Multiple changes in connectivity between buccal ganglia mechanoafferents and motor neurons with different functions after learning that food is inedible in Aplysia.

Changes caused by learning that a food is inedible in Aplysia were examined for fast and slow synaptic connections from the buccal ganglia S1 cluster of mechanoafferents to five followers, in response to repeated stimulus trains. Learning affected only fast connections. For these, unique patterns of change were present in each follower, indicating that learning differentially affects the different branches of the mechanoafferents to their followers. In some followers, there were increases in either excitatory or inhibitory connections, and in others, there were decreases. Changes in connectivity resulted from changes in the amplitude of excitation or inhibition, or as a result of the number of connections, or of both. Some followers also exhibited changes in either within or between stimulus train plasticity as a result of learning. In one follower, changes differed from the different areas of the S1 cluster. The patterns of changes in connectivity were consistent with the behavioral changes produced by learning, in that they would produce an increase in the bias to reject or to release food, and a decrease in the likelihood to respond to food.

Repeated stimulation of feeding mechanoafferents in Aplysia generates responses consistent with the release of food.

How does repeated stimulation of mechanoafferents affect feeding motor neurons? Monosynaptic connections from a mechanoafferent population in the Aplysia buccal ganglia to five motor followers with different functions were examined during repeated stimulus trains. The mechanoafferents produced both fast and slow synaptic outputs, which could be excitatory or inhibitory. In contrast, other Aplysia mechanoafferents produce only fast excitation on their followers. In addition, patterns of synaptic connections were different to the different motor followers. Some followers received both fast excitation and fast inhibition, whereas others received exclusively fast excitation. All followers showed strong decreases in fast postsynaptic potential (PSP) amplitude within a stimulus train. Fast and slow synaptic connections were of net opposite signs in some followers but not in others. For one follower, synaptic contacts were not uniform from all subareas of the mechanoafferent cluster. Differences in properties of the buccal ganglia mechanoafferents and other Aplysia mechanoafferents may arise because the buccal ganglia neurons innervate the interior of the feeding apparatus, rather than an external surface, and connect to motor neurons for muscles with different motor functions. Fast connection patterns suggest that these synapses may be activated when food slips, biasing the musculature to release food. The largest slow inhibitory synaptic PSPs may contribute to a delay in the onset of the next behavior. Additional functions are also possible.

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.

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.

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.

Selective Infrared Neural Inhibition Can Be Reproduced by Resistive Heating.

OBJECTIVES: Small-diameter afferent axons carry various sensory signals that are critical for vital physiological conditions but sometimes contribute to pathologies. Infrared (IR) neural inhibition (INI) can induce selective heat block of small-diameter axons, which holds potential for translational applications such as pain management. Previous research suggested that IR-heating-induced acceleration of voltage-gated potassium channel kinetics is the mechanism for INI. Therefore, we hypothesized that other heating methods, such as resistive heating (RH) in a cuff, could reproduce the selective inhibition observed in INI. MATERIALS AND METHODS: We conducted ex vivo nerve-heating experiments on pleural-abdominal connective nerves of Aplysia californica using both IR and RH. We fabricated a transparent silicone nerve cuff for simultaneous IR heating, RH, and temperature measurements. Temperature elevations (ΔT) on the nerve surface were recorded for both heating modalities, which were tested over a range of power levels that cover a similar ΔT range. We recorded electrically evoked compound action potentials (CAPs) and segmented them into fast and slow subcomponents on the basis of conduction velocity differences between the large and small-diameter axonal subpopulations. We calculated the normalized inhibition strength and inhibition selectivity index on the basis of the rectified area under the curve of each subpopulation. RESULTS: INI and RH showed a similar selective inhibition effect on CAP subcomponents for slow-conducting axons, confirmed by the inhibition probability vs ΔT dose-response curve based on approximately 2000 CAP measurements. The inhibition selectivity indexes of the two heating modalities were similar across six nerves. RH only required half the total electrical power required by INI to achieve a similar ΔT. SIGNIFICANCE: We show that selective INI can be reproduced by other heating modalities such as RH. RH, because of its high energy efficiency and simple design, can be a good candidate for future implantable neural interface designs.

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.

Multiple Local Synaptic Modifications at Specific Sensorimotor Connections after Learning Are Associated with Behavioral Adaptations That Are Components of a Global Response Change.

Learning causes local changes in synaptic connectivity and coordinated, global changes affecting many aspects of behavior. How do local synaptic changes produce global behavioral changes? In the hermaphroditic mollusc Aplysia, after learning that food is inedible, memory is expressed as bias to reject a food and to reduce responses to that food. We now show that memory is also expressed as an increased bias to reject even a nonfood object. The increased bias to rejection is partially explained by changes in synaptic connections from primary mechanoafferents to five follower neurons with well defined roles in producing different feeding behaviors. Previously, these mechanoafferents had been shown to play a role in memory consolidation. Connectivity changes differed for each follower neuron: the probability that cells were connected changed; excitation changed to inhibition and vice versa; and connection amplitude changed. Thus, multiple neural changes at different sites underlie specific aspects of a coordinated behavioral change. Changes in the connectivity between mechanoafferents and their followers cannot account for all of the behavioral changes expressed after learning, indicating that additional synaptic sites are also changed. Access to the circuit controlling feeding can help determine the logic and cellular mechanisms by which multiple local synaptic changes produce an integrated, global change in behavior.SIGNIFICANCE STATEMENT How do local changes in synapses affect global behavior? Studies on invertebrate preparations usually examine synaptic changes at specific neural sites, producing a specific behavioral change. However, memory may be expressed by multiple behavioral changes. We report that a change in behavior after learning in Aplysia is accomplished, in part, by regulating connections between mechanoafferents and their synaptic followers. For some followers, the connection probabilities change; for others, the connection signs are reversed; in others, the connection strength is modified. Thus, learning produces changes in connectivity at multiple sites, via multiple synaptic mechanisms that are consistent with the observed behavioral change.

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.

Identifying the Role of Block Length in Neural Heat Block to Reduce Temperatures During Infrared Neural Inhibition.

BACKGROUND AND OBJECTIVES: The objective of this study is to assess the hypothesis that the length of axon heated, defined here as block length (BL), affects the temperature required for thermal inhibition of action potential propagation applied using laser heating. The presence of such a phenomenon has implications for how this technique, called infrared neural inhibition (INI), may be applied in a clinically safe manner since it suggests that temperatures required for therapy may be reduced through the proper spatial application of light. Here, we validate the presence of this phenomenon by assessing how the peak temperatures during INI are reduced when two different BLs are applied using irradiation from either one or two adjacent optical fibers. STUDY DESIGN/MATERIALS AND METHODS: Assessment of the role of BL was carried out over two phases. First, a computational proof of concept was performed in the neural conduction simulation environment, NEURON, simulating the response of action potentials to increased temperatures applied at different full-width at half-maxima (FWHM) along axons. Second, ex vivo validation of these predictions was performed by measuring the radiant exposure, peak temperature rise, and FWHM of heat distributions associated with INI from one or two adjacent optical fibers. Electrophysiological assessment of radiant exposures at inhibition threshold were carried out in ex vivo Aplysia californica (sea slug) pleural abdominal nerves ( n = 6), an invertebrate with unmyelinated axons. Measurement of the maximum temperature rise required for induced heat block was performed in a water bath using a fine wire thermocouple. Finally, magnetic resonance thermometry (MRT) was performed on a nerve immersed in saline to assess the elevated temperature distribution at these radiant exposures. RESULTS: Computational modeling in NEURON provided a theoretical proof of concept that the BL is an important factor contributing to the peak temperature required during neural heat block, predicting a 11.7% reduction in temperature rise when the FWHM along an axon is increased by 42.9%. Experimental validation showed that, when using two adjacent fibers instead of one, a 38.5 ± 2.2% (mean ± standard error of the mean) reduction in radiant exposure per pulse per fiber threshold at the fiber output (P = 7.3E-6) is measured, resulting in a reduction in peak temperature rise under each fiber of 23.5 ± 2.1% ( P = 9.3E-5) and 15.0 ± 2.4% ( P = 1.4E-3) and an increase in the FWHM of heating by 37.7 ± 6.4% ( P = 1E-3), 68.4 ± 5.2% ( P = 2.4E-5), and 51.9 ± 9.9% ( P = 1.7E-3) in three MRT slices. CONCLUSIONS: This study provides the first experimental evidence for a phenomenon during the heat block in which the temperature for inhibition is dependent on the BL. While more work is needed to further reduce the temperature during INI, the results highlight that spatial application of the temperature rise during INI must be considered. Optimized implementation of INI may leverage this cellular response to provide optical modulation of neural signals with lower temperatures over greater time periods, which may increase the utility of the technique for laboratory and clinical use. Lasers Surg. Med. © 2019 Wiley Periodicals, Inc.

Successful and unsuccessful attempts to swallow in a reduced Aplysia preparation regulate feeding responses and produce memory at different neural sites.

Sensory feedback shapes ongoing behavior and may produce learning and memory. Motor responses to edible or inedible food in a reduced Aplysia preparation were examined to test how sensory feedback affects behavior and memory. Feeding patterns were initiated by applying a cholinomimetic onto the cerebral ganglion. Feedback from buccal muscles increased the response variability and response rate. Repeated application of the cholinomimetic caused decreased responses, expressed in part by lengthening protractions. Swallowing strips of "edible" food, which in intact animals induces learning that enhances ingestion, increased the response rate, and shortened the protraction length, reflecting more swallowing. Testing memory by repeating the procedure prevented the decrease in response rate observed with the cholinomimetic alone, and shortened protractions. Training with "inedible" food that in intact animals produces learning expressed by decreased responses caused lengthened protractions. Testing memory by repeating the procedure did not cause decreased responses or lengthened protractions. After training and testing with edible or inedible food, all preparations were exposed to the cholinomimetic alone. Preparations previously trained with edible food displayed memory expressed as decreased protraction length. Preparations previously trained with inedible food showed decreases in many response parameters. Memory for inedible food may arise in part via a postsynaptic decrease in response to acetylcholine released by afferents sensing food. The lack of change in response number, and in the time that responses are maintained during the two training sessions preceding application of the cholinomimetic alone suggests that memory expression may differ from behavioral changes during training.

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.

Preparing the periphery for a subsequent behavior: motor neuronal activity during biting generates little force but prepares a retractor muscle to generate larger forces during swallowing in Aplysia.

Some behaviors occur in obligatory sequence, such as reaching before grasping an object. Can the earlier behavior serve to prepare the musculature for the later behavior? If it does, what is the underlying neural mechanism of the preparation? To address this question, we examined two feeding behaviors in the marine mollusk Aplysia californica, one of which must precede the second: biting and swallowing. Biting is an attempt to grasp food. When that attempt is successful, the animal immediately switches to swallowing to ingest food. The main muscle responsible for pulling food into the buccal cavity during swallowing is the I3 muscle, whose motor neurons B6, B9, and B3 have been previously identified. By performing recordings from these neurons in vivo in intact, behaving animals or in vitro in a suspended buccal mass preparation, we demonstrated that the frequencies and durations of these motor neurons increased from biting to swallowing. Using the physiological patterns of activation to drive these neurons intracellularly, we further demonstrated that activating them using biting-like frequencies and durations, either alone or in combination, generated little or no force in the I3 muscle. When biting-like patterns preceded swallowing-like patterns, however, the forces during the subsequent swallowing-like patterns were significantly enhanced. Sequences of swallowing-like patterns, either with these neurons alone or in combination, further enhanced forces in the I3 muscle. These results suggest a novel mechanism for enhancing force production in a muscle, and may be relevant to understanding motor control in vertebrates.

Communication-Microelectrode Detection of Cholesterol Efflux from the Human Buccel Mucosa.

It has previously demonstrated that cholesterol efflux from the cell plasma membrane is increased in a mouse model of cystic fibrosis (CF) compared to a wild-type control. A noninvasive means of characterizing plasma membrane cholesterol efflux at the surface of airway tissue of CF patients is needed to extend the trends found in animal models of CF to the human disease state. Microelectrode-induced cholesterol efflux from the plasma membrane of cells at the surface of tissue is proposed as a strategy to demonstrate increased cholesterol efflux for CF in human subjects. Data demonstrating detection of cholesterol efflux from the human buccal mucosa is reported as proof-of-concept for an in vivo diagnostic assay.

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.

Modeling of the dorsal gradient across species reveals interaction between embryo morphology and Toll signaling pathway during evolution.

Morphogenetic gradients are essential to allocate cell fates in embryos of varying sizes within and across closely related species. We previously showed that the maternal NF-κB/Dorsal (Dl) gradient has acquired different shapes in Drosophila species, which result in unequally scaled germ layers along the dorso-ventral axis and the repositioning of the neuroectodermal borders. Here we combined experimentation and mathematical modeling to investigate which factors might have contributed to the fast evolutionary changes of this gradient. To this end, we modified a previously developed model that employs differential equations of the main biochemical interactions of the Toll (Tl) signaling pathway, which regulates Dl nuclear transport. The original model simulations fit well the D. melanogaster wild type, but not mutant conditions. To broaden the applicability of this model and probe evolutionary changes in gradient distributions, we adjusted a set of 19 independent parameters to reproduce three quantified experimental conditions (i.e. Dl levels lowered, nuclear size and density increased or decreased). We next searched for the most relevant parameters that reproduce the species-specific Dl gradients. We show that adjusting parameters relative to morphological traits (i.e. embryo diameter, nuclear size and density) alone is not sufficient to reproduce the species Dl gradients. Since components of the Tl pathway simulated by the model are fast-evolving, we next asked which parameters related to Tl would most effectively reproduce these gradients and identified a particular subset. A sensitivity analysis reveals the existence of nonlinear interactions between the two fast-evolving traits tested above, namely the embryonic morphological changes and Tl pathway components. Our modeling further suggests that distinct Dl gradient shapes observed in closely related melanogaster sub-group lineages may be caused by similar sequence modifications in Tl pathway components, which are in agreement with their phylogenetic relationships.