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The paper analyses stochastic systems describing reacting molecular systems with a combination of two types of state spaces, a finite-dimensional, and an infinite dimenional part. As a typical situation consider the interaction of larger macro-molecules, finite and small in numbers per cell (like protein complexes), with smaller, very abundant molecules, for example metabolites. We study the construction of the continuum approximation of the associated Master Equation (ME) by using the Trotter approximation [27]. The continuum limit shows regimes where the finite degrees of freedom evolve faster than the infinite ones. Then we develop a rigourous asymptotic adiabatic theory upon the condition that the jump process arising from the finite degrees of freedom of the Markov Chain (MC, typically describing conformational changes of the macro-molecules) occurs with large frequency. In a second part of this work, the theory is applied to derive typical enzyme kinetics in an alternative way and interpretation within this framework.
In this paper we consider deterministic limits of molecular stochastic systems with finite and infinite degrees of freedom. The method to obtain the deterministic vector field is based on the continuum limit of such microscopic systems which has been
We study the behavior of a moving wall in contact with a particle gas and subjected to an external force. We compare the fluctuations of the system observed in the microcanonical and canonical ensembles, at varying the number of particles. Static and
Most biological processes are described as a series of interactions between proteins and other molecules, and interactions are in turn described in terms of atomic structures. To annotate protein functions as sets of interaction states at atomic reso
The titled subject has attracted much interest. Here we summarize the substantial results obtained by a physical model of protein evolution based on hydropathic domain dynamics. In a recent Letter eighteen biologists suggested that the titled subject
Certain short polycations, such as TAT and polyarginine, rapidly pass through the plasma membranes of mammalian cells by an unknown mechanism called transduction as well as by endocytosis and macropinocytosis. These cell-penetrating peptides (CPPs) p