Sabok-Sayr Seyed A, Olson Wilma K
Department of Physics and Astronomy, Rutgers University, Piscataway, NJ, United States of America.
Department of Chemistry and Chemical Biology, Rutgers University, Piscataway, NJ, United States of America.
J Phys A Math Theor. 2020 Oct;53(43). doi: 10.1088/1751-8121/abb480. Epub 2020 Oct 9.
We introduce an analytical method to generate the pathway of a closed protein-bound DNA minicircle. We develop an analytical equation to connect two open curves smoothly and use the derived expressions to join the ends of two helical pathways and form models of nucleosome-decorated DNA minicircles. We find that the simplest smooth connector which satisfies the boundary conditions at the end points and the length requirement for such connections to be a quartic function on the -plane and linear along the -direction. This is a general method which can be used to connect any two open curves with well defined mathematical definitions as well as pairs of discrete systems found experimentally. We used this method to describe the configurations of torsionally relaxed, 360-base pair DNA rings with two evenly-spaced, ideal nucleosomes. We considered superhelical nucleosomal pathways with different levels of DNA wrapping and allowed for different inter-nucleosome orientations. We completed the DNA circles with the smooth connectors and studied the associated bending and electrostatic energies for different configurations in the absence and presence of salt. The predicted stable states bear close resemblance to reconstituted minicircles observed under low and high salt conditions.
我们介绍一种分析方法来生成封闭的蛋白质结合DNA小环的路径。我们推导了一个解析方程，用于平滑连接两条开放曲线，并使用所得表达式连接两条螺旋路径的末端，从而构建核小体修饰的DNA小环模型。我们发现，满足端点边界条件以及此类连接长度要求的最简单平滑连接体是平面上的四次函数且沿方向呈线性。这是一种通用方法，可用于连接任何具有明确数学定义的两条开放曲线以及实验中发现的离散系统对。我们使用此方法描述了具有两个均匀间隔的理想核小体的360碱基对扭转松弛DNA环的构型。我们考虑了具有不同DNA缠绕水平的超螺旋核小体路径，并允许不同的核小体间取向。我们用平滑连接体完成DNA环，并研究了在有无盐的情况下不同构型的相关弯曲和静电能。预测的稳定状态与在低盐和高盐条件下观察到的重构小环非常相似。
