Kinetic behavior of the general modifier mechanism of Botts and Morales with non-equilibrium binding

Abstract

In this paper, we perform a complete analysis of the kinetic behavior of the general modifier mechanism of Botts and Morales in both equilibrium steady states and non-equilibrium steady states (NESS). Enlightened by the non-equilibrium theory of Markov chains, we introduce the net flux into discussion and acquire an expression of product rate in NESS, which has clear biophysical significance. Up till now, it is a general belief that being an activator or an inhibitor is an intrinsic property of the modifier. However, we reveal that this traditional point of view is based on the equilibrium assumption. A modifier may no longer be an overall activator or inhibitor when the reaction system is not in equilibrium. Based on the regulation of enzyme activity by the modifier concentration, we classify the kinetic behavior of the modifier into three categories, which are named hyperbolic behavior, bellshaped behavior, and switching behavior, respectively. We show that the switching phenomenon, in which a modifier may convert between an activator and an inhibitor when the modifier concentration varies, occurs only in NESS. Effects of drugs on the Pgp ATPase activity, where drugs may convert from activators to inhibitors with the increase of the drug concentration, are taken as a typical example to demonstrate the occurrence of the switching phenomenon.

Overshoot in biological systems modelled by Markov chains: a non‐equilibrium dynamic phenomenon

“…If the exchange with the environment is sustained, then the living system always approaches a steady state far from equilibrium. Recent studies show that many important biological phenomena, such as coherence resonance in excitable systems [35], unidirectional movement of molecular motors [37] and switching behaviour of the general modifier mechanism of Botts and Morales [10], fail to occur in systems which will finally approach an equilibrium steady state. This suggests that sustained energy consumption is required for living systems to perform these important biological functions.…”

“…The specific meaning of these states varies from systems to systems. Each state can represent a binding state of an enzyme molecule [10], a conformational state of a receptor molecule [14,15,[25][26][27], a cellular state of a cell population [13] and so on. We further assume that the system has an observable f. If the system is in state i, the observation of the system will be f i .…”

“…A two-state system is always an equilibrium system which will finally approach an equilibrium steady state, whereas a system with three or more states may be a non-equilibrium system which will finally approach a non-equilibrium steady state [34][35][36]. Here, we have used the concepts of equilibrium and non-equilibrium steady states in non-equilibrium statistical physics, where the steady state of a system is called equilibrium if each pair of states i and j of the system satisfies the detailed balance condition m i q ij = m j q ji (10) (otherwise, the steady state of the system is called nonequilibrium) where μ i is the steady-state probability of state i and q ij is the transition rate from state i to state j. In the following discussion, a system which will finally approach an equilibrium (non-equilibrium) steady state is referred to as an equilibrium (non-equilibrium) system.…”

Molecular and cellular factors control signal transduction via switchable allosteric modulator proteins (SAMPs)

“…For the modulator protein to be in detailed balance, the following relations must hold at steady state [ 41 ]: …”

Representação do efeito de inibição enzimática reversível para o modelo cinético de Michaelis-Menten no estado transiente

“…2015 Nessa proposta aparecem dois novos complexos enzimáticos: EI representa o complexo de inibição e ESI é o complexo intermediário de inibição. Nesse mecanismo geral aparece, também, a representação de uma substância I que será responsável pela inibição.Em alguns trabalhos da literatura, a substância que propicia o efeito de inibição é representada por R, sendo tratada como uma molécula modificada no processo enzimático(JIA et al, 2012).…”