title: Monte Carlo simulations of enzymatic reactions in crowded media. Effect of the enzyme-obstacle relative size.
abstract: We perform Monte Carlo simulations in three-dimensional (3D) lattice in order to study diffusion-controlled and mixed activation-diffusion reactions following an irreversible Michaelis-Menten scheme in crowded media. The simulation data reveal the rate coefficient dependence on time for diffusion-controlled bimolecular reactions developing in three-dimensional media with obstacles, as predicted by fractal kinetics approach. For the cases of mixed activation-diffusion reactions, the fractality of the reaction decreases as the activation control increases. We propose a modified form of the Zipf-Mandelbrot equation to describe the time dependence of the rate coefficient, k(t)=k0(1+t/τ)(-)(h). This equation provides a good description of the fractal regime and it may be split into two terms: one that corresponds to the initial rate constant (k0) and the other one correlated with the kinetics fractality. Additionally, the proposed equation contains and links two limit expressions corresponding to short and large periods of time: k1=k0 (for t≪τ) that relates to classical kinetics and the well-known Kopelman's equation k∼t(-)(h) (for t≫τ) associated to fractal kinetics. The τ parameter has the meaning of a crossover time between these two limiting behaviours. The value of k0 is mainly dependent on the excluded volume and the enzyme-obstacle relative size. This dependence can be explained in terms of the radius of an average confined volume that every enzyme molecule feels, and correlates very well with the crossover length obtained in previous studies of enzyme diffusion in crowding media.
authors.affiliation: Department of Biology-Chemistry, West University of Timisoara, Pestalozzi 16, 300311 Timisoara, Romania(1); University Al.I. Cuza from Iaşi, 11 Carol I, Iasi, Romania(2).
authors.forename: Laura
authors.initials: L
authors.lastname: Pitulice
authors.affiliation: Physical Chemistry Department and Research Institute of Theoretical and Computational Chemistry (IQTCUB) of Barcelona University (UB), C/Marti i Franquès, 1, E-08028 Barcelona, Catalonia, Spain.
authors.forename: Eudald
authors.initials: E
authors.lastname: Vilaseca
authors.affiliation: Physical Chemistry Department and Research Institute of Theoretical and Computational Chemistry (IQTCUB) of Barcelona University (UB), C/Marti i Franquès, 1, E-08028 Barcelona, Catalonia, Spain.
authors.forename: Isabel
authors.initials: I
authors.lastname: Pastor
authors.affiliation: Physical Chemistry Department and Research Institute of Theoretical and Computational Chemistry (IQTCUB) of Barcelona University (UB), C/Marti i Franquès, 1, E-08028 Barcelona, Catalonia, Spain.
authors.forename: Sergio
authors.initials: S
authors.lastname: Madurga
authors.affiliation: Chemistry Department, University of Lleida (UdL), Lleida, Catalonia, Spain.
authors.forename: Josep Lluís
authors.initials: JL
authors.lastname: Garcés
authors.affiliation: Department of Biology-Chemistry, West University of Timisoara, Pestalozzi 16, 300311 Timisoara, Romania(1).
authors.forename: Adriana
authors.initials: A
authors.lastname: Isvoran
authors.affiliation: Physical Chemistry Department and Research Institute of Theoretical and Computational Chemistry (IQTCUB) of Barcelona University (UB), C/Marti i Franquès, 1, E-08028 Barcelona, Catalonia, Spain. Electronic address: fmas@ub.edu.
authors.forename: Francesc
authors.initials: F
authors.lastname: Mas
mesh_terms: D000465:Algorithms; D003198:Computer Simulation; D004798:Enzymes / Q000378:metabolism*; D017709:Fractals; D007700:Kinetics; D055641:Mathematical Concepts; D008954:Models, Biological; D009010:Monte Carlo Method
chemical_list: D004798:Enzymes
keywords: Diffusion limited reactions; Fractal kinetics; Macromolecular crowding; Michaelis–Menten mechanism; Monte Carlo simulations; Time dependent rate coefficient