Multifractality in intracellular enzymatic reactions

Enzymatic kinetics adjust well to the Michaelis-Menten paradigm in homogeneous media with dilute, perfectly mixed reactants. These conditions are quite different from the highly structured cell plasm, so applications of the classic kinetics theory to this environment are rather limited. Cytoplasmic structure produces molecular crowding and anomalous diffusion of substances, modifying the mass action kinetic laws. The reaction coefficients are no longer constant but time-variant, as stated in the fractal kinetics theory. Fractal kinetics assumes that enzymatic reactions on such heterogeneous media occur within a non-Euclidian space characterized by a certain fractal dimension, this fractal dimension gives the dependence on time of the kinetic coefficients. In this work, stochastic simulations of enzymatic reactions under molecular crowding have been completed, and kinetic coefficients for the reactions, including the Michaelis-Menten parameter K_M, were calculated. The simulations results led us to confirm the time dependence of michaelian kinetic parameter for the enzymatic catalysis. Besides, other chaos related phenomena were pointed out from the obtained K_M time series, such as the emergence of strange attractors and multifractality.