A quantum compatible classical continuum model explains mechanical responses of cell membranes and membrane crosslinkers

Abstract

Both classical mechanics and quantum mechanics explain the Brownian motion. However, it is unclear whether they are compatible with each other as the physical and mathematical identity of the wavefunction in quantum mechanics has been elusive. Here, a continuum theory using grammars in classical mechanics modeling but compatible with the quantum wavefunction is introduced. The theory explains the confined Brownian motion of cell membrane inclusions interacting with extracellular matrices or cytoskeletons via elastic molecular crosslinkers. This crosslinker theory is combined into the Canham-Helfrich-Evans model for fluid membranes. Calculations through the provision of a finite element method for the combined theory reproduced measured data from adhesion molecular machineries and cell membranes. Overall, by providing physical and mathematical interpretations of the quantum wavefunction, the presented theoretical model provides improved capabilities for the realistic simulation of classical and quantum biomechanical aspects of cell membranes and membrane linker proteins.