Coleman B D, Swigon D, Tobias I
Department of Mechanics and Materials Science Rutgers, The State University of New Jersey, Piscataway, New Jersey 08854, USA.
Phys Rev E Stat Phys Plasmas Fluids Relat Interdiscip Topics. 2000 Jan;61(1):759-70. doi: 10.1103/physreve.61.759.
Configurations of protein-free DNA miniplasmids are calculated with the effects of impenetrability and self-contact forces taken into account by using exact solutions of Kirchhoff's equations of equilibrium for elastic rods of circular cross section. Bifurcation diagrams are presented as graphs of excess link, DeltaL, versus writhe, W, and the stability criteria derived in paper I of this series are employed in a search for regions of such diagrams that correspond to configurations that are stable, in the sense that they give local minima to elastic energy. Primary bifurcation branches that originate at circular configurations are composed of configurations with D(m) symmetry (m=2,3,...). Among the results obtained are the following. (i) There are configurations with C2 symmetry forming secondary bifurcation branches which emerge from the primary branch with m=3, and bifurcation of such secondary branches gives rise to tertiary branches of configurations without symmetry. (ii) Whether or not self-contact occurs, a noncircular configuration in the primary branch with m=2, called branch alpha, is stable when for it the derivative dDeltaL/dW, computed along that branch, is strictly positive. (iii) For configurations not in alpha, the condition dDeltaL/dW>0 is not sufficient for stability; in fact, each nonplanar contact-free configuration that is in a branch other than alpha is unstable. A rule relating the number of points of self-contact and the occurrence of intervals of such contact to the magnitude of DeltaL, which in paper I was found to hold for segments of DNA subject to strong anchoring end conditions, is here observed to hold for computed configurations of protein-free miniplasmids.
通过使用圆形横截面弹性杆的基尔霍夫平衡方程的精确解，计算无蛋白质DNA微型质粒的构型，并考虑不可穿透性和自接触力的影响。分岔图以过量连环数ΔL与扭曲数W的关系图形式呈现，并且采用本系列论文I中推导的稳定性标准来寻找该图中对应于稳定构型的区域，这里的稳定是指它们使弹性能达到局部最小值。起源于圆形构型的主要分岔分支由具有D(m)对称性（m = 2,3,...）的构型组成。得到的结果如下。(i) 存在具有C2对称性的构型形成二级分岔分支，这些分支从m = 3的主要分支中出现，并且这种二级分支的分岔产生了无对称性的三级分支构型。(ii) 无论是否发生自接触，当沿着主要分支中m = 2的非圆形构型（称为分支α）计算的导数dΔL/dW严格为正时，该构型是稳定的。(iii) 对于不在α分支中的构型，条件dΔL/dW > 0不足以保证稳定性；实际上，除α分支外的其他分支中的每个非平面无接触构型都是不稳定的。在论文I中发现的一个将自接触点的数量和这种接触的区间的出现与ΔL的大小相关的规则，在这里被观察到对于无蛋白质微型质粒的计算构型也成立。
