Shiferaw, Y. | bioRxiv Science

bioRxiv2020

Buffering and total calcium levels determine the presence of oscillatory regimes in cardiac cells

Calcium oscillations and waves are often behind instances of extra depolarization in cardiac cells, eventually giving rise to life-threatening arrhythmias. In this work, we study the conditions for the appearance of calcium oscillations in both a detailed subcellular model of calcium dynamics and a minimal model that takes into account just the minimal ingredients of the calcium toolkit. To avoid the effects of homeostatic changes and the interaction with the action potential we consider the somewhat artificial condition of a cell without pacing and with no calcium exchange with the extracellular medium. This permits us to isolate the main reasons responsible for the oscillations by controlling externally the total calcium content of the cell. We find that as the calcium content is increased, the system transitions between two stationary states, corresponding to one with closed ryanodine receptors (RyR) and most calcium in the cell stored in the sarcoplasmic reticulum (SR), and another, with open RyRs and a depleted SR. In between these states, calcium oscillations may appear. This transition depends very sensitively in the amount of buffering in the cell. We find, for instance, that at high values of calsequestrin (CSQ) oscillations disappear, while they are present for a broad range of parameters at low values of CSQ. Using the minimal model, we can relate the stability of the oscillating state to the nullcline structure of the system, and find that its range of existence is bounded by a homoclinic and a Hopf bifurcation. Author summaryIn cardiac cells, calcium plays a very important role. An increase in calcium levels is the trigger used by the cell to initiate contraction. Besides, calcium modulates several transmembrane currents, affecting the cell transmembrane potential. Thus, dysregulations in calcium handling have been associated with the appearance of arrhythmias. Often, this dysregulation results in the appearance of periodic calcium waves or global oscillations, providing a pro-arrhythmic substrate. In this paper, we study the onset of calcium oscillations in cardiac cells using both a detailed subcellular model of calcium dynamics and a minimal model that takes into account just the minimal ingredients of the calcium toolkit. Both reproduce the main experimental results and link this behavior with the presence of different steady-state solutions and bifurcations that depend on the total amount of calcium in the cell and in the level of buffering present. We expect that this work will help to clarify the conditions under which calcium oscillations appear in cardiac myocytes and, therefore, will represent a step further in the understanding of the origin of cardiac arrhythmias.

biophysics↗

bioRxiv2019

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

AbstractVentricular contraction is roughly proportional to the amount of calcium released from the Sarcoplasmic Reticulum (SR) during systole. While it is rather straightforward to measure calcium levels and contractibility under different physiological condition, the complexity of calcium handling during systole and diastole has made the prediction of its release at steady state impossible. Here we approach the problem analyzing the evolution of intracellular and extracellular calcium fluxes during a single beat which is away from homeostatic balance. Using an in-silico subcellular model of rabbit ventricular myocyte, we show that the high dimensional nonlinear problem of finding the steady state can be reduced to a two-variable general equilibrium condition where pre-systolic calcium level in the cytosol and in the SR must fulfill simultaneously two different equalities. This renders calcium homeostasis as a problem that can be studied in terms of its equilibrium structure, leading to precise predictions of steady state from single-beat measurements. We show how changes in ionic channels modify the general equilibrium as shocks would do in general equilibrium macroeconomic models. This allows us to predict when an enhanced entrance of calcium in the cell reduces its contractibility and explain why SERCA gene therapy, a change in calcium handling to treat heart failure, might fail to improve contraction even when it successfully increases SERCA expression. Author summaryCardiomyocytes, upon voltage excitation, release calcium, which leads to cell contraction. However, under some pathological conditions, calcium handling is impaired. Recently, SERCA gene therapy, whose aim is to improve Ca2+ sequestration by the Sarcoplasmic Reticulum (SR), has failed to improve the prognosis of patients with Heart Failure. This, together with recent counterintuitive results in calcium handling, has highlighted the need for a framework to understand calcium homeostasis across species and pathologies. We show here that the proper framework is a general equilibrium approach of two independent variables. The development of this framework allows us to find a possible mechanism for the failure of SERCA gene therapy even when it manages to increase Ca SERCA expression.

systems biology↗