Shape-Aware Diffusivity of DNA Binding Proteins Undergoing Rotation-Coupled Sliding Dynamics along DNA

DNA-binding proteins locate their targets by sliding along DNA in a rotation-coupled manner, synchronizing axial motion with helical rotation. The classical Bagchi-Blainey-Xie (BBX) model provides a hydrodynamic description of this process but treats proteins as spheres with fitted radii. Here we introduce BBXB, a shape-aware generalization that explicitly incorporates molecular anisotropy by deriving translational and rotational frictions from the protein's three-dimensional structure via Happel-Brenner integrals. A single roughness parameter accounts for energy-landscape effects arising from rugged protein-DNA interactions. Applied to the Lac repressor and hOgg1 glycosylase, BBXB reproduces experimental single-molecule diffusion coefficients within a factor of 2, substantially improving on the original BBX model without adjustable radii. Across a panel of 27 structurally diverse DNA-binding proteins (spanning spherical to highly anisotropic shapes), BBXB predictions show a strong linear correlation with SoMo/GRPY hydrodynamic benchmarks (R² ≈ 0.99), while remaining systematically lower due to roughness corrections. Heatmap and friction-budget analyses reveal that rotational drag dominates total dissipation and increases with both shape anisotropy and offset distance from the DNA axis. Together, BBXB establishes a predictive and parameter-free hydrodynamic framework that quantitatively links molecular shape to one-dimensional rotation-coupled sliding dynamics of protein-DNA complexes.