Mechanical reconfiguration mediates swallowing and rejection in Aplysia californica

Full Hill-type muscle model of the I1/I3 retractor muscle complex in Aplysia californica

The coordination of complex behavior requires knowledge of both neural dynamics and the mechanics of the periphery. The feeding system of Aplysia californica is an excellent model for investigating questions in soft body systems' neuromechanics because of its experimental tractability. Prior work has attempted to elucidate the mechanical properties of the periphery by using a Hill-type muscle model to characterize the force generation capabilities of the key protractor muscle responsible for moving Aplysia's grasper anteriorly, the I2 muscle. However, the I1/I3 muscle, which is the main driver of retractions of Aplysia's grasper, has not been characterized. Because of the importance of the musculature's properties in generating functional behavior, understanding the properties of muscles like the I1/I3 complex may help to create more realistic simulations of the feeding behavior of Aplysia, which can aid in greater understanding of the neuromechanics of soft-bodied systems. To bridge this gap, in this work, the I1/I3 muscle complex was characterized using force-frequency, length-tension, and force-velocity experiments and showed that a Hill-type model can accurately predict its force-generation properties. Furthermore, the muscle's peak isometric force and stiffness were found to exceed those of the I2 muscle, and these results were analyzed in the context of prior studies on the I1/I3 complex's kinematics in vivo.

A computational neural model that incorporates both intrinsic dynamics and sensory feedback in the Aplysia feeding network

Studying the nervous system underlying animal motor control can shed light on how animals can adapt flexibly to a changing environment. We focus on the neural basis of feeding control in Aplysia californica. Using the Synthetic Nervous System framework, we developed a model of Aplysia feeding neural circuitry that balances neurophysiological plausibility and computational complexity. The circuitry includes neurons, synapses, and feedback pathways identified in existing literature. We organized the neurons into three layers and five subnetworks according to their functional roles. Simulation results demonstrate that the circuitry model can capture the intrinsic dynamics at neuronal and network levels. When combined with a simplified peripheral biomechanical model, it is sufficient to mediate three animal-like feeding behaviors (biting, swallowing, and rejection). The kinematic, dynamic, and neural responses of the model also share similar features with animal data. These results emphasize the functional roles of sensory feedback during feeding.

Variational and phase response analysis for limit cycles with hard boundaries, with applications to neuromechanical control problems

Motor systems show an overall robustness, but because they are highly nonlinear, understanding how they achieve robustness is difficult. In many rhythmic systems, robustness against perturbations involves response of both the shape and the timing of the trajectory. This makes the study of robustness even more challenging. To understand how a motor system produces robust behaviors in a variable environment, we consider a neuromechanical model of motor patterns in the feeding apparatus of the marine mollusk Aplysia californica (Shaw et al. in J Comput Neurosci 38(1):25-51, 2015; Lyttle et al. in Biol Cybern 111(1):25-47, 2017). We established in (Wang et al. in SIAM J Appl Dyn Syst 20(2):701-744, 2021. https://doi.org/10.1137/20M1344974 ) the tools for studying combined shape and timing responses of limit cycle systems under sustained perturbations and here apply them to study robustness of the neuromechanical model against increased mechanical load during swallowing. Interestingly, we discover that nonlinear biomechanical properties confer resilience by immediately increasing resistance to applied loads. In contrast, the effect of changed sensory feedback signal is significantly delayed by the firing rates' hard boundary properties. Our analysis suggests that sensory feedback contributes to robustness in swallowing primarily by shifting the timing of neural activation involved in the power stroke of the motor cycle (retraction). This effect enables the system to generate stronger retractor muscle forces to compensate for the increased load, and hence achieve strong robustness. The approaches that we are applying to understanding a neuromechanical model in Aplysia, and the results that we have obtained, are likely to provide insights into the function of other motor systems that encounter changing mechanical loads and hard boundaries, both due to mechanical and neuronal firing properties.

How octopus arm muscle contractile properties and anatomical organization contribute to the arm functional specialization

Octopus arms are highly flexible structures capable of complex motions and are used in a wide repertoire of behaviors. Movements are generated by the coordinated summation of innervation signals to packed arrays of muscles oriented in different directions and moving based on their anatomical relationships. In this study, we investigated the interplay between muscle biomechanics and anatomical organization in the Octopus vulgaris arm to elucidate their role in different arm movements. We performed isometric and isotonic force measurements on isolated longitudinal (L) and transverse (T) arm muscles and showed that L has a higher rate of activation and relaxation, lower twitch-to-tetanus ratio, and lower passive tension than T muscles, thus prompting their use as faster and slower muscles, respectively. This points to the use of L in more graded responses, such as those involved in precise actions, and T in intense and sustained actions, such as motion stabilization and posture maintenance. Once activated, the arm muscles exert forces that cause deformations of the entire arm, which are determined by the amount, location, properties and orientation of their fibers. Here, we show that, although continuous, the arm manifests a certain degree of morphological specialization, where the arm muscles have a different aspect ratio along the arm. This possibly supports the functional specialization of arm portion observed in various motions, such as fetching and crawling. Hence, the octopus arm as a whole can be seen as a 'reservoir' of possibilities where different types of motion may emerge at the limb level through the co-option of the muscle contractile properties and structural arrangement.

Dynamical consequences of sensory feedback in a half-center oscillator coupled to a simple motor system

We investigate a simple model for motor pattern generation that combines central pattern generator (CPG) dynamics with a sensory feedback (FB) mechanism. Our CPG comprises a half-center oscillator with conductance-based Morris-Lecar model neurons. Output from the CPG drives a push-pull motor system with biomechanics based on experimental data. A sensory feedback conductance from the muscles allows modulation of the CPG activity. We consider parameters under which the isolated CPG system has either "escape" or "release" dynamics, and we study both inhibitory and excitatory feedback conductances. We find that increasing the FB conductance relative to the CPG conductance makes the system more robust against external perturbations, but more susceptible to internal noise. Conversely, increasing the CPG conductance relative to the FB conductance has the opposite effects. We find that the "closed-loop" system, with sensory feedback in place, exhibits a richer repertoire of behaviors than the "open-loop" system, with motion determined entirely by the CPG dynamics. Moreover, we find that purely feedback-driven motor patterns, analogous to a chain reflex, occur only in the inhibition-mediated system. Finally, for pattern generation systems with inhibition-mediated sensory feedback, we find that the distinction between escape- and release-mediated CPG mechanisms is diminished in the presence of internal noise. Our observations support an anti-reductionist view of neuromotor physiology: Understanding mechanisms of robust motor control requires studying not only the central pattern generator circuit in isolation, but the intact closed-loop system as a whole.

Control for multifunctionality: bioinspired control based on feeding in Aplysia californica

Animals exhibit remarkable feats of behavioral flexibility and multifunctional control that remain challenging for robotic systems. The neural and morphological basis of multifunctionality in animals can provide a source of bioinspiration for robotic controllers. However, many existing approaches to modeling biological neural networks rely on computationally expensive models and tend to focus solely on the nervous system, often neglecting the biomechanics of the periphery. As a consequence, while these models are excellent tools for neuroscience, they fail to predict functional behavior in real time, which is a critical capability for robotic control. To meet the need for real-time multifunctional control, we have developed a hybrid Boolean model framework capable of modeling neural bursting activity and simple biomechanics at speeds faster than real time. Using this approach, we present a multifunctional model of Aplysia californica feeding that qualitatively reproduces three key feeding behaviors (biting, swallowing, and rejection), demonstrates behavioral switching in response to external sensory cues, and incorporates both known neural connectivity and a simple bioinspired mechanical model of the feeding apparatus. We demonstrate that the model can be used for formulating testable hypotheses and discuss the implications of this approach for robotic control and neuroscience.

Computational model of the distributed representation of operant reward memory: combinatoric engagement of intrinsic and synaptic plasticity mechanisms

Operant reward learning of feeding behavior in Aplysia increases the frequency and regularity of biting, as well as biases buccal motor patterns (BMPs) toward ingestion-like BMPs (iBMPs). The engram underlying this memory comprises cells that are part of a central pattern generating (CPG) circuit and includes increases in the intrinsic excitability of identified cells B30, B51, B63, and B65, and increases in B63-B30 and B63-B65 electrical synaptic coupling. To examine the ways in which sites of plasticity (individually and in combination) contribute to memory expression, a model of the CPG was developed. The model included conductance-based descriptions of cells CBI-2, B4, B8, B20, B30, B31, B34, B40, B51, B52, B63, B64, and B65, and their synaptic connections. The model generated patterned activity that resembled physiological BMPs, and implementation of the engram reproduced increases in frequency, regularity, and bias. Combined enhancement of B30, B63, and B65 excitabilities increased BMP frequency and regularity, but not bias toward iBMPs. Individually, B30 increased regularity and bias, B51 increased bias, B63 increased frequency, and B65 decreased all three BMP features. Combined synaptic plasticity contributed primarily to regularity, but also to frequency and bias. B63-B30 coupling contributed to regularity and bias, and B63-B65 coupling contributed to all BMP features. Each site of plasticity altered multiple BMP features simultaneously. Moreover, plasticity loci exhibited mutual dependence and synergism. These results indicate that the memory for operant reward learning emerged from the combinatoric engagement of multiple sites of plasticity.

Soft-surface grasping: radular opening in Aplysia californica

Grasping soft, irregular material is challenging both for animals and robots. The feeding systems of many animals have adapted to this challenge. In particular, the feeding system of the marine mollusk Aplysia californica, a generalist herbivore, allows it to grasp and ingest seaweeds of varying shape, texture and toughness. On the surface of the grasper of A. californica is a structure known as the radula, a thin flexible cartilaginous sheet with fine teeth. Previous in vitro studies suggested that intrinsic muscles, I7, are responsible for opening the radula. Lesioning I7 in vivo does not prevent animals from grasping and ingesting food. New in vitro studies demonstrate that a set of fine muscle fibers on the ventral surface of the radula - the sub-radular fibers (SRFs) - mediate opening movements even if the I7 muscles are absent. Both in vitro and in vivo lesions demonstrate that removing the SRFs leads to profound deficits in radular opening, and significantly reduces feeding efficiency. A theoretical biomechanical analysis of the actions of the SRFs suggests that they induce the radular surface to open around a central crease in the radular surface and to arch the radular surface, allowing it to softly conform to irregular material. A three-dimensional model of the radular surface, based on in vivo observations and magnetic resonance imaging of intact animals, provides support for the biomechanical analysis. These results suggest how a soft grasper can work during feeding, and suggest novel designs for artificial soft graspers.

Robustness, flexibility, and sensitivity in a multifunctional motor control model

Motor systems must adapt to perturbations and changing conditions both within and outside the body. We refer to the ability of a system to maintain performance despite perturbations as "robustness," and the ability of a system to deploy alternative strategies that improve fitness as "flexibility." Different classes of pattern-generating circuits yield dynamics with differential sensitivities to perturbations and parameter variation. Depending on the task and the type of perturbation, high sensitivity can either facilitate or hinder robustness and flexibility. Here we explore the role of multiple coexisting oscillatory modes and sensory feedback in allowing multiphasic motor pattern generation to be both robust and flexible. As a concrete example, we focus on a nominal neuromechanical model of triphasic motor patterns in the feeding apparatus of the marine mollusk Aplysia californica. We find that the model can operate within two distinct oscillatory modes and that the system exhibits bistability between the two. In the "heteroclinic mode," higher sensitivity makes the system more robust to changing mechanical loads, but less robust to internal parameter variations. In the "limit cycle mode," lower sensitivity makes the system more robust to changes in internal parameter values, but less robust to changes in mechanical load. Finally, we show that overall performance on a variable feeding task is improved when the system can flexibly transition between oscillatory modes in response to the changing demands of the task. Thus, our results suggest that the interplay of sensory feedback and multiple oscillatory modes can allow motor systems to be both robust and flexible in a variable environment.

Motor neuronal activity varies least among individuals when it matters most for behavior

How does motor neuronal variability affect behavior? To explore this question, we quantified activity of multiple individual identified motor neurons mediating biting and swallowing in intact, behaving Aplysia californica by recording from the protractor muscle and the three nerves containing the majority of motor neurons controlling the feeding musculature. We measured multiple motor components: duration of the activity of identified motor neurons as well as their relative timing. At the same time, we measured behavioral efficacy: amplitude of grasping movement during biting and amplitude of net inward food movement during swallowing. We observed that the total duration of the behaviors varied: Within animals, biting duration shortened from the first to the second and third bites; between animals, biting and swallowing durations varied. To study other sources of variation, motor components were divided by behavior duration (i.e., normalized). Even after normalization, distributions of motor component durations could distinguish animals as unique individuals. However, the degree to which a motor component varied among individuals depended on the role of that motor component in a behavior. Motor neuronal activity that was essential for the expression of biting or swallowing was similar among animals, whereas motor neuronal activity that was not essential for that behavior varied more from individual to individual. These results suggest that motor neuronal activity that matters most for the expression of a particular behavior may vary least from individual to individual. Shaping individual variability to ensure behavioral efficacy may be a general principle for the operation of motor systems.

The significance of dynamical architecture for adaptive responses to mechanical loads during rhythmic behavior

Many behaviors require reliably generating sequences of motor activity while adapting the activity to incoming sensory information. This process has often been conceptually explained as either fully dependent on sensory input (a chain reflex) or fully independent of sensory input (an idealized central pattern generator, or CPG), although the consensus of the field is that most neural pattern generators lie somewhere between these two extremes. Many mathematical models of neural pattern generators use limit cycles to generate the sequence of behaviors, but other models, such as a heteroclinic channel (an attracting chain of saddle points), have been suggested. To explore the range of intermediate behaviors between CPGs and chain reflexes, in this paper we describe a nominal model of swallowing in Aplysia californica. Depending upon the value of a single parameter, the model can transition from a generic limit cycle regime to a heteroclinic regime (where the trajectory slows as it passes near saddle points). We then study the behavior of the system in these two regimes and compare the behavior of the models with behavior recorded in the animal in vivo and in vitro. We show that while both pattern generators can generate similar behavior, the stable heteroclinic channel can better respond to changes in sensory input induced by load, and that the response matches the changes seen when a load is added in vivo. We then show that the underlying stable heteroclinic channel architecture exhibits dramatic slowing of activity when sensory and endogenous input is reduced, and show that similar slowing with removal of proprioception is seen in vitro. Finally, we show that the distributions of burst lengths seen in vivo are better matched by the distribution expected from a system operating in the heteroclinic regime than that expected from a generic limit cycle. These observations suggest that generic limit cycle models may fail to capture key aspects of Aplysia feeding behavior, and that alternative architectures such as heteroclinic channels may provide better descriptions.

Neuromechanical simulation

The importance of the interaction between the body and the brain for the control of behavior has been recognized in recent years with the advent of neuromechanics, a field in which the coupling between neural and biomechanical processes is an explicit focus. A major tool used in neuromechanics is simulation, which connects computational models of neural circuits to models of an animal's body situated in a virtual physical world. This connection closes the feedback loop that links the brain, the body, and the world through sensory stimuli, muscle contractions, and body movement. Neuromechanical simulations enable investigators to explore the dynamical relationships between the brain, the body, and the world in ways that are difficult or impossible through experiment alone. Studies in a variety of animals have permitted the analysis of extremely complex and dynamic neuromechanical systems, they have demonstrated that the nervous system functions synergistically with the mechanical properties of the body, they have examined hypotheses that are difficult to test experimentally, and they have explored the role of sensory feedback in controlling complex mechanical systems with many degrees of freedom. Each of these studies confronts a common set of questions: (i) how to abstract key features of the body, the world and the CNS in a useful model, (ii) how to ground model parameters in experimental reality, (iii) how to optimize the model and identify points of sensitivity and insensitivity, and (iv) how to share neuromechanical models for examination, testing, and extension by others.

The brain in its body: motor control and sensing in a biomechanical context

Although it is widely recognized that adaptive behavior emerges from the ongoing interactions among the nervous system, the body, and the environment, it has only become possible in recent years to experimentally study and to simulate these interacting systems. We briefly review work on molluscan feeding, maintenance of postural control in cats and humans, simulations of locomotion in lamprey, insect, cat and salamander, and active vibrissal sensing in rats to illustrate the insights that can be derived from studies of neural control and sensing within a biomechanical context. These studies illustrate that control may be shared between the nervous system and the periphery, that neural activity organizes degrees of freedom into biomechanically meaningful subsets, that mechanics alone may play crucial roles in enforcing gait patterns, and that mechanics of sensors is crucial for their function.

Multifunctional pattern-generating circuits

The ability of distinct anatomical circuits to generate multiple behavioral patterns is widespread among vertebrate and invertebrate species. These multifunctional neuronal circuits are the result of multistable neural dynamics and modular organization. The evidence suggests multifunctional circuits can be classified by distinct architectures, yet the activity patterns of individual neurons involved in more than one behavior can vary dramatically. Several mechanisms, including sensory input, the parallel activity of projection neurons, neuromodulation, and biomechanics, are responsible for the switching between patterns. Recent advances in both analytical and experimental tools have aided the study of these complex circuits.

The kinematics of multifunctionality: comparisons of biting and swallowing in Aplysia californica

What are the mechanisms of multifunctionality, i.e. the use of the same peripheral structures for multiple behaviors? We studied this question using the multifunctional feeding apparatus of the marine mollusk Aplysia californica, in which the same muscles mediate biting (an attempt to grasp food) and swallowing (ingestion of food). Biting and swallowing responses were compared using magnetic resonance imaging of intact, behaving animals and a three-dimensional kinematic model. Biting is associated with larger amplitude protractions of the grasper (radula/odontophore) than swallowing, and smaller retractions. Larger biting protractions than in swallowing appear to be due to a more anterior position of the grasper as the behavior begins, a larger amplitude contraction of protractor muscle I2, and contraction of the posterior portion of the I1/I3/jaw complex. The posterior I1/I3/jaw complex may be context-dependent, i.e. its mechanical context changes the direction of the force it exerts. Thus, the posterior of I1/I3 may aid protraction near the peak of biting, whereas the entire I1/I3/jaw complex acts as a retractor during swallowing. In addition, larger amplitude closure of the grasper during swallowing allows an animal to exert more force as it ingests food. These results demonstrate that differential deployment of the periphery can mediate multifunctionality.

Neuromechanics of multifunctionality during rejection in Aplysia californica

How are the same muscles and neurons used to generate qualitatively different behaviors? We studied this question by analyzing the biomechanical and neural mechanisms of rejection responses in the marine mollusk Aplysia californica and compared these mechanisms with those used to generate swallowing responses (Ye et al., 2006). During rejection, the central grasper of the feeding structure closes to push inedible food out of the buccal cavity. This contrasts with swallowing, during which the grasper is open as it moves toward the jaws (protracts). We examined how the shape change of the grasper during rejection mechanically reconfigured the surrounding musculature. Grasper shape change increased the effectiveness of protractor muscle I2. The closed grasper alters the function of another muscle, the hinge, which becomes capable of inducing ventral rotations of rejected material. In contrast, during large-amplitude swallows, the hinge muscle mediates dorsal rotations of ingested material. Finally, after the grasper opens, its change in shape induces a delay in the activation of other surrounding muscles, the I1/I3/jaw complex, whose premature activation would close the halves of the grasper and induce it to pull inedible material back inward. The delay in activation of the I1/I3/jaw complex is partially attributable to identified multiaction neurons B4/B5. The results suggest that multifunctionality emerges from a periphery in which flexible coalitions of muscles may perform different functions in different mechanical contexts and in which neural circuitry is capable of reorganizing to exploit these coalitions by changes in phasing, duration, and intensity of motor neuronal activation.