Likelihood-based non-Markovian models from molecular dynamics.

SignificanceThe analysis of complex systems with many degrees of freedom generally involves the definition of low-dimensional collective variables more amenable to physical understanding. Their dynamics can be modeled by generalized Langevin equations, whose coefficients have to be estimated from simulations of the initial high-dimensional system. These equations feature a memory kernel describing the mutual influence of the low-dimensional variables and their environment. We introduce and implement an approach where the generalized Langevin equation is designed to maximize the statistical likelihood of the observed data. This provides an efficient way to generate reduced models to study dynamical properties of complex processes such as chemical reactions in solution, conformational changes in biomolecules, or phase transitions in condensed matter systems.

Free energy calculations and unbiased molecular dynamics targeting the liquid-liquid transition in water no man's land.

The existence of a first-order phase transition between a low-density liquid (LDL) and a high-density liquid (HDL) form of supercooled water has been a central and highly debated issue of physics and chemistry for the last three decades. We present a computational study that allows us to determine the free-energy landscapes of supercooled water over a wide range of pressure and temperature conditions using the TIP4P/2005 force field. Our approach combines topology-based structural transformation coordinates, state-of-the-art free-energy calculation methods, and extensive unbiased molecular dynamics. All our diverse simulations cannot detect any barrier within the investigated timescales and system size, for a discontinuous transition between the LDL and HDL forms throughout the so-called "no man's land," until the onset of the solid, non-diffusive amorphous forms.

Inferring free-energy barriers and kinetic rates from molecular dynamics via underdamped Langevin models.

Rare events include many of the most interesting transformation processes in condensed matter, from phase transitions to biomolecular conformational changes to chemical reactions. Access to the corresponding mechanisms, free-energy landscapes and kinetic rates can in principle be obtained by different techniques after projecting the high-dimensional atomic dynamics on one (or a few) collective variable. Even though it is well-known that the projected dynamics approximately follows - in a statistical sense - the generalized, underdamped or overdamped Langevin equations (depending on the time resolution), to date it is nontrivial to parameterize such equations starting from a limited, practically accessible amount of non-ergodic trajectories. In this work we focus on Markovian, underdamped Langevin equations, that arise naturally when considering, e.g., numerous water-solution processes at sub-picosecond resolution. After contrasting the advantages and pitfalls of different numerical approaches, we present an efficient parametrization strategy based on a limited set of molecular dynamics data, including equilibrium trajectories confined to minima and few hundreds transition path sampling-like trajectories. Employing velocity autocorrelation or memory kernel information for learning the friction and likelihood maximization for learning the free-energy landscape, we demonstrate the possibility to reconstruct accurate barriers and rates both for a benchmark system and for the interaction of carbon nanoparticles in water.

CO2 Capture and Release in Amine Solutions: To What Extent Can Molecular Simulations Help Understand the Trends?

Absorption in amine solutions is a well-established advanced technology for CO2 capture. However, the fundamental aspects of the chemical reactions occurring in solution still appear to be unclear. Our previous investigation of aqueous monoethanolamine (MEA) and 2-amino-2-methyl-1,3-propanediol (AMPD), based on ab initio molecular dynamics simulations aided with metadynamics, provided new insights into the reaction mechanisms leading to CO2 capture and release with carbamate formation and dissociation. In particular, the role of water-strongly underestimated in previous computational studies-was established as essential in determining the development of all relevant reactions. In this article, we apply the same simulation protocol to other relevant primary amines, namely, a sterically hindered amine (2-amino-2-methyl-1-propanol (AMP)) and an aromatic amine (benzylamine (BZA)). We also discuss the case of CO2 capture with the formation of bicarbonate. New information is thus obtained that extends our understanding. However, quantitative predictions obtained using molecular simulations suffer from several methodological problems, and comparison among different chemical species is especially demanding. We clarify these problems further with a discussion of previous attempts to explain the different behaviors of AMP and MEA using other types of models and computations.

Critical Assessment of Data-Driven versus Heuristic Reaction Coordinates in Solution Chemistry.

Reaction coordinates are an essential ingredient of theoretical studies of rare events in chemistry and physics because they carry information about reaction mechanism and allow the computation of free-energy landscapes and kinetic rates. We present a critical assessment of the merits and disadvantages of heuristic reaction coordinates, largely employed today, with respect to coordinates optimized on the basis of reliable transition-path sampling data. We take as a test bed multinanosecond ab initio molecular dynamics simulations of chloride SN2 substitution on methyl chloride in explicit water. The computational protocol we devise allows the unsupervised optimization of agnostic coordinates able to account for solute and solvent contributions, yielding a free-energy reconstruction of quality comparable to the best heuristic coordinates without requiring chemical intuition.

Carbon Dioxide under Earth Mantle Conditions: From a Molecular Liquid through a Reactive Fluid to Polymeric Regimes.

In both its gaseous and condensed forms, carbon dioxide has an ever-increasing impact on Earth's chemistry and human life and activities. However, many aspects of its high-pressure phase diagram remain unclear. In this work, we present a complete structural characterization of carbon dioxide fluids under geological conditions using extensive ab initio molecular dynamics simulations throughout a wide pressure and temperature range, corresponding to Earth's lower mantle. We identify and describe four different disordered regimes, including two polymeric forms and two molecular ones, all within the geothermal conditions of the lower mantle. At pressures below 40 GPa, we find that the molecular liquid becomes very reactive above 2000 K: the C-O double bond routinely breaks, resulting in small and transient chains composed of CO2 units and frequently leading to an exchange of oxygen atoms between molecules. At higher pressures, in addition to the polymeric fluid previously reported at 3000 K, we find a polymeric system with glass-like behavior at lower temperatures, suggesting a complex interplay between kinetics and stability.

Impurity diffusion in magic-size icosahedral clusters.

Atomic diffusion is at the basis of chemical ordering transformations in nanoalloys. Understanding the diffusion mechanisms at the atomic level is therefore a key issue in the study of the thermodynamic behavior of these systems and, in particular, of their evolution from out-of-equilibrium chemical ordering types often obtained in the experiments. Here, the diffusion is studied in the case of a single-atom impurity of Ag or Au moving within otherwise pure magic-size icosahedral clusters of Cu or Co by means of two different computational techniques, i.e., molecular dynamics and metadynamics. Our simulations reveal unexpected diffusion pathways, in which the displacement of the impurity is coupled with the creation of vacancies in the central part of the cluster. We show that the observed mechanism is quite different from the vacancy-mediated diffusion processes identified so far, and we demonstrate that it can be related to the presence of non-homogeneous compressive stress in the inner part of the icosahedral structure.

Formation of nucleobases in a Miller-Urey reducing atmosphere.

The Miller-Urey experiments pioneered modern research on the molecular origins of life, but their actual relevance in this field was later questioned because the gas mixture used in their research is considered too reducing with respect to the most accepted hypotheses for the conditions on primordial Earth. In particular, the production of only amino acids has been taken as evidence of the limited relevance of the results. Here, we report an experimental work, combined with state-of-the-art computational methods, in which both electric discharge and laser-driven plasma impact simulations were carried out in a reducing atmosphere containing NH3 + CO. We show that RNA nucleobases are synthesized in these experiments, strongly supporting the possibility of the emergence of biologically relevant molecules in a reducing atmosphere. The reconstructed synthetic pathways indicate that small radicals and formamide play a crucial role, in agreement with a number of recent experimental and theoretical results.

Holo-like and Druggable Protein Conformations from Enhanced Sampling of Binding Pocket Volume and Shape.

Understanding molecular recognition of small molecules by proteins in atomistic detail is key for drug design. Molecular docking is a widely used computational method to mimic ligand-protein association in silico. However, predicting conformational changes occurring in proteins upon ligand binding is still a major challenge. Ensemble docking approaches address this issue by considering a set of different conformations of the protein obtained either experimentally or from computer simulations, e.g., molecular dynamics. However, holo structures prone to host (the correct) ligands are generally poorly sampled by standard molecular dynamics simulations of the apo protein. In order to address this limitation, we introduce a computational approach based on metadynamics simulations called ensemble docking with enhanced sampling of pocket shape (EDES) that allows holo-like conformations of proteins to be generated by exploiting only their apo structures. This is achieved by defining a set of collective variables that effectively sample different shapes of the binding site, ultimately mimicking the steric effect due to the ligand. We assessed the method on three challenging proteins undergoing different extents of conformational changes upon ligand binding. In all cases our protocol generates a significant fraction of structures featuring a low RMSD from the experimental holo geometry. Moreover, ensemble docking calculations using those conformations yielded in all cases native-like poses among the top-ranked ones.

On the link between polyamorphism and liquid-liquid transition: The case of salty water.

We investigate a LiCl:6D2O water solution in the deep undercooled regime as a function of pressure by neutron diffraction, small angle neutron scattering, and molecular dynamics simulations. We probe the structure of the undercooled liquid and the existence of density fluctuations in the system along isotherms just above the observed first-order-like polymorphic transition in the solid between a high density amorphous (s-HDA) and a very high density amorphous (s-VHDA) form [L. E. Bove et al., Phys. Rev. Lett. 106, 125701 (2011)]. We observe a continuous pressure evolution of the structure factor of the liquid and the absence of density fluctuations when crossing the continuation line of the s-HDA and s-VHDA boundary. These results indicate that no liquid-liquid transition is observed in the system in correspondence with the solid polyamorphism.

Combining theoretical and experimental data to decipher CFTR 3D structures and functions.

Cryo-electron microscopy (cryo-EM) has recently provided invaluable experimental data about the full-length cystic fibrosis transmembrane conductance regulator (CFTR) 3D structure. However, this experimental information deals with inactive states of the channel, either in an apo, quiescent conformation, in which nucleotide-binding domains (NBDs) are widely separated or in an ATP-bound, yet closed conformation. Here, we show that 3D structure models of the open and closed forms of the channel, now further supported by metadynamics simulations and by comparison with the cryo-EM data, could be used to gain some insights into critical features of the conformational transition toward active CFTR forms. These critical elements lie within membrane-spanning domains but also within NBD1 and the N-terminal extension, in which conformational plasticity is predicted to occur to help the interaction with filamin, one of the CFTR cellular partners.

Formamide reaction network in gas phase and solution via a unified theoretical approach: Toward a reconciliation of different prebiotic scenarios.

Increasing experimental and theoretical evidence points to formamide as a possible hub in the complex network of prebiotic chemical reactions leading from simple precursors like H2, H2O, N2, NH3, CO, and CO2 to key biological molecules like proteins, nucleic acids, and sugars. We present an in-depth computational study of the formation and decomposition reaction channels of formamide by means of ab initio molecular dynamics. To this aim we introduce a new theoretical method combining the metadynamics sampling scheme with a general purpose topological formulation of collective variables able to track a wide range of different reaction mechanisms. Our approach is flexible enough to discover multiple pathways and intermediates starting from minimal insight on the systems, and it allows passing in a seamless way from reactions in gas phase to reactions in liquid phase, with the solvent active role fully taken into account. We obtain crucial new insight into the interplay of the different formamide reaction channels and into environment effects on pathways and barriers. In particular, our results indicate a similar stability of formamide and hydrogen cyanide in solution as well as their relatively facile interconversion, thus reconciling experiments and theory and, possibly, two different and competing prebiotic scenarios. Moreover, although not explicitly sought, formic acid/ammonium formate is produced as an important formamide decomposition byproduct in solution.

Prebiotic synthesis of nucleic acids and their building blocks at the atomic level - merging models and mechanisms from advanced computations and experiments.

The origin of life on Earth is one of the most fascinating questions of contemporary science. Extensive research in the past decades furnished diverse experimental proposals for the emergence of first informational polymers that could form the basis of the early terrestrial life. Side by side with the experiments, the fast development of modern computational chemistry methods during the last 20 years facilitated the use of in silico modelling tools to complement the experiments. Modern computations can provide unique atomic-level insights into the structural and electronic aspects as well as the energetics of key prebiotic chemical reactions. Many of these insights are not directly obtainable from the experimental techniques and the computations are thus becoming indispensable for proper interpretation of many experiments and for qualified predictions. This review illustrates the synergy between experiment and theory in the origin of life research focusing on the prebiotic synthesis of various nucleic acid building blocks and on the self-assembly of nucleotides leading to the first functional oligonucleotides.

Systematic comparison of crystalline and amorphous phases: Charting the landscape of water structures and transformations.

Systematically resolving different crystalline phases starting from the atomic positions, a mandatory step in algorithms for the prediction of structures or for the simulation of phase transitions, can be a non-trivial task. Extending to amorphous phases and liquids which lack the discrete symmetries, the problem becomes even more difficult, involving subtle topological differences at medium range that, however, are crucial to the physico-chemical and spectroscopic properties of the corresponding materials. Typically, system-tailored order parameters are devised, like global or local symmetry indicators, ring populations, etc. We show that a recently introduced metric provides a simple and general solution to this intricate problem. In particular, we demonstrate that a map can be traced displaying distances among water phases, including crystalline as well as amorphous states and the liquid, consistently with experimental knowledge in terms of phase diagram, structural features, and preparation routes.

Data-Driven Path Collective Variables.

Identifying optimal collective variables to model transformations using atomic-scale simulations is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables that can be thought of as a data-driven generalization of the path collective variable concept. It consists of a kernel ridge regression of the committor probability, which encodes a transformation's progress. The resulting collective variable is one-dimensional, interpretable, and differentiable, making it appropriate for enhanced sampling simulations requiring biasing. We demonstrate the validity of the method on two different applications: a precipitation model and the association of Li+ and F- in water. For the former, we show that global descriptors such as the permutation invariant vector allow reaching an accuracy far from the one achieved via simpler, more intuitive variables. For the latter, we show that information correlated with the transformation mechanism is contained in the first solvation shell only and that inertial effects prevent the derivation of optimal collective variables from the atomic positions only.

Nucleation process of a fibril precursor in the C-terminal segment of amyloid-ß.

By extended atomistic simulations in explicit solvent and bias-exchange metadynamics, we study the aggregation process of 18 chains of the C-terminal segment of amyloid-ß, an intrinsically disordered protein involved in Alzheimer's disease and prone to form fibrils. Starting from a disordered aggregate, we are able to observe the formation of an ordered nucleus rich in beta sheets. The rate limiting step in the nucleation pathway involves crossing a barrier of approximately 40 kcal/mol and is associated with the formation of a very specific interdigitation of the side chains belonging to different sheets. This structural pattern is different from the one observed experimentally in a microcrystal of the same system, indicating that the structure of a "nascent" fibril may differ from the one of an "extended" fibril.

Structural cluster analysis of chemical reactions in solution.

We introduce a simple and general approach to the problem of clustering structures from atomic trajectories of chemical reactions in solution. By considering distance metrics which are invariant under permutation of identical atoms or molecules, we demonstrate that it is possible to automatically resolve as distinct structural clusters the configurations corresponding to reactants, products, and transition states, even in presence of atom-exchanges and of hundreds of solvent molecules. Our approach strongly simplifies the analysis of large trajectories and it opens the way to the construction of kinetic network models of activated processes in solution employing the available efficient schemes developed for proteins conformational ensembles.

Critical comparison of general-purpose collective variables for crystal nucleation.

The nucleation of crystals is a prominent phenomenon in science and technology that still lacks a full atomic-scale understanding. Much work has been devoted to identifying order parameters able to track the process, from the inception of early nuclei to their maturing to critical size until growth of an extended crystal. We critically assess and compare two powerful distance-based collective variables, an effective entropy derived from liquid state theory and the path variable based on permutation invariant vectors using the Kob-Andersen binary mixture and a combination of enhanced-sampling techniques. Our findings reveal a comparable ability to drive nucleation when a bias potential is applied, and comparable free-energy barriers and structural features. Yet, we also found an imperfect correlation with the committor probability on the barrier top which was bypassed by changing the order parameter definition.