Temporal Modulation of a Spatially Periodic Potential for Kinetically Governed Oriented Motion

Resonant response to temperature modulation for enzymatic dynamics characterization

We consider enzymes involved in a three-state Michaelis-Menten kinetics and submitted to well-chosen temperature modulations of small amplitude. From the first-order amplitudes of concentration oscillations, we design a response function that is maximum for targeted values of the chemical relaxation times. This resonant function can be used to screen a large set of enzymes and identify the one governed by the desired kinetics. The method gives access to all the dynamical parameters of the targeted enzyme without resorting to a fit. We show how to estimate the precision of this parameter determination and give some hints for experimental validation.

Response to a temperature modulation as a signature of chemical mechanisms

We consider n reactive species involved in unimolecular reactions and submitted to a temperature modulation of small amplitude. We determine the conditions on the rate constants for which the deviations from the equilibrium concentrations of each species can be optimized and find the analytical expression of the frequency associated with an extremum of concentration shift in the case n=3. We prove that the frequency dependence of the displacement of equilibrium gives access to the number n of species involved in the mechanism. We apply the results to the case of the transformation of a reactant into a product through a possible reactive intermediate and find the order relation obeyed by the activation energies of the different barriers. The results typically apply to enzymatic catalysis with kinetics of Michaelis-Menten type.