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The kinetics of bleaching in single-molecule fluorescence spectroscopy (SMS) is studied using renewal theory. A five-state model of a dye molecule is considered where bleaching occurs from the excited triplet states. An exact formalism is developed to calculate the distributions of the bleaching number (i.e., the number of photon counts) and bleaching time (i.e., the time before photobleaching). For photostable dyes those distributions are well approximated by exponential distributions determined by the average bleaching number ν and the average bleaching time τ respectively. Exact formulation is developed to calculate ν and τ in terms of the transition rate constants. For photostable dyes the exact ν and τ are well approximated by expressions derived from a steady-state solution to the kinetic rate equations describing the molecule. The theory implies that experimental multiexponential fits to the distributions of the bleaching number and bleaching time are an indication that the SMS system is heterogeneous.

IntroductionManual lymphatic drainage (MLD) is an adjunctive method of chronic venous disease (CVD) therapy. Evaluation of the change at the clinical stage, hemodynamic parameters and quality of life (QoL) following venous system surgery in CVD patients undergoing MLD preoperatively are the most interesting aspects of the study.Material and methodsThe CVD patients qualified for elective surgery of the venous system were randomly divided into 2 groups: the MLD group (n = 38) and the control group (n = 32). In the preoperative period, the MLD group underwent a series of MLD through a period of 2 weeks. The control group did not undergo MLD preoperatively. Both groups were evaluated for CVD staging on the day of qualification for surgery and between 25 and 30 days post-operatively. Additionally, the MLD group was evaluated after the series of MLD. The CVD staging was evaluated in both groups with a QoL questionnaire (CIVIQ), CEAP classification, foot volumetry (FV) and venous refilling time (VRT).ResultsParameter values obtained in the MLD group (before treatment/after MLD/after surgery): CEAP 2.23/2.15/2.10, VRT 15/13/15.6, FV 3625/3472/3418, CIVIQ-complaints: 54.4/43.8/38.2 and CIVIQ-meaning: 57.3/49.3/43.1. Parameter values obtained in control group (before surgery/after surgery): CEAP 2.4/2.12, VRT 13/14.9, FV 3581/3559, CIVIQ-complaints: 51.9/38.7 and CIVIQ-meaning: 53.7/40.6. The CVD patients statistically improved in CEAP staging, FV and QoL in both groups (p < 0.05).ConclusionsThe MLD alone significantly reduced FV in patients with CVD, also improving their QoL. The MLD applied in CVD patients at the preoperative stage results in better surgical outcome, which is demonstrated by reduced disease progression, FV reduction and improvement in the QoL.

The statistical nonequilibrium thermodynamic theory of diffusion-influenced reactions is extended to nonstationary situations. Coupled dynamic equations for the average concentrations and the radial distribution function are derived, and, in the low density limit, applied to study the approach of the reversible reaction A+B⇄C to equilibrium. Two types of rate coefficients for the bimolecular reaction are discussed: (i) molecular rate coefficient describing the rates of elementary reactive events, and (ii) phenomenological rate constants defined via the macroscopic rate equations. In contrast to the phenomenological rate constant, the molecular forward rate coefficient ceases to depend on diffusion when the reaction reaches equilibrium. If the relaxation time for the reaction is much greater than that for diffusion, the classical expressions of Eigen for the linearized relaxation rate near equilibrium are recovered. A close relationship between the classical approach, the pseudo-steady-state approximation, and Onsager’s regression hypothesis is demonstrated. The relation between the present results and those recently put forward in the literature is discussed.