Comparison between the predictions of diffusion-reaction models and localized Ca2+ transients in amphibian skeletal muscle fibers

A 3D diffusional-compartmental model of the calcium dynamics in cytosol, sarcoplasmic reticulum and mitochondria of murine skeletal muscle fibers

Variations of free calcium concentration ([Ca2+]) are powerful intracellular signals, controlling contraction as well as metabolism in muscle cells. To fully understand the role of calcium redistribution upon excitation and contraction in skeletal muscle cells, the local [Ca2+] in different compartments needs to be taken into consideration. Fluorescent probes allow the determination of [Ca2+] in the cytosol where myofibrils are embedded, the lumen of the sarcoplasmic reticulum (SR) and the mitochondrial matrix. Previously, models have been developed describing intracellular calcium handling in skeletal and cardiac muscle cells. However, a comprehensive model describing the kinetics of the changes in free calcium concentration in these three compartments is lacking. We designed a new 3D compartmental model of the half sarcomere with radial symmetry, which accounts for diffusion of Ca2+ into the three compartments and simulates its dynamics at rest and at various rates of stimulation in mice skeletal muscle fibers. This model satisfactorily reproduces both the amplitude and time course of the variations of [Ca2+] in the three compartments in mouse fast fibers. As an illustration of the applicability of the model, we investigated the effects of Calsequestrin (CSQ) ablation. CSQ is the main Ca2+ buffer in the SR, localized in close proximity of its calcium release sites and near to the mitochondria. CSQ knock-out mice muscles still preserve a near-normal contractile behavior, but it is unclear whether this is caused by additional SR calcium buffering or a significant contribution of calcium entry from extracellular space, via stored-operated calcium entry (SOCE). The model enabled quantitative assessment of these two scenarios by comparison to measurements of local calcium in the cytosol, the SR and the mitochondria. In conclusion, the model represents a useful tool to investigate the impact of protein ablation and of pharmacological interventions on intracellular calcium dynamics in mice skeletal muscle.

Quantitative optical nanophysiology of Ca2+ signaling at inner hair cell active zones

Ca²⁺ influx triggers the release of synaptic vesicles at the presynaptic active zone (AZ). A quantitative characterization of presynaptic Ca²⁺ signaling is critical for understanding synaptic transmission. However, this has remained challenging to establish at the required resolution. Here, we employ confocal and stimulated emission depletion (STED) microscopy to quantify the number (20-330) and arrangement (mostly linear 70 nm × 100-600 nm clusters) of Ca²⁺ channels at AZs of mouse cochlear inner hair cells (IHCs). Establishing STED Ca²⁺ imaging, we analyze presynaptic Ca²⁺ signals at the nanometer scale and find confined elongated Ca²⁺ domains at normal IHC AZs, whereas Ca²⁺ domains are spatially spread out at the AZs of bassoon-deficient IHCs. Performing 2D-STED fluorescence lifetime analysis, we arrive at estimates of the Ca²⁺ concentrations at stimulated IHC AZs of on average 25 µM. We propose that IHCs form bassoon-dependent presynaptic Ca²⁺-channel clusters of similar density but scalable length, thereby varying the number of Ca²⁺ channels amongst individual AZs.

The sensitivity of fast muscle contractile function to the major components of the sarcomere Ca(2+)-cycling system

A reaction-diffusion model of a muscle sarcomere was developed to evaluate the sensitivity of force characteristics to diffusion and Ca(2+)-cycling components. The model compared well to experimental force measurements. Diffusion led to Ca(2+) gradients that enhanced maximal force and accelerated relaxation compared to when diffusion was infinitely fast. However, a modest increase in sarcomere length or radius led to a decrease in maximal force. Lowering the Ca(2+) release rate caused a lower maximal force, but increasing the rate led to only modest gains in maximal force while incurring much greater ATP costs associated with reuptake. Greater parvalbumin binding rates decreased maximal force but enhanced relaxation, and this effect was magnified when Ca(2+) uptake rates were lowered as may occur during fatigue. These results show a physiological set of parameters that lead to a functional sarcomere of known dimensions and contractile function, and the effects of parameter variation on muscle function.

Microdomain calcium fluctuations as a colored noise process

Calcium ions play a key role in subcellular signaling as localized transients of the intracellular calcium concentration modify the activity of ion channels, enzymes and transcription factors, among others. The intracellular calcium concentration is inherently noisy, as diffusion, the transient binding to and dissociation from buffer molecules and stochastically gating calcium channels contribute to the fluctuations of the local copy number of Ca²⁺ ions. We study the properties of the fluctuating calcium concentration in sub-femtoliter volumes using an exact stochastic simulation algorithm and approximations to the exact stochastic solution. It is shown that the time course of the local calcium concentration represents a colored noise process whose autocorrelation time is a function of buffer kinetics and diffusion constants. Using the chemical Langevin description and the excess buffer approximation of the process, fast approximative algorithms and theoretical connections to the Ornstein-Uhlenbeck process are obtained. In a generic example, we show how calcium noise can couple to the dynamics of a single variable moving in a double-well potential, leading to a colored noise induced transition. Our work shows how a multitude of intracellular signaling pathways may be influenced by the inherent stochasticity of calcium signals, a key messenger in virtually any cell type, and how the calcium signal can be implemented efficiently in cellular signaling models.

Intracellular calcium movements during excitation-contraction coupling in mammalian slow-twitch and fast-twitch muscle fibers

In skeletal muscle fibers, action potentials elicit contractions by releasing calcium ions (Ca²⁺) from the sarcoplasmic reticulum. Experiments on individual mouse muscle fibers micro-injected with a rapidly responding fluorescent Ca²⁺ indicator dye reveal that the amount of Ca²⁺ released is three- to fourfold larger in fast-twitch fibers than in slow-twitch fibers, and the proportion of the released Ca²⁺ that binds to troponin to activate contraction is substantially smaller.

A coupled electromechanical model for the excitation-dependent contraction of skeletal muscle

This work deals with the development and implementation of an electromechanical skeletal muscle model. To this end, a recently published hyperelastic constitutive muscle model with transversely isotropic characteristics, see Ehret et al. (2011), has been weakly coupled with Ohm's law describing the electric current. In contrast to the traditional way of active muscle modelling, this model is rooted on a non-additive decomposition of the active and passive components. The performance of the proposed modelling approach is demonstrated by the use of three-dimensional illustrative boundary-value problems that include electromechanical analysis on tissue strips. Further, simulations on the biceps brachii muscle document the applicability of the model to realistic muscle geometries.

Functional expression of transgenic 1sDHPR channels in adult mammalian skeletal muscle fibres

We investigated the effects of the overexpression of two enhanced green fluorescent protein (EGFP)-tagged α1sDHPR variants on Ca2+ currents (ICa), charge movements (Q) and SR Ca2+ release of muscle fibres isolated from adult mice. Flexor digitorum brevis (FDB)muscles were transfected by in vivo electroporation with plasmids encoding for EGFP-α1sDHPR-wt and EGFP-α1sDHPR-T935Y (an isradipine-insensitive mutant). Two-photon laser scanning microscopy (TPLSM) was used to study the subcellular localization of transgenic proteins, while ICa, Q and Ca2+ release were studied electrophysiologically and optically under voltage-clamp conditions. TPLSM images demonstrated that most of the transgenic α1sDHPR was correctly targeted to the transverse tubular system (TTS). Immunoblotting analysis of crude extracts of transfected fibres demonstrated the synthesis of bona fide transgenic EGFP-α1sDHPR-wt in quantities comparable to that of native α1sDHPR. Though expression of both transgenic variants of the alpha subunit of the dihydropyridine receptor (α1sDHPR) resulted in ∼50% increase in Q, they surprisingly had no effect on the maximal Ca2+ conductance (gCa) nor the SR Ca2+ release. Nonetheless, fibres expressing EGFP-α1sDHPR-T935Y exhibited up to 70% isradipine-insensitive ICa (ICa-ins) with a right-shifted voltage dependence compared to that in control fibres. Interestingly, Qand SRCa2+ release also displayed right-shifted voltage dependence in fibres expressing EGFP-α1sDHPR-T935Y. In contrast, the midpoints of the voltage dependence of gCa, Q and Ca2+ release were not different from those in control fibres and in fibres expressing EGFP-α1sDHPR-wt. Overall, our results suggest that transgenic α1sDHPRs are correctly trafficked and inserted in the TTS membrane, and that a substantial fraction of the mworks as conductive Ca2+ channels capable of physiologically controlling the release of Ca2+ from the SR. A plausible corollary of this work is that the expression of transgenic variants of the α1sDHPR leads to the replacement of native channels interacting with the ryanodine receptor 1 (RyR1), thus demonstrating the feasibility of molecular remodelling of the triads in adult skeletal muscle fibres.

Luminal Ca(2+) content regulates intracellular Ca(2+) release in subepicardial myocytes of intact beating mouse hearts: effect of exogenous buffers

Ca(+)-induced Ca(2+) release tightly controls the function of ventricular cardiac myocytes under normal and pathological conditions. Two major factors contributing to the regulation of Ca(2+) release are the cytosolic free Ca(2+) concentration and sarcoplasmic reticulum (SR) Ca(2+) content. We hypothesized that the amount of Ca(2+) released from the SR during each heart beat strongly defines the refractoriness of Ca(2+) release. To test this hypothesis, EGTA AM, a high-affinity, slow-association rate Ca(2+) chelator, was used as a tool to modify luminal SR Ca(2+) content. An analysis of the cytosolic and luminal SR Ca(2+) dynamics recorded from the epicardial layer of intact mouse hearts indicated that the presence of EGTA reduced the diastolic SR free Ca(2+) concentration and fraction of SR Ca(2+) depletion during each beat. In addition, this maneuver shortened the refractory period and accelerated the restitution of Ca(2+) release. As a consequence of the accelerated restitution, the frequency dependence of Ca(2+) alternans was significantly shifted toward higher heart rates, suggesting a role of luminal SR Ca(2+) in the genesis of this highly arrhythmogenic phenomenon. Thus, intra-SR Ca(2+) dynamics set the refractoriness and frequency dependence of Ca(2+) transients in subepicardial ventricular myocytes.

Dystrophic skeletal muscle fibers display alterations at the level of calcium microdomains

The spatiotemporal properties of the Ca(2+)-release process in skeletal muscle fibers from normal and mdx fibers were determined using the confocal-spot detection technique. The Ca(2+) indicator OGB-5N was used to record action potential-evoked fluorescence signals at consecutive locations separated by 200 nm along multiple sarcomeres of FDB fibers loaded with 10- and 30-mM EGTA. Three-dimensional reconstructions of fluorescence transients demonstrated the existence of microdomains of increased fluorescence around the Ca(2+)-release sites in both mouse strains. The Ca(2+) microdomains in mdx fibers were regularly spaced along the fiber axis, displaying a distribution similar to that seen in normal fibers. Nevertheless, both preparations differed in that in 10-mM EGTA Ca(2+) microdomains had smaller amplitudes and were wider in mdx fibers than in controls. In addition, Ca(2+)-dependent fluorescence transients recorded at selected locations within the sarcomere of mdx muscle fibers were not only smaller, but also slower than their counterparts in normal fibers. Notably, differences in the spatial features of the Ca(2+) microdomains recorded in mdx and normal fibers, but not in the amplitude and kinetics of the Ca(2+) transients, were eliminated in 30-mM EGTA. Our results consistently demonstrate that Ca(2+)-release flux calculated from release sites in mdx fibers is uniformly impaired with respect to those normal fibers. The Ca(2+)-release reduction is consistent with that previously measured using global detection techniques.

Simulation of Ca2+ movements within the sarcomere of fast-twitch mouse fibers stimulated by action potentials

Ca²⁺ release from the sarcoplasmic reticulum (SR) of skeletal muscle takes place at the triadic junctions; following release, Ca²⁺ spreads within the sarcomere by diffusion. Here, we report multicompartment simulations of changes in sarcomeric Ca²⁺ evoked by action potentials (APs) in fast-twitch fibers of adult mice. The simulations include Ca²⁺ complexation reactions with ATP, troponin, parvalbumin, and the SR Ca²⁺ pump, as well as Ca²⁺ transport by the pump. Results are compared with spatially averaged Ca²⁺ transients measured in mouse fibers with furaptra, a low-affinity, rapidly responding Ca²⁺ indicator. The furaptra Δf_CaD signal (change in the fraction of the indicator in the Ca²⁺-bound form) evoked by one AP is well simulated under the assumption that SR Ca²⁺ release has a peak of 200–225 μM/ms and a FDHM of ∼1.6 ms (16°C). Δf_CaD elicited by a five-shock, 67-Hz train of APs is well simulated under the assumption that in response to APs 2–5, Ca²⁺ release decreases progressively from 0.25 to 0.15 times that elicited by the first AP, a reduction likely due to Ca²⁺ inactivation of Ca²⁺ release. Recovery from inactivation was studied with a two-AP protocol; the amplitude of the second release recovered to >0.9 times that of the first with a rate constant of 7 s⁻¹. An obvious feature of Δf_CaD during a five-shock train is a progressive decline in the rate of decay from the individual peaks of Δf_CaD. According to the simulations, this decline is due to a reduction in available Ca²⁺ binding sites on troponin and parvalbumin. The effects of sarcomere length, the location of the triadic junctions, resting [Ca²⁺], the parvalbumin concentration, and possible uptake of Ca²⁺ by mitochondria were also investigated. Overall, the simulations indicate that this reaction-diffusion model, which was originally developed for Ca²⁺ sparks in frog fibers, works well when adapted to mouse fast-twitch fibers stimulated by APs.

Calcium microdomains in regulated exocytosis

Katz and co-workers showed that Ca(2+) triggers exocytosis. The existence of sub-micrometer domains of greater than 100 microM [Ca(2+)](i) was postulated on theoretical grounds. Using a modified, low-affinity aequorin, Llinas et al. were the first to demonstrate the existence of Ca(2+) 'microdomains' in squid presynaptic terminals. Over the past several years, it has become clear that individual Ca(2+) nano- and microdomains forming around the mouth of voltage-gated Ca(2+) channels ascertain the tight coupling of fast synaptic vesicle release to membrane depolarization by action potentials. Recent work has established different geometric arrangements of vesicles and Ca(2+) channels at different central synapses and pointed out the role of Ca(2+) syntillas - localized, store operated Ca(2+) signals - in facilitation and spontaneous release. The coupling between Ca(2+) increase and evoked exocytosis is more sluggish in peripheral terminals and neuroendocrine cells, where channels are less clustered and Ca(2+) comes from different sources, including Ca(2+) influx via the plasma membrane and the mobilization of Ca(2+) from intracellular stores. Finally, also non- (electrically) excitable cells display highly localized Ca(2+) signaling domains. We discuss in particular the organization of structural microdomains of Bergmann glia, specialized astrocytes of the cerebellum that have only recently been considered as secretory cells. Glial microdomains are the spatial substrate for functionally segregated Ca(2+) signals upon metabotropic activation. Our review emphasizes the large diversity of different geometric arrangements of vesicles and Ca(2+) sources, leading to a wide spectrum of Ca(2+) signals triggering release.

Calcium release domains in mammalian skeletal muscle studied with two-photon imaging and spot detection techniques

The spatiotemporal characteristics of the Ca(2+) release process in mouse skeletal muscle were investigated in enzymatically dissociated fibers from flexor digitorum brevis (FDB) muscles, using a custom-made two-photon microscope with laser scanning imaging (TPLSM) and spot detection capabilities. A two-microelectrode configuration was used to electrically stimulate the muscle fibers, to record action potentials (APs), and to control their myoplasmic composition. We used 125 muM of the low-affinity Ca(2+) indicator Oregon green 488 BAPTA-5N (OGB-5N), and 5 or 10 mM of the Ca(2+) chelator EGTA (pCa 7) in order to arrest fiber contraction and to constrain changes in the [Ca(2+)] close to the release sites. Image and spot data showed that the resting distribution of OGB-5N fluorescence was homogeneous along the fiber, except for narrow peaks ( approximately 23% above the bulk fluorescence) centered at the Z-lines, as evidenced by their nonoverlapping localization with respect to di-8-ANEPPS staining of the transverse tubules (T-tubules). Using spot detection, localized Ca(2+) transients evoked by AP stimulation were recorded from adjacent longitudinal positions 100 nm apart. The largest and fastest DeltaF/F transients were detected at sites flanking the Z-lines and colocalized with T-tubules; the smallest and slowest were detected at the M-line, whereas transients at the Z-line showed intermediate features. Three-dimensional reconstructions demonstrate the creation of two AP-evoked Ca(2+) release domains per sarcomere, which flank the Z-line and colocalize with T-tubules. In the presence of 10 mM intracellular EGTA, these domains are formed in approximately 1.4 ms and dissipate within approximately 4 ms, after the peak of the AP. Their full-width at half-maximum (FWHM), measured at the time that Ca(2+) transients peaked at T-tubule locations, was 0.62 mum, similar to the 0.61 mum measured for di-8-ANEPPS profiles. Both these values exceed the limit of resolution of the optical system, but their similarity suggests that at high [EGTA] the Ca(2+) domains in adult mammalian muscle fibers are confined to Ca(2+) release sites located at the junctional sarcoplasmic reticulum (SR).

Propagation in the transverse tubular system and voltage dependence of calcium release in normal and mdx mouse muscle fibres

Using a two-microelectrode voltage clamp technique, we investigated possible mechanisms underlying the impaired excitation-contraction coupling in skeletal muscle fibres of the mdx mouse, a model of the human disease Duchenne muscular dystrophy. We evaluated the role of the transverse tubular system (T-system) by using the potentiometric indicator di-8 ANEPPS, and that of the sarcoplasmic reticulum (SR) Ca2+ release by measuring Ca2+ transients with a low affinity indicator in the presence of high EGTA concentrations under voltage clamp conditions. We observed minimal differences in the T-system structure and the T-system electrical propagation was not different between normal and mdx mice. Whereas the maximum Ca2+ release elicited by voltage pulses was reduced by approximately 67% in mdx fibres, in agreement with previous results obtained using AP stimulation, the voltage dependence of SR Ca2+ release was identical to that seen in normal fibres. Taken together, our data suggest that the intrinsic ability of the sarcoplasmic reticulum to release Ca2+ may be altered in the mdx mouse.

The action potential-evoked sarcoplasmic reticulum calcium release is impaired in mdx mouse muscle fibres

The mdx mouse, a model of the human disease Duchenne muscular dystrophy, has skeletal muscle fibres which display incompletely understood impaired contractile function. We explored the possibility that action potential-evoked Ca(2+) release is altered in mdx fibres. Action potential-evoked Ca(2+)-dependent fluorescence transients were recorded, using both low and high affinity Ca(2+) indicators, from enzymatically isolated fibres obtained from extensor digitorum longus (EDL) and flexor digitorum brevis (FDB) muscles of normal and mdx mice. Fibres were immobilized using either intracellular EGTA or N-benzyl-p-toluene sulphonamide, an inhibitor of the myosin II ATPase. We found that the amplitude of the action potential-evoked Ca(2+) transients was significantly decreased in mdx mice with no measured difference in that of the surface action potential. In addition, Ca(2+) transients recorded from mdx fibres in the absence of EGTA also displayed a marked prolongation of the slow decay phase. Model simulations of the action potential-evoked transients in the presence of high EGTA concentrations suggest that the reduction in the evoked sarcoplasmic reticulum Ca(2+) release flux is responsible for the decrease in the peak of the Ca(2+) transient in mdx fibres. Since the myoplasmic Ca(2+) concentration is a critical regulator of muscle contraction, these results may help to explain the weakness observed in skeletal muscle fibres from mdx mice and, possibly, Duchenne muscular dystrophy patients.

Comparison between the predictions of diffusion-reaction models and localized Ca2+ transients in amphibian skeletal muscle fibers

We developed a three-dimensional cylindrical diffusion-reaction model of a single amphibian myofibril in which Ca(2+) release occurred only at the Z-line. The model incorporated diffusion of Ca(2+), Mg(2+), and all relevant buffer species, as well as the kinetic binding reactions between the buffers and appropriate ions. Model data was blurred according to a Gaussian approximation of the point spread function of the microscope and directly compared with experimental data obtained using the confocal spot methodology. The flux parameters were adjusted until the simulated Z-line transient matched the experimental one. This model could not simultaneously predict key parameters of the experimental M- and Z-line transients, even when model parameters were adjusted to unreasonably extreme values. Even though the model was accurate in predicting the Z-line transient under conditions of high [EGTA], it predicted a significantly narrower Ca(2+) domain than observed experimentally. We modified the model to incorporate a broader band of release centered at the Z-line. This extended release model was superior both in simultaneously predicting critical features of the Z- and M-line transients as well as the domain profile under conditions of high [EGTA]. We conclude that a model of release occurring exclusively at the Z-line cannot explain our experimental data and suggest that Ca(2+) may be released from a broader region of the sarcoplasmic reticulum than just the T-tubule-sarcoplasmic reticulum junction.