Indirect readout: detection of optimized subsequences and calculation of relative binding affinities using different DNA elastic potentials

Essential biological processes require that proteins bind to a set of specific DNA sites with tuned relative affinities. We focus on the indirect readout mechanism and discuss its theoretical description in relation to the present understanding of DNA elasticity on the rigid base pair level. Combining existing parametrizations of elastic potentials for DNA, we derive elastic free energies directly related to competitive binding experiments, and propose a computationally inexpensive local marker for elastically optimized subsequences in protein-DNA co-crystals. We test our approach in an application to the bacteriophage 434 repressor. In agreement with known results we find that indirect readout dominates at the central, non-contacted bases of the binding site. Elastic optimization involves all deformation modes and is mainly due to the adapted equilibrium structure of the operator, while sequence-dependent elasticity plays a minor role. These qualitative observations are robust with respect to current parametrization uncertainties. Predictions for relative affinities mediated by indirect readout depend sensitively on the chosen parametrization. Their quantitative comparison with experimental data allows for a critical evaluation of DNA elastic potentials and of the correspondence between crystal and solution structures. The software written for the presented analysis is included as Supplementary Data.