Monotonicity and Bistability of Calcium/Calmodulin-Dependent Protein Kinase-Phosphatase Activation

Calcium/calmodulin-dependent protein kinase II (CaMKII) is thought to be a key contributor to the induction of long-term potentiation (LTP). Researchers have developed a variety of mathematical models of CaMKII activation intended to produce simulation output that agrees with empirical observations. This paper focuses on one such model to which recent theoretical results for input-output monotone systems are applied. Several key findings in the literature are reproduced using simple algebraic computations as opposed to exhaustive, simulation-based analysis. In particular, it is confirmed that bistability exists over a range of calcium concentrations that nominally includes the intracellular resting level and switching between high activation and low activation states is described by a hysteresis curve.