Probing Dynamic Disorder in Single Molecule Event Statistics

Abstract

The molecular aspect of a reaction governs the applied methodology and the corresponding properties of a reaction under investigation. Unlike ensemble measurement techniques, single- molecule (SM) studies provide platforms for analysing individual molecular activities and accessing several dynamics aspects like the lifetime of intermediates, the temporal fluctuations in the reaction rates, the rate-determining step, predicting reaction mechanisms, the correlation between events, the probability distribution function (PDF) associated with a stochastic process and related statistical measurements. For analytically analysing these stochastic networks, one requires appropriate theoretical frameworks for constructing the PDF of interest. The thesis titled ‘Probing Dynamic Disorder in Single-Molecule Event Statistics’ emphasises on some applications of the theoretical formalisms (the first-passage time distribution formalism and the waiting-time distribution formalism) for mathematically modelling SM reaction networks associated with an enzyme and a nanoparticle (NP). We have implemented discrete-state models on enzymatic systems undergoing reversible interconversions between different conformational states and calculated the noise. We have also applied these frameworks on NP catalysed reactions for exploring the underlying dynamics of chemical reactions and quantifying the temporal activity fluctuations. Stochastic processes can also be modelled using continuous modelling methods. We have developed a theoretical method to derive the PDF of time taken by a molecule in crossing a barrier (the transit time distribution) using a generalized Langevin Equation (GLE) comprising different force components. All these theoretical investigations and numerical analyses provide platforms for a better understanding of biochemical/biophysical processes.