Natural neural output that produces highly variable locomotory movements

A hierarchical model for external electrical control of an insect, accounting for inter-individual variation of muscle force properties

Cyborg control of insect movement is promising for developing miniature, high-mobility, and efficient biohybrid robots. However, considering the inter-individual variation of the insect neuromuscular apparatus and its neural control is challenging. We propose a hierarchical model including inter-individual variation of muscle properties of three leg muscles involved in propulsion (retractor coxae), joint stiffness (pro- and retractor coxae), and stance-swing transition (protractor coxae and levator trochanteris) in the stick insect Carausius morosus. To estimate mechanical effects induced by external muscle stimulation, the model is based on the systematic evaluation of joint torques as functions of electrical stimulation parameters. A nearly linear relationship between the stimulus burst duration and generated torque was observed. This stimulus-torque characteristic holds for burst durations of up to 500ms, corresponding to the stance and swing phase durations of medium to fast walking stick insects. Hierarchical Bayesian modeling revealed that linearity of the stimulus-torque characteristic was invariant, with individually varying slopes. Individual prediction of joint torques provides significant benefits for precise cyborg control.

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.

Decentralized control of insect walking: A simple neural network explains a wide range of behavioral and neurophysiological results

Controlling the six legs of an insect walking in an unpredictable environment is a challenging task, as many degrees of freedom have to be coordinated. Solutions proposed to deal with this task are usually based on the highly influential concept that (sensory-modulated) central pattern generators (CPG) are required to control the rhythmic movements of walking legs. Here, we investigate a different view. To this end, we introduce a sensor based controller operating on artificial neurons, being applied to a (simulated) insectoid robot required to exploit the "loop through the world" allowing for simplification of neural computation. We show that such a decentralized solution leads to adaptive behavior when facing uncertain environments which we demonstrate for a broad range of behaviors never dealt with in a single system by earlier approaches. This includes the ability to produce footfall patterns such as velocity dependent "tripod", "tetrapod", "pentapod" as well as various stable intermediate patterns as observed in stick insects and in Drosophila. These patterns are found to be stable against disturbances and when starting from various leg configurations. Our neuronal architecture easily allows for starting or interrupting a walk, all being difficult for CPG controlled solutions. Furthermore, negotiation of curves and walking on a treadmill with various treatments of individual legs is possible as well as backward walking and performing short steps. This approach can as well account for the neurophysiological results usually interpreted to support the idea that CPGs form the basis of walking, although our approach is not relying on explicit CPG-like structures. Application of CPGs may however be required for very fast walking. Our neuronal structure allows to pinpoint specific neurons known from various insect studies. Interestingly, specific common properties observed in both insects and crustaceans suggest a significance of our controller beyond the realm of insects.

Computational geometric tools for quantitative comparison of locomotory behavior

A fundamental challenge for behavioral neuroscientists is to accurately quantify (dis)similarities in animal behavior without excluding inherent variability present between individuals. We explored two new applications of curve and shape alignment techniques to address this issue. As a proof-of-concept we applied these methods to compare normal or alarmed behavior in pairs of medaka (Oryzias latipes). The curve alignment method we call Behavioral Distortion Distance (BDD) revealed that alarmed fish display less predictable swimming over time, even if individuals incorporate the same action patterns like immobility, sudden changes in swimming trajectory, or changing their position in the water column. The Conformal Spatiotemporal Distance (CSD) technique on the other hand revealed that, in spite of the unpredictability, alarmed individuals exhibit lower variability in overall swim patterns, possibly accounting for the widely held notion of "stereotypy" in alarm responses. More generally, we propose that these new applications of established computational geometric techniques are useful in combination to represent, compare, and quantify complex behaviors consisting of common action patterns that differ in duration, sequence, or frequency.

Swing Velocity Profiles of Small Limbs Can Arise from Transient Passive Torques of the Antagonist Muscle Alone

In large limbs, changing motor neuron activity typically controls within-movement velocity. For example, sequential agonist-antagonist-agonist motor neuron firing typically underlies the slowing often present at the end of human reaches. In physiological movements of large limbs, antagonistic muscle passive torque is generally negligible. In small limbs, alternatively, passive torques can determine limb rest position, generate restoring movements to it, and decrease agonist-generated movement amplitude and velocity maxima. These observations suggest that, in small limbs, passive forces might also control velocity changes within movements. We investigated this issue in stick insect middle leg femur-tibia (FT) joint. During swing, the FT joint extensor muscle actively shortens and the flexor muscle passively lengthens. As in human reaching, after its initial acceleration, FT joint velocity continuously decreases. We measured flexor passive forces during imposed stretches spanning the ranges of FT joint angles, angular velocities, and movement amplitudes present in leg swings. The viscoelastic "transient" passive force that occurs during and soon after stretch depended on all three variables and could be tens of times larger than the "steady-state" passive force commonly measured long after stretch end. We combined these data, the flexor and extensor moment arms, and an existing extensor model to simulate FT joint swing. To measure only passive (flexor) muscle-dependent effects, we used constant extensor activations in these simulations. In simulations using data from ten flexor muscles, flexor passive torque could always produce swings with, after swing initiation, continuously decreasing velocities. Antagonist muscle passive torques alone can thus control within-movement velocity.

Joint torques in a freely walking insect reveal distinct functions of leg joints in propulsion and posture control

Determining the mechanical output of limb joints is critical for understanding the control of complex motor behaviours such as walking. In the case of insect walking, the neural infrastructure for single-joint control is well described. However, a detailed description of the motor output in form of time-varying joint torques is lacking. Here, we determine joint torques in the stick insect to identify leg joint function in the control of body height and propulsion. Torques were determined by measuring whole-body kinematics and ground reaction forces in freely walking animals. We demonstrate that despite strong differences in morphology and posture, stick insects show a functional division of joints similar to other insect model systems. Propulsion was generated by strong depression torques about the coxa-trochanter joint, not by retraction or flexion/extension torques. Torques about the respective thorax-coxa and femur-tibia joints were often directed opposite to fore-aft forces and joint movements. This suggests a posture-dependent mechanism that counteracts collapse of the leg under body load and directs the resultant force vector such that strong depression torques can control both body height and propulsion. Our findings parallel propulsive mechanisms described in other walking, jumping and flying insects, and challenge current control models of insect walking.

Patterns of variation in feeding strike kinematics of juvenile ghost praying mantis (Phyllocrania paradoxa): are components of the strike stereotypic?

Functional systems, such as feeding mechanics, often involve the evolution of several components of the musculoskeletal system that are moved in coordination to capture prey. Because these systems often involve the quick movement of several structures, some feeding systems have been hypothesized to be stereotypic. While the motor activity patterns are often stereotyped, the subsequent kinematics can be variable, many times in response to variation in prey stimulus (e.g., prey position). Patterns of feeding kinematics have been well studied among vertebrates, with less attention on invertebrate systems. The goal of this study was to examine the amount of stereotypy in the feeding strike kinematics of praying mantises. We filmed 8 juvenile ghost praying mantises (Phyllocrania paradox) at 1000 Hz, across several days within instar 7. We digitized several points that represent the movement of the coxa, trochanter-femur and tibia of the raptorial foreleg to obtain a set of kinematics including angles and angular velocities of the joint, as well as body lunge. Using the coefficient of variation, we found less stereotypy in the approach stage of the strike compared to the sweep. Using Bonferroni corrected Pearson's correlations of kinematics with prey position we found few traits related to prey position with the exception of some kinematics of the coxa joint and the amount of lunge used during the strike. Our results suggest that several components of the praying mantis strike are stereotypic, while others exhibit flexibility to ensure successful capture of the prey.

Sensory-Motor Integration: More Variability Reduces Individuality

Motor neural networks and muscles produce identifiably common outputs, such as a trot or gallop, despite varations in intrinsic properties across individuals. New work shows that sensory input can induce the requisite decrease in across-individual variability even as it increases within-individual variability.

Designing responsive pattern generators: stable heteroclinic channel cycles for modeling and control

A striking feature of biological pattern generators is their ability to respond immediately to multisensory perturbations by modulating the dwell time at a particular phase of oscillation, which can vary force output, range of motion, or other characteristics of a physical system. Stable heteroclinic channels (SHCs) are a dynamical architecture that can provide such responsiveness to artificial devices such as robots. SHCs are composed of sequences of saddle equilibrium points, which yields exquisite sensitivity. The strength of the vector fields in the neighborhood of these equilibria determines the responsiveness to perturbations and how long trajectories dwell in the vicinity of a saddle. For SHC cycles, the addition of stochastic noise results in oscillation with a regular mean period. In this paper, we parameterize noise-driven Lotka-Volterra SHC cycles such that each saddle can be independently designed to have a desired mean sub-period. The first step in the design process is an analytic approximation, which results in mean sub-periods that are within 2% of the specified sub-period for a typical parameter set. Further, after measuring the resultant sub-periods over sufficient numbers of cycles, the magnitude of the noise can be adjusted to control the mean period with accuracy close to that of the integration step size. With these relationships, SHCs can be more easily employed in engineering and modeling applications. For applications that require smooth state transitions, this parameterization permits each state's distribution of periods to be independently specified. Moreover, for modeling context-dependent behaviors, continuously varying inputs in each state dimension can rapidly precipitate transitions to alter frequency and phase.

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.

Motor circuit-specific burst patterns drive different muscle and behavior patterns

In the isolated CNS, different modulatory inputs can enable one motor network to generate multiple output patterns. Thus far, however, few studies have established whether different modulatory inputs also enable a defined network to drive distinct muscle and movement patterns in vivo, much as they enable these distinctions in behavioral studies. This possibility is not a foregone conclusion, because additional influences present in vivo (e.g., sensory feedback, hormonal modulation) could alter the motor patterns. Additionally, rhythmic neuronal activity can be transformed into sustained muscle contractions, particularly in systems with slow muscle dynamics, as in the crab (Cancer borealis) stomatogastric system used here. We assessed whether two different versions of the biphasic (protraction, retraction) gastric mill (chewing) rhythm, triggered in the isolated stomatogastric system by the modulatory ventral cardiac neurons (VCNs) and postoesophageal commissure (POC) neurons, drive different muscle and movement patterns. One distinction between these rhythms is that the lateral gastric (LG) protractor motor neuron generates tonic bursts during the VCN rhythm, whereas its POC-rhythm bursts are divided into fast, rhythmic burstlets. Intracellular muscle fiber recordings and tension measurements show that the LG-innervated muscles retain the distinct VCN-LG and POC-LG neuron burst structures. Moreover, endoscope video recordings in vivo, during VCN-triggered and POC-triggered chewing, show that the lateral teeth protraction movements exhibit the same, distinct protraction patterns generated by LG in the isolated nervous system. Thus, the multifunctional nature of an identified motor network in the isolated CNS can be preserved in vivo, where it drives different muscle activity and movement patterns.

Determining all parameters necessary to build Hill-type muscle models from experiments on single muscles

Characterizing muscle requires measuring such properties as force-length, force-activation, and force-velocity curves. These characterizations require large numbers of data points because both what type of function (e.g., linear, exponential, hyperbolic) best represents each property, and the values of the parameters in the relevant equations, need to be determined. Only a few properties are therefore generally measured in experiments on any one muscle, and complete characterizations are obtained by averaging data across a large number of muscles. Such averaging approaches can work well for muscles that are similar across individuals. However, considerable evidence indicates that large inter-individual variation exists, at least for some muscles. This variation poses difficulties for across-animal averaging approaches. Methods to fully describe all muscle's characteristics in experiments on individual muscles would therefore be useful. Prior work in stick insect extensor muscle has identified what functions describe each of this muscle's properties and shown that these equations apply across animals. Characterizing these muscles on an individual-by-individual basis therefore requires determining only the values of the parameters in these equations, not equation form. We present here techniques that allow determining all these parameter values in experiments on single muscles. This technique will allow us to compare parameter variation across individuals and to model muscles individually. Similar experiments can likely be performed on single muscles in other systems. This approach may thus provide a widely applicable method for characterizing and modeling muscles from single experiments.

Hill-type muscle model parameters determined from experiments on single muscles show large animal-to-animal variation

Models built using mean data can represent only a very small percentage, or none, of the population being modeled, and produce different activity than any member of it. Overcoming this "averaging" pitfall requires measuring, in single individuals in single experiments, all of the system's defining characteristics. We have developed protocols that allow all the parameters in the curves used in typical Hill-type models (passive and active force-length, series elasticity, force-activation, force-velocity) to be determined from experiments on individual stick insect muscles (Blümel et al. 2012a). A requirement for means to not well represent the population is that the population shows large variation in its defining characteristics. We therefore used these protocols to measure extensor muscle defining parameters in multiple animals. Across-animal variability in these parameters can be very large, ranging from 1.3- to 17-fold. This large variation is consistent with earlier data in which extensor muscle responses to identical motor neuron driving showed large animal-to-animal variability (Hooper et al. 2006), and suggests accurate modeling of extensor muscles requires modeling individual-by-individual. These complete characterizations of individual muscles also allowed us to test for parameter correlations. Two parameter pairs significantly co-varied, suggesting that a simpler model could as well reproduce muscle response.

Using individual-muscle specific instead of across-muscle mean data halves muscle simulation error

Hill-type parameter values measured in experiments on single muscles show large across-muscle variation. Using individual-muscle specific values instead of the more standard approach of across-muscle means might therefore improve muscle model performance. We show here that using mean values increased simulation normalized RMS error in all tested motor nerve stimulation paradigms in both isotonic and isometric conditions, doubling mean simulation error from 9 to 18 (different at p < 0.0001). These data suggest muscle-specific measurement of Hill-type model parameters is necessary in work requiring highly accurate muscle model construction. Maximum muscle force (F (max)) showed large (fourfold) across-muscle variation. To test the role of F (max) in model performance we compared the errors of models using mean F (max) and muscle-specific values for the other model parameters, and models using muscle-specific F (max) values and mean values for the other model parameters. Using muscle-specific F (max) values did not improve model performance compared to using mean values for all parameters, but using muscle-specific values for all parameters but F (max) did (to an error of 14, different from muscle-specific, mean all parameters, and mean only F (max) errors at p ≤ 0.014). Significantly improving model performance thus required muscle-specific values for at least a subset of parameters other than F (max), and best performance required muscle-specific values for this subset and F (max). Detailed consideration of model performance suggested that remaining model error likely stemmed from activation of both fast and slow motor neurons in our experiments and inadequate specification of model activation dynamics.

Relating neuronal to behavioral performance: variability of optomotor responses in the blowfly

Behavioral responses of an animal vary even when they are elicited by the same stimulus. This variability is due to stochastic processes within the nervous system and to the changing internal states of the animal. To what extent does the variability of neuronal responses account for the overall variability at the behavioral level? To address this question we evaluate the neuronal variability at the output stage of the blowfly's (Calliphora vicina) visual system by recording from motion-sensitive interneurons mediating head optomotor responses. By means of a simple modelling approach representing the sensory-motor transformation, we predict head movements on the basis of the recorded responses of motion-sensitive neurons and compare the variability of the predicted head movements with that of the observed ones. Large gain changes of optomotor head movements have previously been shown to go along with changes in the animals' activity state. Our modelling approach substantiates that these gain changes are imposed downstream of the motion-sensitive neurons of the visual system. Moreover, since predicted head movements are clearly more reliable than those actually observed, we conclude that substantial variability is introduced downstream of the visual system.

Neural control of unloaded leg posture and of leg swing in stick insect, cockroach, and mouse differs from that in larger animals

Stick insect (Carausius morosus) leg muscles contract and relax slowly. Control of stick insect leg posture and movement could therefore differ from that in animals with faster muscles. Consistent with this possibility, stick insect legs maintained constant posture without leg motor nerve activity when the animals were rotated in air. That unloaded leg posture was an intrinsic property of the legs was confirmed by showing that isolated legs had constant, gravity-independent postures. Muscle ablation experiments, experiments showing that leg muscle passive forces were large compared with gravitational forces, and experiments showing that, at the rest postures, agonist and antagonist muscles generated equal forces indicated that these postures depended in part on leg muscles. Leg muscle recordings showed that stick insect swing motor neurons fired throughout the entirety of swing. To test whether these results were specific to stick insect, we repeated some of these experiments in cockroach (Periplaneta americana) and mouse. Isolated cockroach legs also had gravity-independent rest positions and mouse swing motor neurons also fired throughout the entirety of swing. These data differ from those in human and horse but not cat. These size-dependent variations in whether legs have constant, gravity-independent postures, in whether swing motor neurons fire throughout the entirety of swing, and calculations of how quickly passive muscle force would slow limb movement as limb size varies suggest that these differences may be caused by scaling. Limb size may thus be as great a determinant as phylogenetic position of unloaded limb motor control strategy.

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.

Noise in the nervous system

Noise--random disturbances of signals--poses a fundamental problem for information processing and affects all aspects of nervous-system function. However, the nature, amount and impact of noise in the nervous system have only recently been addressed in a quantitative manner. Experimental and computational methods have shown that multiple noise sources contribute to cellular and behavioural trial-to-trial variability. We review the sources of noise in the nervous system, from the molecular to the behavioural level, and show how noise contributes to trial-to-trial variability. We highlight how noise affects neuronal networks and the principles the nervous system applies to counter detrimental effects of noise, and briefly discuss noise's potential benefits.

Slow temporal filtering may largely explain the transformation of stick insect (Carausius morosus) extensor motor neuron activity into muscle movement

Understanding how nervous systems generate behavior requires understanding how muscles transform neural input into movement. The stick insect extensor tibiae muscle is an excellent system in which to study this issue because extensor motor neuron activity is highly variable during single leg walking and extensor muscles driven with this activity produce highly variable movements. We showed earlier that spike number, not frequency, codes for extensor amplitude during contraction rises, which implies the muscle acts as a slow filter on the time scale of burst interspike intervals (5-10 ms). We examine here muscle response to spiking variation over entire bursts, a time scale of hundreds of milliseconds, and directly measure muscle time constants. Muscle time constants differ during contraction and relaxation, and contraction time constants, although variable, are always extremely slow (200-700 ms). Models using these data show that extremely slow temporal filtering alone can explain much of the observed transform properties. This work also revealed an unexpected (to us) ability of slow filtering to transform steadily declining inputs into constant amplitude outputs. Examination of the effects of time constant variability on model output showed that variation within an SD primarily altered output amplitude, but variation across the entire range also altered contraction shape. These substantial changes suggest that understanding the basis of this variation is central to predicting extensor activity and that the animal could theoretically vary muscle time constant to match extensor response to changing behavioral need.

The extensor tibiae muscle of the stick insect: biomechanical properties of an insect walking leg muscle

We investigated the properties of the extensor tibiae muscle of the stick insect (Carausius morosus) middle leg. Muscle geometry of the middle leg was compared to that of the front and hind legs and to the flexor tibiae, respectively. The mean length of the extensor tibiae fibres is 1.41+/-0.23 mm and flexor fibres are 2.11+/-0.30 mm long. The change of fibre length with joint angle was measured and closely follows a cosine function. Its amplitude gives effective moment arm lengths of 0.28+/-0.02 mm for the extensor and 0.56+/-0.04 mm for the flexor. Resting extensor tibiae muscle passive tonic force increased from 2 to 5 mN in the maximum femur-tibia (FT)-joint working range when stretched by ramps. Active muscle properties were measured with simultaneous activation (up to 200 pulses s(-1)) of all three motoneurons innervating the extensor tibiae, because this reflects most closely physiological muscle activation during leg swing. The force-length relationship corresponds closely to the typical characteristic according to the sliding filament hypothesis: it has a plateau at medium fibre lengths, declines nearly linearly in force at both longer and shorter fibre lengths, and the muscle's working range lies in the short to medium fibre length range. Maximum contraction velocity showed a similar relationship. The force-velocity relationship was the traditional Hill curve hyperbola, but deviated from the hyperbolic shape in the region of maximum contraction force close to the isometric contraction. Step-like changes in muscle length induced by loaded release experiments characterised the non-linear series elasticity as a quadratic spring.

Different motor neuron spike patterns produce contractions with very similar rises in graded slow muscles

Graded muscles produce small twitches in response to individual motor neuron spikes. During the early part of their contractions, contraction amplitude in many such muscles depends primarily on the number of spikes the muscle has received, not the frequency or pattern with which they were delivered. Stick insect (Carausius morosus) extensor muscles are graded and thus would likely show spike-number dependency early in their contractions. Tonic stimulations of the extensor motor nerve showed that the response of the muscles differed from the simplest form of spike-number dependency. However, these differences actually increased the spike-number range over which spike-number dependency was present. When the motor nerve was stimulated with patterns mimicking the motor neuron activity present during walking, amplitude during contraction rises also depended much more on spike number than on spike frequency. A consequence of spike-number dependency is that brief changes in spike frequency do not alter contraction slope and we show here that extensor motor neuron bursts with different spike patterns give rise to contractions with very similar contraction rises. We also examined in detail the early portions of a large number of extensor motor neuron bursts recorded during single-leg walking and show that these portions of the bursts do not appear to have any common spike pattern. Although alternative explanations are possible, the simplest interpretation of these data is that extensor motor neuron firing during leg swing is not tightly controlled.