Exploring the effects of enforced proximity in enzyme reaction kinetics

With small enough volumes or with suitably low molecular population levels, deterministic and continuous approaches to modeling reactions become problematic. The standard methods of stochastic simulations for these systems assume an exponentially distributed waiting time between reactions. We have developed a stochastic model to simulate reactions in a spherical cell that account for each molecule's movement, and find that the wait-time distribution of a spherical substrate undergoing a three-dimensional random walk until collision with a spherical enzyme, when initially separated by a small enough initial distance, has two distinct components. One is exponential while the other is significantly faster than the exponential component. In single-stage reactions, we find that small volumes (and, consequently, high molecular concentrations) can effect faster-than-exponential interarrival times of substrates and reactive enzymes, a fact not included in the standard approaches. In multi-stage reactions, we find that co-locating successive enzymes in the reaction pathway in close proximity leads to greatly decreased reaction times. This is again attributable to the fast-time component of the molecular wait-time distributions. These findings can suggest improved design of metabolic pathways, and may explain why so many important intracellular reactions occur in relatively small volumes within the cell's organelles.