Delrow J J, Gebe J A, Schurr J M
Department of Chemistry, University of Washington, Seattle 98195-1700, USA.
Biopolymers. 1997 Oct 5;42(4):455-70. doi: 10.1002/(SICI)1097-0282(19971005)42:4<455::AID-BIP8>3.0.CO;2-P.
A 1000 base pair (bp) model supercoiled DNA is simulated using spherical screened Coulomb interactions between subunits on one hand and equivalent hard-cylinder interactions on the other. The amplitudes, or effective charges, of the spherical screened Coulomb electrostatic potentials are chosen so that the electrostatic potential surrounding the middle of a linear array of 2001 subunits (31.8 A diameter) closely matches the solution of the nonlinear Poisson-Boltzmann equation for a cylinder with 12 A radius and the full linear charge density of DNA at all distances beyond the 24 A hard-core diameter. This superposition of spherical screened Coulomb potentials is practically identical to the particular solution of the cylindrical linearized Poisson-Boltzmann equation that matches the solution of the nonlinear Poisson-Boltzmann equation at large distances. The interaction energy between subunits is reckoned from the effective charges according to the standard DLVO expression. The equivalent hard-cylinder diameter is chosen following Stigter's protocol for matching second virial coefficients, but for the full linear charge density of DNA. The electrostatic persistence length of the model with screened Coulomb interactions is extremely sensitive to the (arbitrarily) chosen subunit length at the higher salt concentrations. The persistence length of the hard-cylinder model is adjusted to match that of the screened Coulomb model for each ionic condition. Simulations for a superhelix density sigma = -0.05 using a spherical screened Coulomb interaction plus a 24 A hard-cylinder core (SCPHC) potential indicate that the radius of gyration of this 1000 bp DNA actually undergoes a slight increase as the NaCl concentration is raised from 0.01 to 1.0M. Thus, merely softening the potential from hard-cylinder to screened Coulomb form does not produce a large decrease in radius of gyration with increasing NaCl concentration for DNAs of this size. Radii of gyration, static structure factors, and diffusion coefficients obtained using the equivalent hard-cylinder (EHC) potential agree well with those obtained using the SCPHC potential in 1.0M NaCl, but in 0.1M NaCl the agreement is not as good, and in 0.01M NaCl the agreement is definitely unsatisfactory. These conclusions differ in significant respects from those obtained in previous studies.
一方面，使用亚基之间的球形屏蔽库仑相互作用，另一方面使用等效硬圆柱相互作用，对一个1000碱基对（bp）的模型超螺旋DNA进行模拟。选择球形屏蔽库仑静电势的振幅或有效电荷，使得2001个亚基（直径31.8 Å）线性阵列中间周围的静电势，在所有超过24 Å硬核直径的距离处，紧密匹配半径为12 Å且具有DNA全线性电荷密度的圆柱体的非线性泊松-玻尔兹曼方程的解。这种球形屏蔽库仑势的叠加实际上与圆柱形线性化泊松-玻尔兹曼方程的特定解相同，该特定解在大距离处与非线性泊松-玻尔兹曼方程的解相匹配。亚基之间的相互作用能根据标准的DLVO表达式从有效电荷计算得出。等效硬圆柱直径按照斯蒂格特匹配第二维里系数的方法来选择，但针对的是DNA的全线性电荷密度。在较高盐浓度下，具有屏蔽库仑相互作用的模型的静电持久长度对（任意）选择的亚基长度极为敏感。对于每种离子条件，调整硬圆柱模型的持久长度以使其与屏蔽库仑模型的持久长度相匹配。使用球形屏蔽库仑相互作用加上24 Å硬圆柱核心（SCPHC）势对超螺旋密度σ = -0.05进行模拟表明，随着NaCl浓度从0.01 M提高到1.0 M，这种1000 bp DNA的回转半径实际上略有增加。因此，对于这种大小的DNA，仅仅将势从硬圆柱形式软化到屏蔽库仑形式，并不会随着NaCl浓度的增加而使回转半径大幅减小。使用等效硬圆柱（EHC）势获得的回转半径、静态结构因子和扩散系数，在1.0 M NaCl中与使用SCPHC势获得的结果吻合良好，但在0.1 M NaCl中吻合度没那么好，而在0.01 M NaCl中吻合度肯定不令人满意。这些结论在重要方面与先前研究中获得的结论不同。
