MULTI RESOLUTION DESCRIPTION OF BIOLOGICAL SYSTEMS

生物系统通常代表大分子组装体， 需要大量的资源来模拟全原子方法。 到 模拟这种聚集体，必须使用 蛋白质和DNA。 一个这样的表示是一个弹性杆模型， DNA. 我们应用经典的基尔霍夫方程组[30]， 描述DNA的中心线，曲率和扭曲 *。 我们 使用连续方法[31]求解方程，修改 参数和边界条件的值， 解决方案是已知的期望值。 一个特别的挑战是， 使用DNA横截面的各向异性模型， 表示使得DNA扭曲沿着非均匀分布 中心线 此外，我们修改了方程， DNA的内在扭曲和弯曲。 我们将该方法应用于 被乳糖阻遏物结合的DNA片段（见重点部分 本报告）。 利用边界条件， 晶体结构[25]揭示了DNA环的两种可能形状。 基尔霍夫方程组的成功解表明， 它们可以应用于其他生物系统，例如，DNA 包裹着核小体 由于解的分叉， 基尔霍夫方程可能会在未来的应用中带来问题，我们 通过提取以下振荡分量修改了方程： DNA的内在扭曲导致的解决方案。

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.