Showing papers by "Federico Morán published in 2002"

Memory effects and oscillations in single-molecule kinetics

Abstract: An exactly solvable model for single-molecule kinetics is suggested, based on the following assumptions: (i) A single molecule can exist in different chemical states and the random transitions from one chemical state to another can be described by a local master equation with time-dependent transition rates. (ii) Because of conformational and other intramolecular fluctuations the rate coefficients in the master equation are random functions of time; their stochastic properties are represented in terms of a set of control parameters. We assume that the fluctuating rate coefficients fulfill a separability condition, that is, they are made up of the multiplicative contributions of two factors: (a) a universal factor, which depends on the vector of control parameters and is the same for all chemical transformation processes and (b) process-dependent factors, which depend on the initial and final chemical states of the molecule but are independent of the control parameters. For systems with two chemical states the condition of separability is automatically fulfilled. We introduce an intrinsic time scale, which makes it possible to compute theoretically various experimental observables, such as the correlation functions of the fluorescent signal. We analyze the connections between the condition of separability and detailed balance, and discuss the possible cause of chemical oscillations in single molecule kinetics. We show that the intrinsic dynamics of the molecule, expressed by the fluctuations of the control parameters, may lead to damped oscillations of the correlation functions of the fluorescent signal. The influence of the random fluctuations on the control parameters may be described by a renormalized master equation with nonfluctuating apparent rate coefficients. The apparent rate coefficients do not have to obey a condition of detailed balance, even though the real rate coefficients do obey such a condition. It follows that the renormalized master equation may have damped oscillatory solutions.

Neutrality condition and response law for nonlinear reaction-diffusion equations, with application to population genetics.

Abstract: We study a general class of nonlinear macroscopic evolution equations with "transport" and "reaction" terms which describe the dynamics of a species of moving individuals (atoms, molecules, quasiparticles, organisms, etc.). We consider that two types of individuals exist, "not marked" and "marked," respectively. We assume that the concentrations of both types of individuals are measurable and that they obey a neutrality condition, that is, the kinetic and transport properties of the "not marked" and "marked" individuals are identical. We suggest a response experiment, which consists in varying the fraction of "marked" individuals with the preservation of total fluxes, and show that the response of the system can be represented by a linear superposition law even though the underlying dynamics of the system is in general highly nonlinear. The linear response law is valid even for large perturbations and is not the result of a linearization procedure but rather a necessary consequence of the neutrality condition. First, we apply the response theorem to chemical kinetics, where the "marked species" is a molecule labeled with a radioactive isotope and there is no kinetic isotope effect. The susceptibility function of the response law can be related to the reaction mechanism of the process. Secondly we study the geographical distribution of the nonrecurrent, nonreversible neutral mutations of the nonrecombining portion of the Y chromosome from human populations and show that the fraction of mutants at a given point in space and time obeys a linear response law of the type introduced in this paper. The theory may be used for evaluating the geographic position and the moment in time where and when a mutation originated.

Delayed response in tracer experiments and fragment-carrier approach to transit time distributions in nonlinear chemical kinetics

Abstract: A delayed response tracer experiment is suggested, based on the following constraints: (1) The kinetics of the process can be expressed by local evolution equations without delays, for example by the mass action law. (2) The kinetic isotope effect can be neglected, that is, the rate coefficients for labeled and unlabeled chemicals are the same. (3) The total fluxes of the various chemicals are generally time dependent, but are not modified by the presence of the labeled compounds. (4) The experiment consists in the measurement of the time dependence of the fractions βu, u = 1, 2,… of labeled chemicals in the output fluxes as functionals of the time dependence of the fractions αu, u = 1, 2,… of labeled chemicals in the input fluxes, which are controlled by the researcher. We show that the output fluxes are related to the input fluxes by a linear delayed superposition theorem: βu(t) = ∑u′ ∫ χuu′(t,t′)αu′(t′)dt′, where χuu′(t,t′), is a delayed susceptibility function, which is related to the probability density of the transit time, that is, the time necessary for a molecular fragment to cross the system. This linear superposition law is not the result of a linearization procedure and holds even if the underlying kinetic equations are highly nonlinear. We establish a relationship between the transit time probability densities and the lifetime distributions of the various species in the system. The law permits extracting information about the mechanism and kinetics of chemical processes from response experiments.