Physical Foundation of Biomolecular Interactions

National Library Of Medicine

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Abstract

Biomolecular interactions define the internal mechanics of functioning of a biological system: how transcription factors recognize their DNA binding sites, how proteins interact and form complexes, how molecular receptors bind to only certain ligands, and so on. Since many biological molecules bear considerable electric charge, electrostatic interactions are among the most important when studying biomolecular interactions. However, electrostatic interactions in biological systems are difficult to calculate accurately in practice. Aside from the significant charges carried by biomolecules such as DNA and proteins, dielectric properties of the solvent itself, namely, water, result in nontrivial electrostatic effects. Furthermore, hydrogen bonds, known to be involved in numerous important interactions, such as helix formation in both DNA and proteins, are essentially electrostatic in origin. Indeed, it seems that electrostatic effects often drive the physical-chemical processes in biological systems and, thereby, determine biological functions. Therefore, any attempt to perform molecular dynamics (MD) simulations of biological systems requires an adequate description of these electrostatic forces. Previously, we have developed a rigorous surface charge method (SCM) to calculate the crucial electrostatic forces in a biomolecular system. Exact analytical results have been obtained for systems with sufficient symmetry. For example, we developed methods to compute the electrostatic forces for a biomolecular system in which the atoms are represented by spheres. The method is rigorous in the context of the model and the accuracy can be tuned to any desired level. Our efforts in the past years have been to extend this exact formalism to a more realistic and flexible model in which a biomolecule is represented by an arbitrary surface. One way to do so is to incorporate intrinsic multipole moments other than just point charges. This should provide a reasonably good description of the system when the separation between biomolecules is large enough. We have developed such a formalism which can compute electrostatic energy to arbitrary precision. Nevertheless, there is still room for improvement and challenges to meet. As for the improvement part, bypassing the need of calculating Wigner rotation matrix elements for every pair of spheres could drastically speed up the computation. As for the challenges part, it is known that under physiological conditions, the biomolecules are mostly found in electrolyte solution. One choice is to explicitly introduce ions as small dielectric spheres, but one will end up spending too much in computational resources on billions of objects whose individual dynamics do not matter. Having an implicit ion approach is desirable but challenging. Even Lev Landau, possibly the most famous Russian Nobel Laureate, worked on this problem but obtained only an approximate pairwise force between two macro dielectric spheres. In the past few years, we have made progress in overcoming the need to compute the Wigner rotation matrix elements and meeting the challenge of devising a rigorous implicit ion formalism. In 2019, we successfully reformulated the SCM to be a Wigner-rotation-Matrix-free formalism for inclusion of intrinsic multipoles, which was published in Physical Review E. After that, we immediately worked on the implicit ion problem. Finally, the last piece of the puzzle for a rigorous implicit ion formalism was found in the later part of 2020. We now have a full implicit ion formalism, covering Landau's approximation as a special case, that also does not require Wigner rotation for its application. Last year we focused on investigating the outcome from the rigorous ionic screening formalism by examining a few dielectric spheres immersed in electrolyte as the testing ground. Surprising results were obtained and published in the European Journal of Physics E. This year we examined the full implicit ion formalism in the limit of strong ionic screening, developing a rigorous expansion that we expect to provide insight into the qualitative behavior of biomolecular interaction under these conditions. We also have applied the rigorous ionic screening formalism to a planar geometry that represents electrostatic interaction of biomolecules at close approach but is exact in the context of the model and discovered a much more complex and nuanced behavior of electrostatic forces than one would expect in such a symmetric system.