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Michel D.,University Of Rennes1 Irset | Ruelle P.,Catholic University of Louvain
Journal of Mathematical Chemistry | Year: 2013

The Michaelis-Menten enzymatic reaction is sufficient to perceive many subtleties of network modeling, including the concentration and time scales separations, the formal equivalence between bulk phase and single-molecule approaches, or the relationships between single-cycle transient probabilities and steady state rates. Seven methods proposed by different authors and yielding the same famous Michaelis-Menten equation, are selected here to illustrate the kinetic and probabilistic use of rate constants and to review basic techniques for handling them. Finally, the general rate of an ordered multistep reaction, of which the Michaelis-Menten reaction is a particular case, is deduced from a Markovian approach. © 2013 Springer Science+Business Media New York. Source

Michel D.,University Of Rennes1 Irset
Journal of Theoretical Biology | Year: 2013

The quasi-equilibrium approximation is acceptable when molecular interactions are fast enough compared to circuit dynamics, but is no longer allowed when cellular activities are governed by rare events. A typical example is the lactose operon (lac), one of the most famous paradigms of transcription regulation, for which several theories still coexist to describe its behaviors. The lac system is generally analyzed by using equilibrium constants, contradicting single-event hypotheses long suggested by Novick and Weiner (1957). Enzyme induction as an all-or-none phenomenon. Proc. Natl. Acad. Sci. USA 43, 553-566) and recently refined in the study of (Choi et al., 2008. A stochastic single-molecule event triggers phenotype switching of a bacterial cell. Science 322, 442-446). In the present report, a lac repressor (LacI)-mediated DNA immunoprecipitation experiment reveals that the natural LacI-lac DNA complex built in vivo is extremely tight and long-lived compared to the time scale of lac expression dynamics, which could functionally disconnect the abortive expression bursts and forbid using the standard modes of lac bistability. As alternatives, purely kinetic mechanisms are examined for their capacity to restrict induction through: (i) widely scattered derepression related to the arrival time variance of a predominantly backward asymmetric random walk and (ii) an induction threshold arising in a single window of derepression without recourse to nonlinear multimeric binding and Hill functions. Considering the complete disengagement of the lac repressor from the lac promoter as the probabilistic consequence of a transient stepwise mechanism, is sufficient to explain the sigmoidal lac responses as functions of time and of inducer concentration. This sigmoidal shape can be misleadingly interpreted as a phenomenon of equilibrium cooperativity classically used to explain bistability, but which has been reported to be weak in this system. © 2013 Elsevier Ltd. Source

Michel D.,University Of Rennes1 Irset
Physica A: Statistical Mechanics and its Applications | Year: 2013

Although first-order rate constants are basic ingredients of physical chemistry, biochemistry and systems modeling, their innermost nature is derived from complex physical chemistry mechanisms. The present study suggests that equivalent conclusions can be more straightly obtained from simple statistics. The different facets of kinetic constants are first classified and clarified with respect to time and energy and the equivalences between traditional flux rate and modern probabilistic modeling are summarized. Then, a naive but rigorous approach is proposed to concretely perceive how the Arrhenius law naturally emerges from the geometric distribution. It appears that (1) the distribution in time of chemical events as well as (2) their mean frequency, are both dictated by randomness only and as such, are accurately described by time-based and spatial exponential processes respectively. © 2013 Elsevier B.V. All rights reserved. Source

Michel D.,University Of Rennes1 Irset
Biochimie | Year: 2016

A long standing debate in biochemistry is to determine whether the conformational changes observed during biomolecular interactions proceed through conformational selection (of preexisting isoforms) or induced fit (ligand-induced 3D reshaping). The latter mechanism had been invoked in certain circumstances, for example to explain the non-Michaelian activity of monomeric enzymes like glucokinase. But the relative importance of induced fit has been recently depreciated in favor of conformational selection, assumed to be always sufficient, predominant in general and in particular for glucokinase. The relative contributions of conformational selection and induced fit are reconsidered here in and out of equilibrium, in the light of earlier concepts such as the cyclic equilibrium rule and the turning wheel of Wyman, using single molecule state probability, one-way fluxes and net fluxes. The conditions for a switch from conformational selection to induced fit at a given ligand concentration are explicitly determined. Out of equilibrium, the inspection of the enzyme states circuit shows that conformational selection alone would give a Michaelian reaction rate but not the established nonlinear behaviour of glucokinase. Moreover, when induced fit and conformational selection coexist and allow kinetic cooperativity, the net flux emerging in the linkage cycle necessarily corresponds to the induced fit path. © 2016 Elsevier B.V. and Société Française de Biochimie et Biologie Molé Source

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