Fig 1.
Schematic representation of the 3D compartmental diffusional model of murine skeletal muscle.
The unit cell of the skeletal muscle fiber, the half sarcomere, is approximated as a cylinder, so that rotational symmetry allows for analysis in 2D space. This space is occupied by three main compartments: sarcoplasmic reticulum, cytosolic space and mitochondrion. The sarcoplasmic reticulum is divided into m longitudinal sub-compartments and the cytosolic space is divided into m longitudinal and n-1 radial sub-compartments. Diffusion of Ca2+ ions is analyzed between sub-compartments. The mitochondrial compartment is close, but external, to extramyofibrillar space (EF). The mitochondrial calcium uniporter (MCU in black) and sodium calcium exchanger (NCE in red) sense the [Ca2+] in the sub-compartment 125 nm away from the RyR, toward Z-line. Several buffers are present in distinct sub-compartments: calsequestrin (CSQ) and additional buffers (AB) in sarcoplasmic reticulum, parvalbumin (PVA) in all cytosolic spaces, troponin in the myofibrillar spaces, and a mitochondrial buffer (B) in the mitochondrial matrix. Store operated Ca2+ entry (SOCE) is depicted by the vertical arrows from the T-tubular network extended toward the Z-line (green).
Table 1.
Experimental [Ca2+] in μM for WT muscle fibers.
These values are averages measured at steady state during stimulation trains at various rates (60, 20, 5, and 1 Hz).
Fig 2.
Experimental data and model simulations of calcium transients in a 2 s 60Hz stimulation train.
Experimental data (left column, from [12] and [13] [Ca2+] calculated from Fura 2 ratio and YFP/CFP ratios according to the equations reported in S5 File) and simulations (right column) of the [Ca2+] transients in the cytosol (top), SR (middle) and mitochondrion (bottom) during a 2s stimulation train at 60 Hz. It can be seen that the steady-state values reached in the experiments agree well with the model simulations. In addition the time courses agree rather well considering that the model is based solely on previously published parameters. The amplitude of the oscillations in the model simulations are larger than in the experimental recordings, but this is as expected because the experimental recordings were smoothed by an x-point running average to reduce noise. In the inset of the cytosolic calcium simulation (top-right) the local Ca2+ concentration is shown (dotted line) in the element (microdomain) in front of MCU and NCE and compared to the average cytosolic [Ca2+], showing an approximately two-fold increase. The lower-right panel shows the asymmetry in the rising phase (at the beginning of the train of stimuli), and at the decay phase (at the end of the train of stimuli) in the simulated mitochondrial [Ca2+].
Fig 3.
Simulation of the free calcium concentrations.
Simulation of the free calcium concentrations in the three compartments at 1 and 60 Hz in the WT model at the beginning and at the end of the train of stimulation. Red lines represent the mean value (“m” for the cytosolic space) or the steady value before the beginning of the next stimulus (“s” in SR and mitochondrion). Above each panel the values for m or s are reported.
Fig 4.
Comparison between the simulation and experiments in WT muscle fibers.
The simulated [Ca2+]reached at steady state in the three compartments and the experimental data for 1, 5, 20 and 60 Hz in WT mouse fibers are compared with experimental values. The free model parameters are adjusted to fit the data at 60 Hz. [Ca2+] is reported in μM in cytosol or mitochondrion (black and red lines, respectively) or in mM for SR (blue line). Dotted lines: experimental data; continuous lines: model predictions.
Table 2.
Experimental average [Ca2+] in μM for CSQ-KO mouse muscle fibers measured in the steady state attained during stimulation trains at various rates (1, 5, 20, 60 Hz).
Fig 5.
Simulation of the free calcium concentrations in CSQ-KO with an AB buffering capacity of 10% of that of CSQ.
Simulation of the free calcium concentrations in the three compartments at 1 and 60 Hz as predicted by the model without CSQ (CSQ-KO) with a AB buffering capacity of 10% of that of CSQ and with doubled Pmax value. Red lines represent the mean value (“m” for the cytosolic space) or the steady value before the beginning of the next stimulus (“s” in SR and mitochondrion). Above each panel the values for m or s are reported.
Fig 6.
Comparison between the simulation and experiments in CSQ-KO with an AB buffering capacity of 10% of that of CSQ.
Comparison between the simulated steady state [Ca2+] in the three compartments and the experimental data for 1, 5, 20 and 60 Hz in CSQ-KO mouse with 10% of total calcium bound in the SR at rest accounted by AB and with doubled Pmax value. [Ca2+] is reported in μM in cytosol or mitochondrion (black and red lines, respectively) or in mM for SR (blue line). Dotted lines stand for experimental data, continuous lines for simulations. The model without CSQ (CSQ-KO), with 10% of AB capacity and double Pmax fails to match the observed values in all three compartments, with predicted values lower than experimental data.
Fig 7.
Comparison between the simulation and experiments in CSQ-KO with an AB buffering capacity of 20% of that of CSQ.
Comparison between the simulated steady state [Ca2+] in the three compartments and the experimental data for 1, 5, 20 and 60 Hz in CSQ-KO mouse with increased AB buffering to 20% of the capacity of CSQ. [Ca2+] is reported in μM in cytosol or mitochondrion (black and red lines, respectively) or in mM for SR (blue line). Dotted lines stand for experimental data, continuous lines for simulations.
Table 3.
Simulated/Experimental ratio for [Ca2+] in μM for WT and CSQ-KO fibers, assuming the amount bound by secondary buffer capacity at 10% or at 20%.
The values are calculated at the steady state during the trains of stimulations, as in the Figs 3, 6 and 7.