MULTI RESOLUTION DESCRIPTION OF BIOLOGICAL SYSTEMS

生物系统通常代表大分子组件， 需要巨大的资源才能用全原子方法模拟。至 要模拟这样的聚合，必须使用简化的 蛋白质和DNA。一种这样的表示是弹性杆模型 DNA我们将经典的Kirchhoff方程组[30]应用于 用它的中心线、曲率和扭曲来描述DNA。我们 使用延拓法[31]来求解方程，修改 参数和边界条件来自精确的 解已知所需的值。一个特别的挑战是 使用DNA横截面的各向异性模型，例如 表示法使DNA扭曲沿方向非均匀分布 中线。此外，我们对公式进行了修改，以包括 DNA固有的扭曲和弯曲。我们将该方法应用于 由乳糖抑制因子结合的DNA片段(见重点部分 本报告的一部分)。边界条件离子的使用 晶体结构[25]揭示了DNA环的两种可能形状。 Kirchhoff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 包裹在核小体周围。由于解的分叉 基尔霍夫方程在未来的应用中可能会带来问题，我们 通过提取振动分量修改了方程 脱氧核糖核酸的内在扭曲引起的溶液。

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.