Monte Carlo Simulations of Enzyme Reactions in Two Dimensions: Fractal Kinetics and Spatial Segregation

Abstract

Conventional equations for enzyme kinetics are based on mass-action laws, that may fail in low-dimensional and disordered media such as biological membranes. We present Monte Carlo simulations of an isolated Michaelis-Menten enzyme reaction on two-dimensional lattices with varying obstacle densities, as models of biological membranes. The model predicts that, as a result of anomalous diffusion on these low-dimensional media, the kinetics are of the fractal type. Consequently, the conventional equations for enzyme kinetics fail to describe the reaction. In particular, we show that the quasi-stationary-state assumption can hardly be retained in these conditions. Moreover, the fractal characteristics of the kinetics are increasingly pronounced as obstacle density and initial substrate concentration increase. The simulations indicate that these two influences are mainly additive. Finally, the simulations show pronounced S-P segregation over the lattice at obstacle densities compatible with in vivo conditions. This phenomenon could be a source of spatial self organization in biological membranes.

Superdiffusion in a Model for Diffusion in a Molecularly Crowded Environment

“…This understanding is needed to correctly describe passive intracellular transport, as this process may regulate important cellular properties: signal transduction [1], gene transcription [2], reaction kinetics [3], and regulation of cell polarization [4].…”

Space in systems biology of signaling pathways – towards intracellular molecular crowding in silico

“…The molecule can propagate either along its velocity vector or according to its diffusion rate to arrive at another lattice site, and then collide or react with other molecules. CA can be used to simulate reaction and diffusion at both microscopic [7,[31][32][33][34] (Fig. 1(c)) and mesoscopic ( Fig.…”

Monte Carlo simulations of enzymatic reactions in crowded media. Effect of the enzyme-obstacle relative size

“…There are numerous published papers with regard to simulations of diffusion processes [4-7, 10-12, 17, 19-20] and chemical reactions in crowded media [40][41][42][43][44][45][46][47][50][51][52][53][54][55][56]. Macromolecular crowding can lead to anomalous diffusion more likely when low dimension environments are considered especially up to percolation threshold [41].…”

“…Berry [52] studied a native Michaelis-Menten reaction scheme using a Monte Carlo simulation on two-dimensional lattice with cyclic boundary conditions. He used immobile obstacles varying their densities from zero to the percolation threshold.…”