Biological systems often represent macromolecular assemblies that require enormous resources to be simulated by all-atom methods. To simulate such aggregates, one has to use reduced representations of proteins and DNA. One such representation is an elastic rod model of DNA. We applied a classical Kirchhoff system of equations [30] to describe DNA in terms of its center-line, curvatures and twist*. We used a continuation method [31] to solve the equations, modifying parameters and boundary conditions from the values for which an exact solution is known to the desired values. A particular challenge was to use the anisotropic model of DNA cross-section, as such representation renders the DNA twist non-uniformly distributed along the center-line. In addition, we modified the equations to include the intrinsic twist and curvatures of DNA. We applied the method to the DNA segment bound by lactose repressor (see the Highlight section of this report). The use of boundary condit ions obtained from the crystal structure [25] revealed two possible shapes of the DNA loop. The successful solution of the Kirchhoff system of equations suggests that they may be applied to other biological systems, e.g., DNA wrapped around nucleosomes. Since the bifurcation of the solution to the Kirchhoff equations may pose a problem in future applications, we have modified the equations by extracting the oscillatory component of the solution caused by the intrinsic twist of the DNA.
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