Monte Carlo simulation of multiple attack mechanism of β-amylase-catalyzed reaction

Abstract

β‐Amylase (EC 3.2.1.2) produces maltose (dimer) from the nonreducing ends of α‐1,4 glucosidic bonds of substrates like maltooligosaccharides, amylose, and amylopectin. The enzyme releases several maltose molecules from a single enzyme‐substrate complex without dissociation by multiple or repetitive attack containing many branching reaction paths. The Monte Carlo method was applied to the simulation of the β‐amylase‐catalyzed reaction including the multiple attack mechanism. The simulation starts from a single enzyme molecule and a finite number of substrate molecules. The selection of the substrate by the enzyme and degree of multiple attack proceeds by random numbers produced from a computer. The simulation was carried out until the whole substrate and the intermediate molecules were consumed. The simulated data were compared with experimental data of sweet potato β‐amylase using heptamer, octamer, nanomer, and 11‐mer as substrates. The only adjustable parameter for odd‐numbered substrates was the probability of multiple attack, while an additional adjustable parameter (a correction factor due to low reactivity of tetramer) was needed for even‐numbered substrates. © 1997 John Wiley & Sons, Inc. Biopoly 42: 831–836, 1997

Monte Carlo simulation of hyaluronidase reaction involving hydrolysis, transglycosylation and condensation

“…Analysis of the kinetic mechanism by using differential equations from steady-state enzyme kinetics is unsuitable, due to the large number of adjustable parameters involved. In the present study, the Monte Carlo method [9][10][11][12] was applied to the kinetic analysis of the hyaluronidase reaction. Since the Monte Carlo algorithm is simple, the progress of product distribution is simulated with minimum adjustable parameters.…”

Modelling Reactions Catalysed by Carbohydrate-Active Enzymes

“…To treat such enzymes, Hiroshi Nakatani employed Monte Carlo simulations and described in a series of papers various models of the action of enzymes on soluble carbohydrate polymers. In [33,23] a model of the action of β -amylase is presented, which takes into account the possibility of repeated attack of the enzyme without dissociation of the substrate. In [34] a conceptually similar model is discussed which describes the action of α-glucanotransferases, which include central enzymes in the starch degradation pathway such as DPE1.…”

“…As a consequence, various Monte Carlo based modelling approaches have been applied to simulate the action of polymer-active enzymes [33,34,35,23,29,28,13] (see review in the previous section). Such approaches have the advantage that not all possible configurations have to be known a priori.…”

“…However, in many of these simulations, the temporal progress of the catalytic action was simulated only as a function of the reaction coordinate (see e.g. [33,34,35]) and it was difficult to relate the substrate formation with the actual time passed. In [25] and [41] the Monte Carlo approach was slightly modified and simulated using a Gillespie algorithm [17], allowing to explicitly include the time coordinate.…”

“…Notwithstanding our lack of understanding of far-from-equilibrium states, Monte-Carlo simulations [33,34,35] and Gillespie algorithms [25,41] allow for a precise prediction and explanation of the temporal evolution of polymer mixtures in in vitro experiments towards equilibrium. Our new theoretical understanding of polymer-active enzymes allows us now to define adequate kinetic parameters.…”