowing for cognitive processing downstream. Here we show that plasticity in sensory neurons mediates a behavioral switch in C. elegans between attraction to NaCl in naïve animals and avoidance of NaCl in preconditioned animals, called gustatory plasticity. Ca²⁺ imaging in ASE and ASH NaCl sensing neurons reveals multiple cell-autonomous and distributed circuit adaptation mechanisms. A computational model quantitatively accounts for observed behaviors and reveals roles for sensory neurons in the control and modulation of motor behaviors, decision making and navigational strategy. Sensory adaptation dynamically alters the encoding of the environment. Rather than encoding the stimulus directly, therefore, we propose that these C. elegans sensors dynamically encode a context-dependent value of the stimulus. Our results demonstrate how adaptive sensory computation can directly control an animal’s behavioral state.

Martijn Dekkers and Felix Salfelder et al. combine experimental approaches and mathematical modeling to determine the contribution of the two main NaCl sensory neurons (termed ASEL and ASER) and the nociceptive neurons (termed ASH) in C. elegans to the context-dependent switching between NaCl attraction and avoidance. Their results show that regulated sensitivity of these sensory neurons to NaCl allows the animal to dynamically modulate its behavioral response and suggest a role for sensory modulation in balancing exploration and exploitation during foraging.

Social Integrating Robots Suggest Mitigation Strategies for Ecosystem Decay

We develop here a novel hypothesis that may generate a general research framework of how autonomous robots may act as a future contingency to counteract the ongoing ecological mass extinction process. We showcase several research projects that have undertaken first steps to generate the required prerequisites for such a technology-based conservation biology approach. Our main idea is to stabilise and support broken ecosystems by introducing artificial members, robots, that are able to blend into the ecosystem's regulatory feedback loops and can modulate natural organisms' local densities through participation in those feedback loops. These robots are able to inject information that can be gathered using technology and to help the system in processing available information with technology. In order to understand the key principles of how these robots are capable of modulating the behaviour of large populations of living organisms based on interacting with just a few individuals, we develop novel mathematical models that focus on important behavioural feedback loops. These loops produce relevant group-level effects, allowing for robotic modulation of collective decision making in social organisms. A general understanding of such systems through mathematical models is necessary for designing future organism-interacting robots in an informed and structured way, which maximises the desired output from a minimum of intervention. Such models also help to unveil the commonalities and specificities of the individual implementations and allow predicting the outcomes of microscopic behavioural mechanisms on the ultimate macroscopic-level effects. We found that very similar models of interaction can be successfully used in multiple very different organism groups and behaviour types (honeybee aggregation, fish shoaling, and plant growth). Here we also report experimental data from biohybrid systems of robots and living organisms. Our mathematical models serve as building blocks for a deep understanding of these biohybrid systems. Only if the effects of autonomous robots onto the environment can be sufficiently well predicted can such robotic systems leave the safe space of the lab and can be applied in the wild to be able to unfold their ecosystem-stabilising potential.

Movements, embodiment and the emergence of decisions. Insights from insect navigation

We readily infer that animals make decisions, but what this implies is usually not clearly defined. The notion of 'decision-making' ultimately stems from human introspection, and is thus loaded with anthropomorphic assumptions. Notably, the decision is made internally, is based on information, and precedes the goal directed behaviour. Also, making a decision implies that 'something' did it, thus hints at the presence of a cognitive mind, whose existence is independent of the decision itself. This view may convey some truth, but here I take the opposite stance. Using examples from research in insect navigation, this essay highlights how apparent decisions can emerge without a brain, how actions can precede information or how sophisticated goal directed behaviours can be implemented without neural decisions. This perspective requires us to shake off the idea that behaviour is a consequence of the brain; and embrace the concept that movements arise from - as much as participate in - distributed interactions between various computational centres - including the body - that reverberate in closed-loop with the environment. From this perspective we may start to picture how a cognitive mind can be the consequence, rather than the cause, of such neural and body movements.

Chemosensory signal transduction in Caenorhabditis elegans

Chemosensory neurons translate perception of external chemical cues, including odorants, tastants, and pheromones, into information that drives attraction or avoidance motor programs. In the laboratory, robust behavioral assays, coupled with powerful genetic, molecular and optical tools, have made Caenorhabditis elegans an ideal experimental system in which to dissect the contributions of individual genes and neurons to ethologically relevant chemosensory behaviors. Here, we review current knowledge of the neurons, signal transduction molecules and regulatory mechanisms that underlie the response of C. elegans to chemicals, including pheromones. The majority of identified molecules and pathways share remarkable homology with sensory mechanisms in other organisms. With the development of new tools and technologies, we anticipate that continued study of chemosensory signal transduction and processing in C. elegans will yield additional new insights into the mechanisms by which this animal is able to detect and discriminate among thousands of chemical cues with a limited sensory neuron repertoire.

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.

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.

Can Signal Delay be Functional? Including Delay in Evolved Robot Controllers

Engineers, control theorists, and neuroscientists often view the delay imposed by finite signal propagation velocities as a problem that needs to be compensated for or avoided. In this article, we consider the alternative possibility that in some cases, signal delay can be used functionally, that is, as an essential component of a cognitive system. To investigate this idea, we evolve a minimal robot controller to solve a basic stimulus-distinction task. The controller is constrained so that the solution must utilize a delayed recurrent signal. Different from previous evolutionary robotics studies, our controller is modeled using delay differential equations, which (unlike the ordinary differential equations of conventional continuous-time recurrent neural networks) can accurately capture delays in signal propagation. We analyze the evolved controller and its interaction with its environment using classical dynamical systems techniques. The analysis shows what kinds of invariant sets underlie the various successful and unsuccessful performances of the robot, and what kinds of bifurcations produce these invariant sets. In the second phase of our analysis, we turn our attention to the parameter θ, which describes the amount of signal delay included in the model. We show how the delay destabilizes certain attractors that would exist if there were no delay and creates other stable attractors, resulting in an agent that performs well at the target task.

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.

A Gate-and-Switch Model for Head Orientation Behaviors in Caenorhabditis elegans

The nervous system seamlessly integrates perception and action. This ability is essential for stable representation of and appropriate responses to the external environment. How the sensorimotor integration underlying this ability occurs at the level of individual neurons is of keen interest. In Caenorhabditis elegans, RIA interneurons receive input from sensory pathways and have reciprocal connections with head motor neurons. RIA simultaneously encodes both head orientation and sensory stimuli, which may allow it to integrate these two signals to detect the spatial distribution of stimuli across head sweeps and generate directional head responses. Here, we show that blocking synaptic release from RIA disrupts head orientation behaviors in response to unilaterally presented stimuli. We found that sensory encoding in RIA is gated according to head orientation. This dependence on head orientation is independent of motor encoding in RIA, suggesting a second, posture-dependent pathway upstream of RIA. This gating mechanism may allow RIA to selectively attend to stimuli that are asymmetric across head sweeps. Attractive odor removal during head bends triggers rapid head withdrawal in the opposite direction. Unlike sensory encoding, this directional response is dependent on motor inputs to and synaptic output from RIA. Together, these results suggest that RIA is part of a sensorimotor pathway that is dynamically regulated according to head orientation at two levels: the first is a gate that filters sensory representations in RIA, and the second is a switch that routes RIA synaptic output to dorsal or ventral head motor neurons.

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 excitatory ventral cord motor neurons derive rhythm for body undulation

The intrinsic oscillatory activity of central pattern generators underlies motor rhythm. We review and discuss recent findings that address the origin of Caenorhabditis elegans motor rhythm. These studies propose that the A- and mid-body B-class excitatory motor neurons at the ventral cord function as non-bursting intrinsic oscillators to underlie body undulation during reversal and forward movements, respectively. Proprioception entrains their intrinsic activities, allows phase-coupling between members of the same class motor neurons, and thereby facilitates directional propagation of undulations. Distinct pools of premotor interneurons project along the ventral nerve cord to innervate all members of the A- and B-class motor neurons, modulating their oscillations, as well as promoting their bi-directional coupling. The two motor sub-circuits, which consist of oscillators and descending inputs with distinct properties, form the structural base of dynamic rhythmicity and flexible partition of the forward and backward motor states. These results contribute to a continuous effort to establish a mechanistic and dynamic model of the C. elegans sensorimotor system. C. elegans exhibits rich sensorimotor functions despite a small neuron number. These findings implicate a circuit-level functional compression. By integrating the role of rhythm generation and proprioception into motor neurons, and the role of descending regulation of oscillators into premotor interneurons, this numerically simple nervous system can achieve a circuit infrastructure analogous to that of anatomically complex systems. C. elegans has manifested itself as a compact model to search for general principles of sensorimotor behaviours.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.

A programmable platform for sub-second multichemical dynamic stimulation and neuronal functional imaging in C. elegans

Caenorhabditis elegans (C. elegans) is a prominent model organism in neuroscience, as its small stereotyped nervous system offers unique advantages for studying neuronal circuits at the cellular level. Characterizing temporal dynamics of neuronal circuits is essential to fully understand neuronal processing. Characterization of the temporal dynamics of chemosensory circuits requires a precise and fast method to deliver multiple stimuli and monitor the animal's neuronal activity. Microfluidic platforms have been developed that offer an improved control of chemical delivery compared to manual methods. However, stimulating an animal with multiple chemicals at high speed is still difficult. In this work, we have developed a platform that can deliver any sequence of multiple chemical reagents, at sub-second resolution and without cross-contamination. We designed a network of chemical selectors wherein the chemical selected for stimulation is determined by the set of pressures applied to the chemical reservoirs. Modulation of inlet pressures has been automated to create robust, programmable sequences of subsecond chemical pulses. We showed that stimulation with sequences of different chemicals at the second to sub-second range can generate different neuronal activity patterns in chemosensory neurons; we observed previously unseen neuronal responses to a controlled chemical stimulation. Because of the speed and versatility of stimulus generated, this platform opens new possibilities to investigate neuronal circuits.

Cholinergic Sensorimotor Integration Regulates Olfactory Steering

Sensorimotor integration regulates goal-directed movements. We study the signaling mechanisms underlying sensorimotor integration in C. elegans during olfactory steering, when the sinusoidal movements of the worm generate an in-phase oscillation in the concentration of the sampled odorant. We show that cholinergic neurotransmission encodes the oscillatory sensory response and the motor state of head undulations by acting through an acetylcholine-gated channel and a muscarinic acetylcholine receptor, respectively. These signals converge on two axonal domains of an interneuron RIA, where the sensory-evoked signal suppresses the motor-encoding signal to transform the spatial information of the odorant into the asymmetry between the axonal activities. The asymmetric synaptic outputs of the RIA axonal domains generate a directional bias in the locomotory trajectory. Experience alters the sensorimotor integration to generate specific behavioral changes. Our study reveals how cholinergic neurotransmission, which can represent sensory and motor information in the mammalian brain, regulates sensorimotor integration during goal-directed locomotions.

Modulation of sensory information processing by a neuroglobin in Caenorhabditis elegans

Sensory receptor neurons match their dynamic range to ecologically relevant stimulus intensities. How this tuning is achieved is poorly understood in most receptors. The roundworm Caenorhabditis elegans avoids 21% O₂ and hypoxia and prefers intermediate O₂ concentrations. We show how this O₂ preference is sculpted by the antagonistic action of a neuroglobin and an O₂-binding soluble guanylate cyclase. These putative molecular O₂ sensors confer a sigmoidal O₂ response curve in the URX neurons that has highest slope between 15 and 19% O₂ and approaches saturation when O₂ reaches 21%. In the absence of the neuroglobin, the response curve is shifted to lower O₂ values and approaches saturation at 14% O₂ In behavioral terms, neuroglobin signaling broadens the O₂ preference of Caenorhabditis elegans while maintaining avoidance of 21% O₂ A computational model of aerotaxis suggests the relationship between GLB-5-modulated URX responses and reversal behavior is sufficient to broaden O₂ preference. In summary, we show that a neuroglobin can shift neural information coding leading to altered behavior. Antagonistically acting molecular sensors may represent a common mechanism to sharpen tuning of sensory neurons.

On an analogue signal processing circuit in the Nematode C. elegans

In this work we will work on analogue signal processing in the neural circuit of C. elegans which is able to detect the analogue signals from the environment and produce locomotive behaviours which are in accordance with experiments. The signals in C. elegans are processed in a purely analogue procedure, since no action potential has been recorded in its neural activity. We aim to show how signal processing can be executed in analogue domain in a living creature. In order to do that we will model two different behaviours of C. elegans which are generated in the same network of neurons, klinotaxis behaviour and isothermal tracking. We will implement a Genetic Algorithm to find appropriate sets of parameters of the model. Our contribution is to show how relatively straight forward differential equations can lead to relatively complex and different behaviours.

A Computational Model Based on Multi-Regional Calcium Imaging Represents the Spatio-Temporal Dynamics in a Caenorhabditis elegans Sensory Neuron

Due to the huge number of neuronal cells in the brain and their complex circuit formation, computer simulation of neuronal activity is indispensable to understanding whole brain dynamics. Recently, various computational models have been developed based on whole-brain calcium imaging data. However, these analyses monitor only the activity of neuronal cell bodies and treat the cells as point unit. This point-neuron model is inexpensive in computational costs, but the model is unrealistically simplistic at representing intact neural activities in the brain. Here, we describe a novel three-unit Ordinary Differential Equation (ODE) model based on the neuronal responses derived from a Caenorhabditis elegans salt-sensing neuron. We recorded calcium responses in three regions of the ASER neuron using a simple downstep of NaCl concentration. Our simple ODE model generated from a single recording can adequately reproduce and predict the temporal responses of each part of the neuron to various types of NaCl concentration changes. Our strategy which combines a simple recording data and an ODE mathematical model may be extended to realistically understand whole brain dynamics by computational simulation.

Continuous lateral oscillations as a core mechanism for taxis in Drosophila larvae

Taxis behaviour in Drosophila larva is thought to consist of distinct control mechanisms triggering specific actions. Here, we support a simpler hypothesis: that taxis results from direct sensory modulation of continuous lateral oscillations of the anterior body, sparing the need for ‘action selection’. Our analysis of larvae motion reveals a rhythmic, continuous lateral oscillation of the anterior body, encompassing all head-sweeps, small or large, without breaking the oscillatory rhythm. Further, we show that an agent-model that embeds this hypothesis reproduces a surprising number of taxis signatures observed in larvae. Also, by coupling the sensory input to a neural oscillator in continuous time, we show that the mechanism is robust and biologically plausible. The mechanism provides a simple architecture for combining information across modalities, and explaining how learnt associations modulate taxis. We discuss the results in the light of larval neural circuitry and make testable predictions.

DOI:http://dx.doi.org/10.7554/eLife.15504.001

Modeling the thermotaxis behavior of C.elegans based on the artificial neural network

ASBTRACT This research aims at modeling the thermotaxis behavior of C.elegans which is a kind of nematode with full clarified neuronal connections. Firstly, this work establishes the motion model which can perform the undulatory locomotion with turning behavior. Secondly, the thermotaxis behavior is modeled by nonlinear functions and the nonlinear functions are learned by artificial neural network. Once the artificial neural networks have been well trained, they can perform the desired thermotaxis behavior. Last, several testing simulations are carried out to verify the effectiveness of the model for thermotaxis behavior. This work also analyzes the different performances of the model under different environments. The testing results reveal the essence of the thermotaxis of C.elegans to some extent, and theoretically support the research on the navigation of the crawling robots.

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.

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.

A Circuit for Gradient Climbing in C. elegans Chemotaxis

Animals have a remarkable ability to track dynamic sensory information. For example, the nematode Caenorhabditis elegans can locate a diacetyl odor source across a 100,000-fold concentration range. Here, we relate neuronal properties, circuit implementation, and behavioral strategies underlying this robust navigation. Diacetyl responses in AWA olfactory neurons are concentration and history dependent; AWA integrates over time at low odor concentrations, but as concentrations rise, it desensitizes rapidly through a process requiring cilia transport. After desensitization, AWA retains sensitivity to small odor increases. The downstream AIA interneuron amplifies weak odor inputs and desensitizes further, resulting in a stereotyped response to odor increases over three orders of magnitude. The AWA-AIA circuit drives asymmetric behavioral responses to odor increases that facilitate gradient climbing. The adaptation-based circuit motif embodied by AWA and AIA shares computational properties with bacterial chemotaxis and the vertebrate retina, each providing a solution for maintaining sensitivity across a dynamic range.

Dynamical feature extraction at the sensory periphery guides chemotaxis

Behavioral strategies employed for chemotaxis have been described across phyla, but the sensorimotor basis of this phenomenon has seldom been studied in naturalistic contexts. Here, we examine how signals experienced during free olfactory behaviors are processed by first-order olfactory sensory neurons (OSNs) of the Drosophila larva. We find that OSNs can act as differentiators that transiently normalize stimulus intensity—a property potentially derived from a combination of integral feedback and feed-forward regulation of olfactory transduction. In olfactory virtual reality experiments, we report that high activity levels of the OSN suppress turning, whereas low activity levels facilitate turning. Using a generalized linear model, we explain how peripheral encoding of olfactory stimuli modulates the probability of switching from a run to a turn. Our work clarifies the link between computations carried out at the sensory periphery and action selection underlying navigation in odor gradients.

DOI:http://dx.doi.org/10.7554/eLife.06694.001

Fruit flies are attracted to the smell of rotting fruit, and use it to guide them to nearby food sources. However, this task is made more challenging by the fact that the distribution of scent or odor molecules in the air is constantly changing. Fruit flies therefore need to cope with, and exploit, this variation if they are to use odors as cues.

Odor molecules bind to receptors on the surface of nerve cells called olfactory sensory neurons, and trigger nerve impulses that travel along these cells. While many studies have investigated how fruit flies can distinguish between different odors, less is known about how animals can use variation in the strength of an odor to guide them towards its source.

Optogenetics is a technique that allows neuroscientists to control the activities of individual nerve cells, simply by shining light on to them. Because fruit fly larvae are almost transparent, optogenetics can be used on freely moving animals. Now, Schulze, Gomez-Marin et al. have used optogenetics in these larvae to trigger patterns of activity in individual olfactory sensory neurons that mimic the activity patterns elicited by real odors. These virtual realities were then used to study, in detail, some of the principles that control the sensory navigation of a larva—as it moves using a series of forward ‘runs’ and direction-changing ‘turns’.

Olfactory sensory neurons responded most strongly whenever light levels changed rapidly in strength (which simulated a rapid change in odor concentration). On the other hand, these neurons showed relatively little response to constant light levels (i.e., constant odors). This indicates that the activity of olfactory sensory neurons typically represents the rate of change in the concentration of an odor. An independent study by Kim et al. found that olfactory sensory neurons in adult fruit flies also respond in a similar way.

Schulze, Gomez-Marin et al. went on to show that the signals processed by a single type of olfactory sensory neuron could be used to predict a larva's behavior. Larvae tended to turn less when their olfactory sensory neurons were highly active. Low levels and inhibition of activity in the olfactory sensory neurons had the opposite effect; this promoted turning. It remains to be determined how this relatively simple control principle is implemented by the neural circuits that connect sensory neurons to the parts of a larva's nervous system that are involved with movement.

DOI:http://dx.doi.org/10.7554/eLife.06694.002

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.

Regulation of experience-dependent bidirectional chemotaxis by a neural circuit switch in Caenorhabditis elegans

The nematode Caenorhabditis elegans changes its chemotaxis to NaCl depending on previous experience. At the behavioral level, this chemotactic plasticity is generated by reversing the elementary behaviors for chemotaxis, klinotaxis, and klinokinesis. Here, we report that bidirectional klinotaxis is achieved by the proper use of at least two different neural subcircuits. We simulated an NaCl concentration change by activating an NaCl-sensitive chemosensory neuron in phase with head swing and successfully induced klinotaxis-like curving. The curving direction reversed depending on preconditioning, which was consistent with klinotaxis plasticity under a real concentration gradient. Cell-specific ablation and activation of downstream interneurons revealed that ASER-evoked curving toward lower concentration was mediated by AIY interneurons, whereas curving to the opposite direction was not. These results suggest that the experience-dependent bidirectionality of klinotaxis is generated by a switch between different neural subcircuits downstream of the chemosensory neuron.

Multilevel control of run orientation in Drosophila larval chemotaxis

Chemotaxis is a powerful paradigm to study how orientation behavior is driven by sensory stimulation. Drosophila larvae navigate odor gradients by controlling the duration of their runs and the direction of their turns. Straight runs and wide-amplitude turns represent two extremes of a behavioral continuum. Here we establish that, on average, runs curl toward the direction of higher odor concentrations. We find that the orientation and strength of the local odor gradient perpendicular to the direction of motion modulates the orientation of individual runs in a gradual manner. We discuss how this error-correction mechanism, called weathervaning, contributes to larval chemotaxis. We use larvae with a genetically modified olfactory system to demonstrate that unilateral function restricted to a single olfactory sensory neuron (OSN) is sufficient to direct weathervaning. Our finding that bilateral sensing is not necessary to control weathervaning highlights the role of temporal sampling. A correlational analysis between sensory inputs and behavioral outputs suggests that weathervaning results from low-amplitude head casts implemented without interruption of the run. In addition, we report the involvement of a sensorimotor memory arising from previous reorientation events. Together, our results indicate that larval chemotaxis combines concurrent orientation strategies that involve complex computations on different timescales.

Temporal responses of C. elegans chemosensory neurons are preserved in behavioral dynamics

Animals track fluctuating stimuli over multiple timescales during natural olfactory behaviors. Here, we define mechanisms underlying these computations in Caenorhabditis elegans. By characterizing neuronal calcium responses to rapidly fluctuating odor sequences, we show that sensory neurons reliably track stimulus fluctuations relevant to behavior. AWC olfactory neurons respond to multiple odors with subsecond precision required for chemotaxis, whereas ASH nociceptive neurons integrate noxious cues over several seconds to reach a threshold for avoidance behavior. Each neuron's response to fluctuating stimuli is largely linear and can be described by a biphasic temporal filter and dynamical model. A calcium channel mutation alters temporal filtering and avoidance behaviors initiated by ASH on similar timescales. A sensory G-alpha protein mutation affects temporal filtering in AWC and alters steering behavior in a way that supports an active sensing model for chemotaxis. Thus, temporal features of sensory neurons can be propagated across circuits to specify behavioral dynamics.

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.

The role of multiple chemotactic mechanisms in a model of chemotaxis in C. elegans: different mechanisms are specialised for different environments

Unlike simpler organisms, C. elegans possesses several distinct chemosensory pathways and chemotactic mechanisms. These mechanisms and pathways are individually capable of driving chemotaxis in a chemical concentration gradient. However, it is not understood if they are redundant or co-operate in more sophisticated ways. Here we examine the specialisation of different chemotactic mechanisms in a model of chemotaxis to NaCl. We explore the performance of different chemotactic mechanisms in a range of chemical gradients and show that, in the model, far from being redundant, the mechanisms are specialised both for different environments and for distinct features within those environments. We also show that the chemotactic drive mediated by the ASE pathway is not robust to the presence of noise in the chemical gradient. This problem cannot be solved along the ASE pathway without destroying its ability to drive chemotaxis. Instead, we show that robustness to noise can be achieved by introducing a second, much slower NaCl-sensing pathway. This secondary pathway is simpler than the ASE pathway, in the sense that it can respond to either up-steps or down-steps in NaCl but not both, and could correspond to one of several candidates in the literature which we identify and evaluate. This work provides one possible explanation of why there are multiple NaCl sensing pathways and chemotactic mechanisms in C. elegans: rather than being redundant the different pathways and mechanism are specialised both for the characteristics of different environments and for distinct features within a single environment.

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.