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WIREs Comput Mol Sci
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Theoretical models of DNA flexibility

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Abstract DNA sequence‐dependent three‐dimensional structure and mechanical deformability play a large role in biological processes such as protein–DNA interactions, nucleosome positioning, promoter identification, and drug–DNA recognition. On the important scale of 10–100 base pairs, models where DNA bases are represented by interacting rigid bodies have proved useful. We focus on a recently proposed rigid base model with nonlocal, harmonic interaction energy. We discuss the choice of internal coordinates and a method to obtain model parameters from coordinate fluctuations. Parameter transformation upon change of reference strand, coordinate constraints, and models with reduced number of degrees of freedom are described. Relation to traditional local harmonic models is clarified. We outline recent attempts to include anharmonic effects. A rigid base model of a DNA oligomer containing A‐tract is presented as an example. Perspectives of model development and application are discussed. This article is categorized under: Electronic Structure Theory > Density Functional Theory

A DNA double‐stranded oligomer of the sequence GGCA4T4GCC at atomic resolution (left) and in the rigid base representation as created by the 3DNA program (right).

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Probability distribution functions (pdf) of twist and slide for the A4A5 step of the simulated oligomer. The moderately anharmonic distributions can be decomposed into Gaussian‐like contributions corresponding to backbone substates. Both backbone fragments can be in BI substate (BI/BI, green), or one in BI and the other in BII (BI/BII, blue). The third possible backbone state BII/BII is very rare and plays no significant role in the decomposition. Dotted lines mark data for trajectory halves.

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Nondimensionalized stiffness matrix for the full, nonlocal rigid base model. The columns are ordered as follows: the entries for the intra‐base pair coordinates buckle, propeller, opening, shear, stretch, and stagger are above the nucleotide symbol; the entries for the step coordinates tilt, roll, twist, shift, slide, rise are to the right. The ordering of rows is analogous. The thick red line marks the region of nonzero entries for the nearest neighbor base–base interaction scheme described in the text.

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Diagonal stiffness constants from the full stiffness matrix (Eqs. (1) and (2), red), the single‐coordinate stiffness constants (Eq. (7), black), and diagonal stiffness constants for the model of independent base pairs and steps (Eqs. (5) and (6), blue). Crosses indicate values for the trajectory halves.

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Equilibrium values of the internal coordinates propeller and roll as a function of the sequence. Crosses indicate values from the halves of the MD trajectory. The large negative propeller is characteristic for A‐tracts.

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