Investigating Nanoparticle-cancer cell membrane Interactions using a modified Jarzynski Free-Energy Estimator to Eliminate Non-conservative Forces*

Despite extensive research and progress in the field of drug design for cancer therapy, cancer is still a leading cause of death worldwide. Chemotherapy is standard practice for cancer treatment and has an enormous impact on patient quality of life, as it can be the only effective treatment for advanced metastatic tumors; however, it often leads to a chemoresistant state in which cancer cells no longer respond to administered drugs. To study the interactions of drugs and nanoparticles (NPs)  with the lipidomic component of the membrane of chemoresistance cancer cells at the most basic level, we need to use computational methods. Computational methods to understand interactions in bio-systems are however limited to time scales typically much shorter than in Nature. For instance, on the molecular level, interactions between NPs and membranes are vital in complex biomolecular processes such as cellular uptake. This can be remedied by the application of e.g. Jarzynski’s equality where thermodynamic properties are extracted from non-equilibrium

simulations. Although, the out of equilibrium work leads to non-conservative forces. We here propose a correction Pair Forces method, that removes non-conservative forces, which can be assigned to the free energy calculations. The method simultaneously considers pair forces (forward and backward forces) of pulling NPs through the membrane. Our proposed method leads to decreasing the error of non-equilibrium simulations, enhancing the statistics  (growing sample sizes from N to 2N to enhance the accuracy of results), using conservative force to obtain equilibrated free energy, and reducing simulation time. To present the method, we consider interactions between anti-cancer drugs and NPs for non-symmetric and symmetrical membranes. Our results show that this leads to much improvement in free energy. Although here we have demonstrated the application of the method in molecular dynamics simulation, it could be applied to experimental approaches.