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 2.596 nm (+0.049/-0.045) (dark) and 4.04 nm (+0.92/-0.45) (lit) in the wild type, and 2.55 nm (+0.13/-0.11) (dark) and 4.4 nm (+1.6/-0.9) (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.