Predicting Diffusion Coefficients of DNA-Protein Complexes by Convex Hull Modelling

Abstract

The recent development of single-molecule diffusometry establishes the diffusion coefficient as a new observable in single-molecule experiments to visualize biomolecular interactions. To decipher the rich information available from these experiments, accurate modeling of the hydrodynamic properties of biomolecular complexes is needed. Currently available tools for predicting diffusion coefficients of biomolecules, such as Hydropro and HullRad, rely on the existence of atomic coordinates for the molecule of interest. Composite molecular complexes that lack detailed Protein Data Bank entries, but can be modeled structurally from their constituent parts (i.e. a complex with multiple proteins bound to a single DNA) are frequently encountered in experiments but cannot yet be properly modeled for hydrodynamic properties. We present a simple program to predict the diffusion coefficients of composite DNA-protein complexes. Our algorithm extends the computational framework introduced by Fleming et al. in the HullRad software to construct a convex hull of the molecular complex and then uses an ellipsoidal approximation to compute hydrodynamic parameters. In order to construct the convex hull of the whole complex, the algorithm incorporates a priori knowledge of the complex such as the crystal structures of the constituent biomolecules, binding site positions, geometry and mechanics of DNA duplexes. The program is computationally efficient, integrates naturally with PyMOL, and outputs the 3D convex hull for visualization. We validate the program by accurately predicting hydrodynamic parameters of known crystal structures of DNA-protein complexes. We then predict diffusion coefficients of the restriction enzyme BamHI bound to double strand DNA of different lengths and compare these predictions with single-molecule diffusometry measurements. We envision that this program will aid researchers in using diffusion coefficient to identify and characterize relevant biological structures at the nanometer scale.