Spatially Confined Reactions: Stochastic Effects in Signaling Reactions at the Membrane

Signaling reactions often originate at the membrane, where competing membrane reactions decide if and how the signal will be passed on to downstream signaling cascades. In some cases, membrane reactions can even lead to polarization of signaling molecules that convey spatial information to downstream pathways. Due to the microscopic size of cellular structures, reactions at the membrane are confined and limited to low molecular copy numbers. Signaling decisions are therefore subject to strong stochastic effects. Understanding how membrane reactions can be influenced by stochastic effects is an imperative step toward deciphering the molecular logic of cellular signaling. However, the space of possibilities remains sparsely mapped. In this dissertation, I aim to expand our understanding of this topic by studying two-dimensional confinement effects on phosphatidylinositol signaling and small GTPase signaling reactions, both of which are ubiquitous membrane signaling mediators. Reducing the size of the membrane can lead to two distinct types of stochastic effects: size-dependent reaction speed and stochastic bistability. The underlying physical mechanism is intrinsically stochastic and cannot be predicted by classical deterministic kinetics. The biochemical requirements and potential cellular regulation of these stochastic effects are further discussed. In membranes with asymmetric shapes, the difference in local stochastic effects that the reaction experiences could emerge as stochastic polarization. This stochastic polarization has no analog in continuum reaction-diffusion systems and exhibits a striking ability to polarize in a consistent direction when constrained to cellular shapes. The requirements of size-dependent reaction speed, stochastic bistability, and stochastic polarization are very basic, and largely met in cellular environments, such that many membrane signaling reactions may be subject to these effects. Overall, the discussions here provide a basis to understand how the size and shape of the membrane can be a regulating factor of biochemical reactions and further influence living phenomena