In this thesis three case studies of stochastic effects in biological signaling systems are presented. The opening of Ca release channels, clustered at discrete sites on the endoplasmic reticulum, can lead to large scale intracellular calcium waves. Experiments in Xenopus oocytes have shown the inter-wave intervals for these waves have a standard deviation much smaller than the mean and that the background [Ca²⁺] exhibits a slow rise during the interwave interval. In Chapter III we modeled this process and confirmed slow rise of Ca increases the cooperativity between the openings of the clusters. Moreover, a slow kinetics of Ca pump proteins is important for the accumulation of background Ca.

Cardiac calcium release channels are reported to have sub-conducting states when FK-506 binding protein (FKBP) level is low. This has important implications for heart failure, where it has been hypothesized that hyperphosphorylation of calcium channel by β-adrenergic stimulation results in a loss of FKBP binding, which can lead to a persistent leak and a reduced SR calcium content. In Chapter IV we modeled the gating of the channel via an allosteric interaction between its subunits and coupled this dynamics with the excitation-contraction (E-C) cycle of cardiac myocytes. We find the level of cooperativity can have a dramatic effect on the cardiac E-C coupling gain and that this gain exhibits a clear maximum. These findings are compared to currently available data from different species and allows for an evaluation of the heart failure scenario.

Cells often measure their local environment via the interaction of diffusible chemical signals with membrane receptors. At the level of a single receptor, this process is inherently stochastic, but cells can contain many such receptors to reduce the variability in the detected signal by suitable averaging. In Chapter V, we use explicit Monte Carlo simulations and analytical calculations to characterize the noise level as a function of the number of receptors. We show that the residual noise approaches zero and that the correlation time diverges for large receptor numbers. This result has important implications for such processes as eukaryotic chemotaxis.