Quadratic response of a chemical reaction to external oscillations

Stochastic pumping of non-equilibrium steady-states: how molecules adapt to a fluctuating environment

In the absence of input energy, a chemical reaction in a closed system ineluctably relaxes toward an equilibrium state governed by a Boltzmann distribution. The addition of a catalyst to the system provides a way for more rapid equilibration toward this distribution, but the catalyst can never, in and of itself, drive the system away from equilibrium. In the presence of external fluctuations, however, a macromolecular catalyst (e.g., an enzyme) can absorb energy and drive the formation of a steady state between reactant and product that is not determined solely by their relative energies. Due to the ubiquity of non-equilibrium steady states in living systems, the development of a theory for the effects of external fluctuations on chemical systems has been a longstanding focus of non-equilibrium thermodynamics. The theory of stochastic pumping has provided insight into how a non-equilibrium steady-state can be formed and maintained in the presence of dissipation and kinetic asymmetry. This effort has been greatly enhanced by a confluence of experimental and theoretical work on synthetic molecular machines designed explicitly to harness external energy to drive non-equilibrium transport and self-assembly.

Nonlinear response theory in chemical kinetics

A theory of nonlinear response of chemical kinetics, in which multiple perturbations are used to probe the time evolution of nonlinear chemical systems, is developed. Expressions for nonlinear chemical response functions and susceptibilities, which can serve as multidimensional measures of the kinetic pathways and rates, are derived. A new class of multidimensional measures that combine multiple perturbations and measurements is also introduced. Nonlinear fluctuation-dissipation relations for steady-state chemical systems, which replace operations of concentration measurement and perturbations, are proposed. Several applications to the analysis of complex reaction mechanisms are provided.

Determination of the six rate constants of a three-state enzymatic network and a noninvasive test of detailed balance

The Michaelis-Menten mechanism is unanimously recognized by experimentalists and theoreticians as the reference model for the description of enzymatic catalysis. The recent explosion in the diversity of fluorescent probes solves the problem of in situ observation of proteins and the experimental investigation of enzymatic dynamics, which determines the Michaelis constant or a small number of relaxation times, is becoming more and more common. We propose a protocol for the full characterization of enzyme kinetics in the framework of the Michaelis-Menten mechanism. The method relies on the measurement of the oscillation amplitude of the enzymatic concentrations, when the biological medium is submitted to a temperature modulation of a few degrees. Analytical expressions of all the rate constants as functions of the concentration amplitudes are derived. The noninvasive character of the perturbation and the assessable uncertainty on the rate constant values make an in situ test of detailed balance possible.

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.

Resonance of relaxation time in the temperature modulated Schlögl model

We show the possibility to accelerate-in a resonant way-a nonlinear chemical reaction by imposing a small temperature modulation. This classical resonance, which happens for particular modulation frequencies, is illustrated on the athermic cubic Schlogl model, which allows us to get analytical expressions for both the reaction relaxation time and the frequency-resonant delay.

Molecular change signal-to-noise criteria for interpreting experiments involving exposure of biological systems to weakly interacting electromagnetic fields

We describe an approach to aiding the design and interpretation of experiments involving biological effects of weakly interacting electromagnetic fields that range from steady (dc) to microwave frequencies. We propose that if known biophysical mechanisms cannot account for an inferred, underlying molecular change signal-to-noise ratio, (S/N)gen, of a observed result, then there are two interpretation choices: (1) there is an unknown biophysical mechanism with stronger coupling between the field exposure and the ongoing biochemical process, or (2) the experiment is responding to something other than the field exposure. Our approach is based on classical detection theory, the recognition that weakly interacting fields cannot break chemical bonds, and the consequence that such fields can only alter rates of ongoing, metabolically driven biochemical reactions, and transport processes. The approach includes both fundamental chemical noise (molecular shot noise) and other sources of competing chemical change, to be compared quantitatively to the field induced change for the basic case that the field alters a single step in a biochemical network. Consistent with pharmacology and toxicology, we estimate the molecular dose (mass associated with field induced molecular change per mass tissue) resulting from illustrative low frequency field exposures for the biophysical mechanism of voltage gated channels. For perspective, we then consider electric field-mediated delivery of small molecules across human skin and into individual cells. Specifically, we consider the examples of iontophoretic and electroporative delivery of fentanyl through skin and electroporative delivery of bleomycin into individual cells. The total delivered amount corresponds to a molecular change signal and the delivery variability corresponds to generalized chemical noise. Viewed broadly, biological effects due to nonionizing fields may include animal navigation, medical applications, and environmental hazards. Understanding necessary conditions for such effects can be based on a unified approach: quantitative comparison of the estimated chemical change due to a particular electromagnetic field exposure to that due to competing influences, with both estimates based on a biophysical mechanism model within the context of a model of a biological system.

Advantages of external periodic events to the evolution of biochemical oscillatory reactions

We compare, by calculations on a simple model of glycolysis, the evolutionary development of oscillatory reaction mechanisms in the presence and absence of external periodic events, such as an oscillatory or constant influx of glucose in an open reaction system. The chosen model has autonomous oscillations for given choices of the parameters of the feedback loops responsible for the oscillations, and for a given range of the total adenylate pool concentration. We change first one, then two of the parameters, so that there are no autonomous oscillations, and then vary these parameters with a genetic algorithm method in which the parameters are represented by binary strings that evolve by selection, crossover, and mutations; the optimization goal is the attainment of a high ATP/ADP concentration ratio in the system. This goal is taken to provide evolutionary advantages and is shown to be achieved more quickly in the presence of external periodic events, rather than constant influx of glucose. The results suggest the possibility of the enhanced evolutionary development of oscillatory biological reactions at shores where waves impinge on rocks and bring nutrients periodically. Measurements have shown that animals and plants grow more rapidly in the presence of such wave action than in its absence.

Towards a chemically driven molecular electron pump

Charge can be pumped through a tiny gated portal from a reservoir at low electrochemical potential to one at the same or higher electrochemical potential by cyclically modulating the portal and gate energies. A theoretically and experimentally well established mechanism is Thouless adiabatic pumping, achieved by a precisely timed out-of-phase modulation of at least two parameters of the system. Here we show that stochastic modulation between two configurations of gate and portal energies can drive efficient pumping by a different, nonadiabatic, mechanism that may provide a basis for chemically driven electron pumping through a molecular wire.