Fast and Robust 2D Inverse Laplace Transformation of Single-Molecule Fluorescence Lifetime Data

Abstract

Fluorescence spectroscopy at the single-molecule scale has been indispensable for studying conformational dynamics and rare states of biological macromolecules. Single-molecule 2D-fluorescence lifetime correlation spectroscopy (sm-2D-FLCS) is an emerging technique that holds great promise for the study of protein and nucleic acid dynamics as it 1) resolves conformational dynamics using a single chromophore, 2) measures forward and reverse transitions independently, and 3) has a dynamic window ranging from microseconds to seconds. However, the calculation of a 2D fluorescence relaxation spectrum requires an inverse Laplace transition (ILT), which is an ill-conditioned inversion that must be estimated numerically through a regularized minimization. The current methods for performing ILTs of fluorescence relaxation can be computationally inefficient, sensitive to noise corruption, and difficult to implement. Here, we adopt an approach developed for NMR spectroscopy (T1-T2 relaxometry) to perform 1D and 2D-ILTs on single-molecule fluorescence spectroscopy data using singular-valued decomposition and Tikhonov regularization. This approach provides fast, robust, and easy to implement Laplace inversions of single-molecule fluorescence data. Significance StatementInverse Laplace transformations are a powerful approach for analyzing relaxation data. The inversion computes a relaxation rate spectrum from experimentally measured temporal relaxation, circumventing the need to choose appropriate fitting functions. They are routinely performed in NMR spectroscopy and are becoming increasing used in single-molecule fluorescence experiments. However, as Laplace inversions are ill-conditioned transformations, they must be estimated from regularization algorithms that are often computationally costly and difficult to implement. In this work, we adopt an algorithm first developed for NMR relaxometry to provide fast, robust, and easy to implement 1D and 2D inverse Laplace transformations on single-molecule fluorescence data.