Related papers: The Quasi-Steady State Assumption in an Enzymatica…
The Michaelis-Menten mechanism is probably the best known model for an enzyme-catalyzed reaction. For spatially homogeneous concentrations, QSS reductions are well known, but this is not the case when chemical species are allowed to…
The celebrated Michaelis-Menten (MM) expression provides a fundamental relation between the rate of enzyme catalysis and substrate concentration. The validity of this classical expression is, however, restricted to macroscopic amounts of…
In biochemical networks, reactions often occur on disparate timescales and can be characterized as either "fast" or "slow." The quasi-steady state approximation (QSSA) utilizes timescale separation to project models of biochemical networks…
The application of the standard quasi-steady-state approximation to the Michaelis--Menten reaction mechanism is a textbook example of biochemical model reduction, derived using singular perturbation theory. However, determining the specific…
Mathematical analysis of mass action models of large complex chemical systems is typically only possible if the models are reduced. The most common reduction technique is based on quasi-steady state assumptions. To increase the accuracy of…
The classic Michaelis-Menten equation describes the catalytic activities for ensembles of enzyme molecules very well. But recent single-molecule experiment showed that the waiting time distribution and other properties of single enzyme…
The century-long Michaelis-Menten rate law and its modifications in the modeling of biochemical rate processes stand on the assumption that the concentration of the complex of interacting molecules, at each moment, rapidly approaches an…
It is well known in enzyme kinetics that the Michaelis-Menten (MM) equation is applicable only to enzymes in the steady state. We show that the result obtained in the previous work [Phys. Rev. Lett. 107, 218301 (2011)] is inconsistent with…
We study a class of Stochastic Differential Equations (SDEs) with jumps modeling multistage Michaelis--Menten enzyme kinetics, in which a substrate is sequentially transformed into a product via a cascade of intermediate complexes. These…
The present work revisits the reduction of the nonlinear dynamics of an electromechanical system through a quasi-steady state hypothesis, discussing the fundamental aspects of this type of approach and clarifying some confusing points found…
Previous studies have primarily focused on the nonequilibrium thermodynamics of chemical reaction networks (CRNs) occurring in closed systems. In contrast, CRNs in open systems exhibit much richer nonequilibrium phenomena due to sustained…
In a conformational nonequilibrium steady state (cNESS), enzyme turnover is modulated by the underlying conformational dynamics. Based on a discrete kinetic network model, we use the integrated probability flux balance method to derive the…
In the framework of the theory of open systems based on completely positive quantum dynamical semigroups, we give a description of the dynamics of entanglement for a system consisting of two uncoupled harmonic oscillators interacting with a…
We develop a theory of enzyme catalysis within biological cells where the substrate concentration [S](t) is time dependent, in contrast to the Michaelis-Menten theory that assumes a steady state. We find that the time varying concentration…
Partial equilibrium approximation (PEA) and quasi-steady-state approximation (QSSA) are two classical methods for reducing complex macroscopic chemical reactions into simple computable ones. Previous studies mainly focus on the accuracy of…
Nonequilibrium thermodynamics of a system situated in a sustained environment with influx and efflux is usually treated as a subsystem in a larger, closed "universe". It remains a question what the minimally required description for the…
The adiabatic approximation exhibits wide applicability in quantum mechanics, providing a simple approach for nontransitional dynamics in quantum systems governed by slowly varying time-dependent Hamiltonians. However, the standard…
The theory of biochemical processes needs simple but realistic models of phenomena underlying microscopic dynamics of proteins. Many experiments performed in the 1980s have demonstrated that within the protein native state, apart from usual…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
All biological processes are controlled by complex systems of enzymatic chemical reactions. Although the majority of enzymatic networks have very elaborate structures, there are many experimental observations indicating that some turnover…