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Application of enhanced sampling approaches to the early stages of mineralization
Published in Elaine DiMasi, Laurie B. Gower, Biomineralization Sourcebook, 2014
approach is a powerful methodology that is also shedding light on the in uence of organic interfaces on the crystallization of calcium carbonate. Notably, Freeman et al. (Quigley et al., 2009) show that metadynamics can predict the experimentally observed orientation of calcite crystals on carboxyl-terminated self-assembled monolayers and that the crystallization mechanism is not strictly a matter of lattice epitaxy but rather involves the concomitant restructuring of both the monolayer and amorphous phase throughout the phase transition. Freeman et al. are also applying metadynamics to probe the interactions between the eggshell protein OC-17 and anhydrous ACC (Freeman et al., 2010, 2011, 2012) and have shown in this particular instance that binding to the protein likely destabilizes the amorphous phase and accelerates the formation of calcite (Freeman et al., 2010). 18.3.3 PARALLEL TEMPERING AND REPLICAEXCHANGE MOLECULAR DYNAMICS In the previous sections, two methods are presented (umbrella sampling and metadynamics) by which passage of the system through bottlenecks in the free energy landscape is facilitated by the application of a suitable bias. Replica-exchange molecular dynamics (REMD) (Sugita and Okamoto, 1999), which is based on the parallel tempering Monte Carlo sampling scheme (Earl and Deem, 2005; Freeman, 2000; Frenkel and Smit, 2002), is a fundamentally different approach whereby exploration of the energy landscape is enhanced, in principle, without introducing a bias to the system. In standard parallel tempering, several noninteracting copies (or replicas) of the system are all initiated
Accurate meso-scale dynamics by kinetic Monte Carlo simulation via free energy multicanonical sampling: oxygen vacancy diffusion in BaTiO3
Published in Science and Technology of Advanced Materials: Methods, 2021
Hiroya Nakata, Masaaki Araidai, Shandan Bai, Hiromichi Hirano, Tomofumi Tada
The extraction of all possible events depending on temperature is itself quite a difficult task. For example, when a system with rugged free-energy landscapes is a target, a lot of computational time would be required to achieve thermal equilibrium. Then, conventional canonical simulations tend to miss many rare but important events for accurate simulations. Recently, some generalized-ensemble methods [28–30], such as umbrella sampling [31], parallel tempering (replica exchange) [32–36], adaptive biasing force method [37], metadynamics [38], and the multicanonical (MUCA) ensemble method [39–44], have been intensively developed to perform simulations of such a system. Among them, the MUCA ensemble method is especially suitable for the preprocessing of kMC simulation, because the probability distribution function of the MUCA ensemble is a constant within an energy window of interest, which facilitates exhaustive structure samplings within the temperature window. Such an artificial ensemble is made by knowing the density of states of system. In this study, we perform the Monte Carlo simulations with suitable transition rates to find out it. Once we acquire the density of states, we can get the entropy. As a result, we can obtain the statistical quantities in the canonical ensemble, namely free energy, within a range of target temperatures.
Machine learning for collective variable discovery and enhanced sampling in biomolecular simulation
Published in Molecular Physics, 2020
Hythem Sidky, Wei Chen, Andrew L. Ferguson
The application of artificial biasing potentials in the collective variables identified by DMAPS is made challenging by the absence of an explicit and differentiable mapping between the atomic coordinates and the DMAPS CVs. The out-of-sample extension techniques discussed in Section 2.2 furnish approximate projections for new data and enable energy biases to be applied in Monte-Carlo simulations as perturbations to the unbiased Hamiltonian conditioned on the current value of the DMAPS CVs [169–171]. The approximations introduced by these extrapolations, however, typically render them too numerically unstable for reliable derivative calculation and the implementation of force biases in molecular dynamics simulation. One solution to this problem is offered by the diffusion nets (DNETS) approach of Mishne et al., who train an ANN encoder to learn a functional map from the atomic coordinates to the low-dimensional DMAPS embeddings [172]. By construction, this map is both explicit and differentiable, opening the door to its use within off-the-shelf molecular dynamics enhanced sampling techniques such as umbrella sampling or metadynamics. The authors also train a ANN decoder to reconstruct molecular configurations from the DMAPS manifold, which may also be useful in ‘hallucinating’ new molecular configurations outside the currently explored phase space that may then be lifted and used to initialise new simulations in the mould of iMapD.
Free energy reaction root mapping of alanine tripeptide in water
Published in Molecular Physics, 2019
Yuki Mitsuta, Johannes Kästner, Shusuke Yamanaka, Takashi Kawakami, Mitsutaka Okumura
In the case of thermodynamic conditions, we are interested in the potential of mean force (PMF) [11], which can be calculated by where , T is the temperature, is the Boltzmann’s constant, and is the partition function and is the probability distribution of the system along reaction coordinates () In these equations, is the number of degrees of freedom, is the energy of certain point and is the Dirac delta function. The PMF provides the free energy difference along . Many methods to calculate PMF with molecular dynamics (MD) simulation are available, such as blue moon sampling [6,12], slow growth [13–15], steered molecular dynamics [16–19], metadynamics [20–22] and umbrella sampling [23,24].