Single-molecule reaction-diffusion.

We propose capturing reaction-diffusion on a molecule-by-molecule basis from the fastest acquirable timescale, namely individual photon arrivals. We illustrate our method on the intrinsically disordered human protein linker histone H1.0 and its chaperone prothymosin α, as these diffuse through an illuminated confocal spot and interact, forming larger ternary complexes on millisecond timescales. Most importantly, single-molecule reaction-diffusion (smRD) reveals single-molecule properties without the requirement to trap or otherwise confine molecules to surfaces. We achieve smRD within a Bayesian paradigm and term our method Bayes-smRD. Bayes-smRD is further free of the average, bulk results inherent to analyzing long photon arrival traces by fluorescence correlation spectroscopy. In learning from mere thousands of photon arrivals, continuous spatial positions, and discrete conformational and photophysical state changes, Bayes-smRD estimates kinetic parameters on a molecule-by-molecule basis with two to three orders of magnitude less data than tools such as fluorescence correlation spectroscopy, thereby also dramatically reducing sample photodamage.