Cytosolic Ca²⁺ gradients and mitochondrial Ca²⁺ uptake in resting muscle fibers: A model analysis

Abstract

Calcium ions (Ca²⁺) enter mitochondria via the mitochondrial Ca²⁺ uniporter, driven by electrical and concentration gradients. In this regard, transgenic mouse models, such as calsequestrin knockout (CSQ-KO) mice, with higher mitochondrial Ca²⁺ concentrations ([Ca²⁺]_mito), should display higher cytosolic Ca²⁺ concentrations ([Ca²⁺]_cyto). However, repeated measurements of [Ca²⁺]_cyto in quiescent CSQ-KO fibers never showed a difference between WT and CSQ-KO. Starting from the consideration that fluorescent Ca²⁺ probes (Fura-2 and Indo-1) measure averaged global cytosolic concentrations, in this report we explored the role of local Ca²⁺ concentrations (i.e., Ca²⁺ microdomains) in regulating mitochondrial Ca²⁺ in resting cells, using a multicompartmental diffusional Ca²⁺ model. Progressively including the inward and outward fluxes of sarcoplasmic reticulum (SR), extracellular space, and mitochondria, we explored their contribution to the local Ca²⁺ distribution within the cell.

The model predicts Ca²⁺ concentration gradients with hot spots or microdomains even at rest, minor but similar to those of evoked Ca²⁺ release. Due to their specific localization close to Ca²⁺ release units (CRU), mitochondria could take up Ca²⁺ directly from high-concentration microdomains, thus sensibly raising [Ca²⁺]_mito, despite minor, possibly undetectable, modifications of the average [Ca²⁺]_cyto.

Why it matters

In skeletal muscle, Ca²⁺ enters the inner mitochondrial membrane via the mitochondrial Ca²⁺ uniporter (MCU) to regulate metabolic activation and apoptosis. Due to the proximity of the MCU to the ryanodine receptor type-1 (RyR1), which releases Ca²⁺ in the myoplasm during stimulation, mitochondria take advantage of a locally high [Ca²⁺] named microdomains. Here, we show, by means of a numerical model, that these microdomains are present also in resting fibers, induced by RyR1 leakage. These “resting microdomains” become even more relevant in the calsequestrin knockout (CSQ-KO) mouse model where the RyR1 leakage is enhanced. These resting microdomains can explain the observed mitochondrial [Ca²⁺] at rest in CSQ-KO fibers, with a minimum, possibly undetectable, variation in the average cytosolic [Ca²⁺].

Introduction

In skeletal muscle fibers, the sarcoplasmic reticulum (SR) is both the largest intracellular Ca²⁺ store and the only compartment able to quickly release and reuptake Ca²⁺. In this way, SR links the sarcolemma electrical activity to myofibrillar force generation. The relevance of mitochondrial Ca²⁺ uptake to regulate ATP synthesis is widely accepted, but their ability to store Ca²⁺ has been debated for many years. Recently, the determination of mitochondrial Ca²⁺ content, using the membrane lysis method (1), has definitely confirmed that, in skeletal muscle, mitochondria are endowed with a high Ca²⁺-buffering capacity.

Interestingly, the lysis method showed that total mitochondrial calcium content is increased in two transgenic mouse models with a Ca²⁺ leak through SR ryanodine receptor type-1 (RyR1) Ca²⁺ channel: a gain of function RyR1 knockin and the calsequestrin knockout (CSQ-KO) mice (1). In RYR1 models, a direct comparison between total mitochondrial calcium and free mitochondrial Ca²⁺ ([Ca²⁺]_mito) showed the high buffering power of the organelle, while a comparison with previously published data on free cytosolic Ca²⁺ ([Ca²⁺]_cyto) suggested a high sensitivity of [Ca²⁺]_mito to small changes in [Ca²⁺]_cyto (2). Similar conclusions were suggested also for CSQ-KO mice; however, for this mouse model, these relationships were only extrapolated without using data on [Ca²⁺]_mito and [Ca²⁺]_cyto present in the literature (3,4,5,6). While the higher total mitochondrial calcium is consistent with previous data that report an increased [Ca²⁺]_mito in CSQ-KO mice, [Ca²⁺]_cyto was never found to be higher compared with WT mice.

By combining previously published data (1,1,6), here we aim at exploring further the role of [Ca²⁺]_cyto on mitochondrial Ca²⁺ accumulation in resting skeletal muscle fibers and, by means of theoretical and numerical methods, the specific dependence on the local Ca²⁺ concentration. Our results suggest that a small, possibly undetectable, difference in the averaged [Ca²⁺]_cyto can be associated with the increment in total and free mitochondrial calcium levels thanks to the existence of the “microdomains,” where the [Ca²⁺]_cyto is locally higher than the average value due to their peculiar position. Their existence is well established during contraction (7) but their role in resting muscle is much less considered.

The buffering power of mitochondria in WT and CSQ-KO fibers

The free [Ca²⁺]_mito was determined in FDB fibers of CSQ-KO male mice using the cameleon-4mtD3cpv sensor by Scorzeto et al. (6) (see Fig. 1). Males were chosen because they showed a more severe phenotype than females, in particular the hyperthermic crises were more frequent (8,9). In quiescent fibers, the free [Ca²⁺]_mito was higher in CSQ-KO (0.23 μmol/L_mito) than in WT (0.16 μmol/L_mito). Combining the [Ca²⁺]_mito determined by Scorzeto et al. (6) with the total mitochondrial calcium content determined with the lysis method by Lamboley et al. (1), the buffering power in quiescent CSQ-KO fibers can be quantified as follows.

Figure 1.

(A) Resting cytosolic free Ca²⁺ (means ± SEM) concentration determined with Fura-2 (5,6), (B) resting local peri-mitochondrial free Ca²⁺ concentration estimated by Seng et al. (2), (C) resting free Ca²⁺ concentration (means ± SEM) in the mitochondrial matrix measured with cameleon 4mtD3cpv (6) and relevant calibration curve, (D) resting total mitochondrial calcium concentration (means ± SD) measured with the lysis method by Lamboley et al. (1). No experimental measurements are available for cytosolic concentration in WT females and for mitochondrial concentration in WT and CSQ-KO females (see text).

Extrapolated from Fig. 5 in (1), the values of total mitochondrial calcium per fiber liter are 0.06 and 0.25 mmol/L_fiber for WT and CSQ-KO, respectively. Assuming a mitochondrial volume of 5% of total fiber volume in WT and 8% (i.e., 60% higher (6,10)) in CSQ-KO, the total calcium concentrations per mitochondria liter become 0.06/0.05 = 1.2 mmol/L_mito and 0.25/0.08 = 3.12 mmol/L_mito for WT and for CSQ-KO, respectively. The buffering power can therefore be estimated to be 1200/0.16 μmol/L_mito = 7500 and 3120/0.23 μmol/L_mito = 13565 for WT and CSQ-KO, respectively. It is worth underlining that the values reported by Scorzeto et al. (6) refer to deletion of both CSQ1 and CSQ2 (double knockout), while the data of Lamboley et al. (1) refer to CSQ1 ablation. Actually, the difference is small as CSQ2 is a minor isoform in fast fibers and, as shown by Tomasi et al. (11), the ablation of CSQ1 alone leads to a reorganization of the terminal cisternae with a severe (up to 80%) reduction of other triadic proteins, among them CSQ2, triadin, and sarcalumenin.

The values of buffering power calculated above are fully comparable with those determined: 1) by Lamboley et al. (1) for skeletal muscle fibers of WT and RYR1 mutation, 2) by Madsen (12) in mitochondria isolated from human skeletal muscle biopsy, and 3) in liver, brain, and heart (13,14). The higher buffering power in CSQ-KO may be explained through an adaptive response to the genetic ablation of the CSQ. However, it may also be a consequence of a strong cooperativity in the mitochondrial buffers, as is the case for CSQ itself (15,16). A variable buffering power in cardiac mitochondria assuming the presence of multiple molecular species acting as a calcium buffer has been proposed in (14).

A high cytosolic Ca²⁺ concentration is needed to increase mitochondrial Ca²⁺ uptake

Ca²⁺ enters the inner mitochondrial membrane via the mitochondrial Ca²⁺ uniporter (MCU), driven by an electrochemical gradient. Thus, to a first approximation, a higher free [Ca²⁺]_mito should imply a higher [Ca²⁺]_cyto. Accordingly, the interpretation proposed by Lamboley et al. (1) was that the higher total mitochondrial calcium content in CSQ-KO than WT muscles requires a quite higher [Ca²⁺]_cyto in the former case. However, their approach to describe the relationship between total mitochondrial calcium and average free cytosolic Ca²⁺, despite informative, had some limits, which possibly overestimated the needed increase in [Ca²⁺]_cyto. The relationship, substantially based on male CSQ1-KO and heterozygous and homozygous RYR1 knockin mice data, was shifted to a resting [Ca²⁺]_cyto in WT of only 50 nM, a choice which emphasized the differences between phenotypes. Moreover, as also acknowledged by Lamboley et al. (1) , the local Ca²⁺ concentration at the mitochondrial microdomain likely plays a crucial role in defining the resting [Ca²⁺]_mito, but this was not considered in that study. As a result, they concluded that a [Ca²⁺]_cyto more than three times higher in CSQ-KO than in WT fibers, was necessary to explain the greater calcium accumulation in the mitochondria. This conclusion is in sharp contrast with the direct measurements, as such a difference was never detected either with Indo-1 (17,18) or with Fura-2 (3,4,5,6), a high-affinity probe with a K_d = 145 nM (data sheet Thermo Fisher), thus perfectly suitable to detect variations of the resting [Ca²⁺]_cyto (see Fig. 1 A).

Importantly, a leaky RyR1 is not sufficient to alter resting [Ca²⁺]_cyto by itself. According to the “cell boundary theorem” (19), steady-state [Ca²⁺]_cyto in quiescent fibers is determined solely by exchanges with the extracellular space through the sarcolemma, while changes of Ca²⁺ fluxes within intracellular compartments cannot modify it permanently. In other words, [Ca²⁺]_cyto depends on the balance between Ca²⁺ influx and efflux at the plasma membrane, which can be translated in mathematical terms as follows (19):

$$\frac{\mathrm{d}{\left[{Ca}^{2+}\right]}_{cyto}}{dt}=influx\left({\left[{Ca}^{2+}\right]}_{ext},{\left[{Ca}^{2+}\right]}_{cyto}\right)-efflux\left({\left[{Ca}^{2+}\right]}_{ext},{\left[{Ca}^{2+}\right]}_{cyto}\right)-removal\left({\left[{Ca}^{2+}\right]}_{org},{\left[{Ca}^{2+}\right]}_{cyto}\right)+release\left({\left[{Ca}^{2+}\right]}_{org},{\left[{Ca}^{2+}\right]}_{cyto}\right)$$ (1)

where influx and efflux represent the Ca²⁺ exchanged with the external space, and removal and release the exchanges with a particular organelle org. At the truly steady-state, when $\mathrm{d}{\left[{Ca}^{2+}\right]}_{cyto}/dt=0$, the last two terms must be equal, and therefore also the first two terms equate each other, so:

$$influx\left({\left[{Ca}^{2+}\right]}_{ext},{\left[{Ca}^{2+}\right]}_{cyto}\right)=efflux\left({\left[{Ca}^{2+}\right]}_{ext},{\left[{Ca}^{2+}\right]}_{cyto}\right)$$ (2)

which, considering the constancy of [Ca²⁺]_ext and assuming a one-to-one matching between [Ca²⁺]_cyto and the fluxes, leads to the conclusion that only a modification of the exchanges with the external space can regulate [Ca²⁺]_cyto.

Thus, a higher [Ca²⁺]_cyto would require either a decreased efflux, via the Na⁺/Ca²⁺ exchanger or the plasma membrane Ca²⁺ ATPase (PMCA), or an enhanced influx via store-operated Ca²⁺ entry (SOCE). Lamboley et al. (1) have shown an altered Ca²⁺ permeability of the transverse tubular system membrane. A constitutively active SOCE through the recently described intracellular SR/transverse-tubule junctions at the I band of the sarcomere named Ca²⁺ entry units, was reported in both fast- and slow-twitch fibers from CSQ-KO mice, likely as a compensative mechanism for the massive reduction of total SR calcium content observed in these animals (20,21). These modifications can then be responsible for an altered [Ca²⁺]_cyto, but for a quantitative understanding of their role we must consider also the influence of the steady-state Ca²⁺ gradients generated by RyR1 leaks, as shown in the next section.

In fibers with leaky SR, mitochondria might take up Ca²⁺ from microdomains

In understanding the discrepancy between higher mitochondrial Ca²⁺ concentration and unchanged free [Ca²⁺]_cyto we noted that measurements of [Ca²⁺]_cyto at rest, carried out with Fura-2 or other probes, only yielded an average or pooled [Ca²⁺]_cyto. As we discussed in a recent review (22), at the mitochondria-CRU microdomain distance (∼140 nm) (23) a free Ca²⁺ concentration higher than the pooled or averaged cytosolic concentration can be expected, not only during Ca²⁺ release events but also in the presence of Ca²⁺ leakage.

In the “global version” of the cell boundary theorem reported above, in Eqs. 1 and 2, without a structural modification of the channels/pumps that support efflux and influx, the two fluxes keep a constant dependence of [Ca²⁺]_cyto on [Ca²⁺]_ext, and therefore any perturbation is fated to reach the sole value that equilibrates the two fluxes. However, as already noted by Ríos (19), in the presence of gradients within the cell, Eq. 1 is true only after “integration over the entire plasmalemma.” Alternatively, considering that the exchanges occur in a finite number of structures, we can write:

$$\frac{\mathrm{d}{\left[{Ca}^{2+}\right]}_{cyto}}{dt}=\sum _{ic}\left[influx\left({\left[{Ca}^{2+}\right]}_{ext},{\left[{Ca}^{2+}\right]}_{cyto}^{ic}\right)\right]-\sum _{ec}\left[efflux\left({\left[{Ca}^{2+}\right]}_{ext},{\left[{Ca}^{2+}\right]}_{cyto}^{ec}\right)\right]-removal\left({\left[{Ca}^{2+}\right]}_{org},{\left[{Ca}^{2+}\right]}_{cyto}\right)+release\left({\left[{Ca}^{2+}\right]}_{org},{\left[{Ca}^{2+}\right]}_{cyto}\right)$$ (3)

This “local version” of the cell boundary theorem considers the local [Ca²⁺]_cyto in front of each influx (ic) or efflux (ec) channel/pump. The local version of the theorem is equivalent to the global version if we include a function “g,” which, accounting for the geometrical and diffusional constraint in the cell, links the two concentrations through [Ca²⁺]^ic/ec_cyto = g([Ca²⁺]_cyto). In this way, the new equation is again a function of the sole variable [Ca²⁺]_cyto in the steady state. However, if the gradient generated by a different value of the removal and release fluxes is big enough to sensibly affect the function g, then the modification has an implicit effect also on the shape of the influx (g([Ca²⁺]_cyto)) and efflux (g([Ca²⁺]_cyto)), pointing to a different value for the [Ca²⁺]_cyto at the equilibrium.

The previous reasoning implies that the effects of changes in the internal fluxes on the average [Ca²⁺]_cyto can only be evaluated taking into account also the local [Ca²⁺] gradients. Therefore, we quantified the magnitude of the [Ca²⁺] gradient with a diffusion rate of Ca²⁺ equal to 3 × 10^–6 cm²/s (24), generated by a leaky RyR1 in a quiescent sarcomere, of 2.5 μm length and 0.5 μm radius, improving our previous diffusional model (see supporting material) of a half-sarcomere of a WT fast skeletal muscle, which includes the major buffers and organelles, and refining the mesh with 50 longitudinal and 20 radial compartments (25). We progressively included into the model the inward and outward fluxes to explore their contribution to the local Ca²⁺ concentration. In each version of the model we kept fixed the uptake capacity of the SERCA pumps, described as a series of saturable first-order pumps distributed along the SR with maximum cumulative uptake rate of 5.6 mmol/s/L_fiber at 25°C (from 4 mmol/s/L_fiber at 20°C with Q10 = 2) and K_d = 0.5 μM (26). As a simplest case (Fig. 2, case 1) we hypothesized that the leakage of the RyR1, located on the SR at 500 nm from the Z-line, as it is the case for mammalian, and specifically mice, fast skeletal muscle (27), is fully balanced by the continuous uptake of the SERCA pumps. When the constant rate of the RyR1 leak is modulated to keep the average [Ca²⁺]_cyto at the resting level of 100 nM, the resulting local [Ca²⁺] in the microdomain close to mitochondria is about 50% higher. The calculated RyR1 leakage resulted to be 255 μmol/s/L_fiber.

Figure 2.

Cytosolic [Ca²⁺] in a quiescent half-sarcomere of a fast-twitch WT mouse fiber with increasing complexity of the internal and external Ca²⁺ fluxes. Case 1: the leakage of the RyR1, located on the SR at 500 nm from the Z-line, is fully balanced by the continuous uptake by the SERCA pumps, described as a series of saturable first-order pumps distributed along the SR with maximum cumulative uptake rate of 4 mmol/s/L_fiber and K_d = 0.5 μM (26). The constant rate of the RyR1 leak is modulated to keep the average cytosolic [Ca²⁺] at the physiological level of 100 nM. The position of the RyR1 is indicated by the yellow arrow, the red arrows indicate the positions of the SERCA. The white dashed line indicates the likely location of the closest compartment of an intermyofibrillar mitochondrion at 140 nm from the CRU (23). Case 2 introduces a non-RyR1 leakage in the SR of 75% of the SERCA uptake rate. Case 3 includes also Ca²⁺ fluxes with the extracellular space and can represent the WT situation. Percentages in red indicate the increase in the local mitochondrial microdomain concentration with respect to the bulk level.

For a Figure360 author presentation of this figure, see https://doi.org/10.1016/j.bpr.2023.100117.

This was, however, the simplest case, which did not include Ca²⁺ influx and efflux across the sarcolemma. To reach a more realistic situation, we included first a non-RyR1 leakage in the SR, which can account for three-fourths of the total reuptake of SERCA in resting muscle, as estimated by Barclay and Launikonis starting from the rate of heat output from noncontracting human forearm muscles (26). In this case (Fig. 2, case 2), the constant RyR1 leak calculated to keep the [Ca²⁺]_cyto resting level at 100 nM was lower and the local [Ca²⁺] in the mitochondrial microdomain was 20% higher than that level. Moreover, the gradient was even more reduced when we included in the model the Ca²⁺ exchange with the extracellular space. We hypothesized (Fig. 2, case 3) an extrusion of Ca²⁺ through the PMCA of the 10% of the total RyR1 leakage (26), located in the junctional space, i.e., same cytosolic compartment of the RyR1, balanced by a series of influxes disposed along the SR, to mimic the SOCE. The localization of these outward and inward fluxes reduces the gradient generated by the RyR1 leak, creating a sort of shortcut in the mathematical model, bringing an amount of Ca²⁺ from the triad directly to the uptake compartments. Although relatively small, it is sufficient to reduce the gradient in the local [Ca²⁺] of the mitochondrial microdomain, which is now 19% higher than the bulk level. We considered this last case as representative of the WT cells. The RyR1 leakage, which keeps the average [Ca²⁺]_cyto to 100 nM in this more realistic case, is computed to be about 50 μM/s/L_fiber (Table 1). This value is compatible with the value of 17 μmol/s/L_fiber obtained in the model proposed in (1) considering that in that study a basal level of [Ca²⁺]_cyto of only 50 nM has been imposed.

Table 1.

Comparison of the fluxes and Ca²⁺ concentrations in the WT and in the CSQ-KO with two different leaks in the RyR (see text)

	RyR1 (μM/s)	[Ca2+]cyto (nM)	[Ca2+]microdomain (nM)	[Ca2+]mito nM
WT	50	100	119	160
RyR1 ×2.3	130	117	140	230
RyR1 ×5	250	142	189	420

Next, we used the model to estimate the sole effect of an increased RyR1 leakage, as observed in CSQ-KO muscles, on both the average [Ca²⁺]_cyto and on the local [Ca²⁺] of the mitochondrial microdomain. Although the CSQ ablation possibly affects to a different extent several model parameters, we adopted a ceteris paribus approach, where the estimated increase in RyR1 leakage is the sole parameter modified along with the absence of the CSQ buffer in the SR. We aimed at showing how much the increase in RyR1 leakage alone can influence the mitochondrial Ca²⁺ uptake. First, we explored the impact of a fivefold increase of the leakage. This means a constant leak of 250 μmol/s/L_fiber, close to what was estimated by a previous work for CSQ-KO cells (238.5 μmol/s/L_fiber) (1). Without further modifications of other fluxes, the increased RyR1 leak generates an average [Ca²⁺]_cyto of 142 nM, with an increase of the [Ca²⁺] in the mitochondrial microdomains of +35% (192 nM, Fig. 3, case 4). When the RyR1 leakage is chronically raised, a simultaneous increase in Ca²⁺ extrusion, through PMCA, and reuptake, through SOCE, is observed (28). PMCA is very close to RyR1 and highly sensitive to local [Ca²⁺] in the junctional space (1), while SOCE, activated to keep constant the SR Ca²⁺ content, releases Ca²⁺ in a close proximity with the SERCA (29). When we included a faster Ca²⁺ exchange with the extracellular space, as previously observed in this mouse model (20), increasing the extracellular flux from 10 to 50% of the RyR1 leak in the WT case, the average [Ca²⁺]_cyto value was almost unaffected, while the local [Ca²⁺] of the mitochondrial microdomain decreased to 189 nM (+33% with respect to the bulk value, Fig. 3, case 5). Interestingly, this local value is very close to the Ca²⁺ concentration extrapolated in (1) from the relationship between total mitochondrial calcium and average [Ca²⁺]_cyto as described above.

Figure 3.

Cytosolic [Ca²⁺] in a quiescent half-sarcomere of a fast-twitch CSQ-KO mouse fiber with increasing complexity of the internal and external Ca²⁺ fluxes. Description as in Fig. 2, with an increased RyR1 leak of a factor of 5. Case 4: Ca²⁺ exchange with the extracellular space is kept as in the WT case 3. Case 5 accounts for a greater Ca²⁺ exchange with the extracellular space, representative of the CSQ-KO situation.

Our simulation predicts that the presence of higher local [Ca²⁺] might provide an acceptable explanation of the [Ca²⁺]_mito higher in CSQ-KO than in WT even in the presence of a similar resting global [Ca²⁺]_cyto. Interestingly, the privileged location of the mitochondria suggests that, in the presence of leakage from SR, they might contribute to stabilize or prevent increase in average [Ca²⁺]_cyto and, at the same time, enhance the leakage via ROS and RNS generation. The cystein thiol groups of RYR1 and SERCA are well-known targets of ROS/RNS (for a review, see (30)). In addition, the increased free [Ca²⁺]_mito would boost ATP production, which is beneficial to support the SERCA-mediated SR refilling. The recent demonstration that RyR1 Ca²⁺ leak determines a standing [Ca²⁺] gradient between RyR1 and SERCA (31) is consistent with this view.

The Ca²⁺ uptake via MCU is not the only determinant of mitochondrial calcium content

Next, we made an attempt to estimate the resting [Ca²⁺]_mito generated by the different gradient in [Ca²⁺]_cyto in WT and in CSQ-KO cases including into the model a mitochondrial compartment located at about 140 nm from the RyR1. In this context it is worth underlining that intramitochondrial free and total calcium concentrations are not simply determined by the influx via the MCU complex driven by the Ca²⁺ electrochemical gradient. The kinetic balance of Ca²⁺ accumulation by mitochondria can be described more correctly by the equation

$$\frac{\mathrm{d}{\left[{Ca}^{2+}\right]}_{mito}}{dt}=J_{in}-J_{out}-J_b$$ (4)

where $J_b=\mathrm{\Sigma }\left(k_{on}{\left[{Ca}^{2+}\right]}_{mito}\left[B_{tot}-B_{Ca}\right]-k_{off}\left[B_{Ca}\right]\right)$, k_on, and K_off are the rate constants of the buffer, and B_tot and B_Ca are the total and Ca²⁺-bound concentrations, respectively, of intramitochondrial buffers (see (22)).

As underlined by Eq. 4, the mitochondrial ability to accumulate Ca²⁺ does not depend only on the MCU-mediated influx, but also on the buffer capacity and on outflow via the sodium-calcium-lithium exchanger (NCLX) or via permeability transition pore. It is plausible that the increased SR Ca²⁺ leakage determined by constitutive ablation of CSQ or gain-of-function RYR1 mutations could induce adaptive response of the mitochondria. An increased mitochondrial density has been observed in CSQ-KO fibers (10) and swollen mitochondria can be found in fibers with RYR1 mutations (32). As discussed above, the comparison between the total and free mitochondrial calcium determined by our group and others points to an increased buffer capacity in CSQ-KO fibers, eventually reducing the free Ca²⁺ during transient states. An increased influx, or a decreased efflux, can instead increase [Ca²⁺]_mito in resting CSQ-KO fibers. However, lacking experimental data, and with the aim of analyzing the effect of RyR1 leakage in a ceteris paribus approach, in the following we kept the values of MCU and NCLX parameters equal in WT and CSQ-KO. Thus, in an attempt to reproduce the balance of these two fluxes in WT and CSQ-KO cells, we simulated MCU as a saturable first-order kinetics, with V_max = 22.4 μmol/s/L_fiber (from (33) adapted at 25°C with a Q10 of 2) and cooperativity of 2 (25), while Ca²⁺ extruded through NCLX was simulated as proposed in (34) with a 3:1 stoichiometry for Na⁺ and Ca²⁺. Maximum extrusion velocity was imposed to match the measured resting [Ca²⁺]_mito in WT of 160 nM (6). Cooperativity in the MCU Ca²⁺ uptake represents the changes in the calcium affinity of the MCU induced by [Ca²⁺]_cyto via MICU1/2 subunits (35). Keeping these values constant, the model indicated that the predicted increase of local [Ca²⁺] in the mitochondrial microdomain with a fivefold increase of RyR1 leak would lead to a resting [Ca²⁺]_mito of 420 nM, higher than that observed experimentally by Scorzeto et al. (6). A value closer to that seen experimentally (230 nM) was reached imposing a factor of 2.3 in the RyR1 leak in CSQ-KO compared with WT (Fig. 4). This value required a local [Ca²⁺] in the mitochondrial microdomain at 140 nM, and the average [Ca²⁺]_cyto to 117 nM, only 17% higher than the WT counterpart, and possibly below the resolution obtained experimentally with Fura-2 measurements (Table 1).

Figure 4.

Mitochondrial free calcium concentration in WT and in CSQ-KO with two different RyR1 leakages, 2.3 and 5 times greater, respectively, than in WT.

Conclusion

The present results contribute to the quantitative understanding of how local gradients or hotspots/microdomains are generated, not only during contraction but also at rest, and how relevant they are to mitochondrial Ca²⁺ regulation.

Some limits must be acknowledged both for the numerical model and for the experimental data. Parameters for the maximum fluxes and cooperativities are still under debate in literature and their mathematical representation is necessarily a simplification of the real events. This is particularly true for the mitochondrial model, where the Na⁺ and H⁺ homeostasis is not considered as well as possible variation in the membrane potential.

Our ceteris paribus approach, which imposed for the CSQ-KO simulations the same parameters used for the WT case, except for the RyR1 leakage, allowed to highlight the crucial role of the RyR1 leakage in determining the mitochondrial calcium content at rest. We acknowledge that modifications in the mitochondrial Ca²⁺ buffer, influx, or efflux would also affect [Ca²⁺]_mito but, to the best of our knowledge, these adaptive alterations due to genetic ablation of the CSQ are not quantitatively characterized experimentally. An extension of the model to include these effects is left for future work. Finally, the existence of a MCU “threshold,” as a minimum level of [Ca²⁺]_cyto that triggers the MCU Ca²⁺ influx, has been hypothesized (36) but, since its existence is still under debate (37), we decided to include these effects in the model through the imposed MCU cooperativity.

As to experimental determination of cytosolic and free mitochondrial [Ca²⁺], it is important to underline the differences between male and female mice in both WT and CSQ-KO (see Fig. 1). Malignant hyperthermia crises occurred much less frequently in females when exposed to anesthetics or to high environmental temperature (8,9). The data suggested that a better redox control in females can explain the sex-related difference (3,4,5). Similarly to RYR1 mutations (32), in CSQ-KO fibers, the Ca²⁺ leakage increases ROS/RNS production, which in turn enhances RyR1 permeability via nitrosylation of cysteine residues (3). It is also worth noting that another important factor is the temperature. The free [Ca²⁺]_cyto and free [Ca²⁺]_mito measurements (5,6), as well as of the total mitochondrial calcium (1,2) in the CSQ-KO model, were obtained at room temperature (25°C). In muscle fibers with leaky RyR1, no difference in [Ca²⁺]_cyto is present at low temperature (38). The difference appears only when temperature is increased toward physiological values (32,39). Finally, the determinations of [Ca²⁺]_cyto were performed in fibers dissociated with collagenase (6), which are partially depolarized (resting potential close to –60 mV, (40)) and this possibly affects the Na⁺/Ca²⁺ exchanger both in CSQ-KO and WT.

Nonetheless, the model prediction demonstrates that the gradients between the CRU and the closest intermyofibrillar mitochondria due to the continuous leakage provides the link to the free and total mitochondrial calcium in resting skeletal muscle. Moreover, the presence of local variations of [Ca²⁺]_cyto at rest explains how the enhanced leakage may not affect substantially the average [Ca²⁺]_cyto. Considering local values is then a necessary step in estimating the average [Ca²⁺]_cyto in CSQ-KO fibers. This is critical, especially in view of the proposed mechanism that the augmented RyR1 leak could be functional in presaturating the troponin to preserve a normal force production despite the reduced SR calcium content and Ca²⁺ release in CSQ-KO fibers (1,10,17).

It is finally worth recalling that mitochondrial Ca²⁺ concentration is of outmost relevance for many biological processes such as regulation of ATP resynthesis, apoptosis, and proteostasis in health and disease (41,42). The control of mitochondrial Ca²⁺ in skeletal muscles is still debated, but there are clear indications that Ca²⁺ leakage from the SR leads to increased [Ca²⁺]_mito, possibly enhancing ROS/RNS production and inducing mitochondrial dysfunction (43,44). In this regard, the role of MCU, electrochemical gradient, and local [Ca²⁺]_cyto is not exhaustive and other components such as the Ca²⁺ efflux from mitochondria would require more attention.

Author contributions

L.M., C.R., and A.M. designed the research. L.M. performed numerical simulation. L.M., C.R., and A.M. analyzed the data. L.M., C.R., and A.M. wrote the paper.

Editor: Howard Young.