Ca2+/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 outputs that agrees with empirical observations. Our research 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 when the system input is constant.
However, the system input is often periodic in experimental settings, so another important part of our research is averaging analysis, which provides us a way to build up an average model that approximates the original system asymptotically as the perturbation tends to zero. Meanwhile, we intend to establish that the CaMKII activation system acts as a low-pass filter which filters out high frequency components in the input signal. Thus the CaMKII activation system with a periodic input can be approximated by an averaged system with a constant input. In this way, not only is the computational burden of the simulation greatly reduced, but also the system analysis can be simplified significantly.