Physical Foundation of Biomolecular Interactions

National Library Of Medicine

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Abstract

Biomolecular interactions determine how transcription factors recognize their DNA binding sites, how proteins interact with each other, and consequently how a biological system functions. 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, the solvent itself, namely, water produces considerable electrostatic effects. Furthermore, hydrogen bonds, known to be involved in 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 will require 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, it will drastically speed up the computational a lot if we can bypass the need of calculating Wigner rotation matrix elements for every pair of spheres. As for the challenges part, it is known that under physiological condition, the biomolecules are mostly present 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 it at some stage 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 perform the Wigner rotation matrix elements and meeting the challenge of devising a rigorous implicit ion formalism. In 2019, we successfully reformulate the SCM to be a Wigner-rotation-Matrix-free formalism for inclusion of intrinsic multipoles. It was published in Physical Review E. We immediately worked the implicit ion problem since. Finally, the last piece of puzzle for a rigorous implicit ion formalism was found in later part of 2020. We now have a full implicit ion formalism, covering Landaus approximation as a special case, that also does not require Wigner rotation for its application.