Combining Graphical and Analytical Methods with Molecular Simulations To Analyze Time-Resolved FRET Measurements of Labeled Macromolecules Accurately

Abstract

Förster resonance energy transfer (FRET) measurements from a donor, D, to an acceptor, A, fluorophore are frequently used in vitro and in live cells to reveal information on the structure and dynamics of DA labeled macromolecules. Accurate descriptions of FRET measurements by molecular models are complicated because the fluorophores are usually coupled to the macromolecule via flexible long linkers allowing for diffusional exchange between multiple states with different fluorescence properties caused by distinct environmental quenching, dye mobilities, and variable DA distances. It is often assumed for the analysis of fluorescence intensity decays that DA distances and D quenching are uncorrelated (homogeneous quenching by FRET) and that the exchange between distinct fluorophore states is slow (quasistatic). This allows us to introduce the FRET-induced donor decay, εD(t), a function solely depending on the species fraction distribution of the rate constants of energy transfer by FRET, for a convenient joint analysis of fluorescence decays of FRET and reference samples by integrated graphical and analytical procedures. Additionally, we developed a simulation toolkit to model dye diffusion, fluorescence quenching by the protein surface, and FRET. A benchmark study with simulated fluorescence decays of 500 protein structures demonstrates that the quasistatic homogeneous model works very well and recovers for single conformations the average DA distances with an accuracy of < 2%. For more complex cases, where proteins adopt multiple conformations with significantly different dye environments (heterogeneous case), we introduce a general analysis framework and evaluate its power in resolving heterogeneities in DA distances. The developed fast simulation methods, relying on Brownian dynamics of a coarse-grained dye in its sterically accessible volume, allow us to incorporate structural information in the decay analysis for heterogeneous cases by relating dye states with protein conformations to pave the way for fluorescence and FRET-based dynamic structural biology. Finally, we present theories and simulations to assess the accuracy and precision of steady-state and time-resolved FRET measurements in resolving DA distances on the single-molecule and ensemble level and provide a rigorous framework for estimating approximation, systematic, and statistical errors.

Toward dynamic structural biology: Two decades of single-molecule Förster resonance energy transfer

“…The nontrivial transformations from uncorrected FRET efficiency E * to corrected FRET efficiency E , and then to inter-dye distance R and to inter-residue distance r , require additional preparations and measurements of control mutants, modeling and simulations, structural convergence procedures, and control and validation of refined structures. Several studies (117–119) have followed this route, reporting successful structure determination (120–122). The information retrieved from smFRET measurements of multiple distances can be used to directly triangulate a structure of a whole or part of a macromolecule, or can be used as experimental constraints for structural simulations (121).…”

Characterizing highly dynamic conformational states: the transcription bubble in RNAP-promoter open complex as an example

“…S16 of the supplementary material) and transformed into apparent mean D-A distances ̅ − , (Eqs. S17, S18, S21 of the supplementary material); (v) steps (i)-(iv) are repeated for all labeled constructs; The more labeled constructs of more reaction coordinates are measured, the more accurate and reliable the dynamic structure determination will be; (vi) the different 19,49 or coarse-grained (CG) [49][50][51] simulations or against database predicted structures 52 .…”

“…Indeed, several groups used this approach in conjunction with 3D structures attained from molecular simualtions (e.g. molecular dynamics, Monte Carlo) [15][16][17][18][19] . This approach allows identification and solving of 3D macromolecular structures that are 'too dynamic' and have not been characterized by classical structural biology techniques.…”

High-throughput smFRET analysis of freely diffusing nucleic acid molecules and associated proteins

“…Combination with microfluidics [4,5], electrokinetic trapping [6] or single-molecule manipulation techniques [7], later enabled studying conformational dynamics in solution at the single-molecule level. Recent developments have mainly focused on improving the reliability and resolution of distance measurements by smFRET [8,9,10], making it a useful complementary technique to X-ray crystallography and single-particle cryo-EM for exploring biomolecular structures. In particular, the ability of solution-based measurements to access molecular dynamics lays the foundation for timeresolved structure determination at the nanometer scale [3,10].…”