Connecting Longitudinal and Transverse Relaxation Rates in Live-Cell NMR

In the cytosolic environment, protein crowding and Brownian motions result in numerous transient encounters. Each such encounter event increases the apparent size of the interacting molecules, leading to slower rotational tumbling. The extent of transient protein complexes formed in live cells can conveniently be quantified by an apparent viscosity, based on NMR-detected spin-relaxation measurements, that is, the longitudinal (T₁) and transverse (T₂) relaxation. From combined analysis of three different proteins and surface mutations thereof, we find that T₂ implies significantly higher apparent viscosity than T₁. At first sight, the effect on T₁ and T₂ seems thus nonunifiable, consistent with previous reports on other proteins. We show here that the T₁ and T₂ deviation is actually not a inconsistency but an expected feature of a system with fast exchange between free monomers and transient complexes. In this case, the deviation is basically reconciled by a model with fast exchange between the free-tumbling reporter protein and a transient complex with a uniform 143 kDa partner. The analysis is then taken one step further by accounting for the fact that the cytosolic content is by no means uniform but comprises a wide range of molecular sizes. Integrating over the complete size distribution of the cytosolic interaction ensemble enables us to predict both T₁ and T₂ from a single binding model. The result yields a bound population for each protein variant and provides a quantification of the transient interactions. We finally extend the approach to obtain a correction term for the shape of a database-derived mass distribution of the interactome in the mammalian cytosol, in good accord with the existing data of the cellular composition.