Reconstructing time-resolved inter-residue distance distributions in a protein ensemble during functional dynamics in solution

Reconstructing time-resolved inter-residue distance distributions during protein functional dynamics in the solution state is known to be a difficult and important problem. This article presents a technique for extracting spin-spin (as a proxy for residue-residue) distance distributions on doubly-spin-labeled proteins from rapid-scan time-resolved Gd-Gd electron paramagnetic resonance (rs-TiGGER) spectra recorded near room temperature in solution at 240 GHz. We use a best-fit technique that convolves a dipolar kernel matrix with an intrinsic, non-dipolar-broadened (single-labeled) spectrum. The kernel incorporates the effect of solution-state tumbling on the dipolar broadening using a correlation function that bridges the static and rapidly tumbling regimes. We apply the technique to AsLOV2 , a protein domain with a dark-state crystal structure that is well-known from X-ray crystallography, but a less well-characterized and disordered tertiary structure that manifests after photoactivation at 450 nm. Informed by principal component analysis, we assume that the underlying distance distribution may be approximated by a sum of two Gaussian distributions. The fits returned time-resolved, light-activated populations with mean distances of (dark) and (lit) in the wild type, and (dark) and (lit) in an N414Q mutant, with nearly complete unfolding (within fit uncertainty) of the active, light-sensitive fraction. The extracted distance distributions and their accompanying uncertainties are consistent within uncertainty with molecular dynamics simulations of the equilibrated protein structure.