title: Effective reaction rates in diffusion-limited phosphorylation-dephosphorylation cycles.
abstract: We investigate the kinetics of the ubiquitous phosphorylation-dephosphorylation cycle on biological membranes by means of kinetic Monte Carlo simulations on the triangular lattice. We establish the dependence of effective macroscopic reaction rate coefficients as well as the steady-state phosphorylated substrate fraction on the diffusion coefficient and concentrations of opposing enzymes: kinases and phosphatases. In the limits of zero and infinite diffusion, the numerical results agree with analytical predictions; these two limits give the lower and the upper bound for the macroscopic rate coefficients, respectively. In the zero-diffusion limit, which is important in the analysis of dense systems, phosphorylation and dephosphorylation reactions can convert only these substrates which remain in contact with opposing enzymes. In the most studied regime of nonzero but small diffusion, a contribution linearly proportional to the diffusion coefficient appears in the reaction rate. In this regime, the presence of opposing enzymes creates inhomogeneities in the (de)phosphorylated substrate distributions: The spatial correlation function shows that enzymes are surrounded by clouds of converted substrates. This effect becomes important at low enzyme concentrations, substantially lowering effective reaction rates. Effective reaction rates decrease with decreasing diffusion and this dependence is more pronounced for the less-abundant enzyme. Consequently, the steady-state fraction of phosphorylated substrates can increase or decrease with diffusion, depending on relative concentrations of both enzymes. Additionally, steady states are controlled by molecular crowders which, mostly by lowering the effective diffusion of reactants, favor the more abundant enzyme.
authors.affiliation: College of Inter-Faculty Individual Studies in Mathematics and Natural Sciences, University of Warsaw, 02-089 Warsaw, Poland.
authors.forename: Paulina
authors.initials: P
authors.lastname: Szymańska
authors.affiliation: Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland.
authors.forename: Marek
authors.initials: M
authors.lastname: Kochańczyk
authors.affiliation: Institute of Applied Mathematics and Mechanics, University of Warsaw, 02-097 Warsaw, Poland.
authors.forename: Jacek
authors.initials: J
authors.lastname: Miękisz
authors.affiliation: Institute of Fundamental Technological Research, Polish Academy of Sciences, 02-106 Warsaw, Poland and Department of Statistics, Rice University, Houston, Texas 77005, USA.
authors.forename: Tomasz
authors.initials: T
authors.lastname: Lipniacki
mesh_terms: D003198:Computer Simulation; D004058:Diffusion; D007700:Kinetics; D008566:Membranes / Q000378:metabolism; D008954:Models, Biological; D009010:Monte Carlo Method; D010744:Phosphoric Monoester Hydrolases / Q000378:metabolism; D010766:Phosphorylation; D010770:Phosphotransferases / Q000378:metabolism
chemical_list: D010770:Phosphotransferases; D010744:Phosphoric Monoester Hydrolases