Spontaneous Ca2+ release from the sarcoplasmic reticulum limits Ca2+- dependent twitch potentiation in individual cardiac myocytes. A mechanism for maximum inotropy in the myocardium

We hypothesized that the occurrence of spontaneous Ca2+ release from the sarcoplasmic reticulum (SR), in diastole, might be a mechanism for the saturation of twitch potentiation common to a variety of inotropic perturbations that increase the total cell Ca. We used a videomicroscopic technique in single cardiac myocytes to quantify the amplitude of electrically stimulated twitches and to monitor the occurrence of the mechanical manifestation of spontaneous SR Ca2+ release, i.e., the spontaneous contractile wave. In rat myocytes exposed to increasing bathing [Ca2+] (Cao) from 0.25 to 10 mM, the Cao at which the peak twitch amplitude occurred in a given cell was not unique but varied with the rate of stimulation or the presence of drugs: in cells stimulated at 0.2 Hz in the absence of drugs, the maximum twitch amplitude occurred in 2 mM Cao; a brief exposure to 50 nM ryanodine before stimulation at 0.2 Hz shifted the Cao of the maximum twitch amplitude to 7 mM. In cells stimulated at 1 Hz in the absence of drugs, the maximum twitch amplitude occurred in 4 mM Cao; 1 microM isoproterenol shifted the Cao of the maximum twitch amplitude to 3 mM. Regardless of the drug or the stimulation frequency, the Cao at which the twitch amplitude saturated varied linearly with the Cao at which spontaneous Ca2+ release first occurred, and this relationship conformed to a line of identity (r = 0.90, p = less than 0.001, n = 25). The average peak twitch amplitude did not differ among these groups of cells. In other experiments, (a) the extent of rest potentiation of the twitch amplitude in rat myocytes was also limited by the occurrence of spontaneous Ca2+ release, and (b) in both rat and rabbit myocytes continuously stimulated in a given Cao, the twitch amplitude after the addition of ouabain saturated when spontaneous contractile waves first appeared between stimulated twitches. A mathematical model that incorporates this interaction between action potential-mediated SR Ca2+ release and the occurrence of spontaneous Ca2+ release in individual cells predicted the shape of the Cao-twitch relationship observed in other studies in intact muscle. Thus, the occurrence of spontaneous SR Ca2+ release is a plausible mechanism for the saturation of the inotropic response to Ca2+ in the intact myocardium.     

The kinetics relating calcium and force in skeletal muscle.

The kinetics relating Ca2+ transients and muscle force were examined using data obtained with the photoprotein aequorin in skeletal muscles of the rat, barnacle, and frog. These data were fitted by various models using nonlinear methods for minimizing the least mean square errors. Models in which Ca2+ binding to troponin was rate limiting for force production did not produce good agreement with the observed data, except for a small twitch of the barnacle muscle. Models in which cross-bridge kinetics were rate limiting also did not produce good agreement with the observed data, unless the detachment rate constant was allowed to increase sharply on the falling phase of tension production. Increasing the number of cross-bridge states did not dramatically improve the agreement between predicted and observed force. We conclude that the dynamic relationship between Ca2+ transients and force production in intact muscle fibers under physiological conditions can be approximated by a model in which (a) two Ca2+ ions bind rapidly to each troponin molecule, (b) force production is limited by the rate of formation of tightly bound cross-bridges, and (c) the rate of cross-bridge detachment increases rapidly once tension begins to decline and free Ca2+ levels have fallen to low values after the last stimulus. Such a model can account not only for the pattern of force production during a twitch and tetanus, but also the complex, nonlinear pattern of summation which is observed during an unfused tetanus at intermediate rates of stimulation.     

Side peak suppression in responses of an across-frequency integration model to stimuli of varying bandwidth as demonstrated analytically and by implementation

Multiplication-like sound localization models are subjected to phase ambiguities for high-frequency tonal stimuli as multiplication creates several equivalent response peaks in tuning curves. By increasing the bandwidth of the stimulus, phase ambiguities can be reduced, which is often referred to as side peak suppression. In this study we present a Jeffress-based sound localization model, and determine side peak suppression analytically. The results were verified with an implementation of the same model, and compared to physiological data of barn owls. Three types of stimuli were analyzed: pure-tone stimuli, two-tone complexes with varying frequency distances, and noise signals with variable bandwidths. As an additional parameter we also determined the half-width of the main response peak to examine the scaling of tuning curves in azimuth. Results showed that side peak suppression did not only depend on bandwidth, but also on the center frequency and the distance of the side peak to the main response peak. In particular, the analytical model predicted that side peak suppression is a function of relative bandwidth, whereas half-width is inversely proportional to center frequency, with a proportionality factor depending on relative bandwidth. The analytical approach and the implementation yielded equivalent tuning curves (deviation < 1 %). Moreover, the electrophysiological data recorded in barn owls closely matched the predicted tuning curves.     

Ca2+ Dynamics during Membrane Excitation of Green Alga Chara: Model Simulations and Experimental Data

Kinetic investigations of stimulus response coupling in the green alga Chara have revealed that an intermediate second messenger is formed in the process of membrane excitation. This second messenger links electrical stimulation to the mobilization of Ca2+ from internal stores. In the present work, the experimentally based kinetic model, which describes the stimulus-dependent production of the second messenger and Ca2+ mobilization, is combined with a model for inositol 1,4,5-trisphosphate (IP3)-and Ca2+-sensitive gating of a Ca2+-release channel in endomembranes of animal cells. The combination of models allows a good simulation of experimental data, including the all-or-none-type dependence of the Ca2+ response on stimulus duration and complex phase locking phenomena for the dependence of the Ca2+ response on stimulation frequency. The model offers a molecular explanation for the refractory phenomenon in Chara, assigning it to the life time of an inactive state of the Ca2+-release channel. The model furthermore explains the steep dependence of excitation on strength/duration of electrical stimulation as a consequence of an interplay of the dynamical variables in the model.     

Effects of elastic loads on the contractions of cat muscles

The nerves to plantaris and soleus muscles in the cat were stimulated with maximal single shocks and with random stimulus trains which produced partially fused contractions. In order to obtain information on the mechanism of muscular contraction, the effects of allowing the muscles to shorten against various elastic loads were studied in the time domain and in the frequency domain. When springs of increasing stiffness were placed in series with the muscle, the twitch tension increased greatly. The gain of the frequency response curve was also much greater with stiffer springs. The shape of the frequency response curve for plantaris muscle could usually be described by that expected for a second-order system with two real time constants or rate constants. The rate constants changed in qualitatively similar ways in response to increased stiffness of an elastic load, increased muscle length and increased mean rate of nerve stimulation. These results are in agreement with the hypothesis that the linear responses of muscles working against elastic loads are determined by the values of two rate constants. Thus, of the many processes associated with contraction, only two are rate-limiting: one associated with the viscoelastic properties of muscle and the second associated with the reuptake of Ca into the sarcoplasmic reticulum. Non-linear aspects of muscular contraction are also discussed. These are more prominent in soleus muscle than in plantaris muscle.Graduate student of the Medical Research Council of Canada.Formerly a Post-doctoral Fellow of the Muscular Dystrophy Association of Canada.     

Modeling of the effect of modulated electromagnetic radiation on animal cells

Frequency-dependent modifications of intracellular free calcium concentration ([Ca2+]i) in neutrophils exposures to modulated extremely high frequency electromagnetic radiation were analyzed using a special mathematical model for [Ca2+]i oscillations. The model took into account the activation of Ca2+ influx into the cell by cytosolic Ca2+ and Ca(2+)-induced Ca2+ release from intracellular stores. The calcium channels of plasma membrane were chosen as a target for the influence of harmonic signal and additive noise in the model. The model simulation showed that in response to modulating signal, the rise in [Ca2+]i, has frequency dependence and phase dependence in relation to the moment of chemical stimulation. The phase-frequency dependence of the effect was observed at a certain sequence of delivery of chemical stimulus and modulating signal to the cell. At intensities of modulating signals exceeding the threshold, a rise in [Ca2+]i, reaching a level of more than 50% of the initial level, was observed at a frequency of about 1 Hz and in the phase range of 0.3-2.5 radians. The effect was found only at high intensities of chemical stimulus. The additive noise introduced into the system modified qualitatively and quantitatively the phase-frequency characteristics of the cell response to the modulating signal. An increase in noise intensity resulted in a displacement of the average frequency of the band of rise in [Ca2+]i, and then the emergence of a set of bands with a greater Q-factors. The analysis of dynamics of the nonlinear system in terms of the stability theory showed that, as the intensity of chemical stimulus increases, the system transits by means of a series of bifurcations from regular driving to chaotic, and then to oscillations, induced by a modulating harmonic signal. The boundary of the transition of oscillations from chaotic to induced ones corresponds to a specific "threshold" of the intensity of chemical stimulus for the significant rise in [Ca2+]i in response to the modulating signal. The results of the model analysis are in good correspondence with the experimental data obtained earlier, namely, with the effects of modulated extremely high-frequency electromagnetic radiation on neutrophils, which were observed only in the presence of Ca2+ in extracellular medium and at high concentrations of calcium ionophore A23187. Thus, as the characteristic frequency of the quasi-periodic process of calcium signalling in the cell coincides with the frequency of external field, a narrow-band rise in [Ca2+]i is observed, which can result in a modification of the functional activity of the cell.     

The Pattern of Activation in the Sartorius Muscle of the Frog

The development of isometric twitch tension has been compared with the redevelopment of isometric tension in the fully active frog sartorius muscle following release. At 0°C the rate of rise of isometric twitch tension is the same as that for the muscle in the fully active state at the same tension but not until about 40 msec. after the stimulus and then only for a few milliseconds. The rates of rise of tension in the twitch and in the redevelopment of tension in the fully active muscle appear to be nearly the same at low tensions. Substitution of nitrate for chloride in the Ringer's solution bathing the muscle retards the development of tension during the early part of the contraction phase of the twitch and the effect reaches a maximum within 3 minutes after changing the solutions. These observations have been discussed in connection with some possible patterns of activation and the hypothesis has been advanced that the rate of activation of a sarcomere is determined mainly by the rate at which the transverse component of the link between excitation and contraction is propagated inwards from the periphery to the center of the fiber. This hypothesis has been discussed in relation to others concerning the nature of excitation-contraction coupling.     

Prediction of summation in incompletely fused tetanic contractions of rat muscle

Summation is the accumulating contractile force resulting from sequential activations applied to a muscle without sufficient interval to permit complete relaxation. The purpose of this study was to evaluate summation in the rat medial gastrocnemius muscle, and to determine if the contractile responses during summation could be predicted from the relationship between force and activation pattern. In the first part of this study, the consistency of summation in the rat gastrocnemius muscle was assessed and prediction equations were derived. The second part compared predicted summation with actual contractions obtained in a new set experiments. Summation was assessed by calculation of the contractile response, per stimulation, for up to five stimulating pulses at these frequencies: 20, 40, 60 and 80Hz. This was done by subtraction of the force transient for j-1 pulses of stimulation (where j=1-5 pulses) from the force response with j pulses of stimulation. Each of these force differences was evaluated for peak rate of force development, contraction time and half-relaxation time. Contraction and half-relaxation times changed by only a small magnitude from values obtained for the twitch. Peak rate of force development was proportional to the active force for all force transients obtained by subtraction. The force per activation increased from the first to the fifth stimulus, and was dependent on interpulse delay. In the second series of experiments, the predicted force was related to the actual force for brief tetanic contractions at 40, 50 and 60Hz (r(2)=0.875). These experiments demonstrate that the force response to sequential activations is consistent and predictable. Summation can be predicted, knowing only the amplitude of the twitch contraction and the relationship between delay and force for each activating stimulus.     

Contribution of sarcolemmal sodium-calcium exchange and intracellular calcium release to force development in isolated canine ventricular muscle

The aim of this work was to determine the relationship between peak twitch amplitude and sarcoplasmic reticulum (SR) Ca2+ content during changes of stimulation frequency in isolated canine ventricle, and to estimate the extent to which these changes were dependent upon sarcolemmal Na(+)-Ca2+ exchange. In physiological [Na+]o, increased stimulation frequency in the 0.2-2-Hz range resulted in a positive inotropic effect characterized by an increase in peak twitch amplitude and a decrease in the duration of contraction, measured as changes in isometric force development or unloaded cell shortening in intact muscle and isolated single cells, respectively. Action potentials recorded from single cells indicated that the inotropic effect was associated with a progressive decrease of action potential duration and a marked reduction in average time spent by the cell near the resting potential during the stimulus train. The frequency-dependent increase of peak twitch force was correlated with an increase of Ca2+ uptake into and release from the SR. This was estimated indirectly using the phasic contractile response to rapid (less than 1 s) lowering of perfusate temperature from 37 degrees C to 0-2 degrees C and changes of twitch amplitude resulting from perturbations in the pattern of electrical stimulation. Lowering [Na+]o from 140 to 70 mM resulted in an increase of contractile strength, which was accompanied by a similar increase of apparent SR Ca2+ content, both of which could be abolished by exposure to ryanodine (1 x 10(-8) M), caffeine (3 x 10(-3) M), or nifedipine (2 x 10(-6) M). Increased stimulation frequency in 70 mM [Na+]o resulted in a negative contractile staircase, characterized by a graded decrease of peak isometric force development or unloaded cell shortening. SR Ca2+ content estimated under identical conditions remained unaltered. Rate constants derived from mechanical restitution studies implied that the depressant effect of increased stimulation frequency in 70 mM [Na+]o was not a consequence of a decreased rate of refilling of a releasable pool of Ca2+ within the cell. These results demonstrate that frequency-dependent changes of contractile strength and intracellular Ca2+ loading in 140 mM [Na+]o require the presence of a functional sarcolemmal Na(+)-Ca2+ exchange process. The possibility that the negative staircase in 70 mM [Na+]o is related to inhibition of Ca(2+)-induced release of Ca2+ from the SR by various cellular mechanisms is discussed.     

Effects of previous activity on the energetics of activation in frog skeletal muscle

Effects of previous activity on the ability of frog skeletal muscle at 0 degrees C to liberate energy associated with contractile activation, i.e., activation heat (AH), have been examined. Earlier work suggests that activation heat amplitude (as measured from muscles stretched to lengths where active force development is nearly abolished) is related to the amount of Ca2+ released upon stimulation. After a twitch, greater than 2 s is required before a second stimulus (AHt) can liberate the same activation heat as a first stimulus (AH infinity), i.e., (AHt)/(AH infinity) = 1 -0.83 e-1.40t, where t is time in seconds. Caffeine introduces a time delay in the recovery of the ability to generate activation heat after a twitch. After a tetanus, the activation heat is depressed to a greater extent at any time than after a twitch. The activation heat elicited by a stimulus 1 s after a tetanus is depressed progressively with respect to tetanus duration up to 3 s. For tetani of 3, 40, and 80 s duration the postetanus activation heat is comparably depressed. The time-course of the recovery of the ability of the muscle to produce activation heat after a tetanus can be described as (AHt)/(AH infinity) = 1 -0.80 e-0.95t - 0.20 e-0.02t. Greater than 90 s is required before the posttetanus activation heat is equal to the pretetanus value. The faster phase of recovery is similar to recovery after the twitch and the slower phase may be associated with the return of calcium to the terminal cisternae from uptake sites in the longitudinal sarcoplasmic reticulum.     

Mechanism for the opioid-induced twitch potentiations of frog's skeletal muscle

The twitch-potentiating effects of opioids in the frog's skeletal muscle which are naloxone resistant and nonstereospecific were further studied. The rapid kinetics of the onset and of the offset (following washout) of the opioid effect indicates that the site for this action is the surface membrane of the muscle fibre. On the other hand, the lack of any twitch-potentiating effect by naloxone methylbromide, a quaternary derivative of naloxone, suggests that opioids which potentiate the twitch must enter the lipid phase of the membrane to act. Intracellular microelectrode experiments revealed no relation between the opioid effects on membrane electrical events and twitch potentiation. Blocking slow calcium channels with D-600 did not modify the opioid-induced twitch potentiation. The twitch potentiation was antagonized by increasing the extracellular calcium concentration, [Ca2+]o, to 8.64 mM. The effects of closely spaced multiple electrical pulses revealed that the opioids decreased the summated response relative to predrug controls. The results suggest that opioids facilitate the process of excitation-contraction coupling in the frog's skeletal muscle by the release of an additional amount of "trigger calcium" following a single electrical stimulus, thereby generating a potentiated twitch.     

Effect of twitch interval duration on the contractile function of subsequent twitches in isolated rat, rabbit, and dog myocardium under physiological conditions

Many studies have shown that a change in stimulation frequency leads to altered contractility of the myocardium. However, it remains unclear what changes occur directly after a change in frequency and which ones are a result of the slow processes that lead to the altered homeostasis, which develops after a change in stimulation frequency. To distinguish the immediate from the slow responses, we assessed contractile function in two species that have distinctively different calcium (Ca(2+))-handling properties using a recently developed, randomized pacing protocol. In isolated dog and rat right ventricular trabeculae, twitch contractions at five different cycle lengths within the physiologic range of each species were randomized around a steady-state frequency. We found, in both species, that the duration of the cycle length just prior to the analyzed twitch (primary) positively correlated with the increased force of the analyzed twitch. In sharp contrast, the cycle lengths, one and two more removed from the analyzed twitch ("secondary" and "tertiary"), displayed a negative correlation with force of the analyzed twitch. In additional experiments, assessment of intracellular Ca(2+) transients in rabbit trabeculae revealed that diastolic Ca(2+) levels were closely correlated to contractile function outcome. The relative contribution of the primary cycle length was different between dog (51%) and rat (71%), whereas in neither species was a significant effect on relaxation time observed. With the use of randomized cycle lengths, we have distinguished the intrinsic response from the signaling-mediated effects of frequency-dependent activation on myofilament properties and Ca(2+) handling.     

A quantitative description of the contraction of blood vessels following the release of noradrenaline from sympathetic varicosities

A model is presented that highlights the principal factors determining the form and extent of contraction in arteries upon stimulation of their sympathetic nerve supply. This model incorporates a previous quantitative model of the process of noradrenaline (NAd) diffusion into the vascular media and reuptake into sympathetic varicosities during nerve stimulation (J. Theor. Biol. 226 (2004) 359). It is also dependent on a model of how the subsequent activation of metabotropic receptors initiates a G-protein cascade, resulting in the production of inositol trisphosphate (IP3) and an increase in intracellular calcium concentration, [Ca2+]i, in the smooth muscle cells (J. Theor. Biol. 223 (2003) 93). In the present work we couple this rise in [Ca2+]i to the increase in phosphorylated myosin bound to actin in the cells and hence determine the force development in arteries due to nerve stimulation. The model accounts for force development as a function of [Ca2+]i and for the rate of change of force as a function of the rate of change of [Ca2+]i in single smooth muscle cells. It also accounts for the characteristic time course of the force developed by the media of the rat-tail artery upon nerve stimulation. This consists of a rapid rise to a transient peak followed by a sustained plateau of contraction during the stimulation period, after which the contraction slowly decays back to baseline at a rate dependent on the strength of the stimulation. The model indicates that the transient peak is primarily due to the partial block of the IP3 receptor by the rise in [Ca2+]i and that the main determinant of the equilibrium condition indicated by the plateau phase is the rate of pumping of calcium into the sarcoplasmic reticulum. The relatively slow decline of contraction at the end of nerve stimulation is primarily a consequence of the slow rates of removal of NAd from the media by diffusion and reuptake into the sympathetic varicosities. The model thus provides a quantitative account of vascular smooth muscle contraction upon sympathetic nerve stimulation.     

See globally, spike locally: oscillations in a retinal model encode large visual features

We show that coherent oscillations among neighboring ganglion cells in a retinal model encode global topological properties, such as size, that cannot be deduced unambiguously from their local, time-averaged firing rates. Whereas ganglion cells may fire similar numbers of spikes in response to both small and large spots, only large spots evoke coherent high frequency oscillations, potentially allowing downstream neurons to infer global stimulus properties from their local afferents. To determine whether such information might be extracted over physiologically realistic spatial and temporal scales, we analyzed artificial spike trains whose oscillatory correlations were similar to those measured experimentally. Oscillatory power in the upper gamma band, extracted on single-trials from multi-unit spike trains, supported good to excellent size discrimination between small and large spots, with performance improving as the number of cells and/or duration of the analysis window was increased. By using Poisson distributed spikes to normalize the firing rate across stimulus conditions, we further found that coincidence detection, or synchrony, yielded substantially poorer performance on identical size discrimination tasks. To determine whether size encoding depended on contiguity independent of object shape, we examined the total oscillatory activity across the entire model retina in response to random binary images. As the ON-pixel probability crossed the percolation threshold, which marks the sudden emergence of large connected clusters, the total gamma-band activity exhibited a sharp transition, a phenomena that may be experimentally observable. Finally, a reanalysis of previously published oscillatory responses from cat ganglion cells revealed size encoding consistent with that predicted by the retinal model.     

Neural response to very low-frequency sound in the avian cochlear nucleus

Recordings were made in the chick cochlear nucleus from neurons that are sensitive to very low frequency sound. The tuning, discharge rate response and phase-locking properties of these units are described in detail. The principal conclusions are: 1. Low frequency (LF) units respond to sound frequencies between 10-800 Hz. Best thresholds average 60 dB SPL, and are occasionally as low as 40 dB SPL. While behavioral thresholds in this frequency range are not available for the domestic chick, these values are in good agreement with the pigeon behavioral audiogram (Kreithen and Quine 1979). 2. About 60% of the unit population displays tuning curves resembling low-pass filter functions with corner frequencies between 50-250 Hz. The remaining units have broad band-pass tuning curves. Best frequencies range from 50-300 Hz. 3. Spontaneous discharge rate was analyzed quantitatively for LF units recorded from nucleus angularis. The distribution of spontaneous rates for LF units is similar to that seen from higher CF units (300-5000 Hz) found in the same nucleus. However, the spontaneous firing of LF units is considerably more regular than that of their higher CF counterparts. 4. Low frequency units with low spontaneous rates (SR's less than 40 spikes/s) show large driven rate increases and usually saturate by discharging once or twice per stimulus cycle. Higher SR units often show no driven rate increases. 5. All LF units show strong phase-locking at all excitatory stimulus frequencies. Vector strengths as high as 0.98 have been observed at moderate sound levels. 6. The preferred phase of discharge (relative to the sound stimulus) increases with stimulus frequency in a nearly linear manner. This is consistent with the LF units being stimulated by a traveling wave. The slope of these phase-frequency relationships provides an estimate of traveling wave delay. These delays average 7.2 ms, longer than those seen for higher CF auditory brainstem units. These observations suggest that the peripheral site of low frequency sensitivity is the very distal region of the basilar papilla, an area whose morphology differs significantly from the rest of the chick basilar papilla. 7. LF units are described whose response to sound is inhibitory at frequencies above 50 Hz.     

Enhanced skeletal muscle contraction with myosin light chain phosphorylation by a calmodulin-sensing kinase

Repetitive low frequency stimulation results in potentiation of twitch force development in fast-twitch skeletal muscle due to myosin regulatory light chain (RLC) phosphorylation by Ca(2+)/calmodulin (CaM)-dependent skeletal muscle myosin light chain kinase (skMLCK). We generated transgenic mice that express an skMLCK CaM biosensor in skeletal muscle to determine whether skMLCK or CaM is limiting to twitch force potentiation. Three transgenic mouse lines exhibited up to 22-fold increases in skMLCK protein expression in fast-twitch extensor digitorum longus muscle containing type IIa and IIb fibers, with comparable expressions in slow-twitch soleus muscle containing type I and IIa fibers. The high expressing lines showed a more rapid RLC phosphorylation and force potentiation in extensor digitorum longus muscle with low frequency electrical stimulation. Surprisingly, overexpression of skMLCK in soleus muscle did not recapitulate the fast-twitch potentiation response despite marked enhancement of both fast-twitch and slow-twitch RLC phosphorylation. Analysis of calmodulin binding to the biosensor showed a frequency-dependent activation to a maximal extent of 60%. Because skMLCK transgene expression is 22-fold greater than the wild-type kinase, skMLCK rather than calmodulin is normally limiting for RLC phosphorylation and twitch force potentiation. The kinase activation rate (10.6 s(-1)) was only 3.6-fold slower than the contraction rate, whereas the inactivation rate (2.8 s(-1)) was 12-fold slower than relaxation. The slower rate of kinase inactivation in vivo with repetitive contractions provides a biochemical memory via RLC phosphorylation. Importantly, RLC phosphorylation plays a prominent role in skeletal muscle force potentiation of fast-twitch type IIb but not type I or IIa fibers.     

Relationship between numbers and frequencies of stimuli in human muscle fatigue

The effect of stimulus frequency on the rate of muscle fatigue has been studied on dorsiflexor muscles of the human ankle. It was found that significantly fewer stimuli were required to abolish twitch and tetanic torque when the stimuli were delivered at 15 Hz rather than 30 Hz. At both stimulus frequencies twitch torque disappeared before tetanic torque. The difference in numbers of stimuli required for fatigue was not due to impaired excitation of muscle fibers at either of the two frequencies. At both stimulating frequencies, twitch fatigue appeared to be due to a defect in excitation-contraction coupling and/or the contractile machinery.     

Responses of cells in the somatosensory cortex of unanaesthetized cats after sinusoidal displacements of single vibrissae

Summary Neurones in the somatosensory cortex of unanaesthetized restrained cats were recorded during single trapezoid and repetitive sinusoidal displacements of single vibrissae. Responses to trapezoid displacements were similar to those described previously in anaesthetized cats (Hellweg et al., 1977).During repetitive mechanical stimulation cortical cells showed adaptive behaviour so that at higher stimulation frequencies the number of cell discharges per stimulus cycle decreased. The ability to follow the repetition of the stimulus at a one to one ratio was lost in the frequency range between 20 Hz and 60 Hz. A few exceptional cells, while not following at a one to one ratio, still showed some periodicities in their response histograms corresponding to repetition rates of up to 100 Hz. In about 10% of the cells nonmonotonic functions between stimulation frequency and response per cycle were found. These nonmonotonic functions as well as the different adaptive behaviour of cells could not be predicted on the basis of their response to trapezoid stimuli.Measurements of the phase differences between stimulus cycle and response peaks during repetitive stimulation showed that both can vary as a function of stimulation frequency. It is discussed whether these findings could be compatible with the concept of phase coding in the somatosensory cortex.     

Modeling of summation of individual twitches into unfused tetanus for various types of rat motor units.

Repeated stimulation of motor units (MUs) causes an increase of the force output that cannot be explained by linear summation of equal twitches evoked by the same stimulation pattern. To explain this phenomenon, an algorithm for reconstructing the individual twitches, that summate into an unfused tetanus is described in the paper. The algorithm is based on an analytical function for the twitch course modeling. The input parameters of this twitch model are lead time, contraction and half-relaxation times and maximal force. The measured individual twitches and unfused tetani at 10, 20, 30 and 40 Hz stimulation frequency of three rat motor units (slow, fast resistant to fatigue and fast fatigable) are processed. It is concluded that: (1) the analytical function describes precisely the course of individual twitches; (2) the summation of equal twitches does not follow the results from the experimentally measured unfused tetani, the differences depend on the type of the MU and are bigger for higher values of stimulation frequency and fusion index; (3) the reconstruction of individual twitches from experimental tetanic records can be successful if the tetanus is feebly fused (fusion index up to 0.7); (4) both the maximal forces and time parameters of individual twitches subtracted from unfused tetani change and influence the course of each tetanus. A discrepancy with respect to the relaxation phase was observed between experimental results and model prediction for tetani with fusion index exceeding 0.7. This phase was predicted longer than the experimental one for better fused tetani. Therefore, a separate series of physiological experiments and then, more complex model are necessary for explanation of this distinction.     

Frequency response model of skeletal muscle and its association with contractile properties of skeletal muscle

The aims of the present study were to develop a mathematical model of the skeletal muscle based on the frequency transfer function, referred to as frequency response model, and to presume the relationship between the model elements and skeletal muscle contractile properties. Twitch force in elbow flexion was elicited by applying a single electrical stimulation to the motor point of biceps brachii muscles, and then analyzed visually by the Bode gain and phase diagram of the force signal. The frequency response model was represented by a frequency transfer function consisting of five basic control elements (proportional element, dead time element, and three first-order lag elements). The model element constants were estimated by best-fitting to the Bode gain and phase diagram of the twitch force signal. The proportional constant and the dead time in the frequency response model correlated significantly with the peak torque and the latency in the actual twitch force, respectively. In addition, the time constants of the three first-order lag elements in the model correlated strongly with the contraction time and the half relaxation time in the actual twitch force. The results suggested a possibility that the individual elements in the frequency response model would reflect the biochemical and biomechanical properties in the excitation–contraction coupling process of skeletal muscle.