Fig 1.
Structure of the computational ventricular rabbit cardiomyocyte model.
Panel (1): Scheme of the three-dimensional model where the cardiomyocyte is divided into thousands of 3d stacked Calcium Release Units (highlighted one in red). Panel (2): Depiction of the basic structure of the CaRUs showing the L-type Calcium Channels (LCC) in the vicinity of the Ryanodine Receptor (RyR), the SERCA pump and the Na-Ca Exchanger. The different states of the LCC and the RyR2 are also depicted. Panel (3): Typical cytosolic (orange) and SR (blue) free calcium transients in the rabbit ventricular model (described in Methods) at a voltage-clamped pacing rate of 2 Hz.
Fig 2.
Example of counterintuitive calcium homeostatic regulations.
Panel (1): Evolution of the SR free calcium concentration when, at a time marked by a black vertical line, the conductivity of the LCC is increased (left) or decreased (right). An increase in intake via the LCC leads to a cardiomyocyte with higher calcium average concentrations in the SR. Panel (2): Response of the cardiomyocyte to an increase in LCC conductivity, as in the first panel, when its buffering and SERCA uptake is different. Now, the increased intake via LCC is homeostatically regulated in a completely different way. The higher level of calcium intake leads to an even larger extrusion for the SR leading to a lower calcium load.
Fig 3.
Schematics of the procedure to reconstruct one of the nullclines of the system.
The nullcline corresponds to the partial equilibrium where the intake of calcium into the SR equals its release, where we have multiplied all ΔQ by the volume of the cytosol, to obtain this value in femtomols (fmol). The main central graph reproduces total release ΔQrel and uptake ΔQup as a function of the initial free concentrations in the cytosol ci(t = 0) and SR cSR(t = 0). The nullcline is determined by the line where both surfaces cross. For each initial condition, one single transient is simulated and the release JRyR and uptake JSrCa computed and shown in the upper graphs. The integrated values are indicated in the bar graph below and then placed as elements of the surface. The whole surface is constructed by reproducing this procedure with multiple different initial calcium concentrations where all other initial variables are in their fast equilibrium approximation.
Fig 4.
General equilibrium. Prediction of steady-state from the nullclines crossing.
Panel (1): The first two surfaces indicate the total amount of calcium entering ΔQin and leaving ΔQout the cell, computed following the same procedure explained in Fig 3. Below we compute the surfaces corresponding to release and uptake of calcium from the SR. On the right, we plot the two nullclines that correspond to the crossing of the previous surfaces. The f-nullcline is the set of initial ci and csr where ΔQin = ΔQout while the g-nullcline corresponds to the crossing between release ΔQrel and uptake ΔQup. The point where both nullclines cross gives the steady state of the system (ci, cSR) where concentrations return to the same pre-systolic values after a stimulation. Notice that the parameters of the model fix this crossing precisely at the expected value of roughly 150nM in the cytosol and 40 μmol/Lcyt in the SR, which correspond to a local concentration of free calcium in the SR csr at roughly 500 μM, given the volume ratio between SR and cytosol. We notice that this free calcium concentration corresponds to 100 μmol/Lcyt of total calcium in the SR, free and bound to CSQ, as reported in [42]. Panel (2): Steady state from single beat measurements at 2 Hz described in the top panel with modification of the rabbit model where the conductivity of LCC is increased. The prediction of thesteady state obtained from the global equilibrium as a function of the LCC conductivity fits very well the computed steady-state obtained after letting the system evolve for 100 beats.
Fig 5.
Shocks in general equilibrium models. Change in SERCA uptake is a two-nullcline shock.
Panel (1): We show a hypothetical change in the cell that only affects one of the four surfaces. This produces a change in one of the nullclines. As an example, we pick an increase of the ΔQup surface. This leads to a shift of the g-nullcline to the right compared with the previous case, resulting in a lower diastolic level in the cytosol but larger in the SR. Panel (2): Effect of changing the maximum uptake of the SERCA pump from 0.15 μ M/ms to 0.3 μ M/ms in our rabbit model. Increasing the function of SERCA does not only affect the g-nullcline, expected since the uptake is larger, but also affects how well the exchanger works shifting also the f-nullcline to the right. The end result is similar to the previous case.
Fig 6.
Homeostatic response of increasing SERCA uptake with normal and low RyR channel conductivity.
Panel (1): Dependence of pre-systolic values of free calcium concentrations in the SR and in the cytosol at steady state with maximum uptake of SERCA pump vup in the rabbit model. On the right, the relative increase of calcium during the calcium transient as a function of the maximum SERCA uptake νup. We take 100% to be the transient with the standard νup = 0.5 μM/ms. Panel (2): We present the same graphs as in the first panel but for a cell where the single channel conductivity of the RyR has been reduced. In this situation, the calcium transient is always lower than before and it does not improve as the uptake of SERCA is larger.
Fig 7.
Schematics of possible SERCA gene therapy outcomes.
Schematics of how SERCA gene therapy may fail in certain cells. A) During SERCA gene therapy a sudden increase in maximum SERCA uptake does not change initially the LCC or the release but it decreases NCX function as it decreases cytosolic calcium. This necessarily leads to a state of calcium unbalance that must be rebalanced again. B) Homeostasis will always fix and rebalance the system. However, the particulars of how this is done are not universal. They depend on the nullcline structure and reaction to shocks. For instance, in a healthy rabbit, the cell increases total calcium content by increasing considerably the calcium in the SR while diminishing cytosolic calcium levels. This increase in SR calcium results in a higher transient that allows a higher extraction of calcium through the NCX, even if diastolic calcium is reduced. However, it can happen that the RyR has a weak sensitivity to SR calcium content, so release remains almost constant. Since uptake is increased, the diastolic cytosolic level has to be increased to allow calcium extrusion through the NCX, then the transient is decreased, which results in decreased contractibility despite a stronger SERCA.