Muscle active force-length curve explained by an electrophysical model of interfilament spacing.

The active isometric force-length relation (FLR) of striated muscle sarcomeres is central to understanding and modeling muscle function. The mechanistic basis of the descending arm of the FLR is well explained by the decreasing thin:thick filament overlap that occurs at long sarcomere lengths. The mechanistic basis of the ascending arm of the FLR (the decrease in force that occurs at short sarcomere lengths), alternatively, has never been well explained. Because muscle is a constant-volume system, interfilament lattice distances must increase as sarcomere length shortens. This increase would decrease thin and thick-filament electrostatic interactions independently of thin:thick filament overlap. To examine this effect, we present here a fundamental, physics-based model of the sarcomere that includes filament molecular properties, calcium binding, sarcomere geometry including both thin:thick filament overlap and interfilament radial distance, and electrostatics. The model gives extremely good fits to existing FLR data from a large number of different muscles across their entire range of measured activity levels, with the optimized parameter values in all cases lying within anatomically and physically reasonable ranges. A local first-order sensitivity analysis (varying individual parameters while holding the values of all others constant) shows that model output is most sensitive to a subset of model parameters, most of which are related to sarcomere geometry, with model output being most sensitive to interfilament radial distance. This conclusion is supported by re-running the fits with only this parameter subset being allowed to vary, which increases fit errors only moderately. These results show that the model well reproduces existing experimental data, and indicate that changes in interfilament spacing play as central a role as changes in filament overlap in determining the FLR, particularly on its ascending arm.

Neuromodulation Can Be Simple: Myoinhibitory Peptide, Contained in Dedicated Regulatory Pathways, Is the Only Neurally-Mediated Peptide Modulator of Stick Insect Leg Muscle.

In the best studied cases (Aplysia feeding, crustacean stomatogastric system), peptidergic modulation is mediated by large numbers of peptides. Furthermore, in Aplysia, excitatory motor neurons release the peptides, obligatorily coupling target activation and modulator release. Vertebrate nervous systems typically contain about a hundred peptide modulators. These data have created a belief that modulation is, in general, complex. The stick insect leg is a well-studied locomotory model system, and the complete stick insect neuropeptide inventory was recently described. We used multiple techniques to comprehensively examine stick insect leg peptidergic modulation. Single-cell mass spectrometry (MS) and immunohistochemistry showed that myoinhibitory peptide (MIP) is the only neuronal (as opposed to hemolymph-borne) peptide modulator of all leg muscles. Leg muscle excitatory motor neurons contained no neuropeptides. Only the common inhibitor (CI) and dorsal unpaired median (DUM) neuron groups, each neuron of which innervates a group of functionally-related leg muscles, contained MIP. We described MIP transport to, and receptor presence in, one leg muscle, the extensor tibiae (ExtTi). MIP application reduced ExtTi slow fiber force and shortening by about half, increasing the muscle's ability to contract and relax rapidly. These data show neuromodulation does not need to be complex. Excitation and modulation do not need to be obligatorily coupled (Aplysia feeding). Modulation does not need to involve large numbers of peptides, with the attendant possibility of combinatorial explosion (stomatogastric system). Modulation can be simple, mediated by dedicated regulatory neurons, each innervating a single group of functionally-related targets, and all using the same neuropeptide.SIGNIFICANCE STATEMENT Vertebrate and invertebrate nervous systems contain large numbers (around a hundred in human brain) of peptide neurotransmitters. In prior work, neuropeptide modulation has been complex, either obligatorily coupling postsynaptic excitation and modulation, or large numbers of peptides modulating individual neural networks. The complete stick insect neuropeptide inventory was recently described. We comprehensively describe here peptidergic modulation in the stick insect leg. Surprisingly, out of the large number of potential peptide transmitters, only myoinhibitory peptide (MIP) was present in neurons innervating leg muscles. Furthermore, the peptide was present only in dedicated regulatory neurons, not in leg excitatory motor neurons. Peptidergic modulation can thus be simple, neither obligatorily coupling target activation and modulation nor involving so many peptides that combinatorial explosion can occur.

Choline and NMDG directly reduce outward currents: reduced outward current when these substances replace Na+ is alone not evidence of Na+-activated K+ currents.

Choline chloride is often, and N-methyl-d-glucamine (NMDG) sometimes, used to replace sodium chloride in studies of sodium-activated potassium channels. Given the high concentrations used in sodium replacement protocols, it is essential to test that it is not the replacement substances themselves, as opposed to the lack of sodium, that cause any observed effects. We therefore compared, in lobster stomatogastric neurons and leech Retzius cells, the effects of applying salines in which choline chloride replaced sodium chloride, and in which choline hydroxide or sucrose was added to normal saline. We also tested, in stomatogastric neurons, the effect of adding NMDG to normal saline. These protocols allowed us to measure the direct effects (i.e., effects not due to changes in sodium concentration or saline osmolarity or ionic strength) of choline on stomatogastric and leech currents, and of NMDG on stomatogastric currents. Choline directly reduced transient and sustained depolarization-activated outward currents in both species, and NMDG directly reduced transient depolarization-activated outward currents in stomatogastric neurons. Experiments with lower choline concentrations showed that adding as little as 150 mM (stomatogastric) or 5 mM (leech) choline reduced at least some depolarization-activated outward currents. Reductions in outward current with choline chloride or NMDG replacement alone are thus not evidence of sodium-activated potassium currents. NEW & NOTEWORTHY We show that choline or N-methyl-d-glucamine (NMDG) directly (i.e., not due to changes in extracellular sodium) decrease outward currents. Prior work studying sodium-activated potassium channels in which sodium was replaced with choline or NMDG without an addition control may therefore be artifactual.

Cell dialysis by sharp electrodes can cause nonphysiological changes in neuron properties.

We recorded from lobster and leech neurons with two sharp electrodes filled with solutions often used with these preparations (lobster: 0.6 M K2SO4 or 2.5 M KAc; leech: 4 M KAc), with solutions approximately matching neuron cytoplasm ion concentrations, and with 6.5 M KAc (lobster, leech) and 0.6 M KAc (lobster). We measured membrane potential, input resistance, and transient and sustained depolarization-activated outward current amplitudes in leech and these neuron properties and hyperpolarization-activated current time constant in lobster, every 10 min for 60 min after electrode penetration. Neuron properties varied with electrode fill. For fills with molarities ≥2.5 M, neuron properties also varied strongly with time after electrode penetration. Depending on the property being examined, these variations could be large. In leech, cell size also increased with noncytoplasmic fills. The changes in neuron properties could be due to the ions being injected from the electrodes during current injection. We tested this possibility in lobster with the 2.5 M KAc electrode fill by making measurements only 10 and 60 min after penetration. Neuron properties still changed, although the changes were less extreme. Making measurements every 2 min showed that the time-dependent variations in neuron properties occurred in concert with each other. Neuron property changes with high molarity electrode-fill solutions were great enough to decrease neuron firing strongly. An experiment with (14)C-glucose electrode fill confirmed earlier work showing substantial leak from sharp electrodes. Sharp electrode work should thus be performed with cytoplasm-matched electrode fills.

Limb coordination: Coming together to bounce along.

Experimental, modeling, and robotic research shows that switching of sea stars from crawling to bouncing gaits does not require centralized neural control. Bouncing can instead arise cooperatively, with synchronization of sea star tube feet occurring by locally acting mechanisms alone.

Contamination of current-clamp measurement of neuron capacitance by voltage-dependent phenomena.

Measuring neuron capacitance is important for morphological description, conductance characterization, and neuron modeling. One method to estimate capacitance is to inject current pulses into a neuron and fit the resulting changes in membrane potential with multiple exponentials; if the neuron is purely passive, the amplitude and time constant of the slowest exponential give neuron capacitance (Major G, Evans JD, Jack JJ. Biophys J 65: 423-449, 1993). Golowasch et al. (Golowasch J, Thomas G, Taylor AL, Patel A, Pineda A, Khalil C, Nadim F. J Neurophysiol 102: 2161-2175, 2009) have shown that this is the best method for measuring the capacitance of nonisopotential (i.e., most) neurons. However, prior work has not tested for, or examined how much error would be introduced by, slow voltage-dependent phenomena possibly present at the membrane potentials typically used in such work. We investigated this issue in lobster (Panulirus interruptus) stomatogastric neurons by performing current clamp-based capacitance measurements at multiple membrane potentials. A slow, voltage-dependent phenomenon consistent with residual voltage-dependent conductances was present at all tested membrane potentials (-95 to -35 mV). This phenomenon was the slowest component of the neuron's voltage response, and failure to recognize and exclude it would lead to capacitance overestimates of several hundredfold. Most methods of estimating capacitance depend on the absence of voltage-dependent phenomena. Our demonstration that such phenomena make nonnegligible contributions to neuron responses even at well-hyperpolarized membrane potentials highlights the critical importance of checking for such phenomena in all work measuring neuron capacitance. We show here how to identify such phenomena and minimize their contaminating influence.

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.

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.

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.

Non-linear multimodal integration in a distributed premotor network controls proprioceptive reflex gain in the insect leg.

Producing context-appropriate motor acts requires integrating multiple sensory modalities. Presynaptic inhibition of proprioceptive afferent neurons1-4 and afferents of different modalities targeting the same motor neurons (MNs)5-7 underlies some of this integration. However, in most systems, an interneuronal network is interposed between sensory afferents and MNs. How these networks contribute to this integration, particularly at single-neuron resolution, is little understood. Context-specific integration of load and movement sensory inputs occurs in the stick insect locomotory system,6,8-12 and both inputs feed into a network of premotor nonspiking interneurons (NSIs).8 We analyzed how load altered movement signal processing in the stick insect femur-tibia (FTi) joint control system by tracing the interaction of FTi movement13-15 (femoral chordotonal organ [fCO]) and load13,15,16 (tibial campaniform sensilla [CS]) signals through the NSI network to the slow extensor tibiae (SETi) MN, the extensor MN primarily active in non-walking animals.17-19 On the afferent level, load reduced movement signal gain by presynaptic inhibition. In the NSI network, graded responses to movement and load inputs summed nonlinearly, increasing the gain of NSIs opposing movement-induced reflexes and thus decreasing the SETi and extensor tibiae muscle movement reflex responses. Gain modulation was movement-parameter specific and required presynaptic inhibition. These data suggest that gain changes in distributed premotor networks, specifically the relative weighting of antagonistic pathways, could be a general mechanism by which multiple sensory modalities are integrated to generate context-appropriate motor activity.

Correlation between ranges of leg walking angles and passive rest angles among leg types in stick insects.

Because of scaling issues, passive muscle and joint forces become increasingly important as limb size decreases.1-3 In some small limbs, passive forces can drive swing in locomotion,4,5 and antagonist passive torques help control limb swing velocity.6 In stance, minimizing antagonist muscle and joint passive forces could save energy. These considerations predict that, for small limbs, evolution would result in the angle range over which passive forces are too small to cause limb movement (called "resting-state range" in prior insect work4 and "area of neutral equilibrium" in physics and engineering) correlating with the limb's typical working range, usually that in locomotion. We measured the most protracted and retracted thorax-femur (ThF) angles of the pro- (front), meso- (middle), and metathoracic (hind) leg during stick insect (Carausius morosus) walks. This ThF working range differed in the three leg types, being more posterior in more posterior legs. In other experiments, we manually protracted or retracted the denervated front, middle, and hind legs. Upon release, passive forces moved the leg in the opposite direction (retraction or protraction) until it reached the most protracted or most retracted edge of the ThF resting-state range. The ThF resting-state angle ranges correlated with the leg-type working range, being more posterior in more posterior legs. The most protracted ThF walking angles were more retracted than the post-protraction ThF angles, and the most retracted ThF walking angles were similar to the post-retraction ThF angles. These correlations of ThF working- and resting-state ranges could simplify motor control and save energy. These data also provide an example of evolution altering behavior by changing passive muscle and joint properties.7.

Motor control: Elephant trunks ignore the many and choose a few.

The elephant trunk is a muscular hydrostat with essentially infinite freedom of movement. Utilizing all this range would be extremely complex. A new analysis shows that elephants simplify such 'overchoice' by using twelve motor primitives that can generate most observed trunk movements.

Sensory feedback induced by front-leg stepping entrains the activity of central pattern generators in caudal segments of the stick insect walking system.

Legged locomotion results from a combination of central pattern generating network (CPG) activity and intralimb and interlimb sensory feedback. Data on the neural basis of interlimb coordination are very limited. We investigated here the influence of stepping in one leg on the activities of neighboring-leg thorax-coxa (TC) joint CPGs in the stick insect (Carausius morosus). We used a new approach combining single-leg stepping with pharmacological activation of segmental CPGs, sensory stimulation, and additional stepping legs. Stepping of a single front leg could activate the ipsilateral mesothoracic TC CPG. Activation of the metathoracic TC CPG required that both ipsilateral front and middle legs were present and that one of these legs was stepping. Unlike the situation in real walking, ipsilateral mesothoracic and metathoracic TC CPGs activated by front-leg stepping fired in phase with the front-leg stepping. Local (intralimb) sensory feedback from load sensors could override this intersegmental influence of front-leg stepping, shifting retractor motoneuron activity relative to the front-leg step cycle and thereby uncoupling them from front-leg stepping. These data suggest that front-leg stepping in isolation would result in in-phase activity of all ipsilateral legs, and functional stepping gaits (in which the three ipsilateral legs do not step in synchrony) emerge because of local load sensory feedback overriding this in-phase influence.

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.

Slow conductances could underlie intrinsic phase-maintaining properties of isolated lobster (Panulirus interruptus) pyloric neurons.

The rhythmic pyloric network of the lobster stomatogastric system approximately maintains phase (that is, the burst durations and durations between the bursts of its neurons change proportionally) when network cycle period is altered by current injection into the network pacemaker (Hooper, 1997a,b). When isolated from the network and driven by rhythmic hyperpolarizing current pulses, the delay to firing after each pulse of at least one network neuron type [pyloric (PY)] varies in a phase-maintaining manner when cycle period is varied (Hooper, 1998). These variations require PY neurons to have intrinsic mechanisms that respond to changes in neuron activity on time scales at least as long as 2 s. Slowly activating and deactivating conductances could provide such a mechanism. We tested this possibility by building models containing various slow conductances. This work showed that such conductances could indeed support intrinsic phase maintenance, and we show here results for one such conductance, a slow potassium conductance. These conductances supported phase maintenance because their mean activation level changed, hence altering neuron postinhibition firing delay, when the rhythmic input to the neuron changed. Switching the sign of the dependence of slow-conductance activation and deactivation on membrane potential resulted in neuron delays switching to change in an anti-phase-maintaining manner. These data suggest that slow conductances or similar slow processes such as changes in intracellular Ca(2+) concentration could underlie phase maintenance in pyloric network neurons.

Direct evidence that stomatogastric (Panulirus interruptus) muscle passive responses are not due to background actomyosin cross-bridges.

Muscles respond to imposed length changes with rapid, large force changes followed by slow relaxations to new steady-state forces. These responses were originally believed to arise from background levels of actomyosin binding. Discovery of giant sarcomere-spanning proteins suggested muscle passive responses could arise from length changes of elastic domains present in these proteins. However, direct evidence that actomyosin plays little role in passive muscle force responses to imposed length changes has not been provided. We show here that a poison of actomyosin interaction, thiourea, does not alter initial force changes or subsequent relaxations of lobster stomatogastric muscles. These data provide direct evidence that background actomyosin cross-bridge formation likely plays, at most, a small role in muscle passive responses to length changes. Thiourea does not alter lobster muscle electrical responses to motor nerve stimulation, although in this species it does cause tonic motor nerve firing. This firing limits the utility of thiourea to study lobster muscle electrical responses to motor nerve stimulation. However, it is unclear whether thiourea induces such motor nerve firing in other animals. Thiourea may therefore provide a convenient technique to measure muscle electrical responses to motor nerve input without the confounding difficulties caused by muscle contraction.

Invertebrate muscles: thin and thick filament structure; molecular basis of contraction and its regulation, catch and asynchronous muscle.

This is the second in a series of canonical reviews on invertebrate muscle. We cover here thin and thick filament structure, the molecular basis of force generation and its regulation, and two special properties of some invertebrate muscle, catch and asynchronous muscle. Invertebrate thin filaments resemble vertebrate thin filaments, although helix structure and tropomyosin arrangement show small differences. Invertebrate thick filaments, alternatively, are very different from vertebrate striated thick filaments and show great variation within invertebrates. Part of this diversity stems from variation in paramyosin content, which is greatly increased in very large diameter invertebrate thick filaments. Other of it arises from relatively small changes in filament backbone structure, which results in filaments with grossly similar myosin head placements (rotating crowns of heads every 14.5 nm) but large changes in detail (distances between heads in azimuthal registration varying from three to thousands of crowns). The lever arm basis of force generation is common to both vertebrates and invertebrates, and in some invertebrates this process is understood on the near atomic level. Invertebrate actomyosin is both thin (tropomyosin:troponin) and thick (primarily via direct Ca(++) binding to myosin) filament regulated, and most invertebrate muscles are dually regulated. These mechanisms are well understood on the molecular level, but the behavioral utility of dual regulation is less so. The phosphorylation state of the thick filament associated giant protein, twitchin, has been recently shown to be the molecular basis of catch. The molecular basis of the stretch activation underlying asynchronous muscle activity, however, remains unresolved.

Operant Learning: Octopus Arms Need Brains to Learn Their Way.

Octopus arm nervous systems have great arm-local information processing capabilities, raising the possibility each arm functions semi-independently. A recent two-choice behavioral study suggests, however, that the brain is required to learn, and choose in each trial, correct arm direction.