DNA nano-mechanics: how proteins deform the double helix

DNA nano-mechanics: how proteins deform the double helix Nils B. Becker∗ Laboratoire de Physique de l'École Normale Supérieure, Université de Lyon, France Ralf Everaers Laboratoire de Physique de l'École Normale Supérieure, Université de Lyon, France October 29, 2018 Abstract It is a standard exercise in mechanical engineer- ing to infer the external forces and torques on a body from a given static shape and known elastic properties. Here we apply this kind of analysis to distorted double-helical DNA in complexes with proteins: We extract the lo- cal mean forces and torques acting on each base-pair of bound DNA from high-resolution complex structures. Our analysis relies on known elastic potentials and a careful choice of coordinates for the well-established rigid base-pair model of DNA. The results are ro- bust with respect to parameter and confor- mation uncertainty. They reveal the com- plex nano-mechanical patterns of interaction between proteins and DNA. Being non-trivially and non-locally related to observed DNA con- formations, base-pair forces and torques pro- vide a new view on DNA-protein binding that complements structural analysis. ∗Corresponding author. Address: Labo de Physique de l'ENS, 46 allée de l'Italie, 69007 Lyon, France Introduction A large class of DNA-binding proteins induce deformations of the DNA double helix which are essential in biochemical processes such as transcription regulation, DNA packing and replication [1]. Insight into the mechanism of binding largely depends on high-resolution structures of DNA-protein complexes. A rst step in their analysis consists of a description of DNA conformation in the complex, often in terms of a suitably reduced set of degrees of freedom such as the rigid base-pair parameters, e.g. [2]. As a second step, sites of local DNA de- formation can be identied by comparison with ensembles of uctuating DNA conformations. This allows to quantify deformation strength in terms of a free energy. Here we take the analysis a step further by extracting the points of attack, magnitudes and directions of forces acting between protein and DNA in the com- plex. The basic idea of inferring the force on an elastic body from its deformation is as com- monplace as stepping on a scale to measure one's weight. We propose to apply the same idea to DNA-protein complexes, using DNA as a nanoscale force probe calibrated by a known elastic potential. That is, starting 1 arXiv:0809.3938v2 [q-bio.BM] 17 Dec 2008 DNA nano-mechanics 2 from the coarse-grained mean conformation of a piece of bound DNA as extracted from a high- resolution structural model, we infer the corre- sponding coarse-grained static mean forces re- quired for that conformation. To implement this idea, we use the rigid base-pair level of coarse-graining. Correspondingly, our analysis results in a DNA base-pair step elastic energy prole, complemented by the set of mean forces and torques by which the protein acts on each DNA base-pair. This article focuses on the theoretical basis, implementation, range of applicability and val- idation of DNA nano-mechanics analysis. We begin by discussing the statistical mechanics of the mechanical equilibrium in DNA-protein complexes in section Background. We also mo- tivate our choice of the rigid base-pair level of coarse-graining which, unlike standard molecu- lar mechanics with atomistic force elds, allows reliable extraction of mean forces within the ex- perimentally available resolution. Our matrix formalism for force and torque calculations is described in section DNA nano-mechanics, and implementation and parameter choice details are given in Methods. In the Results section, we present exemplary force and torque calcu- lations for several high-resolution NMR and x- ray complex structures. These examples show the robustness of the analysis with respect to experimental and parameter uncertainties, and demonstrate the key features of base-pair forces and torques described in the Discussion sec- tion: Base-pair forces and DNA deformation are nontrivially and non-locally related, and they allow to discriminate force-transmitting and non-transmitting protein-DNA contacts. Based on these features, DNA nano-mechanics analysis has a number of promising applica- tions, such as validation and design of coarse- grained molecular models for multi-scale sim- ulations, and identication of target sites for structure-changing mutations in protein-DNA complexes. These are expanded upon in the reduced coordinate A(x) A(x)-fx slope -f slope A'(xd) free energy xd x1 x2 Figure 1: Constraint force fd and externally applied force f in a stereotyped double-well free energy landscape, and thermal distribu- tion (solid lines). Under an external force f, the landscape is tilted (dashed lines). Conclusion section. Background The statistical mechanics of DNA can be de- scribed on multiple levels of coarse-graining, depending on the required amount of detail. For a chosen set of red

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