Scaling of buccal mass growth and muscle activation determine the duration of feeding behaviours in the marine mollusc Aplysia californica.

The mechanical forces experienced during movement and the time constants of muscle activation are important determinants of the durations of behaviours, which may both be affected by size-dependent scaling. The mechanics of slow movements in small animals are dominated by elastic forces and are thus quasistatic (i.e. always near mechanical equilibrium). Muscular forces producing movement and elastic forces resisting movement should scale identically (proportional to mass2/3), leaving the scaling of the time constant of muscle activation to play a critical role in determining behavioural duration. We tested this hypothesis by measuring the duration of feeding behaviours in the marine mollusc Aplysia californica whose body sizes spanned three orders of magnitude. The duration of muscle activation was determined by measuring the time it took for muscles to produce maximum force as A. californica attempted to feed on tethered inedible seaweed, which provided an in vivo approximation of an isometric contraction. The timing of muscle activation scaled with mass0.3. The total duration of biting behaviours scaled identically, with mass0.3, indicating a lack of additional mechanical effects. The duration of swallowing behaviour, however, exhibited a shallower scaling of mass0.17. We suggest that this was due to the allometric growth of the anterior retractor muscle during development, as measured by micro-computed tomography (micro-CT) scans of buccal masses. Consequently, larger A. californica did not need to activate their muscles as fully to produce equivalent forces. These results indicate that muscle activation may be an important determinant of the scaling of behavioural durations in quasistatic systems.

Navigation by magnetic signatures in a realistic model of Earth's magnetic field.

Certain animal species use the Earth's magnetic field (i.e. magnetoreception) alongside their other sensory modalities to navigate long distances that include continents and oceans. It is hypothesized that several animals use geomagnetic parameters, such as field intensity and inclination, to recognize specific locations or regions, potentially enabling migration without a pre-surveyed map. However, it is unknown how animals use geomagnetic information to generate guidance commands, or where in the world this type of strategy would maximize an animal's fitness. While animal experiments have been invaluable in advancing this area, the phenomenon is difficult to studyin vivoorin situ, especially on the global scale where the spatial layout of the geomagnetic field is not constant. Alongside empirical animal experiments, mathematical modeling and simulation are complementary tools that can be used to investigate animal navigation on a global scale, providing insights that can be informative across a number of species. In this study, we present a model in which a simulated animal (i.e. agent) navigates via an algorithm which determines travel heading based on local and goal magnetic signatures (here, combinations of geomagnetic intensity and inclination) in a realistic model of Earth's magnetic field. By varying parameters of the navigation algorithm, different regions of the world can be made more or less reliable to navigate. We present a mathematical analysis of the system. Our results show that certain regions can be navigated effectively using this strategy when these parameters are properly tuned, while other regions may require more complex navigational strategies. In a real animal, parameters such as these could be tuned by evolution for successful navigation in the animal's natural range. These results could also help with developing engineered navigation systems that are less reliant on satellite-based methods.

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.

Use of an invertebrate animal model (Aplysia californica) to develop novel neural interfaces for neuromodulation.

New tools for monitoring and manipulating neural activity have been developed with steadily improving functionality, specificity, and reliability, which are critical both for mapping neural circuits and treating neurological diseases. This review focuses on the use of an invertebrate animal, the marine mollusk Aplysia californica, in the development of novel neurotechniques. We review the basic physiological properties of Aplysia neurons and discuss the specific aspects that make it advantageous for developing novel neural interfaces: First, Aplysia nerves consist only of unmyelinated axons with various diameters, providing a particularly useful model of the unmyelinated C fibers in vertebrates that are known to carry important sensory information, including those that signal pain. Second, Aplysia's neural tissues can last for a long period in an ex vivo experimental setup. This allows comprehensive tests such as the exploration of parameter space on the same nerve to avoid variability between animals and minimize animal use. Third, nerves in large Aplysia can be many centimeters in length, making it possible to easily discriminate axons with different diameters based on their conduction velocities. Aplysia nerves are a particularly good approximation of the unmyelinated C fibers, which are hard to stimulate, record, and differentiate from other nerve fibers in vertebrate animal models using epineural electrodes. Fourth, neurons in Aplysia are large, uniquely identifiable, and electrically compact. For decades, researchers have used Aplysia for the development of many novel neurotechnologies. Examples include high-frequency alternating current (HFAC), focused ultrasound (FUS), optical neural stimulation, recording, and inhibition, microelectrode arrays, diamond electrodes, carbon fiber microelectrodes, microscopic magnetic stimulation and magnetic resonance electrical impedance tomography (MREIT). We also review a specific example that illustrates the power of Aplysia for accelerating technology development: selective infrared neural inhibition of small-diameter unmyelinated axons, which may lead to a translationally useful treatment in the future. Generally, Aplysia is suitable for testing modalities whose mechanism involves basic biophysics that is likely to be similar across species. As a tractable experimental system, Aplysia californica can help the rapid development of novel neuromodulation technologies.

Carbon fiber electrodes for intracellular recording and stimulation.

Objective.To understand neural circuit dynamics, it is critical to manipulate and record many individual neurons. Traditional recording methods, such as glass microelectrodes, can only control a small number of neurons. More recently, devices with high electrode density have been developed, but few of them can be used for intracellular recording or stimulation in intact nervous systems. Carbon fiber electrodes (CFEs) are 8µm-diameter electrodes that can be assembled into dense arrays (pitches ⩾ 80µm). They have good signal-to-noise ratios (SNRs) and provide stable extracellular recordings both acutely and chronically in neural tissuein vivo(e.g. rat motor cortex). The small fiber size suggests that arrays could be used for intracellular stimulation.Approach.We tested CFEs for intracellular stimulation using the large identified and electrically compact neurons of the marine molluskAplysia californica. Neuron cell bodies inAplysiarange from 30µm to over 250µm. We compared the efficacy of CFEs to glass microelectrodes by impaling the same neuron's cell body with both electrodes and connecting them to a DC coupled amplifier.Main results.We observed that intracellular waveforms were essentially identical, but the amplitude and SNR in the CFE were lower than in the glass microelectrode. CFE arrays could record from 3 to 8 neurons simultaneously for many hours, and many of these recordings were intracellular, as shown by simultaneous glass microelectrode recordings. CFEs coated with platinum-iridium could stimulate and had stable impedances over many hours. CFEs not within neurons could record local extracellular activity. Despite the lower SNR, the CFEs could record synaptic potentials. CFEs were less sensitive to mechanical perturbations than glass microelectrodes.Significance.The ability to do stable multi-channel recording while stimulating and recording intracellularly make CFEs a powerful new technology for studying neural circuit dynamics.

Shape versus timing: linear responses of a limit cycle with hard boundaries under instantaneous and static perturbation.

When dynamical systems that produce rhythmic behaviors operate within hard limits, they may exhibit limit cycles with sliding components, that is, closed isolated periodic orbits that make and break contact with a constraint surface. Examples include heel-ground interaction in locomotion, firing rate rectification in neural networks, and stick-slip oscillators. In many rhythmic systems, robustness against external perturbations involves response of both the shape and the timing of the limit cycle trajectory. The existing methods of infinitesimal phase response curve (iPRC) and variational analysis are well established for quantifying changes in timing and shape, respectively, for smooth systems. These tools have recently been extended to nonsmooth dynamics with transversal crossing boundaries. In this work, we further extend the iPRC method to nonsmooth systems with sliding components, which enables us to make predictions about the synchronization properties of weakly coupled stick-slip oscillators. We observe a new feature of the isochrons in a planar limit cycle with hard sliding boundaries: a nonsmooth kink in the asymptotic phase function, originating from the point at which the limit cycle smoothly departs the constraint surface, and propagating away from the hard boundary into the interior of the domain. Moreover, the classical variational analysis neglects timing information and is restricted to instantaneous perturbations. By defining the "infinitesimal shape response curve" (iSRC), we incorporate timing sensitivity of an oscillator to describe the shape response of this oscillator to parametric perturbations. In order to extract timing information, we also develop a "local timing response curve" (lTRC) that measures the timing sensitivity of a limit cycle within any given region. We demonstrate in a specific example that taking into account local timing sensitivity in a nonsmooth system greatly improves the accuracy of the iSRC over global timing analysis given by the iPRC.

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.

Rapid Adaptation to Changing Mechanical Load by Ordered Recruitment of Identified Motor Neurons.

As they interact with their environment and encounter challenges, animals adjust their behavior on a moment-to-moment basis to maintain task fitness. This dynamic process of adaptive motor control occurs in the nervous system, but an understanding of the biomechanics of the body is essential to properly interpret the behavioral outcomes. To study how animals respond to changing task conditions, we used a model system in which the functional roles of identified neurons and the relevant biomechanics are well understood and can be studied in intact behaving animals: feeding in the marine mollusc Aplysia We monitored the motor neuronal output of the feeding circuitry as intact animals fed on uniform food stimuli under unloaded and loaded conditions, and we measured the force of retraction during loaded swallows. We observed a previously undescribed pattern of force generation, which can be explained within the appropriate biomechanical context by the activity of just a few key, identified motor neurons. We show that, when encountering load, animals recruit identified retractor muscle motor neurons for longer and at higher frequency to increase retraction force duration. Our results identify a mode by which animals robustly adjust behavior to their environment, which is experimentally tractable to further mechanistic investigation.

neurotic: Neuroscience Tool for Interactive Characterization.

A software tool for synchronization of video with signals would be of broad general use to behavioral neuroscientists. A new program, called neurotic (NEUROscience Tool for Interactive Characterization), allows users to review and annotate signal data synchronized with video, performs simple initial analyses including signal filtering and spike detection, is easy to use, and supports a variety of file formats. The program also facilitates collaborations by using a portable specification for loading and processing data and retrieving data files from online sources. Two examples are shown in which the software is used to explore experimental datasets with extracellular nerve or muscle recordings and simultaneous video of behavior. The configuration specification for controlling how data are located, loaded, processed, and plotted is also summarized. Algorithms for spike detection and burst detection are demonstrated. This new program could be used in many applications in which behavior and signals need to be analyzed together.

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.

Sensory Feedback Reduces Individuality by Increasing Variability within Subjects.

Behavioral variability is ubiquitous [1-6], yet variability is more than just noise. Indeed, humans exploit their individual motor variability to improve tracing and reaching tasks [7]. What controls motor variability? Increasing the variability of sensory input, or applying force perturbations during a task, increases task variability [8, 9]. Sensory feedback may also increase task-irrelevant variability [9, 10]. In contrast, sensory feedback during locust flight or to multiple cortical areas just prior to task performance decreases variability during task-relevant motor behavior [11, 12]. Thus, how sensory feedback affects both task-relevant and task-irrelevant motor outputs must be understood. Furthermore, since motor control is studied in populations, the effects of sensory feedback on variability must also be understood within and across subjects. For example, during locomotion, each step may vary within and across individuals, even when behavior is normalized by step cycle duration [13]. Our previous work demonstrated that motor components that matter for effective behavior show less individuality [14]. Is sensory feedback the mechanism for reducing individuality? We analyzed durations and relative timings of motor pools within swallowing motor patterns in the presence and absence of sensory feedback and related these motor program components to behavior. Here, at the level of identified motor neurons, we show that sensory feedback to motor program components highly correlated with behavioral efficacy reduces variability across subjects but-surprisingly-increases variability within subjects. By controlling intrinsic, individual differences in motor neuronal activity, sensory feedback provides each subject access to a common solution space.

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.

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.