Excited-state reversible geminate recombination with quenching in one dimension

General theory of multistage geminate reactions of isolated pairs of reactants. I. Kinetic equations

General matrix approach to the consideration of multistage geminate reactions of isolated pairs of reactants depending on reactant mobility is formulated on the basis of the concept of "effective" particles. Various elementary reactions (stages of multistage reaction including physicochemical processes of internal quantum state changes) proceeding with the participation of isolated pairs of reactants (or isolated reactants) are taken into account. Investigation has been made in terms of kinetic approach implying the derivation of general (matrix) kinetic equations for local and mean probabilities of finding any of the reaction species in the sample under study (or for local and mean concentrations). The recipes for the calculation of kinetic coefficients of the equations for mean quantities in terms of relative coordinates of reactants have been formulated in the general case of inhomogeneous reacting systems. Important specific case of homogeneous reacting systems is considered.

Green's function for reversible geminate reaction with volume reactivity

The kinetics of a diffusing particle near a reversible trap may be described by an extension of the Feynman-Kac equation to the case of reversible binding, which can occur within a finite reaction sphere. We obtain the Green's function solution for the Laplace transform of this equation when the particle is initially either bound or unbound. We study the solution in the time-domain by either inverting the Laplace transform numerically or propagating the partial differential equation in the time-domain. We show that integrals of this solution over the reaction sphere agree with previously obtained solutions.

Model of the initiation of signal transduction by ligands in a cell culture: simulation of molecules near a plane membrane comprising receptors

Cell communication is a key mechanism in tissue responses to radiation. Several molecules are implicated in radiation-induced signaling between cells, but their contributions to radiation risk are poorly understood. Meanwhile, Green's functions for diffusion-influenced reactions have appeared in the literature, which are applied to describe the diffusion of molecules near a plane membrane comprising bound receptors with the possibility of reversible binding of a ligand and activation of signal transduction proteins by the ligand-receptor complex. We have developed Brownian dynamics algorithms to simulate particle histories in this system which can accurately reproduce the theoretical distribution of distances of a ligand from the membrane, the number of reversibly bound particles, and the number of receptor complexes activating signaling proteins as a function of time, regardless of the number of time steps used for the simulation. These simulations will be of great importance to model interactions at low doses where stochastic effects induced by a small number of molecules or interactions come into play.

Diffusional effects on the reversible excited-state proton transfer. From experiments to Brownian dynamics simulations

We have studied an excited state proton transfer (ESPT) from the cationic "super" photoacid N-methyl 6-hydroxyquinolinium perfluorobutane sulfonate to non-aqueous solvents using picosecond and nanosecond time-resolved fluorescence spectroscopy. Upon the photoinduced adiabatic deprotonation from the hydroxyl moiety, a quinolinium zwitterion with a highly anisotropic charge distribution is formed. Due to the complexity of the resultant photodissociated system, the typical description of the reversible ESPT within the framework of the Spherically Symmetric Diffusion Problem (SSDP) is not possible. Additional complications are caused by the presence of a counteranion particle which affects the proton mobility. To better understand the ESPT process, we have performed extensive Brownian dynamics (BD) simulations of this three-body system as a tool to reveal the nature of the nonstationary interaction potentials and to elucidate the role of a counterion in the diffusion and reactive properties of the proton. Moreover, our results demonstrated that the anisotropy of the potential force can be taken into account after adapting this force for use in the SSDP. The results of both BD simulations and SSDP calculation with the adapted force field were used to fit the experimental kinetics of this three-body problem adequately.

Excited-state reversible geminate recombination in two dimensions

Excited-state reversible geminate recombination with two different lifetimes and quenching is investigated in two dimensions. From the exact Green function in the Laplace domain, analytic expressions of two-dimensional survival and binding probabilities are obtained at short and long times. We find that a new pattern of kinetic transition occurs in two dimensions. The long-time effective survival probabilities show a pattern of (ln t)(-1)-->constant-->e(t) depending on the rate constants while the effective binding probabilities show t(-1)(ln t)(-2)-->t(-1)-->e(t).

Diffusion-influenced excited-state reversible geminate ABCD reaction in the presence of an external field

We obtained the exact Green functions, in the Laplace domain, for a diffusion-influenced excited-state reversible geminate ABCD reaction with two different lifetimes and quenching processes under a constant external field in one dimension. Analytic expressions for the survival probabilities of the initial and final states are obtained in the time domain at short and long times, respectively. The short-time approximations obtained in this work are valid for t</K/(-1), where K depends on several parameters of the system. The analysis of the long-time asymptotic behaviors reveals rather complex kinetic transitions dependent upon the field and lifetimes. We also find a destructive interplay leading to the reduction in the number of kinetic transitions similar to that found for the excited-state geminate ABC reaction with an external field in one dimension.

Transition in the temperature-dependence of GFP fluorescence: from proton wires to proton exit

In green fluorescent protein, photo-excitation leads to excited-state proton transfer from its chromophore, leaving behind a strongly fluorescing anion, while the proton is commonly thought to migrate internally to Glu-222. X-ray data show that the protein contains more extended hydrogen-bonded networks that can support proton migration (i.e., proton wires). Here we study the temperature-dependence of the transient fluorescence from both the acid and anionic forms up to 15 ns. At low temperatures, we find that the (lifetime-corrected) fluorescence of the acidic form decays asymptotically as t(-1/2), following quantitatively the solution of a one-dimensional diffusion equation for reversible geminate recombination with quenching. This indicates proton migration along the internal proton wires. A small degree of geminate proton quenching is attributed to the formation of the zwitterion by proton migration on a side-branch of the proton wire. Above 230 K, the fluorescence kinetics undergo a transition, exhibiting an asymptotic t(-3/2) decay, and the quenching effect disappears. We interpret these findings as evidence for a conformational change enabling the rotation of Thr-203, which eventually allows the proton to escape to the exterior solution.

Exact solution of the excited-state geminate A*+B⇄C*+D reaction with two different lifetimes and quenching

The authors obtain, in the Laplace transform space, the exact analytic solution for the Green function and survival probabilities for the excited-state diffusion-influenced reversible geminate reaction, A*+B <==> C*+D, with two different lifetimes and in the presence of an added quenching process. This extends a previous investigation by Popov and Agmon [J. Chem. Phys. 117, 5770 (2002)] of the ground-state reaction without quenching. The long-time asymptotic behavior of the survival probabilities is obtained in the time domain. It is found to be different from the equal-lifetime case. This paper also provides a useful short-time approximation for the kinetics.

Diffusion-influenced reversible geminate recombination in one dimension. III. Field effect on the excited-state reaction

We obtain exact analytic solutions of the diffusion-influenced excited-state reversible geminate recombination reaction, A* + B<-->(AB)*, with two different lifetimes and quenching under the influence of a constant external field in one dimension. These fundamental solutions generalize two previous results [Kim et al., J. Chem. Phys. 111, 3791 (1999); 114, 3905 (2001)] and provide us with the insight necessary to analyze their specific relations and asymptotic kinetic transition behaviors. We find that the number of kinetic transitions can be changed due to interplay between the field strength and lifetimes. Unlike the previous works, the number of lifetime dependent transitions is found to be one or zero. On the other hand, the number of the field dependent transitions becomes two, one, or zero. We find a new pattern of kinetic transition e(t)-->t(-1/2)-->e(t) when there is only one field dependent transition.

Experimental evidence for a kinetic transition in reversible reactions

We provide a first experimental verification of a theoretical prediction of a kinetic transition in a reversible binding reaction, AB right harpoon over left harpoon A+B, driven by the difference in effective lifetimes of the bound and the unbound states. We consider the kinetics of excited-state proton transfer to solvent from a photoacid whose conjugate anionic base possesses an extremely short unbound anion lifetime. Its solvent variation relative to the overall dissociation rate coefficient induces a transition in the kinetics, from power law to exponential.