An application of computational geometry to solution theory of biomolecule association

肌动蛋白分子在高盐溶液中自发缔合形成肌动蛋白丝，参与细胞运动。应用溶液理论中的扩展标度粒子理论（XSPT）计算了大分子拥挤产生的平均力势。计算结果表明，肌动蛋白二聚体的最稳定构型是由小角X射线散射确定的构型。在高浓度（填充分数>0.6）的拥挤剂、肌动蛋白单体时，计算得到的肌动蛋白二聚体的最稳定构型与肌动蛋白丝中纵向相邻两分子的构型相同，而与水溶液中的构型不同。因此，我们不能通过不同构型下排斥体积的大小来区分大分子拥挤效应的影响。在我们的方法中，计算几何中的阿尔法形状方法被用于解析推导的排斥体积函数的标度参数。α形状方法使XSPT能够结合二聚体的构型和肌动蛋白分子的3-D结构的差异。在这项工作中，我们发现，基本测量理论（FMT），这是一个密度泛函理论，和XSPT的平均力的潜力的解析表达式中只有一项不同。当α形方法也应用于FMT时，FMT和XSPT两种方法得到的由大分子拥挤效应引起的平均力势将夹在真值之间。

Actin molecules, which have functions in cell movement, spontaneously associates to form actin filament at high salt concentration in aquerous solution. Potential of mean force originated from macromolecular crowding was calculated by using extended scaled particle theory (XSPT), which is one of the solution theories. Calculated results show that the most stable configuration of actin dimmer is the one believed from small angle X-ray scattering. At high concentration (packing fraction >0.6) of crowding agents, actin monomers, the most stable configuration of actin dimmer in calculation was the same as that of longitudinal adjacent two molecules in actin filaments and different from that in aquerous solution. Therefore, we cannot distinguish the effect of macromolecular crowding effect by the order of excluded volumes at various configurations. In our methods, alpha shape method in computational geometry was used in analytical derivation of a excluded volume function of scaling parameter. The alpha shape method enabled XSPT to incorporate difference of both configuration of a dimmer and 3-D structure of an actin molecule. In this work, we found Fundamental measure theory (FMT), which is one of the density functional theories, and XSPT differ only one term in the analytical expression of the potential of mean force. Potentials of mean force originated from macromolecular crowding effect by using two methods, FMT and XSPT, sandwiches the true value when the alpha shape method is also applied to FMT.