Enhancing Molecular Dynamics Simulations: From Trajectories to Reaction Rates

Abstract

Advanced methods for estimating reaction rates of rare events in molecular dynamics (MD) simulations are crucial for molecular processes like chemical reactions, nucleation, and pro- tein folding. These processes commonly involve high energy barriers, making them infrequent and challenging to capture with conventional MD due to long waiting times. Some rare event methods apply enhanced sampling techniques where potential energy functions are biased to accelerate molecular transitions. In this thesis, different rare event methods employing enhanced sampling are introduced, applied and compared. A first case study focuses on thermal cis-trans isomerization of retinal, a crucial process in opsins involved in biological light responses. The enormous disparity between accessible simulation times (nanoseconds to microseconds depending on level of theory) and actual reaction times (hours to days) requires careful application of rate theories. Results from rare event methods based in both numerical sampling of transitions and effective dynamics were compared to results from transition state optimization followed by application of Eyring’s transition state theory (TST). Numerical sampling, enabled by infrequent metadynamics simulation, yielded rates in good agreement with Eyring’s TST, especially when the classical limit was enforced. Methods based in ef- fective dynamics proved highly sensitive to the choice of reaction coordinate. Only after optimizing the reaction coordinate using adaptive path collective variables did rates approx- imate those from Eyring’s TST well. Additionally, the thesis explores dynamical reweighting techniques, particularly Girsanov reweighting, to recover kinetics and reaction dynamics from biased simulations. Girsanov reweighting factors were derived for a number of integrators for underdamped Langevin dynamics. The reweighting factors were subsequently tested for a [Ca-Cl]+ dimer system. The dissociation rates obtained from biased trajectories successfully estimated reference rates for the unbiased system, demonstrating the effectiveness of these methods for accurately recovering reaction dynamics as well as their potential for future reaction dynamics studies.