Polymorph specific RMSD local order parameters for molecular crystals and nuclei: α-, β-, and γ-glycine

Impact of Phosphorylation at Various Sites on the Active Pocket of Human Ferrochelatase: Insights from Molecular Dynamics Simulations

Ferrochelatase (FECH) is the terminal enzyme in human heme biosynthesis, catalyzing the insertion of ferrous iron into protoporphyrin IX (PPIX) to form protoheme IX (Heme). Phosphorylation increases the activity of FECH, and it has been confirmed that the activity of FECH phosphorylated at T116 increases. However, it remains unclear whether the T116 site and other potential phosphorylation modification sites collaboratively regulate the activity of FECH. In this study, we identified a new phosphorylation site, T218, and explored the allosteric effects of unphosphorylated (UP), PT116, PT218, and PT116 + PT218 states on FECH in the presence and absence of substrates (PPIX and Heme) using molecular dynamics (MD) simulations. Binding free energies were evaluated with the MM/PBSA method. Our findings indicate that the PT116 + PT218 state exhibits the lowest binding free energy with PPIX, suggesting the strongest binding affinity. Additionally, this state showed a higher binding free energy with Heme compared to UP, which facilitates Heme release. Moreover, employing multiple analysis methods, including free energy landscape (FEL), principal component analysis (PCA), dynamic cross-correlation matrix (DCCM), and hydrogen bond interaction analysis, we demonstrated that phosphorylation significantly affects the dynamic behavior and binding patterns of substrates to FECH. Insights from this study provide valuable theoretical guidance for treating conditions related to disrupted heme metabolism, such as various porphyrias and iron-related disorders.

Resolving Temperature-Dependent Hydrate Nucleation Pathway: The Role of "Transition Layer"

Understanding the nucleation of natural gas hydrate (NGH) at different conditions has important implications to NGH recovery and other industrial applications, such as gas storage and separation. Herein, vast numbers of hydrate nucleation events are traced via molecular dynamics (MD) simulations at different degrees of supercooling (or driving forces). Specifically, to precisely characterize a hydrate nucleus from an aqueous system during the MD simulation, we develop an evolutionary order parameter (OP) to recognize the nucleus size and shape. Subsequently, the free energy landscapes of hydrate during nucleation are explored by using the newly developed OP. The results suggest that at 270 K (or 0.92 Tm supercooling, where Tm is the melting point), the near-rounded nucleus prevails during the nucleation, as described from the classical nucleation theory. In contrast, at relatively strong driving forces of 0.85 and 0.88 Tm, nonclassical nucleation events arise. Specifically, the pathway toward an elongated nucleus becomes as important as the pathway toward a near-rounded nucleus. To explain the distinct nucleation phenomena at different supercoolings, a notion of a "transition layer" (or liquid-blob-like layer) is proposed. Here, the transition layer is to describe the interfacial region between the nucleus and aqueous solution, and this layer entails two functionalities: (1) it tends to retain CH4 depending on the degrees of supercooling and (2) it facilitates collision among CH4, which thus promote the incorporation of CH4 into nucleus. Our simulation indicates that compared to the near-rounded nucleus, the transition layer surrounding the elongated nucleus is more evident with the higher collision rate among CH4 molecules. As such, the transition layer tends to promote the elongated nucleus pathway, while offsetting the cost of larger surface free energy associated with the elongated nucleus. At 0.92 Tm, however, the transition layer gradually disappears, and classical nucleation events dominate. Overall, the notion of "transition layer" offers deeper insight into the NGH nucleation at different degrees of supercooling and could be extended to describe other types of hydrate nucleation.

Collective Variables for Crystallization Simulations-from Early Developments to Recent Advances

Crystallization is an important physicochemical process which has relevance in material science, biology, and the environment. Decades of experimental and theoretical efforts have been made to understand this fundamental symmetry-breaking transition. While experiments provide equilibrium structures and shapes of crystals, they are limited to unraveling how molecules aggregate to form crystal nuclei that subsequently transform into bulk crystals. Computer simulations, mainly molecular dynamics (MD), can provide such microscopic details during the early stage of a crystallization event. Crystallization is a rare event that takes place in time scales much longer than a typical equilibrium MD simulation can sample. This inadequate sampling of the MD method can be easily circumvented by the use of enhanced sampling (ES) simulations. In most of the ES methods, the fluctuations of a system's slow degrees of freedom, called collective variables (CVs), are enhanced by applying a bias potential. This transforms the system from one state to the other within a short time scale. The most crucial part of such CV-based ES methods is to find suitable CVs, which often needs intuition and several trial-and-error optimization steps. Over the years, a plethora of CVs has been developed and applied in the study of crystallization. In this review, we provide a brief overview of CVs that have been developed and used in ES simulations to study crystallization from melt or solution. These CVs can be categorized mainly into four types: (i) spherical particle-based, (ii) molecular template-based, (iii) physical property-based, and (iv) CVs obtained from dimensionality reduction techniques. We present the context-based evolution of CVs, discuss the current challenges, and propose future directions to further develop effective CVs for the study of crystallization of complex systems.

Toward Automated Sampling of Polymorph Nucleation and Free Energies with the SGOOP and Metadynamics

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process and correctly calculating the relative free energies of different polymorphs. Here, we demonstrate, for the prototypical case of urea nucleation from the melt, how one can learn such a one-dimensional reaction coordinate as a function of prespecified order parameters and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of the generic thermodynamic and structural order parameters using the "spectral gap optimization of order parameters (SGOOP)" approach [Tiwary, P. and Berne, B. J. Proc. Natl. Acad. Sci. U.S.A. (2016)] and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insights into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes an accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. We believe the ideas demonstrated in this work will facilitate efficient sampling of nucleation in complex, generic systems.

Solubility curves and nucleation rates from molecular dynamics for polymorph prediction – moving beyond lattice energy minimization

Seeded nucleation simulations allow for the screening of low energy structures to predict final structure present in solution.

Crystal Nucleation in Liquids: Open Questions and Future Challenges in Molecular Dynamics Simulations

The nucleation of crystals in liquids is one of nature's most ubiquitous phenomena, playing an important role in areas such as climate change and the production of drugs. As the early stages of nucleation involve exceedingly small time and length scales, atomistic computer simulations can provide unique insights into the microscopic aspects of crystallization. In this review, we take stock of the numerous molecular dynamics simulations that, in the past few decades, have unraveled crucial aspects of crystal nucleation in liquids. We put into context the theoretical framework of classical nucleation theory and the state-of-the-art computational methods by reviewing simulations of such processes as ice nucleation and the crystallization of molecules in solutions. We shall see that molecular dynamics simulations have provided key insights into diverse nucleation scenarios, ranging from colloidal particles to natural gas hydrates, and that, as a result, the general applicability of classical nucleation theory has been repeatedly called into question. We have attempted to identify the most pressing open questions in the field. We believe that, by improving (i) existing interatomic potentials and (ii) currently available enhanced sampling methods, the community can move toward accurate investigations of realistic systems of practical interest, thus bringing simulations a step closer to experiments.

Modeling Polymorphic Molecular Crystals with Electronic Structure Theory

Interest in molecular crystals has grown thanks to their relevance to pharmaceuticals, organic semiconductor materials, foods, and many other applications. Electronic structure methods have become an increasingly important tool for modeling molecular crystals and polymorphism. This article reviews electronic structure techniques used to model molecular crystals, including periodic density functional theory, periodic second-order Møller-Plesset perturbation theory, fragment-based electronic structure methods, and diffusion Monte Carlo. It also discusses the use of these models for predicting a variety of crystal properties that are relevant to the study of polymorphism, including lattice energies, structures, crystal structure prediction, polymorphism, phase diagrams, vibrational spectroscopies, and nuclear magnetic resonance spectroscopy. Finally, tools for analyzing crystal structures and intermolecular interactions are briefly discussed.

Predicting finite-temperature properties of crystalline carbon dioxide from first principles with quantitative accuracy

The temperature-dependence of the crystalline carbon dioxide (phase I) structure, thermodynamics, and mechanical properties are predicted in excellent agreement with experiment over a 200 K temperature range using high-level electronic structure calculations.

Molecular crystal structures, thermodynamics, and mechanical properties can vary substantially with temperature, and predicting these temperature-dependencies correctly is important for many practical applications in the pharmaceutical industry and other fields. However, most electronic structure predictions of molecular crystal properties neglect temperature and/or thermal expansion, leading to potentially erroneous results. Here, we demonstrate that by combining large basis set second-order Møller–Plesset (MP2) or even coupled cluster singles, doubles, and perturbative triples (CCSD(T)) electronic structure calculations with a quasiharmonic treatment of thermal expansion, experimentally observable properties such as the unit cell volume, heat capacity, enthalpy, entropy, sublimation point and bulk modulus of phase I crystalline carbon dioxide can be predicted in excellent agreement with experiment over a broad range of temperatures. These results point toward a promising future for ab initio prediction of molecular crystal properties at real-world temperatures and pressures.

Order-parameter-aided temperature-accelerated sampling for the exploration of crystal polymorphism and solid-liquid phase transitions

The problem of predicting polymorphism in atomic and molecular crystals constitutes a significant challenge both experimentally and theoretically. From the theoretical viewpoint, polymorphism prediction falls into the general class of problems characterized by an underlying rough energy landscape, and consequently, free energy based enhanced sampling approaches can be brought to bear on the problem. In this paper, we build on a scheme previously introduced by two of the authors in which the lengths and angles of the supercell are targeted for enhanced sampling via temperature accelerated adiabatic free energy dynamics [T. Q. Yu and M. E. Tuckerman, Phys. Rev. Lett. 107, 015701 (2011)]. Here, that framework is expanded to include general order parameters that distinguish different crystalline arrangements as target collective variables for enhanced sampling. The resulting free energy surface, being of quite high dimension, is nontrivial to reconstruct, and we discuss one particular strategy for performing the free energy analysis. The method is applied to the study of polymorphism in xenon crystals at high pressure and temperature using the Steinhardt order parameters without and with the supercell included in the set of collective variables. The expected fcc and bcc structures are obtained, and when the supercell parameters are included as collective variables, we also find several new structures, including fcc states with hcp stacking faults. We also apply the new method to the solid-liquid phase transition in copper at 1300 K using the same Steinhardt order parameters. Our method is able to melt and refreeze the system repeatedly, and the free energy profile can be obtained with high efficiency.

Lattice-switching Monte Carlo method for crystals of flexible molecules

We discuss implementation of the lattice-switching Monte Carlo method (LSMC) as a binary sampling between two synchronized Markov chains exploring separated minima in the potential energy landscape. When expressed in this fashion, the generalization to more complex crystals is straightforward. We extend the LSMC method to a flexible model of linear alkanes, incorporating bond length and angle constraints. Within this model, we accurately locate a transition between two polymorphs of n-butane with increasing density, and suggest this as a benchmark problem for other free-energy methods.

Salting out the polar polymorph: analysis by alchemical solvent transformation

We computationally examine how adding NaCl to an aqueous solution with α- and γ-glycine nuclei alters the structure and interfacial energy of the nuclei. The polar γ-glycine nucleus in pure aqueous solution develops a melted layer of amorphous glycine around the nucleus. When NaCl is added, a double layer is formed that stabilizes the polar glycine polymorph and eliminates the surface melted layer. In contrast, the non-polar α-glycine nucleus is largely unaffected by the addition of NaCl. To quantify the stabilizing effect of NaCl on γ-glycine nuclei, we alchemically transform the aqueous glycine solution into a brine solution of glycine. The alchemical transformation is performed both with and without a nucleus in solution and for nuclei of α-glycine and γ-glycine polymorphs. The calculations show that adding 80 mg/ml NaCl reduces the interfacial free energy of a γ-glycine nucleus by 7.7 mJ/m(2) and increases the interfacial free energy of an α-glycine nucleus by 3.1 mJ/m(2). Both results are consistent with experimental reports on nucleation rates which suggest: J(α, brine) < J(γ, brine) < J(α, water). For γ-glycine nuclei, Debye-Hückel theory qualitatively, but not quantitatively, captures the effect of salt addition. Only the alchemical solvent transformation approach can predict the results for both polar and non-polar polymorphs. The results suggest a general "salting out" strategy for obtaining polar polymorphs and also a general approach to computationally estimate the effects of solvent additives on interfacial free energies for nucleation.