An Efficient Approach for Calculating Free Energy in Molecular Dynamics: Demineralization of Hydroxyapatite as a Case Study

Despite the strength of Molecular Dynamics simulations in providing insights into the microscopic details of phenomenon in many fields in materials science, physics and biology, the biggest barrier is its limited timescale which is several orders of magnitude lower than the timescale of the real-world processes and phenomena being modeled. Free energy calculations are designed as a remedy to this problem that in theory can overcome this barrier. This is particularly relevant for biomineralisation processes such as tooth mineral formation and dissolution, while reflecting a broader challenge in accurately modelling rare events and long-timescale phenomena across complex molecular systems. However, due to the novelty of the field, a number of questions remain outstanding pertaining to the best practice of applying this method. The non-equilibrium work approach based on the Jarzynski equation is one of the most promising free energy calculation methods. However, the biggest challenge for the broader use of this method is the question of how many simulations are required for an accurate free energy estimation. Comparing the free energy results with very long reversible pulling simulations of atom clusters from the surface, each taking 75 days on the 48-core Intel Xeon Platinum 8268 CPUs, in this study we showed that this question is irrelevant and higher quality and better equilibrated initial structures is the proper approach than simply based on the number of simulations. We designed a new adaptive free energy calculation methodology which combines high quality, high computational cost free energy values with lower quality, lower cost values to build up the entire free energy profile. In the best case scenario this method lowers manifold the computational cost required for the non-equilibrium work free energy calculations compared to both the regular method and the reversible simulation.