Currently, a significant barrier to building predictive models of cellular self-assembly processes is that molecular models cannot capture minutes-long dynamics that couple distinct components with active processes, whereas reaction-diffusion models cannot capture structures of molecular assembly. Here, we introduce the nonequilibrium reaction-diffusion self-assembly simulator (NERDSS), which addresses this spatiotemporal resolution gap. NERDSS integrates efficient reactiondiffusion algorithms into generalized software that operates on user-defined molecules through diffusion, binding and orientation, unbinding, chemical transformations, and spatial localization. By connecting the fast processes of binding with the slow timescales of large-scale assembly, NERDSS integrates molecular resolution with reversible formation of ordered, multisubunit complexes. NERDSS encodes models using rule-based formatting languages to facilitate model portability, usability, and reproducibility. Applying NERDSS to steps in clathrin-mediated endocytosis, we design multicomponent systems that can form lattices in solution or on the membrane, and we predict how stochastic but localized dephosphorylation of membrane lipids can drive lattice disassembly. The NERDSS simulations reveal the spatial constraints on lattice growth and the role of membrane localization and cooperativity in nucleating assembly. By modeling viral lattice assembly and recapitulating oscillations in protein expression levels for a circadian clock model, we illustrate the adaptability of NERDSS. NERDSS simulates user-defined assembly models that were previously inaccessible to existing software tools, with broad applications to predicting self-assembly in vivo and designing high-yield assemblies in vitro.

We present new findings about how primary and secondary structure affects the role of fast protein motions in the reaction coordinates of enzymatic reactions. Using transition path sampling and committor distribution analysis, we examined the difference in the role of these fast protein motions in the reaction coordinate of lactate dehydrogenases (LDHs) of Apicomplexa organisms Plasmodium falciparum and Cryptosporidium parvum. Having evolved separately from a common malate dehydrogenase ancestor, the two enzymes exhibit several important structural differences, notably a five-amino acid insertion in the active site loop of P. falciparum LDH. We find that these active site differences between the two organisms’ LDHs likely cause a decrease in the contribution of the previously determined LDH rate-promoting vibration to the reaction coordinate of P. falciparum LDH compared to that of C. parvum LDH, specifically in the coupling of the rate-promoting vibration and the hydride transfer. This effect, while subtle, directly shows how changes in structure near the active site of LDH alter catalytically important motions. Insights provided by studying these alterations would prove to be useful in identifying LDH inhibitors that specifically target the isozymes of these parasitic organisms.

The mechanisms of enzymatic reactions are studied via a host of computational techniques. While previous methods have been used successfully, many fail to incorporate the full dynamical properties of enzymatic systems. This can lead to misleading results in cases where enzyme motion plays a significant role in the reaction coordinate, which is especially relevant in particle transfer reactions where nuclear tunneling may occur. In this chapter, we outline previous methods, as well as discuss newly developed dynamical methods to interrogate mechanisms of enzymatic particle transfer reactions. These new methods allow for the calculation of free energy barriers and kinetic isotope effects (KIEs) with the incorporation of quantum effects through centroid molecular dynamics (CMD) and the full complement of enzyme dynamics through transition path sampling (TPS). Recent work, summarized in this chapter, applied the method for calculation of free energy barriers to reaction in lactate dehydrogenase (LDH) and yeast alcohol dehydrogenase (YADH). It was found that tunneling plays an insignificant role in YADH but plays a more significant role in LDH, though not dominant over classical transfer. Additionally, we summarize the application of a TPS algorithm for the calculation of reaction rates in tandem with CMD to calculate the primary H/D KIE of YADH from first principles. It was found that the computationally obtained KIE is within the margin of error of experimentally determined KIEs, and corresponds to the KIE of particle transfer in the enzyme. These methods provide new ways to investigate enzyme mechanism with the inclusion of protein and quantum dynamics.

In this study, we develop and test a method to determine the rate of particle transfer and kinetic isotope effects in enzymatic reactions, specifically yeast alcohol dehydrogenase (YADH), from first-principles. Transition path sampling (TPS) and normal mode centroid dynamics (CMD) are used to simulate these enzymatic reactions without knowledge of their reaction coordinates and with the inclusion of quantum effects, such as zero-point energy and tunneling, on the transferring particle. Though previous studies have used TPS to calculate reaction rate constants in various model and real systems, it has not been applied to a system as large as YADH. The calculated primary H/D kinetic isotope effect agrees with previously reported experimental results, within experimental error. The kinetic isotope effects calculated with this method correspond to the kinetic isotope effect of the transfer event itself. The results reported here show that the kinetic isotope effects calculated from first-principles, purely for barrier passage, can be used to predict experimental kinetic isotope effects in enzymatic systems.

Proteins with BAR domains function to bind to and remodel biological membranes, where the dimerization of BAR domains is a key step in this function. These domains can dimerize in solution or after localizing to the membrane surface. Here, we characterize the binding thermodynamics of homodimerization between the LSP1 BAR domain proteins in solution, using molecular dynamics (MD) simulations. By combining the MARTINI coarse-grained protein models with enhanced sampling through metadynamics, we construct a two-dimensional free energy surface quantifying the bound versus unbound ensembles as a function of two distance variables. With this methodology, our simulations can simultaneously characterize the structures and relative stabilities of a range of sampled dimers, portraying a heterogeneous and extraordinarily stable bound ensemble, where the proper crystal structure dimer is the most stable in a 100 mM NaCl solution. Nonspecific dimers that are sampled involve contacts that are consistent with experimental structures of higher-order oligomers formed by the LSP1 BAR domain. Because the BAR dimers and oligomers can assemble on membranes, we characterize the relative alignment of the known membrane binding patches, finding that only the specific dimer is aligned to form strong interactions with the membrane. Hence, we would predict a strong selection of the specific dimer in binding to or assembling when on the membrane. Establishing the pairwise stabilities of homodimer contacts is difficult experimentally when the proteins form stable oligomers, but through the method used here, we can isolate these contacts, providing a foundation to study the same interactions on the membrane.