Development and implementation of theoretical models for molecular scale distance distributions for comparison with fluorescence resonance energy transfer measurements

Abstract

The objective of this project is to develop theoretical calculations of molecular scale distance distributions for comparison with those detectable with time resolved fluorescence spectroscopy measurements, emphasizing the frequency domain technique. Fluorescence resonance energy transfer (FRET) measurements are in principle sensitive to donor-acceptor (D-A) distances and distance distribution functions. Heterogeneity of emission rates is interpreted as heterogeneity of D-to-A energy transfer rates and D-to-A distances. The goal of uniting the theoretical and experimental domains is advanced from the theoretical side by two sets of computer programs. The first program is an implementation of the rotational isomeric state (RIS) model as described by Flory (1969) for the end-to-end distance distribution functions of chain-like molecules. Application of the algorithm to alkyl-linker molecules is presented, as well as some work on peptide-linker molecules. Using this program this independent perspective on the shape of the end-to-end distance distribution function is shown to reinforce the shape of a parameterized one recovered from the data. Conversely the RIS model is shown to be consistent with the fluorescence data, for the longer alkyl molecules described here. The second program is an implementation of a Monte Carlo integration over the space of possible donor-acceptors configurations, or Explicit Fluorophore Distribution Simulation (EFDS). In it, models for the distribution functions available to energy transfer acceptors may be tested, with decreased restrictions of assumed symmetry or uniformity of kinetic patterns. The method is shown to be consistent by comparison with solutions based on geometries which are amenable to analytic solutions. This is followed by examples of behavior based on some restrictive geometries. The programs provide an improved mechanism for comparing models described in geometric terms with values from the experimental domain. In so doing, the applicability of the models can be evaluated. It is hoped that quantification of molecular flexibility and configurational heterogeneity will improve the interpretation and utility of fluorescence experiments and ultimately lead to a better understanding of molecular behavior at this scale.