Effect of crowding on protein-protein association in diffusion-limited regime

Abstract

Abstract.In the present paper, we establish a theoretical formalism to study the protein-protein association rate in the framework of diffusion-limited theory. To account for the crowding effect due to the presence of polymer, we particularly take into account the deviation of rotational diffusion of proteins from the Stokes-Einstein-Debye relation. Based on fluid mechanics and depletion theory, a new scaling relation for the retardation factor of the rotational diffusion was proposed. Besides, the crowding-induced interaction energy between the proteins has been also properly introduced into the association rate theory. We apply our theory to calculate the association rate constant of proteins β-lactamase and β-lactamase inhibitor protein in poly(ethylene glycol) solutions. Particular attention is paid to the dependence of the association rate constant on the polymer concentration and polymer molecular weight. The deviation from the simple relation based on Stokes-Einstein approximation is well addressed. We find that our theoretical results show good agreements with the experimental data in the whole concentration region, which demonstrates the validity of our theory.

Diffusion and flow in complex liquids

“…We used the theory to provide a database for rotational diffusion and sliding along a DNA strand in E. coli, which gives parameters necessary for a quantitative description of protein association rates. 42 Another effect which modifies nanoparticle diffusion is related to its interactions (e.g., electrostatics) with surrounding macromolecules. 47,48 This effect can be included in the governing equations used in this article but was neglected in our phenomenological assumptions.…”

“…For example, descriptions of protein-protein association rates require information about both translational and rotational diffusion coefficients of reactants. 42 Based on eqn (14) and the model describing the z(a)/z 0 ratio for cytoplasm of E. coli we provide a database of rotational diffusion coefficients for all proteins and their possible oligomers; see Table S1 from the ESI. † Another example, also related to the diffusion in the cytoplasm of E. coli, is the motion of the transcription factors along a DNA strand described by the model of Blainey et al 43 The model was introduced to describe experiments on interactions of DNA with proteins.…”