Minimal model for calcium alternans due to SR release refractoriness

Area of Science:

• Cardiovascular Physiology
• Computational Biology
• Biophysics

Background:

• Pulsus alternans, characterized by alternating contraction strength, is often linked to intracellular calcium (Ca2+) transient instabilities.
• Two primary mechanisms for Ca2+ alternans are proposed: sarcoplasmic reticulum (SR) Ca2+ load dependence and SR Ca2+ release refractoriness due to ryanodine receptor 2 (RyR2) inactivation.

Purpose of the Study:

• To investigate the relationship between Ca2+ alternans and RyR2 refractoriness using a simplified model.
• To elucidate the fundamental mechanisms driving Ca2+ alternans.

Main Methods:

• Development of a reduced mathematical model focusing on dyadic space Ca2+ concentration and RyR2 recovery dynamics.
• Analysis of a nonlinear equation for dyadic Ca2+ and a relaxation equation for recovered RyR2s.
• Simulation of Ca2+ alternans onset under varying conditions, including inactivation, diffusion, and release conductance.

Main Results:

• Ca2+ alternans can be explained by a simple nonlinear equation for dyadic Ca2+ coupled with RyR2 recovery dynamics.
• Slow RyR2 recovery naturally leads to period doubling bifurcations, resulting in Ca2+ alternans.
• Optimal Ca2+ alternans development requires a specific level of Ca2+ diffusion, with less sensitivity to inactivation or release conductance.

Conclusions:

• The study provides a fundamental understanding of Ca2+ alternans driven by RyR2 refractoriness.
• RyR2 recovery dynamics are a critical determinant of Ca2+ alternans, independent of SR Ca2+ load instability.
• Calcium diffusion plays a crucial role in the onset and development of Ca2+ alternans.