A new mathematical model for molecular dynamics 1: Molecular basis of memory

Abstract

Proteins have been empirically linked to memory. If memory relates to protein structure, then each conformation would_functionally_ code only one bit, making it difficult to explain large memories. Nor is there a simple way to relate memory to protein dynamics on current molecular dynamics (MD), which is memoryless. Here we point out that MD may be modified to involve memory ab initio without any new hypothesis: simply replace the electrostatic (Coulomb) force by the electrodynamic force--which is more accurate. We now need to solve functional differential equations (FDEs), instead of the ordinary differential equations (ODEs) currently solved in MD. Unlike ODEs, retarded FDEs are history-dependent: so memory is already present even at the level of interacting sites within molecules. The resulting increase in computational complexity is within the reach of current computers. While Amdahl's law does pose a challenge to parallelised time-stepping with this model, the compute-intensive part--the force calculation--may still be carried out in parallel. Thus, reformulating MD to use FDEs is feasible, and this could help to understand the possible dynamical basis of memory.