Effective reaction rates for diffusion-limited reaction cycles

• Published in: The Journal of chemical physics Vol. 143; no. 21; p. 215102
• Main Authors: Nałęcz-Jawecki, Paweł, Szymańska, Paulina, Kochańczyk, Marek, Miękisz, Jacek, Lipniacki, Tomasz
• Format: Journal Article
• Language: English
• Published: United States 07.12.2015
• Subjects: Adenosine Triphosphate - metabolism; Animals; Biocatalysis; Computer Simulation; Diffusion; Humans; Kinetics; Models, Biological; Monte Carlo Method; Phosphoric Monoester Hydrolases - metabolism; Phosphorylation; Protein Kinases - metabolism
• ISSN: 1089-7690
• DOI: 10.1063/1.4936131

Biological signals in cells are transmitted with the use of reaction cycles, such as the phosphorylation-dephosphorylation cycle, in which substrate is modified by antagonistic enzymes. An appreciable share of such reactions takes place in crowded environments of two-dimensional structures, such as plasma membrane or intracellular membranes, and is expected to be diffusion-controlled. In this work, starting from the microscopic bimolecular reaction rate constants and using estimates of the mean first-passage time for an enzyme-substrate encounter, we derive diffusion-dependent effective macroscopic reaction rate coefficients (EMRRC) for a generic reaction cycle. Each EMRRC was found to be half of the harmonic average of the microscopic rate constant (phosphorylation c or dephosphorylation d), and the effective (crowding-dependent) motility divided by a slowly decreasing logarithmic function of the sum of the enzyme concentrations. This implies that when c and d differ, the two EMRRCs scale differently with the motility, rendering the steady-state fraction of phosphorylated substrate molecules diffusion-dependent. Analytical predictions are verified using kinetic Monte Carlo simulations on the two-dimensional triangular lattice at the single-molecule resolution. It is demonstrated that the proposed formulas estimate the steady-state concentrations and effective reaction rates for different sets of microscopic reaction rates and concentrations of reactants, including a non-trivial example where with increasing diffusivity the fraction of phosphorylated substrate molecules changes from 10% to 90%.