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1. Weighted ensemble milestoning (WEM): A combined approach for rare event simulations.

   https://doi.org/doi: 10.1063/5.0008028  

   Ray, D; Andricioaei, I. (June 2020, The Journal of chemical physics)

   To directly simulate rare events using atomistic molecular dynamics is a significant challenge in computational biophysics. Well-established enhanced-sampling techniques do exist to obtain the thermodynamic functions for such systems. However, developing methods for obtaining the kinetics of long timescale processes from simulation at atomic detail is comparatively less developed an area. Milestoning and the weighted ensemble (WE) method are two different stratification strategies; both have shown promise for computing long timescales of complex biomolecular processes. Nevertheless, both require a significant investment of computational resources. We have combined WE and milestoning to calculate observables in orders-of-magnitude less central processing unit and wall-clock time. Our weighted ensemble milestoning method (WEM) uses WE simulation to converge the transition probability and first passage times between milestones, followed by the utilization of the theoretical framework of milestoning to extract thermodynamic and kinetic properties of the entire process. We tested our method for a simple one-dimensional double-well potential, for an eleven-dimensional potential energy surface with energy barrier, and on the biomolecular model system alanine dipeptide. We were able to recover the free energy profiles, time correlation functions, and mean first passage times for barrier crossing events at a significantly small computational cost. WEM promises to extend the applicability of molecular dynamics simulation to slow dynamics of large systems that are well beyond the scope of present day brute-force computations. 

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2. REVO: Resampling of ensembles by variation optimization

   https://doi.org/10.1063/1.5100521  

   Donyapour, Nazanin; Roussey, Nicole_M; Dickson, Alex (June 2019, The Journal of Chemical Physics)

   Conventional molecular dynamics simulations are incapable of sampling many important interactions in biomolecular systems due to their high dimensionality and rough energy landscapes. To observe rare events and calculate transition rates in these systems, enhanced sampling is a necessity. In particular, the study of ligand-protein interactions necessitates a diverse ensemble of protein conformations and transition states, and for many systems, this occurs on prohibitively long time scales. Previous strategies such as WExplore that can be used to determine these types of ensembles are hindered by problems related to the regioning of conformational space. Here, we propose a novel, regionless, enhanced sampling method that is based on the weighted ensemble framework. In this method, a value referred to as “trajectory variation” is optimized after each cycle through cloning and merging operations. This method allows for a more consistent measurement of observables and broader sampling resulting in the efficient exploration of previously unexplored conformations. We demonstrate the performance of this algorithm with the N-dimensional random walk and the unbinding of the trypsin-benzamidine system. The system is analyzed using conformation space networks, the residence time of benzamidine is confirmed, and a new unbinding pathway for the trypsin-benzamidine system is found. We expect that resampling of ensembles by variation optimization will be a useful general tool to broadly explore free energy landscapes. 

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3. Direct and Indirect Drivers of Energy and Nutrient Availability in Freshwater Ecosystems Across Spatial Scales

   https://doi.org/10.1029/2022GB007580  

   Fazekas, Hannah M.; Brun, Julien; Wymore, Adam S. (May 2023, Global Biogeochemical Cycles)

   Abstract Freshwater ecosystems reflect the landscapes in which they are embedded. The biogeochemistry of these systems is fundamentally linked to climate and watershed processes that control fluxes of water and the mobilization of energy and nutrients imprinting as variation in stream water chemistry. Disentangling these processes is difficult as they operate at multiple scales varying across space. We examined the relative importance of climate, soil, and watershed characteristics in mediating direct and indirect pathways that influence carbon and nitrogen availability in streams and rivers across spatial scales. Our data set comprised landscape and climatic variables and 37,995 chemistry measurements of carbon and nitrogen across 459 streams and rivers spanning the continental United States. Models explained a small fraction of carbon and nitrogen concentrations at the continental scale (25% and 6%, respectively) but 61% and 40%, respectively, at smaller spatial scales. Hydrometeorological processes were always important in mediating the availability of solutes but the mechanistic implications were variable across spatial scales. The influence of hydrometeorology on concentrations was often not direct, rather it was mediated by soil characteristics for carbon and watershed characteristics for nitrogen. For example, the seasonality of precipitation was often important in determining carbon concentrations through its influence on soil moisture at biogeoclimatic spatial scales, whereas it had a direct influence on concentrations at the continental scale. Our results suggest that hydrometeorological forcing remains the consistent driver of energy and nutrient concentrations but the mechanism influencing patterns varies across broad spatial scales. 

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4. Inferring phenomenological models of first passage processes

   https://doi.org/10.1371/journal.pcbi.1008740  

   Rivera, Catalina; Hofmann, David; Nemenman, Ilya (March 2021, PLOS Computational Biology)

   Faeder, James R. (Ed.)

   Biochemical processes in cells are governed by complex networks of many chemical species interacting stochastically in diverse ways and on different time scales. Constructing microscopically accurate models of such networks is often infeasible. Instead, here we propose a systematic framework for building phenomenological models of such networks from experimental data, focusing on accurately approximating the time it takes to complete the process, the First Passage (FP) time. Our phenomenological models are mixtures of Gamma distributions, which have a natural biophysical interpretation. The complexity of the models is adapted automatically to account for the amount of available data and its temporal resolution. The framework can be used for predicting behavior of FP systems under varying external conditions. To demonstrate the utility of the approach, we build models for the distribution of inter-spike intervals of a morphologically complex neuron, a Purkinje cell, from experimental and simulated data. We demonstrate that the developed models can not only fit the data, but also make nontrivial predictions. We demonstrate that our coarse-grained models provide constraints on more mechanistically accurate models of the involved phenomena. 

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5. Accurate estimates of dynamical statistics using memory

   https://doi.org/10.1063/5.0187145  

   Lorpaiboon, Chatipat; Guo, Spencer C; Strahan, John; Weare, Jonathan; Dinner, Aaron R (February 2024, The Journal of Chemical Physics)

   Many chemical reactions and molecular processes occur on time scales that are significantly longer than those accessible by direct simulations. One successful approach to estimating dynamical statistics for such processes is to use many short time series of observations of the system to construct a Markov state model, which approximates the dynamics of the system as memoryless transitions between a set of discrete states. The dynamical Galerkin approximation (DGA) is a closely related framework for estimating dynamical statistics, such as committors and mean first passage times, by approximating solutions to their equations with a projection onto a basis. Because the projected dynamics are generally not memoryless, the Markov approximation can result in significant systematic errors. Inspired by quasi-Markov state models, which employ the generalized master equation to encode memory resulting from the projection, we reformulate DGA to account for memory and analyze its performance on two systems: a two-dimensional triple well and the AIB9 peptide. We demonstrate that our method is robust to the choice of basis and can decrease the time series length required to obtain accurate kinetics by an order of magnitude. 

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