Numerical methods to determine calcium release flux from calcium transients in muscle cells

Voltage sensor current, SR Ca2+ release, and Ca2+ channel current during trains of action potential-like depolarizations of skeletal muscle fibers

In skeletal muscle, CaV 1.1 serves as the voltage sensor for both excitation-contraction coupling (ECC) and L-type Ca2+ channel activation. We have recently adapted the technique of action potential (AP) voltage clamp (APVC) to monitor the current generated by the movement of intramembrane voltage sensors (IQ ) during single imposed transverse tubular AP-like depolarization waveforms (IQAP ). We now extend this procedure to monitoring IQAP , and Ca2+ currents during trains of tubular AP-like waveforms in adult murine skeletal muscle fibers, and compare them with the trajectories of APs and AP-induced Ca2+ release measured in other fibers using field stimulation and optical probes. The AP waveform remains relatively constant during brief trains (<1 sec) for propagating APs in non-V clamped fibers. Trains of 10 AP-like depolarizations at 10 Hz (900 ms), 50 Hz (180 ms), or 100 Hz (90 ms) did not alter IQAP amplitude or kinetics, consistent with previous findings in isolated muscle fibers where negligible charge immobilization occurred during 100 ms step depolarizations. Using field stimulation, Ca2+ release did exhibit a considerable decline from pulse to pulse during the train, also consistent with previous findings, indicating that the decline of Ca2+ release during a short train of APs is not correlated to modification of charge movement. Ca2+ currents during single or 10 Hz trains of AP-like depolarizations were hardly detectable, were minimal during 50 Hz trains, and became more evident during 100 Hz trains in some fibers. Our results verify predictions on the behavior of the ECC machinery in response to AP-like depolarizations and provide a direct demonstration that Ca2+ currents elicited by single AP-like waveforms are negligible, but can become more prominent in some fibers during short high-frequency train stimulation that elicits maximal isometric force.

Loss of S100A1 expression leads to Ca2+ release potentiation in mutant mice with disrupted CaM and S100A1 binding to CaMBD2 of RyR1

Calmodulin (CaM) and S100A1 fine-tune skeletal muscle Ca2+ release via opposite modulation of the ryanodine receptor type 1 (RyR1). Binding to and modulation of RyR1 by CaM and S100A1 occurs predominantly at the region ranging from amino acid residue 3614-3640 of RyR1 (here referred to as CaMBD2). Using synthetic peptides, it has been shown that CaM binds to two additional regions within the RyR1, specifically residues 1975-1999 and 4295-4325 (CaMBD1 and CaMBD3, respectively). Because S100A1 typically binds to similar motifs as CaM, we hypothesized that S100A1 could also bind to CaMBD1 and CaMBD3. Our goals were: (1) to establish whether S100A1 binds to synthetic peptides containing CaMBD1 and CaMBD3 using isothermal calorimetry (ITC), and (2) to identify whether S100A1 and CaM modulate RyR1 Ca2+ release activation via sites other than CaMBD2 in RyR1 in its native cellular context. We developed the mouse model (RyR1D-S100A1KO), which expresses point mutation RyR1-L3625D (RyR1D) that disrupts the modulation of RyR1 by CaM and S100A1 at CaMBD2 and also lacks S100A1 (S100A1KO). ITC assays revealed that S100A1 binds with different affinities to CaMBD1 and CaMBD3. Using high-speed Ca2+ imaging and a model for Ca2+ binding and transport, we show that the RyR1D-S100A1KO muscle fibers exhibit a modest but significant increase in myoplasmic Ca2+ transients and enhanced Ca2+ release flux following field stimulation when compared to fibers from RyR1D mice, which were used as controls to eliminate any effect of binding at CaMBD2, but with preserved S100A1 expression. Our results suggest that S100A1, similar to CaM, binds to CaMBD1 and CaMBD3 within the RyR1, but that CaMBD2 appears to be the primary site of RyR1 regulation by CaM and S100A1.

Voltage modulates halothane-triggered Ca2+ release in malignant hyperthermia-susceptible muscle

Malignant hyperthermia can result from mutations in the ryanodine receptor that favor anesthetic-induced Ca²⁺ release. Zullo et al. find that membrane potential modulates the effect of the volatile anesthetic halothane on skeletal muscle ryanodine receptors possessing the Y524S mutation.

Malignant hyperthermia (MH) is a fatal hypermetabolic state that may occur during general anesthesia in susceptible individuals. It is often caused by mutations in the ryanodine receptor RyR1 that favor drug-induced release of Ca²⁺ from the sarcoplasmic reticulum. Here, knowing that membrane depolarization triggers Ca²⁺ release in normal muscle function, we study the cross-influence of membrane potential and anesthetic drugs on Ca²⁺ release. We used short single muscle fibers of knock-in mice heterozygous for the RyR1 mutation Y524S combined with microfluorimetry to measure intracellular Ca²⁺ signals. Halothane, a volatile anesthetic used in contracture testing for MH susceptibility, was equilibrated with the solution superfusing the cells by means of a vaporizer system. In the range 0.2 to 3%, the drug causes significantly larger elevations of free myoplasmic [Ca²⁺] in mutant (YS) compared with wild-type (WT) fibers. Action potential–induced Ca²⁺ signals exhibit a slowing of their time course of relaxation that can be attributed to a component of delayed Ca²⁺ release turnoff. In further experiments, we applied halothane to single fibers that were voltage-clamped using two intracellular microelectrodes and studied the effect of small (10-mV) deviations from the holding potential (−80 mV). Untreated WT fibers show essentially no changes in [Ca²⁺], whereas the Ca²⁺ level of YS fibers increases and decreases on depolarization and hyperpolarization, respectively. The drug causes a significant enhancement of this response. Depolarizing pulses reveal a substantial negative shift in the voltage dependence of activation of Ca²⁺ release. This behavior likely results from the allosteric coupling between RyR1 and its transverse tubular voltage sensor. We conclude that the binding of halothane to RyR1 alters the voltage dependence of Ca²⁺ release in MH-susceptible muscle fibers such that the resting membrane potential becomes a decisive factor for the efficiency of the drug to trigger Ca²⁺ release.

Altered Ca(2+) signaling in skeletal muscle fibers of the R6/2 mouse, a model of Huntington's disease

Huntington's disease (HD) is caused by an expanded CAG trinucleotide repeat within the gene encoding the protein huntingtin. The resulting elongated glutamine (poly-Q) sequence of mutant huntingtin (mhtt) affects both central neurons and skeletal muscle. Recent reports suggest that ryanodine receptor-based Ca(2+) signaling, which is crucial for skeletal muscle excitation-contraction coupling (ECC), is changed by mhtt in HD neurons. Consequently, we searched for alterations of ECC in muscle fibers of the R6/2 mouse, a mouse model of HD. We performed fluorometric recordings of action potentials (APs) and cellular Ca(2+) transients on intact isolated toe muscle fibers (musculi interossei), and measured L-type Ca(2+) inward currents on internally dialyzed fibers under voltage-clamp conditions. Both APs and AP-triggered Ca(2+) transients showed slower kinetics in R6/2 fibers than in fibers from wild-type mice. Ca(2+) removal from the myoplasm and Ca(2+) release flux from the sarcoplasmic reticulum were characterized using a Ca(2+) binding and transport model, which indicated a significant reduction in slow Ca(2+) removal activity and Ca(2+) release flux both after APs and under voltage-clamp conditions. In addition, the voltage-clamp experiments showed a highly significant decrease in L-type Ca(2+) channel conductance. These results indicate profound changes of Ca(2+) turnover in skeletal muscle of R6/2 mice and suggest that these changes may be associated with muscle pathology in HD.

Modulation of sarcoplasmic reticulum Ca2+ release in skeletal muscle expressing ryanodine receptor impaired in regulation by calmodulin and S100A1

In vitro, calmodulin (CaM) and S100A1 activate the skeletal muscle ryanodine receptor ion channel (RyR1) at submicromolar Ca(2+) concentrations, whereas at micromolar Ca(2+) concentrations, CaM inhibits RyR1. One amino acid substitution (RyR1-L3625D) has previously been demonstrated to impair CaM binding and regulation of RyR1. Here we show that the RyR1-L3625D substitution also abolishes S100A1 binding. To determine the physiological relevance of these findings, mutant mice were generated with the RyR1-L3625D substitution in exon 74, which encodes the CaM and S100A1 binding domain of RyR1. Homozygous mutant mice (Ryr1(D/D)) were viable and appeared normal. However, single RyR1 channel recordings from Ryr1(D/D) mice exhibited impaired activation by CaM and S100A1 and impaired CaCaM inhibition. Isolated flexor digitorum brevis muscle fibers from Ryr1(D/D) mice had depressed Ca(2+) transients when stimulated by a single action potential. However, during repetitive stimulation, the mutant fibers demonstrated greater relative summation of the Ca(2+) transients. Consistently, in vivo stimulation of tibialis anterior muscles in Ryr1(D/D) mice demonstrated reduced twitch force in response to a single action potential, but greater summation of force during high-frequency stimulation. During repetitive stimulation, Ryr1(D/D) fibers exhibited slowed inactivation of sarcoplasmic reticulum Ca(2+) release flux, consistent with increased summation of the Ca(2+) transient and contractile force. Peak Ca(2+) release flux was suppressed at all voltages in voltage-clamped Ryr1(D/D) fibers. The results suggest that the RyR1-L3625D mutation removes both an early activating effect of S100A1 and CaM and delayed suppressing effect of CaCaM on RyR1 Ca(2+) release, providing new insights into CaM and S100A1 regulation of skeletal muscle excitation-contraction coupling.

S100A1 promotes action potential-initiated calcium release flux and force production in skeletal muscle

The role of S100A1 in skeletal muscle is just beginning to be elucidated. We have previously shown that skeletal muscle fibers from S100A1 knockout (KO) mice exhibit decreased action potential (AP)-evoked Ca(2+) transients, and that S100A1 binds competitively with calmodulin to a canonical S100 binding sequence within the calmodulin-binding domain of the skeletal muscle ryanodine receptor. Using voltage clamped fibers, we found that Ca(2+) release was suppressed at all test membrane potentials in S100A1(-/-) fibers. Here we examine the role of S100A1 during physiological AP-induced muscle activity, using an integrative approach spanning AP propagation to muscle force production. With the voltage-sensitive indicator di-8-aminonaphthylethenylpyridinium, we first demonstrate that the AP waveform is not altered in flexor digitorum brevis muscle fibers isolated from S100A1 KO mice. We then use a model for myoplasmic Ca(2+) binding and transport processes to calculate sarcoplasmic reticulum Ca(2+) release flux initiated by APs and demonstrate decreased release flux and greater inactivation of flux in KO fibers. Using in vivo stimulation of tibialis anterior muscles in anesthetized mice, we show that the maximal isometric force response to twitch and tetanic stimulation is decreased in S100A1(-/-) muscles. KO muscles also fatigue more rapidly upon repetitive stimulation than those of wild-type counterparts. We additionally show that fiber diameter, type, and expression of key excitation-contraction coupling proteins are unchanged in S100A1 KO muscle. We conclude that the absence of S100A1 suppresses physiological AP-induced Ca(2+) release flux, resulting in impaired contractile activation and force production in skeletal muscle.

The auxiliary subunit gamma 1 of the skeletal muscle L-type Ca2+ channel is an endogenous Ca2+ antagonist

Ca2+ channels play crucial roles in cellular signal transduction and are important targets of pharmacological agents. They are also associated with auxiliary subunits exhibiting functions that are still incompletely resolved. Skeletal muscle L-type Ca2+ channels (dihydropyridine receptors, DHPRs) are specialized for the remote voltage control of type 1 ryanodine receptors (RyR1) to release stored Ca2+. The skeletal muscle-specific gamma subunit of the DHPR (gamma 1) down-modulates availability by altering its steady state voltage dependence. The effect resembles the action of certain Ca2+ antagonistic drugs that are thought to stabilize inactivated states of the DHPR. In the present study we investigated the cross influence of gamma 1 and Ca2+ antagonists by using wild-type (gamma+/+) and gamma 1 knockout (gamma-/-) mice. We studied voltage-dependent gating of both L-type Ca2+ current and Ca2+ release and the allosteric modulation of drug binding. We found that 10 microM diltiazem, a benzothiazepine drug, more than compensated for the reduction in high-affinity binding of the dihydropyridine agent isradipine caused by gamma 1 elimination; 5 muM devapamil [(-)D888], a phenylalkylamine Ca2+ antagonist, approximately reversed the right-shifted voltage dependence of availability and the accelerated recovery kinetics of Ca2+ current and Ca2+ release. Moreover, the presence of gamma 1 altered the effect of D888 on availability and strongly enhanced its impact on recovery kinetics demonstrating that gamma 1 and the drug do not act independently of each other. We propose that the gamma 1 subunit of the DHPR functions as an endogenous Ca2+ antagonist whose task may be to minimize Ca2+ entry and Ca2+ release under stress-induced conditions favoring plasmalemma depolarization.

Transient loss of voltage control of Ca2+ release in the presence of maurocalcine in skeletal muscle

In skeletal muscle, sarcoplasmic reticulum (SR) calcium release is controlled by the plasma membrane voltage through interactions between the voltage-sensing dihydropyridine receptor (DHPr) and the ryanodine receptor (RYr) calcium release channel. Maurocalcine (MCa), a scorpion toxin peptide presenting some homology with a segment of a cytoplasmic loop of the DHPr, has been previously shown to strongly affect the activity of the isolated RYr. We injected MCa into mouse skeletal muscle fibers and measured intracellular calcium under voltage-clamp conditions. Voltage-activated calcium transients exhibited similar properties in control and in MCa-injected fibers during the depolarizing pulses, and the voltage dependence of calcium release was similar under the two conditions. However, MCa was responsible for a pronounced sustained phase of Ca(2+) elevation that proceeded for seconds following membrane repolarization, with no concurrent alteration of the membrane current. The magnitude of the underlying uncontrolled extra phase of Ca(2+) release correlated well with the peak calcium release during the pulse. Results suggest that MCa binds to RYr that open on membrane depolarization and that this interaction specifically alters the process of repolarization-induced closure of the channels.

Calcium transients in developing mouse skeletal muscle fibres

Ca(2)(+) transients elicited by action potentials were measured using MagFluo-4, at 20-22 degrees C, in intact muscle fibres enzymatically dissociated from mice of different ages (7, 10, 15 and 42 days). The rise time of the transient (time from 10 to 90% of the peak) was 2.4 and 1.1 ms in fibres of 7- and 42-day-old mice, respectively. The decay of the transient was described by a double exponential function, with time constants of 1.8 and 16.4 ms in adult, and of 4.6 and 105 ms in 7-day-old animals. The fractional recovery of the transient peak amplitude after 10 ms, F(2(10))/F(1), determined using twin pulses, was 0.53 for adult fibres and ranged between 0.03 and 0.60 in fibres of 7-day-old animals This large variance may indicate differences in the extent of inactivation of Ca(2)(+) release, possibly related to the difference in ryanodine receptor composition between young and old fibres. At the 7 and 10 day stages, fibres responded to Ca(2)(+)-free solutions with a larger decrease in the transient peak amplitude (25% versus 11% in adult fibres), possibly indicating a contribution of Ca(2)(+) influx to the Ca(2)(+) transient in younger animals. Cyclopiazonic acid (1 mum), an inhibitor of the sarcoplasmic reticulum (SR) Ca(2)(+)-ATPase, abolished the Ca(2)(+) transient decay in fibres of 7- and 10-day-old animals and significantly reduced its rate in older animals. Analysis of the transients with a Ca(2)(+) removal model showed that the results are consistent with a larger relative contribution of the SR Ca(2)(+) pump and a lower expression of myoplasmic Ca(2)(+) buffers in fibres of young versus old animals.

A model-independent algorithm to derive Ca2+ fluxes underlying local cytosolic Ca2+ transients

Local intracellular Ca(2+) signals result from Ca(2+) flux into the cytosol through individual channels or clusters of channels. To gain a mechanistic understanding of these events we need to know the magnitude and spatial distribution of the underlying Ca(2+) flux. However, this is difficult to infer from fluorescence Ca(2+) images because the distribution of Ca(2+)-bound dye is affected by poorly characterized processes including diffusion of Ca(2+) ions, their binding to mobile and immobile buffers, and sequestration by Ca(2+) pumps. Several methods have previously been proposed to derive Ca(2+) flux from fluorescence images, but all require explicit knowledge or assumptions regarding these processes. We now present a novel algorithm that requires few assumptions and is largely model-independent. By testing the algorithm with both numerically generated image data and experimental images of sparklets resulting from Ca(2+) flux through individual voltage-gated channels, we show that it satisfactorily reconstructs the magnitude and time course of the underlying Ca(2+) currents.

Estimation of initial conditions and parameters of a chaotic evolution process from a short time series

Tracing back to the initial state of a time-evolutionary process using a segment of historical time series may lead to many meaningful applications. In this paper, we present an estimation method that can detect the initial conditions, unobserved time-varying states and parameters of a dynamical (chaotic) system using a short scalar time series that may be contaminated by noise. The technique based on the Newton-Raphson method and the least-squares algorithm is tolerant to large mismatch between the initial guess and actual values. The feasibility and robustness of this method are illustrated via the numerical examples based on the Lorenz system and Rossler system corrupted with Gaussian noise.

Biomimetic model of skeletal muscle isometric contraction: II. A phenomenological model of the skeletal muscle excitation–contraction coupling process

This paper describes a new macroscopic, phenomenological model of the skeletal muscle excitation-contraction coupling process, as represented by four principal and consecutive compartments (biophysical, biochemical, and biomechanical phases) characteristic of isometric excitation-contraction coupling in mammalian skeletal muscle, and coupled by a system of simultaneous, first-order linear ordinary differential equations. The model is based upon biological compartmental transport kinetics and irreversible thermodynamic energy transformation, and represents a distinct improvement over other biomimetic models. The model was derived using physiological parameter data published in the literature, and validated using MATLAB R12.

Voltage-dependent Ca2+ fluxes in skeletal myotubes determined using a removal model analysis

The purpose of this study was to quantify the Ca2+ fluxes underlying Ca2+ transients and their voltage dependence in myotubes by using the "removal model fit" approach. Myotubes obtained from the mouse C2C12 muscle cell line were voltage-clamped and loaded with a solution containing the fluorescent indicator dye fura-2 (200 microM) and a high concentration of EGTA (15 mM). Ca2+ inward currents and intracellular ratiometric fluorescence transients were recorded in parallel. The decaying phases of Ca2+-dependent fluorescence signals after repolarization were fitted by theoretical curves obtained from a model that included the indicator dye, a slow Ca2+ buffer (to represent EGTA), and a sequestration mechanism as Ca2+ removal components. For each cell, the rate constants of slow buffer and transport and the off rate constant of fura-2 were determined in the fit. The resulting characterization of the removal properties was used to extract the Ca2+ input fluxes from the measured Ca2+ transients during depolarizing pulses. In most experiments, intracellular Ca2+ release dominated the Ca2+ input flux. In these experiments, the Ca2+ flux was characterized by an initial peak followed by a lower tonic phase. The voltage dependence of peak and tonic phase could be described by sigmoidal curves that reached half-maximal activation at -16 and -20 mV, respectively, compared with -2 mV for the activation of Ca2+ conductance. The ratio of the peak to tonic phase (flux ratio) showed a gradual increase with voltage as in rat muscle fibers indicating the similarity to EC coupling in mature mammalian muscle. In a subgroup of myotubes exhibiting small fluorescence signals and in cells treated with 30 microM of the SERCA pump inhibitor cyclopiazonic acid (CPA) and 10 mM caffeine, the calculated Ca2+ input flux closely resembled the L-type Ca2+ current, consistent with the absence of SR Ca2+ release under these conditions and in support of a valid determination of the time course of myoplasmic Ca2+ input flux based on the optical indicator measurements.

Voltage-activated calcium signals in myotubes loaded with high concentrations of EGTA

In the present study we describe the analysis of optically recorded whole cell Ca(2+) transients elicited by depolarization in cultured skeletal myotubes. Myotubes were obtained from the mouse muscle-derived cell line C2C12 and from mouse satellite cells. The cells were voltage-clamped and perfused with an artificial intracellular solution containing 15 mM EGTA to ensure that the bulk of the Ca(2+) mobilized by depolarization is bound to this extrinsic buffer. The apparent on- and off-rate constants of EGTA and the dissociation rate constant of fura-2 in the cell were estimated by investigating the Ca(2+)-dependence of kinetic components of the fluorescence decay after repolarization. These parameters were used to calculate the time course of the total voltage-controlled flux of Ca(2+) to the myoplasmic space (Ca(2+) input flux). The validity of the procedure was confirmed by model simulations using artificial Ca(2+) input fluxes. Both C2C12 and primary-cultured myotubes showed a very similar phasic-tonic time course of the Ca(2+) input flux. In most measurements, the input flux was considerably larger and showed a different time course than the estimated Ca(2+) flux carried by the L-type Ca(2+) channels, indicating that it consists mainly of voltage-controlled Ca(2+) release from the sarcoplasmic reticulum. In cells with extremely small fluorescence transients, the calculated input fluxes matched the kinetic characteristics of the Ca(2+) inward current, indicating that Ca(2+) release was absent. These measurements served as a control for the fidelity of the fluorimetric flux analysis. The procedures promise a deeper insight into alterations of Ca(2+) release gating in studies employing myotube expression systems for mutant or chimeric protein components of excitation-contraction coupling.

Sustained release of calcium elicited by membrane depolarization in ryanodine-injected mouse skeletal muscle fibers

The effect of micromolar intracellular levels of ryanodine was tested on the myoplasmic free calcium concentration ([Ca(2+)](i)) measured from a portion of isolated mouse skeletal muscle fibers voltage-clamped at -80 mV. When ryanodine-injected fibers were transiently depolarized to 0 mV, the early decay phase of [Ca(2+)](i) upon membrane repolarization was followed by a steady elevated [Ca(2+)](i) level. This effect could be qualitatively well simulated, assuming that ryanodine binds to release channels that open during depolarization and that ryanodine-bound channels do not close upon repolarization. The amplitude of the postpulse [Ca(2+)](i) elevation depended on the duration of the depolarization, being hardly detectable for pulses shorter than 100 ms, and very prominent for duration pulses of seconds. Within a series of consecutive pulses of the same duration, the effect of ryanodine produced a staircase increase in resting [Ca(2+)](i), the slope of which was approximately twice larger for depolarizations to 0 or +10 mV than to -30 or -20 mV. Overall results are consistent with the "open-locked" state because of ryanodine binding to calcium release channels that open during depolarization. Within the voltage-sensitive range of calcium release, increasing either the amplitude or the duration of the depolarization seems to enhance the fraction of release channels accessible to ryanodine.

Sepsis research in the next millennium: concentrate on the software rather than the hardware

Today the basic principles of septic conditions are understood. Nevertheless, sepsis research has reached a critical point. To integrate our knowledge towards a consistent theory of the disease process and to derive effective therapies, new perspectives for future research that fit the complexity of the problem have to be found. We conducted a review of the literature concerning systemic inflammatory response syndrome (SIRS) and sepsis with particular reference to liver pathophysiology. And compared our findings with characteristic features of complex systems. The complexity of sepsis is broadly recognized. A review of the different aspects of liver inflammation during SIRS and sepsis, i.e. endotoxin challenge, cytokine induced dysfunction, the mechanisms of leukocyte transmigration, and hormonal and neuroendocrine regulatory mechanisms is given. Key aspects of complex systems, including parallelism, locality, emergence, and cross-scale interactions are introduced. We conclude that sepsis research needs new perspectives that allow us to handle the complex interactions occurring during the disease process. We propose to focus research on the interactions between the constituents of the system rather than only describing isolated aspects of the disease process. We also conclude that the ideas and techniques of non-linear systems theory are suitable tools for the analysis of complex and dynamic diseases like SIRS and sepsis.