Lamm G, Wong L, Pack G R
Department of Biomedical Sciences, University of Illinois College of Medicine at Rockford 61107.
Biopolymers. 1994 Feb;34(2):227-37. doi: 10.1002/bip.360340209.
The counterion density and the condensation region around DNA have been examined as functions of both ion size and added-salt concentration using Metropolis Monte Carlo (MC) and Poisson-Boltzmann (PB) methods. Two different definitions of the "bound" and "free" components of the electrolyte ion atmosphere were used to compare these approaches. First, calculation of the ion density in different spatial regions around the polyelectrolyte molecule indicates, in agreement with previous work, that the PB equation does not predict an invariance of the surface concentration of counterions as electrolyte is added to the system. Further, the PB equation underestimates the counterion concentration at the DNA surface, compared to the MC results, the difference being greatest in the grooves, where ionic concentrations are highest. If counterions within a fixed radius of the helical axis are considered to be bound, then the fraction of polyelectrolyte charge neutralized by counterions would be predicted to increase as the bulk electrolyte concentration increases. A second categorization--one in which monovalent cations in regions where the average electrostatic potential is less than -kT are considered to be bound--provides an informative basis for comparison of MC and PB with each other and with counterion-condensation theory. By this criterion, PB calculations on the B form of DNA indicate that the amount of bound counterion charge per phosphate group is about .67 and is independent of salt concentration. A particularly provocative observation is that when this binding criterion is used, MC calculations quantitatively reproduce the bound fraction predicted by counterion-condensation theory for all-atom models of B-DNA and A-DNA as well as for charged cylinders of varying linear charge densities. For example, for B-DNA and A-DNA, the fractions of phosphate groups neutralized by 2 A hard sphere counterions are 0.768 and .817, respectively. For theoretical studies, the radius enclosing the region in which the electrostatic potential is calculated to be less than -kT is advocated as a more suitable binding or condensation radius than that enclosing the fraction of counterions given by (1 - epsilon-1). A comparison of radii calculated using both of these definitions is presented.
利用 metropolis 蒙特卡罗（MC）方法和泊松-玻尔兹曼（PB）方法，研究了 DNA 周围抗衡离子密度和凝聚区域随离子大小和外加盐浓度的变化情况。使用了电解质离子氛围中“束缚”和“自由”成分的两种不同定义来比较这些方法。首先，与先前的工作一致，对聚电解质分子周围不同空间区域的离子密度计算表明，PB 方程并未预测随着向系统中添加电解质，抗衡离子表面浓度的不变性。此外，与 MC 结果相比，PB 方程低估了 DNA 表面的抗衡离子浓度，在离子浓度最高的沟槽中差异最大。如果将螺旋轴固定半径内的抗衡离子视为束缚态，那么随着本体电解质浓度的增加，聚电解质电荷被抗衡离子中和的比例预计会增加。第二种分类方法——将平均静电势小于 -kT 的区域中的单价阳离子视为束缚态——为比较 MC 和 PB 以及与抗衡离子凝聚理论提供了一个有用的基础。根据这个标准，对 B 型 DNA 的 PB 计算表明，每个磷酸基团的束缚抗衡离子电荷量约为 0.67，且与盐浓度无关。一个特别引人深思的观察结果是，当使用这种结合标准时，MC 计算定量地重现了抗衡离子凝聚理论对 B - DNA 和 A - DNA 的全原子模型以及不同线性电荷密度的带电圆柱体所预测的束缚分数。例如，对于 B - DNA 和 A - DNA，被 2 Å 硬球抗衡离子中和的磷酸基团分数分别为 0.768 和 0.817。对于理论研究，与由（1 - ε⁻¹）给出的抗衡离子分数所包围的半径相比，主张将计算出静电势小于 -kT 的区域所包围的半径作为更合适的结合或凝聚半径。文中给出了使用这两种定义计算出的半径的比较。
