Stochastic mapping of the Michaelis-Menten mechanism

Abstract

Potential of mean force between hydrophobic solutes in the Jagla model of water and implications for cold denaturation of proteins J. Chem. Phys. 136, 044512 (2012) Size and shape effects on receptor-mediated endocytosis of nanoparticles J. Appl. Phys. 111, 024702 (2012) Hybrid modeling and simulation of stochastic effects on progression through the eukaryotic cell cycle J. Chem. Phys. 136, 034105 (2012) Amino acid analogues bind to carbon nanotube via π-π interactions: Comparison of molecular mechanical and quantum mechanical calculations JCP: BioChem. Phys. 6, 01B607 (2012) On binding of DNA-bending proteins to DNA minicircles JCP: BioChem. Phys. 6, 01B606 (2012) Additional information on J. Chem. Phys. The Michaelis-Menten mechanism is an extremely important tool for understanding enzymecatalyzed transformation of substrates into final products. In this work, a computationally viable, full stochastic description of the Michaelis-Menten kinetic scheme is introduced based on a stochastic equivalent of the steady-state assumption. The full solution derived is free of restrictions on amounts of substance or parameter values and is used to create stochastic maps of the Michaelis-Menten mechanism, which show the regions in the parameter space of the scheme where the use of the stochastic kinetic approach is inevitable. The stochastic aspects of recently published examples of single-enzyme kinetic studies are analyzed using these maps.

A queueing approach to multi-site enzyme kinetics

“…a traditional two-state Michaelis-Menten approximation with distinct states corresponding to enzyme bound or unbound to substrate. However, even simple deterministic Michaelis-Menten models can be difficult to properly analyse without some form of approximation [2][3][4], and this difficulty is compounded when stochastic dynamics are also considered [5][6][7][8][9][10][11][12]. Given that the majority of cellular processes are governed by enzymatic reactions, progress in the development of intuitive but powerful mathematical approaches to enzymatic kinetics immediately impacts our understanding of many biological networks.…”

Stochastic mapping of first order reaction networks: A systematic comparison of the stochastic and deterministic kinetic approaches

“…Furthermore, the Michaelis-Menten mechanism for enzyme kinetics is also simplified into a pseudo-first order scheme under the limit of low substrate concentration. 13 Two such experiments are shown in Fig. 1: point F describes single enzyme activity studies using Lipase B from Candida Antarctica, 45 whereas line G represents similar experimental studies with a β-galactosidase enzyme.…”

“…(20) and (21), the time dependences of s i,i and s i,j can be given without solving Eq. (13). Therefore, the standard deviation of a i can be calculated.…”

“…Stochastic mapping, which was used in essence in at least three recent articles 8,12,13 but was only named so in the last one, 13 attempts to answer this question by identifying the parameter range of a given kinetic scheme in which only the stochastic approach is viable. These earlier papers were concerned with chiral amplification, 12 extinction phenomena in autocatalysis, 8 and the Michaelis-Menten mechanism.…”

“…These earlier papers were concerned with chiral amplification, 12 extinction phenomena in autocatalysis, 8 and the Michaelis-Menten mechanism. 13 The stochastic region of a given scheme was defined in them as the set of parameter values for which the stochastic approach shows that the relative standard error of the target variable is larger than a pre-set critical value (usually 1%). Kurtz's theorem 14 ensures that the stochastic description of any reactive system converges to the deterministic solution when a) Fax: 36-52-518-660.…”