The affinity-enhancing roles of flexible linkers in two-domain DNA-binding proteins

Recently many attempts have been made to design high-affinity DNA-binding proteins by linking two domains. Here a theory for guiding these designs is presented. Flexible linkers may play three types of roles: (a) linking domains which by themselves are unfolded and bind to DNA only as a folded dimer (as in a designed single-chain Arc repressor), (b) connecting domains which can separately bind to DNA (as in the Oct-1 POU domain), and (c) linking a DNA-binding domain with a dimerization domain (as in the lambda repressor). In (a), the linker keeps the protein as a folded dimer so that it is always DNA-binding-competent. In (b), the linker is predicted to enhance DNA-binding affinity over those of the individual domains (with dissociation constants K(A) and K(B)) by p(d(0))/K(B) or p(d(0))/K(A), where p(d(0)) = (3/4pil(p)bL)(3/2) exp(-3d(0)(2)/4l(p)bL)(1 - 5l(p)/4bL +...) is the probability density for the end-to-end vector of the linker with L residues to have a distance d(0). In (c), the linker is predicted to enhance the binding affinity by K(d)(C)/p(d(0)), where K(d)(C) is the dimer dissociation constant for the dimerization domain. The predicted affinity enhancements are found to be actually reached by the Oct-1 POU domain and lambda repressor. However, there is room for improvement in many of the recently designed proteins. The theoretical limits presented should provide a useful guide for current efforts of designing DNA-binding proteins.