Diffusion limited reactions in poorly mixed environments

Reaction rates and kinetic states form a central paradigm of biochemistry. Understanding and interpreting measured reaction rates is often equivalent to understanding the interactions and workings of a given system. However, the predictions and interpretations of reaction rates often assume a well-mixed environment, throughout which the reactants are evenly distributed. We consider two situations that challenge this approximation. First, we explore mechanisms in which flexible tethers confine diffusing particles, thereby regulating their bimolecular reaction rate. We use theory and simulation to explore how the rate at which the reactants find each other in solution depends upon the polymer properties of the tethers. We identify several biological systems, both synthetic and natural, in which tethering may play important roles in regulating chemical kinetics, and explore one system in depth, the actin-capping protein formin.;Second, we investigate how measurements of bimolecular dissociation rates depend on rapid rebinding events, in which the ligand transiently unbinds and rebinds before mixing in solution. Directly after unbinding, the local concentration of ligand is elevated, creating a poorly mixed environment. We argue that competitors introduced to chase off the ligand can accelerate the apparent dissociation of ligands, because they can interfere with the rapid rebinding events. We design a single molecule colocalization DNA binding experiment to probe the competitor dependence in the measured dissociation rate, and use theory and simulation to estimate the competitor effect. The experiment demonstrates competitor dependence that is consistent with our theory, and we show that in most experimental contexts the competitor will not change the off rate. Furthermore, the theory validates single-molecule colocalization as a method of biochemical kinetic measurement and shows its equivalence to bulk methods.