Hidden peak of radial distribution function and effective attraction between like-charged proteins caused by translational motion of solvent molecules

- Effective interaction between proteins is calculated under weak coupling condition.
- Explicit solvent and implicit solvent models were examined.
- The effects of translational motion of solvent molecules are discussed.
- It must be important, but it must be hidden in the structure factor.

To discuss the effective interactions between macroanions, such as acidic proteins, the radial distribution function between macroanions, gMM(r), was calculated using an integral equation theory with a charged hard spheres model under weak coupling conditions. Explicit and implicit solvent models were examined. The gMM(r) for the explicit solvent model indicated a significant peak at the contact distance, which was caused by the translational motion of solvent molecules. In contrast, the gMM(r) for the implicit solvent model did not indicate any significant peak at the distance because of no explicit solvent particles. Although there was a significant difference in the gMM(r) for the explicit and implicit models, the structure factor SMM(k) was nearly the same and the shapes and peak shifts caused by macroanion concentration changes were also similar to the experimental results. To reproduce the first sharp peak in gMM(r), the structure factor SMM(k) provided by scattering experiments was not sufficiently long for standard analyses. This showed that the results provided by conventional small-angle scattering experiments cannot deny the existence of a first sharp peak in gMM(r).

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