Using Multiorder Time-Correlation Functions (TCFs) To Elucidate Biomolecular Reaction Pathways from Microsecond Single-Molecule Fluorescence Experiments

Abstract

Recent advances in single-molecule fluorescence imaging have made it possible to perform measurements on microsecond time scales. Such experiments have the potential to reveal detailed information about conformational changes in biological macromolecules, including the reaction pathways and dynamics of the rearrangements involved in processes such as sequence-specific DNA ‘breathing’ and the assembly of protein-nucleic acid complexes. Because microsecond resolved single-molecule trajectories often involve ‘sparse’ data – i.e., they contain relatively few data points per unit time – they cannot be easily analyzed using the standard protocols that were developed for single-molecule experiments carried out with tens-of-millisecond time resolution and high ‘data density.’ We here describe a generalized approach, based on time correlation functions (TCFs), to obtain kinetic information from microsecond-resolved single-molecule fluorescence measurements. This approach can be used to identify short-lived intermediates that lie on reaction pathways connecting relatively long-lived reactant and product states. As a concrete illustration of the potential of this methodology for analyzing specific macromolecular systems, we accompany the theoretical presentation with a description of a specific biologically-relevant example drawn from studies of the reaction mechanisms of the assembly of the single-stranded DNA binding protein of the T4 bacteriophage replication complex onto a model DNA replication fork.

Using microsecond single-molecule FRET to determine the assembly pathways of T4 ssDNA binding protein onto model DNA replication forks

“…The significance of the number of decay components of the second-order TCF can be understood in the context of the theory of Markov chains, which describes the kinetics of an equilibrium chemical system that may undergo stochastic transitions between N discrete states (36). Markov chain theory predicts that the second-order TCF contains N -1 decay components (20). Thus, the biexponential decay that we have observed for C ð2Þ ðτÞ implies that N ≥ 3.…”

“…In this work, we apply generalized concepts of time correlation functions (TCFs) to study the ssDNA-(gp32) 2 assembly pathways (20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30). We assume that our single-molecule experiments probe the instantaneous conformational state of the system at equilibrium and that the stochastically fluctuating smFRET efficiency, E FRET , can be directly mapped onto this state.…”

“…An overview of the theoretical method that we implemented for this purpose is given in ref. 20. We note that fourth-order TCFs are important in the analysis of nonlinear spectroscopies, including 2D NMR, 2D IR, and 2D electronic spectroscopy (31).…”

“…Both second-and fourth-order TCFs can be modeled using the theory of Markov chains (20,36). This approach assumes a kinetic scheme, in which N states are interconnected by elementary chemical steps as depicted in Fig.…”

“…The input parameters of the Markov model are the observed fluctuation values δE i assigned to state i and the rate constants k ij associated with forward and backward transitions between states i and j. The values of k ij must satisfy the principles of detailed balance (20). Expressions for calculated second-and fourth-order TCFs are derived in SI Appendix.…”