Dissociation Constants of Weak Acids from ab Initio Molecular Dynamics Using Metadynamics: Influence of the Inductive Effect and Hydrogen Bonding on pK(a) Values

The theoretical estimation of the dissociation constant, or pK(a), of weak acids continues to be a challenging field. Here, we show that ab initio CarParrinello molecular dynamics simulations in conjunction with metadynamics calculations of the free-energy profile of the dissociation reaction provide reasonable estimates of the pK(a) value. Water molecules, sufficient to complete the three hydration shells surrounding the acid molecule, were included explicitly in the computation procedure. The free-energy profiles exhibit two distinct minima corresponding to the dissociated and neutral states of the acid, and the difference in their values provides the estimate for pK(a). We show for a series of organic acids that CPMD simulations in conjunction with metadynamics can provide reasonable estimates of pK(a) values. The acids investigated were aliphatic carboxylic acids, chlorine-substituted carboxylic acids, cis- and trans-butenedioic acid, and the isomers of hydroxybenzoic acid. These systems were chosen to highlight that the procedure could correctly account for the influence of the inductive effect as well as hydrogen bonding on pK(a) values of weak organic acids. In both situations, the CPMD metadynamics procedure faithfully reproduces the experimentally observed trend and the magnitudes of the pK(a) values.

Estimating successive pK(a) values of polyprotic acids from ab initio molecular dynamics using metadynamics: the dissociation of phthalic acid and its isomers

Estimation of the dissociation constant, or pK(a), of weak acids continues to be a central goal in theoretical chemistry. Here we show that ab initio Car-Parrinello molecular dynamics simulations in conjunction with metadynamics calculations of the free energy profile of the dissociation reaction can provide reasonable estimates of the successive pK(a) values of polyprotic acids. We use the distance-dependent coordination number of the protons bound to the hydroxyl oxygen of the carboxylic group as the collective variable to explore the free energy profile of the dissociation process. Water molecules, sufficient to complete three hydration shells surrounding the acid molecule, were included explicitly in the computation procedure. Two distinct minima corresponding to the dissociated and un-dissociated states of the acid are observed and the difference in their free energy values provides the estimate for pK(a), the acid dissociation constant. We show that the method predicts the pK(a) value of benzoic acid in good agreement with experiment and then show using phthalic acid (benzene dicarboxylic acid) as a test system that both the first and second pK(a) values as well, as the subtle difference in their values for different isomers can be predicted in reasonable agreement with experimental data.

Ab Initio Molecular Dynamics Simulations of Amino Acids in Aqueous Solutions: Estimating pK(a) Values from Metadynamics Sampling

Changes in the protonation and deprotonation of amino acid residues in proteins play a key role in many biological processes and pathways. Here, we report calculations of the free-energy profile for the protonation deprotonation reaction of the 20 canonical alpha amino acids in aqueous solutions using ab initio Car-Parrinello molecular dynamics simulations coupled with metad-ynamics sampling. We show here that the calculated change in free energy of the dissociation reaction provides estimates of the multiple pK(a) values of the amino acids that are in good agreement with experiment. We use the bond-length-dependent number of the protons coordinated to the hydroxyl oxygen of the carboxylic and the amine groups as the collective variables to explore the free-energy profiles of the Bronsted acid-base chemistry of amino acids in aqueous solutions. We ensure that the amino acid undergoing dissociation is solvated by at least three hydrations shells with all water molecules included in the simulations. The method works equally well for amino acids with neutral, acidic and basic side chains and provides estimates of the multiple pK(a) values with a mean relative error, with respect to experimental results, of 0.2 pK(a) units.

Locating binding poses in protein-ligand systems using reconnaissance metadynamics

A molecular dynamics-based protocol is proposed for finding and scoring protein-ligand binding poses. This protocol uses the recently developed reconnaissance metadynamics method, which employs a self-learning algorithm to construct a bias that pushes the system away from the kinetic traps where it would otherwise remain. The exploration of phase space with this algorithm is shown to be roughly six to eight times faster than unbiased molecular dynamics and is only limited by the time taken to diffuse about the surface of the protein. We apply this method to the well-studied trypsin-benzamidine system and show that we are able to refind all the poses obtained from a reference EADock blind docking calculation. These poses can be scored based on the length of time the system remains trapped in the pose. Alternatively, one can perform dimensionality reduction on the output trajectory and obtain a map of phase space that can be used in more expensive free-energy calculations.

Exploring the free energy surfaces of clusters using reconnaissance metadynamics

A new approach is proposed for exploring the low-energy structures of small to medium-sized aggregates of atoms and molecules. This approach uses the recently proposed reconnaissance metadynamics method [G. A. Tribello, M. Ceriotti, and M. Parrinello. Proc. Natl. Acad. Sci. U.S.A. 107(41), 17509 (2010)] in tandem with collective variables that describe the average structure of the coordination sphere around the atoms/molecules. We demonstrate this method on both Lennard-Jones and water clusters and show how it is able to quickly find the global minimum in the potential energy surface, while exploring the finite temperature free energy surface. (C) 2011 American Institute of Physics. [doi: 10.1063/1.3628676]

Modified PNA design and synthesis: a novel approach using Molecular Dynamics and Metadynamics

Gli acidi peptido nucleici sono potenti strumenti utilizzati in ambito biotecnologico per colpire DNA o RNA. PNA contenenti basi o backbone modificati sono attualmente studiati per migliorarne le proprietà in ambito biologico. Bersagliare i micro RNA (anti-miR) è particolarmente interessante nell’ottica di future applicazioni terapeutiche, ma strumenti computazionali che aiutino nel design di nuovi PNA anti-miR non sono stati ancora completamente sviluppati. Le proprietà conformazionali del singolo filamento di PNA (non modificato o recante modificazioni in γ) e dei duplex PNA:RNA e i processi di re-annealing e melting sono stati studiati tramite Dinamica Molecolare e Metadinamica. L’approccio computazionale consolidato, assieme a un programma modificato per la generazione delle strutture dei duplex contenenti PNA, è stato utilizzato per il virtual screening di PNA contenenti basi modificate. Sono state inoltre sintetizzate le unità per l’ottenimento del composto più promettente e una funzione idrolitica da legare al monomero finale.

Communication: Benzene dimer-The free energy landscape

Establishing the relative orientation of the two benzene molecules in the dimer has remained an enigmatic challenge. Consensus has narrowed the choice of structures to either a T-shape, that may be tilted, or a parallel displaced arrangement, but the relatively small energy differences makes identifying the global minimum difficult. Here we report an ab initio Car-Parrinello Molecular Dynamics based metadynamics computation of the free-energy landscape of the benzene dimer. Our calculations show that although competing structures may be isoenergetic, free energy always favors a tilted T-shape geometry at all temperatures where the bound benzene dimer exist. (C) 2013 AIP Publishing LLC.

Ab Initio MD Simulations of the Bronsted Acidity of Glutathione in Aqueous Solutions: Predicting pK(a) Shifts of the Cysteine Residue

The tripeptide glutathione (GSH) is one of the most abundant peptides and the major repository for nonprotein sulfur in both animal and plant cells. It plays a critical role in intracellular oxidative stress management by the reversible formation of glutathione disulfide with the thiol-disulfide pair acting as a redox buffer. The state of charge of the ionizable groups of GSH can influence the redox couple, and hence the pK(a) value of the cysteine residue of GSH is critical to its functioning. Here we report ab initio Car-Parrinello molecular dynamics simulations of glutathione solvated by 200 water molecules, all of which are considered in the simulation. We show that the free-energy landscape for the protonation-deprotonation reaction of the cysteine residue of GSH computed using metadynamics sampling provides shift in the dissociation constant values as compared with the isolated accurate estimates of the pK(a) and correctly predicts the cysteine amino acid.

Energetics and Structural Characterization of the large-scale Functional Motion of Adenylate Kinase

Adenylate Kinase (AK) is a signal transducing protein that regulates cellular energy homeostasis balancing between different conformations. An alteration of its activity can lead to severe pathologies such as heart failure, cancer and neurodegenerative diseases. A comprehensive elucidation of the large-scale conformational motions that rule the functional mechanism of this enzyme is of great value to guide rationally the development of new medications. Here using a metadynamics-based computational protocol we elucidate the thermodynamics and structural properties underlying the AK functional transitions. The free energy estimation of the conformational motions of the enzyme allows characterizing the sequence of events that regulate its action. We reveal the atomistic details of the most relevant enzyme states, identifying residues such as Arg119 and Lys13, which play a key role during the conformational transitions and represent druggable spots to design enzyme inhibitors. Our study offers tools that open new areas of investigation on large-scale motion in proteins.

Using sketch-map coordinates to analyze and bias molecular dynamics simulations

When examining complex problems, such as the folding of proteins, coarse grained descriptions of the system drive our investigation and help us to rationalize the results. Oftentimes collective variables (CVs), derived through some chemical intuition about the process of interest, serve this purpose. Because finding these CVs is the most difficult part of any investigation, we recently developed a dimensionality reduction algorithm, sketch-map, that can be used to build a low-dimensional map of a phase space of high-dimensionality. In this paper we discuss how these machine-generated CVs can be used to accelerate the exploration of phase space and to reconstruct free-energy landscapes. To do so, we develop a formalism in which high-dimensional configurations are no longer represented by low-dimensional position vectors. Instead, for each configuration we calculate a probability distribution, which has a domain that encompasses the entirety of the low-dimensional space. To construct a biasing potential, we exploit an analogy with metadynamics and use the trajectory to adaptively construct a repulsive, history-dependent bias from the distributions that correspond to the previously visited configurations. This potential forces the system to explore more of phase space by making it desirable to adopt configurations whose distributions do not overlap with the bias. We apply this algorithm to a small model protein and succeed in reproducing the free-energy surface that we obtain from a parallel tempering calculation.

A self-learning algorithm for biased molecular dynamics

A new self-learning algorithm for accelerated dynamics, reconnaissance metadynamics, is proposed that is able to work with a very large number of collective coordinates. Acceleration of the dynamics is achieved by constructing a bias potential in terms of a patchwork of one-dimensional, locally valid collective coordinates. These collective coordinates are obtained from trajectory analyses so that they adapt to any new features encountered during the simulation. We show how this methodology can be used to enhance sampling in real chemical systems citing examples both from the physics of clusters and from the biological sciences.

Binding of Calcium and Carbonate to Polyacrylates

Polyacrylate molecules can be used to slow the growth of calcium carbonate. However, little is known about the mechanism by which the molecules impede the growth rate. A recent computational study (Bulo et al. Macromolecules 2007, 40, 3437) used metadynamics to investigate the binding of calcium to polyacrylate chains and has thrown some light on the coiling and precipitation of these polymers. We extend these simulations to examine the binding of calcium and carbonate to polyacrylate chains. We show that calcium complexed with both carbonate and polyacrylate is a very stable species. The free energies of calcium-carbonate-polyacrylate complexes, with different polymer configurations, are calculated, and differences in the free energy of the binding of carbonate are shown to be due to differences in the amount of steric hindrance about the calcium, which prevents the approach of the carbonate ion.

Transient Polymorphism in NaCl

We introduce a new, collective variable (CV) that can be used to increase the frequency with which nucleation events are observed in biased atomistic simulations. This CV forces the ions to aggregate into clusters but does not force the ions to order themselves in a particular pattern. We perform metadynamics simulations using this CV in order to examine nucleation in a solution of sodium chloride and find that for small cluster sizes the usual bulk rocksalt structure is less stable than a structure that resembles wurtzite.

PLUMED 2: New feathers for an old bird

Enhancing sampling and analyzing simulations are central issues in molecular simulation. Recently, we introduced PLUMED, an open-source plug-in that provides some of the most popular molecular dynamics (MD) codes with implementations of a variety of different enhanced sampling algorithms and collective variables (CVs). The rapid changes in this field, in particular new directions in enhanced sampling and dimensionality reduction together with new hardware, require a code that is more flexible and more efficient. We therefore present PLUMED 2 here a,complete rewrite of the code in an object-oriented programming language (C++). This new version introduces greater flexibility and greater modularity, which both extends its core capabilities and makes it far easier to add new methods and CVs. It also has a simpler interface with the MD engines and provides a single software library containing both tools and core facilities. Ultimately, the new code better serves the ever-growing community of users and contributors in coping with the new challenges arising in the field.

Program summary

Program title: PLUMED 2

Catalogue identifier: AEEE_v2_0

Program summary URL: http://cpc.cs.qub.ac.uk/summaries/AEEE_v2_0.html

Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland

Licensing provisions: Yes

No. of lines in distributed program, including test data, etc.: 700646

No. of bytes in distributed program, including test data, etc.: 6618136

Distribution format: tar.gz

Programming language: ANSI-C++.

Computer: Any computer capable of running an executable produced by a C++ compiler.

Operating system: Linux operating system, Unix OSs.

Has the code been vectorized or parallelized?: Yes, parallelized using MPI.

RAM: Depends on the number of atoms, the method chosen and the collective variables used.

Classification: 3, 7.7, 23. Catalogue identifier of previous version: AEEE_v1_0.

Journal reference of previous version: Comput. Phys. Comm. 180 (2009) 1961.

External routines: GNU libmatheval, Lapack, Bias, MPI. (C) 2013 Elsevier B.V. All rights reserved.

Probing the Unfolded Configurations of a β-Hairpin Using Sketch-Map

This work examines the conformational ensemble involved in β-hairpin folding by means of advanced molecular dynamics simulations and dimensionality reduction. A fully atomistic description of the protein and the surrounding solvent molecules is used, and this complex energy landscape is sampled by means of parallel tempering metadynamics simulations. The ensemble of configurations explored is analyzed using the recently proposed sketch-map algorithm. Further simulations allow us to probe how mutations affect the structures adopted by this protein. We find that many of the configurations adopted by a mutant are the same as those adopted by the wild-type protein. Furthermore, certain mutations destabilize secondary-structure-containing configurations by preventing the formation of hydrogen bonds or by promoting the formation of new intramolecular contacts. Our analysis demonstrates that machine-learning techniques can be used to study the energy landscapes of complex molecules and that the visualizations that are generated in this way provide a natural basis for examining how the stabilities of particular configurations of the molecule are affected by factors such as temperature or structural mutations.