The mechanisms of the residual force enhancement after stretch of skeletal muscle: non-uniformity in half-sarcomeres and stiffness of titin

When activated skeletal muscles are stretched, the force increases significantly. After the stretch, the force decreases and reaches a steady-state level that is higher than the force produced at the corresponding length during purely isometric contractions. This phenomenon, referred to as residual force enhancement, has been observed for more than 50 years, but the mechanism remains elusive, generating considerable debate in the literature. This paper reviews studies performed with single muscle fibres, myofibrils and sarcomeres to investigate the mechanisms of the stretch-induced force enhancement. First, the paper summarizes the characteristics of force enhancement and early hypotheses associated with non-uniformity of sarcomere length. Then, it reviews new evidence suggesting that force enhancement can also be associated with sarcomeric structures. Finally, this paper proposes that force enhancement is caused by: (i) half-sarcomere non-uniformities that will affect the levels of passive forces and overlap between myosin and actin filaments, and (ii) a Ca(2+)-induced stiffness of titin molecules. These mechanisms are compatible with most observations in the literature, and can be tested directly with emerging technologies in the near future.     

Theoretical and experimental behaviour of the muscle viscosity coefficient during maximal concentric actions

The aim of this study was to calculate the theoretical variation of the nonlinear damping factor (B) as a function of the muscle shortening velocity, and then to compare the theoretical values with the experimental data obtained on both the elbow flexor and the ankle extensor muscles. The theoretical variation of the B factor was determined from a muscle model consisting of a contractile component in parallel with a viscous damper both in series with an elastic component, and by using, the charateristic equation of the force velocity curve. In this muscle model, the viscous element modelled the inability of the muscle to generate as big a contracting force (while shortening) as possible under isometric conditions. Eight volunteer subjects performed maximal concentric elbow flexions and ankle extensions on an isokinetic ergometer at angular velocities of 60, 120, 180, 240, 300 and 360°·s^–1, and held two maximal isometric actions at an elbow angle of 90° (0° corresponds to the full extension) and at an ankle angle of 0° (0° corresponds to the foot flexion of 90° relative to the leg axis). From these measurements, the force and the shortening velocity values of each muscle were determined by using a musculo-skeletal model of the joint. The results showed that the theoretical behaviour of the B factor would seem to be dependent on the shortening velocity and on the parameter which varies according to the muscle fibre type composition and affects the curvature of the force-velocity curve (a_f). For each muscle group, the experimental data of B fitted with the theoretical equation, and the best fit was obtained for an of of 0.28 for the ankle extensor and of 0.32 for the elbow flexor muscles. These results indicated that from the muscle model used in the present study it is possible to describe the mechanical behaviour of the muscle during maximal concentric action.     

Categorization of enzyme deactivations using a series-type mechanism

A series-type enzyme deactivation model involving an active enzyme precursor and a final enzyme state with possible non-zero activity is proposed to categorize enzyme deactivation curves. The enzyme activity is a weighted function of the active enzyme states. The deactivation curves may be broadly classified into two major categories wherein the activity is either always less than or it may be more than the initial activity for some time period. Data taken from the literature may be classified into 14 cases. Complex enzyme deactivation curves exhibiting enzyme stabilization and a flex are some of the features that are classified.     

Stimulation frequency and force potentiation in the human adductor pollicis muscle

The effect of stimulation frequency on twitch force potentiation was examined in the adductor pollicis muscle of ten normal subjects. The ulnar nerve was supramaximally stimulated at the wrist and isometric twitch force was measured from a 3-Hz train lasting 1 s. Test stimulation frequencies of 5, 10, 20, 25, 30, 40, 50 and 100 Hz were applied for 5 s each in random order (5 min apart) and the twitches (3 Hz) were applied immediately before and after (1 s) the test frequency and at intervals up to 5 min afterwards (10 s, and 1, 2 and 5 min). Poststimulation twitches were expressed as a percentage of the prestimulation twitch. Low frequency fatigue was not induced by the protocol since the 20:50 Hz ratio did not alter within each session. The degree of twitch potentiation was frequency dependent, with potentiation increasing up to 50 Hz [mean 173 (SD 16)%] but the effect was markedly less at 100 Hz [mean 133 (SD 25)%, P less than 0.01] for all subjects. The reduced potentiation at 100 Hz may have occurred due to high frequency fatigue produced by the 100-Hz test stimulation train. The optimal frequency of those examined in the experimental group was 50 Hz but this only produced maximal potentiation in six of the ten subjects and 100 Hz always produced less potentiation. These findings have implications for electrical stimulation of muscle in the clinical setting.     

Predicting muscle force generation during fast-starts for the common carp Cyprinus carpio

Muscle contractile properties have been characterised for white myotomal muscle from the common carp Cyprinus carpio at 10, 15, and 20 °C. The time course of muscle force development was measured when one, two, or three stimuli were delivered at the onset of constant velocity shortening. As the shortening velocity increased several parameters decreased including the maximum force, the time course for the contraction and the relative duration of the deactivation compared to the activation. The maximum force and the relative rates of activation to deactivation for the contraction were relatively independent of temperature, whereas the duration of the contraction decreased with increasing temperature. A predictive model was developed which was based on fitting a modified Weibull distribution to these observations. The model was used to interpolate the expected contractile forces during cyclic length-changes. Measured and predicted values for force and power during such cyclic work-loop experiments showed an excellent agreement over the range of shortening regimes typically found during swimming behaviours. However, the predicted force was overestimated during the deactivation phase of the contractions when the shortening velocities exceeded those found during swimming. Accepted: 25 May 1999     

The separation of antagonist from agonist effects of trisubstituted purines on CaV2.2 (N-type) channels

Dihydropyridines can affect L-type calcium channels (CaV1) as either agonists or antagonists. Seliciclib or R-roscovitine, a 2,6,9-trisubstituted purine, is a potent cyclin-dependent kinase inhibitor that induces both agonist and antagonist effects on CaV2 channels (N-, P/Q- and R-type). We studied the effects induced by various trisubstituted purines on CaV2.2 (N-type) channels to learn about chemical structure–function relationships. We found that S-roscovitine and R-roscovitine showed similar potency to inhibit, but agonist activity of S-roscovitine required at least a 20-fold higher concentration, suggesting stereospecificity of the agonist-binding site. The testing of other trisubstituted purines showed a correlation between CaV2.2 inhibition and cyclin-dependent kinase affinity that broke down after determining that a chemically unrelated inhibitor, kenpaullone, was a poor CaV2.2 inhibitor, and a kinase inactive analog (dimethylamino-olomoucine; DMAO) was a strong inhibitor, which together support a kinase independent effect. In fact, like dihydropyridine-induced L-channel inhibition, R-roscovitine left-shifted the closed-state inactivation versus voltage relationship, which suggests that inhibition results from CaV2 channels moving into the inactivated state. Trisubstituted purine antagonists could become clinically important drugs to treat diseases, such as heart failure and neuropathic pain that result from elevated CaV2 channel activity.     

Force depression decays during shortening in the medial gastrocnemius of the rat

Force depression due to shortening of activated skeletal muscles has previously been described to be long lasting during isometric contractions following the shortening. In the present study, using the medial gastrocnemius of the rat, effects of force depression have been made apparent during shortening by computationally partially compensating for the direct effect of shortening velocity due to the tension–velocity relation. Evidence was found for the decay and complete disappearance of force depression already during continuation of the shortening contraction to short muscle lengths.     

Titin-induced force enhancement and force depression: A ‘sticky-spring’ mechanism in muscle contractions?

The sliding filament and crossbridge theories do not suffice to explain a number of muscle experiments. For example, from the entire muscle to myofibrils, predictions of these theories were shown to underestimate the force output during and after active tissue stretch. The converse applies to active tissue shortening.In addition to the crossbridge cycle, we propose that another molecular mechanism is effective in sarcomere force generation. We suggest that, when due to activation, myosin binding sites are available on actin, the giant protein titin's PEVK region attaches itself to the actin filament at those sites. As a result, the molecular spring length is dramatically reduced. This leads to increased passive force when the sarcomere is stretched and to decreased or even negative passive force when the sarcomere shortens. Moreover, during shortening, the proposed mechanism interferes with active-force production by inhibiting crossbridges.Incorporation of a simple ‘sticky-spring’ mechanism model into a Hill-type model of sarcomere dynamics offers explanations for several force-enhancement and force-depression effects. For example, the increase of the sarcomere force compared to the force predicted solely by the sliding filament and crossbridge theories depends on the stretch amplitude and on the working range. The same applies to the decrease of sarcomere force during and after shortening. Using only literature data for its parameterization, the model predicts forces similar to experimental results.     

Interaction between the Postactivation Depression of H Reflex and Long-Lasting Inhibition,Evoked by Stimulation of a Nerve to the Antagonist Muscles,in Humans

In a study on healthy humans, we examined interaction of the inhibitory influences on the H reflex recorded from the m. soleus (the respective EMG discharge, evoked by stimulation of the n. tibialis comm.). Postactivation depression of the reflex was evoked by a preceding conditioning stimulation of the same nerve, while conditioning stimulation of a nerve to the antagonist muscles (n. peroneus comm.) evoked long-lasting inhibition of the reflex, which included two consecutive waves of depression, D ₁ and D ₂. When the intensity of conditioning stimulations slightly exceeded the threshold for the development of inhibitory effects, interaction between postactivation depression and both the D ₁ and D ₂ waves demonstrated mutual facilitation of these effects. When the intensity of conditioning stimuli was increased, facilitation was changed by occlusion. We conclude that afferent impulsation, evoked by homo- and heteronymous conditioning stimulations of the peripheral nerves, converges on common interneuronal populations providing long-lasting suppression of the H reflex, which develops due to depolarization of primary afferent Ia terminals.     

Multisensory integration in the superior colliculus: a neural network model

Neurons in the superior colliculus (SC) are known to integrate stimuli of different modalities (e.g., visual and auditory) following specific properties. In this work, we present a mathematical model of the integrative response of SC neurons, in order to suggest a possible physiological mechanism underlying multisensory integration in SC. The model includes three distinct neural areas: two unimodal areas (auditory and visual) are devoted to a topological representation of external stimuli, and communicate via synaptic connections with a third downstream area (in the SC) responsible for multisensory integration. The present simulations show that the model, with a single set of parameters, can mimic various responses to different combinations of external stimuli including the inverse effectiveness, both in terms of multisensory enhancement and contrast, the existence of within- and cross-modality suppression between spatially disparate stimuli, a reduction of network settling time in response to cross-modal stimuli compared with individual stimuli. The model suggests that non-linearities in neural responses and synaptic (excitatory and inhibitory) connections can explain several aspects of multisensory integration.     

Molecular Dynamics as a Mathematical Mapping. I. Differentiable Force Functions

Abstract

The molecular dynamics technique can be viewed as a deterministic mathematical mapping between, on one side, the force field parameters that describe the potential energy interactions and the input macroscopic conditions, and, on the other, the calculated macroscopic properties of the bulk molecular system.

The differentiability of such a mapping in the conventional molecular dynamics calculations is affected by the discontinuities in particle positions introduced by the periodic boundary conditions and the discontinuities introduced by the minimum image convention and other methods commonly employed to approximate the calculation of interparticle potential and force.

This paper proposes an alternative molecular dynamics framework based on modified force functions which are almost everywhere continuous and differentiable, and exhibit a natural periodicity. These characteristics obviate the need for both the periodic boundary conditions and the minimum image convention, as well as for any corrections for long-range interactions. They also make it possible to apply standard methods of variational calculus for the computation of partial derivatives of the molecular dynamics mapping.

The modified framework is first introduced for the case of simple monoatomic fluids where the nature of the forces exerted between any pair of two particles is identical. A more general model describing the interactions of flexible molecules is then developed. We describe the application of this approach to mixtures of alkane molecules interacting via the NERD force field.     

The Magnitude and Duration of Itch Produced by Intracutaneous Injections of Histamine

The magnitude and duration of itch sensation produced by intracutaneous injection of histamine were determined for humans with the procedure of magnitude estimation scaling. Thirteen subjects received a 10-μ1 intracutaneous injection of histamine at doses of 0.0001, 0.001, 0.01, 0.1, 1, and 10 μg into the volar forearm; eight of these subjects also received a 100-μg dose. One subject received multiple injections over several weeks to determine the reliability of the magnitude estimates of itch. Following each injection, the area of flare and duration of itch were also determined.

Intracutaneous injection of histamine produced a pure sensation of itch, without pain. The magnitude of itch increased in a dose-dependent fashion. The lowest histamine dose that produced itch greater than the itch produced by vehicle was 0.01 μg. The greatest itch was produced by the 100-μg dose. A power function fitted to the mean magnitude estimates had an exponent of 0.17, indicating a negatively accelerating relation between the magnitude of itch and histamine dose. The one subject who received histamine over several weeks gave fairly reproducible estimates of itch magnitude.

The duration of itch and the area of flare also increased in a dose-dependent fashion. The lowest dose of histamine that produced a duration of itch longer than the itch produced by the vehicle was 0.1 μg, while the 100-μg dose produced the longest duration of itch. Although the area of flare increased with each increase in dose from 0.1 to 10 μg, the areas of flare produced by 10 and 100 μg of histamine did not differ.

These results indicate that humans can scale the magnitude of itch produced by histamine in a dose-dependent manner. In addition, the duration of itch and the area of flare produced by histamine are dose-dependent, confirming results of previous investigators. Intracutaneous histamine is easily quantifiable and may thus be a useful stimulus in neurophysiological studies of the peripheral neural mechanisms of itch.     

Shortening-induced force depression is primarily caused by cross-bridges in strongly bound states

The steady-state isometric force following active muscle shortening is smaller than the corresponding force obtained for purely isometric contractions. This so-called residual force depression has been observed consistently for more than half a century, however its mechanism remains a matter of scientific debate. [Maréchal, G., Plaghki, L., 1979. The deficit of the isometric tetanic tension redeveloped after a release of frog muscle at a constant velocity. J. Gen. Physiol. 73, 453–467] suggested that force depression might be caused by alterations in the cross-bridge kinetics following muscle shortening, but there is no research studying force depression systematically for altered cross-bridge kinetic conditions. The purpose of this study was to investigate if force depression affects so-called weakly and strongly bound cross-bridges to the same degree. In order to achieve this aim, we modified the ratio of weakly to strongly bound cross-bridges with 2,3-butanedione monoxime (BDM) in single frog fibers. BDM inhibits the formation of strongly bound cross-bridges in a dose-dependent manner, thus the ratio of weakly to strongly bound cross-bridges could be altered in a systematic way. We found that the absolute amount of force depression was decreased by 50% while the relative amount was decreased by 12% in BDM exposed fibers compared to fibers in normal Ringer's solution. Furthermore, force depression was accompanied by a decrease in stiffness that was much greater in normal compared to BDM exposed fibers, leading to the conclusion that force depression was caused by an inhibition of cross-bridge attachment following fiber shortening and that this inhibition primarily affected cross-bridges in the strongly bound states.     

Inhibitors of sensillar esterase reversibly block the responses of moth pheromone receptor cells

Three volatile alkyl-thio-trifluoro propanones inhibiting the esterase in olfactory sensilla of the silkmoths Antheraea polyphemus and A. pernyi were used to test the hypothesis that enzymatic pheromone degradation is responsible for the decline of the receptor potential after pheromone stimulation. Test stimuli were the pheromone components (E,Z)-6,11-hexadecadienyl acetate, a substrate for the sensillar esterase, and (E,Z)-6,11-hexadecadienal, not degraded by the esterase. Each compound acts on a separate type of receptor cell. In both receptor cell types the trifluoro propanones caused a partially reversible reduction of sensitivity as indicated by smaller receptor potential amplitudes and lower nerve impulse frequencies. Since application of the esterase inhibitors did not prolong the decline of the receptor potential of the acetate cell, the esterase is not responsible for the rapid pheromone deactivation. When the trifluoro propanones were applied after the pheromone at high concentrations, they rapidly inhibited (repolarized) both receptor cell types. Experiments with local application of trifluoro propanones revealed that the inhibitory effect spreads within seconds along the length of the sensillum. The inhibition of the electrophysiological responses might be due to an antagonistic action of the trifluoro propanones at the pheromone-binding sites, either at the receptor molecules or at the pheromone-binding protein. Accepted: 4 February 1998     

Molecular Dynamics as a Mathematical Mapping. III. Efficient Evaluation of the Differentiable Force Functions and Their Derivatives

Abstract

The fully continuous and differentiable framework for performing molecular dynamics calculations introduced in parts I and II of this paper [1,2] requires the evaluation of rather complex force functions and their spatial partial derivatives. This paper presents an efficient interpolation scheme for the evaluation of these quantities over a finite spatial domain.

The modified force function is approximated by a linear combination of Hermite cubic basis functions such that both the interpolant of the force and its spatial derivatives are continuous across the grid boundaries. In order to achieve better accuracy for a given grid size, a nonuniform rectilinear grid is constructed via iterative refinement procedure. The latter guarantees the accuracy of the force computed by interpolation within any specified tolerance > ε O.

For many potential functions of practical interest, it is possible for polynomial interpolants to be constructed for parts of the force functions which are independent of the potential parameters and system density (the so-called “separable force functions”). In such cases, a single interpolation grid which is applicable for a wide range of potential parameters and system densities can be constructed a priori.