Two-variable nullcline analysis of ionic general equilibrium predicts calcium homeostasis in ventricular myocytes
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.