Inferring structure factors of weakly populated excited states in perturbative crystallography experiments

Perturbative X-ray crystallography can visualize functional dynamics and conformational changes in proteins at atomic resolution. During a typical perturbative crystallography experiment, only a fraction of protein molecules in a crystal will be perturbed, or "excited". As a result, the observed data represent a mixture of excited and ground states. The conventional approach to estimating the excited-state structure factor amplitudes is to linearly extrapolate the difference between the structure factor amplitudes of the perturbed and unperturbed data. This approach often fails to yield well-refined structural models because it amplifies experimental errors and neglects phase differences between the ground and excited states. Here, we introduce an approach to estimating excited-state structure factor amplitudes that starts from a statistical prior for the correlations between excited and ground states. Using benchmarks from time-resolved crystallography and a drug-fragment screen, we illustrate how this approach effectively addresses the limitations of traditional extrapolation.