Volodymyr Babin

Adaptively biased molecular dynamics for free energy calculations

We present an adaptively biased molecular dynamics (ABMD) method for the computation of the free energy surface of a reaction coordinate using nonequilibrium dynamics. The ABMD method belongs to the general category of umbrella sampling methods with an evolving biasing potential and is inspired by the metadynamics method. The ABMD method has several useful features, including a small number of control parameters and an O(t) numerical cost with molecular dynamics time t. The ABMD method naturally allows for extensions based on multiple walkers and replica exchange, where different replicas can have different temperatures and/or collective variables. This is beneficial not only in terms of the speed and accuracy of a calculation, but also in terms of the amount of useful information that may be obtained from a given simulation. The workings of the ABMD method are illustrated via a study of the folding of the Ace-GGPGGG-Nme peptide in a gaseous and solvated environment.

Conformations and free energy landscapes of polyproline peptides

The structure of the proline amino acid allows folded polyproline peptides to exist as both left- (PPII) and right-handed (PPI) helices. We have characterized the free energy landscapes of hexamer, nanomer, and tridecamer polyproline peptides in gas phase and implicit water as well as explicit hexane and 1-propanol for the nanomer. To enhance the sampling provided by regular molecular dynamics, we used the recently developed adaptively biased molecular dynamics method, which describes Landau free energy maps in terms of relevant collective variables. These maps, as a function of the collective variables of handedness, radius of gyration, and three others based on the peptide torsion angle ω, were used to determine the relative stability of the different structures, along with an estimate of the transition pathways connecting the different minima. Results show the existence of several metastable isomers and therefore provide a complementary view to experimental conclusions based on photo-induced electron transfer experiments with regard to the existence of stable heterogeneous subpopulations in PPII polyproline.

Reaction path ensemble of the B–Z-DNA transition: a comprehensive atomistic study

Since its discovery in 1979, left-handed Z-DNA has evolved from an in vitro curiosity to a challenging DNA structure with crucial roles in gene expression, regulation and recombination. A fundamental question that has puzzled researchers for decades is how the transition from B-DNA, the prevalent right-handed form of DNA, to Z-DNA is accomplished. Due to the complexity of the B–Z-DNA transition, experimental and computational studies have resulted in several different, apparently contradictory models. Here, we use molecular dynamics simulations coupled with state-of-the-art enhanced sampling techniques operating through non-conventional reaction coordinates, to investigate the B–Z-DNA transition at the atomic level. Our results show a complex free energy landscape, where several phenomena such as over-stretching, unpeeling, base pair extrusion and base pair flipping are observed resulting in interconversions between different DNA conformations such as B-DNA, Z-DNA and S-DNA. In particular, different minimum free energy paths allow for the coexistence of different mechanisms (such as zipper and stretch–collapse mechanisms) that previously had been proposed as independent, disconnected models. We find that the B–Z-DNA transition—in absence of other molecular partners—can encompass more than one mechanism of comparable free energy, and is therefore better described in terms of a reaction path ensemble.

Conformational free energies of methyl-α-L-iduronic and methyl-β-D-glucuronic acids in water

We present a simulation protocol that allows for efficient sampling of the degrees of freedom of a solute in explicit solvent. The protocol involves using a nonequilibrium umbrella sampling method, in this case, the recently developed adaptively biased molecular dynamics method, to compute an approximate free energy for the slow modes of the solute in explicit solvent. This approximate free energy is then used to set up a Hamiltonian replica exchange scheme that samples both from biased and unbiased distributions. The final accurate free energy is recovered via the weighted histogram analysis technique applied to all the replicas, and equilibrium properties of the solute are computed from the unbiased trajectory. We illustrate the approach by applying it to the study of the puckering landscapes of the methyl glycosides of alpha-L-iduronic acid and its C5 epimer beta-D-glucuronic acid in water. Big savings in computational resources are gained in comparison to the standard parallel tempering method.

A Statistical Analysis of the PPII Propensity of Amino Acid Guests in Proline-Rich Peptides

There has been considerable debate about the intrinsic PPII propensity of amino-acid residues in denatured polypeptides. Experimentally, the propensity scale is based on the behavior of guest amino-acid residues placed in the middle of polyproline hosts. We have used classical molecular dynamics simulations, with state-of-the-art force fields to carry out a comprehensive analysis of the conformational equilibria of the proline-based host oligopeptides with single guests. The tracked structural characteristics include the PPII content, the cis/trans isomerization of the prolyl bonds, the puckering of the pyrrolidine rings of the proline residues, and the secondary structural motifs. We find no evidence for an intrinsic PPII propensity in any of the guest amino acids other than proline. Instead, the PPII content as derived from experiments may be explained in terms of: 1), a local correlation between the dihedral angles of the guest amino acid and the proline residue immediately preceding it; and 2), a nonlocal correlation between the cis/trans states of the peptide bonds. In terms of the latter, we find that the presence of a guest (other than proline, tyrosine, or tryptophan) increases the trans content of most of the prolyl bonds, which results in an effective increase of the peptide PPII content. With respect to the local dihedral correlations, we find that these are well described in terms of the so-called odds-ratio statistic. Expressed in terms of free energy language, the PPII content based on the odds-ratio of the relevant residues correlate well with the experimentally measured PPII content.

PPII propensity of multiple-guest amino acids in a proline-rich environment.

There has been considerable debate about the intrinsic PPII propensity of amino acid residues in denatured polypeptides. Experimentally, this scale is based on the behavior of guest amino acid residues placed in the middle of proline-based hosts. We have used classical molecular dynamics simulations combined with replica-exchange methods to carry out a comprehensive analysis of the conformational equilibria of proline-based host oligopeptides with multiple guest amino acids including alanine, glutamine, valine, and asparagine. The tracked structural characteristics include the secondary structural motifs based on the Ramachandran angles and the cis/trans isomerization of the prolyl bonds. In agreement with our recent study of single amino acid guests, we did not observe an intrinsic PPII propensity in any of the guest amino acids in a multiple-guest setting. Instead, the experimental results can be explained in terms of (i) the steric restrictions imposed on the C-terminal guest amino acid that is immediately followed by a proline residue and (ii) an increase in the trans content of the prolyl bonds due to the presence of guest residues. In terms of the latter, we found that the more guests added to the system, the larger the increase in the trans content of the prolyl bonds, which results in an effective increase in the PPII content of the peptide.

Are Long-Range Structural Correlations Behind the Aggregration Phenomena of Polyglutamine Diseases?

We have characterized the conformational ensembles of polyglutamine peptides of various lengths (ranging from to ), both with and without the presence of a C-terminal polyproline hexapeptide. For this, we used state-of-the-art molecular dynamics simulations combined with a novel statistical analysis to characterize the various properties of the backbone dihedral angles and secondary structural motifs of the glutamine residues. For (i.e., just above the pathological length for Huntingtons disease), the equilibrium conformations of the monomer consist primarily of disordered, compact structures with non-negligible -helical and turn content. We also observed a relatively small population of extended structures suitable for forming aggregates including - and -strands, and - and -hairpins. Most importantly, for we find that there exists a long-range correlation (ranging for at least residues) among the backbone dihedral angles of the Q residues. For polyglutamine peptides below the pathological length, the population of the extended strands and hairpins is considerably smaller, and the correlations are short-range (at most residues apart). Adding a C-terminal hexaproline to suppresses both the population of these rare motifs and the long-range correlation of the dihedral angles. We argue that the long-range correlation of the polyglutamine homopeptide, along with the presence of these rare motifs, could be responsible for its aggregation phenomena.

The α‐sheet: A missing‐in‐action secondary structure?

The α‐sheet has been speculated to play a role as a toxic conformer in amyloid diseases. However, except for relatively short fragments, its detection has remained elusive. Here, we present molecular dynamics simulations that support the existence of the α‐sheet as a stable, metastable, or long‐lived secondary structure in polyglutamine and, to a lesser extent, in polyasparagine aggregates. Proteins 2011.

Binding Polymorphism in the DNA Bound State of the Pdx1 Homeodomain

The subtle effects of DNA-protein recognition are illustrated in the homeodomain fold. This is one of several small DNA binding motifs that, in spite of limited DNA binding specificity, adopts crucial, specific roles when incorporated in a transcription factor. The homeodomain is composed of a 3-helix domain and a mobile N-terminal arm. Helix 3 (the recognition helix) interacts with the DNA bases through the major groove, while the N-terminal arm becomes ordered upon binding a specific sequence through the minor groove. Although many structural studies have characterized the DNA binding properties of homeodomains, the factors behind the binding specificity are still difficult to elucidate. A crystal structure of the Pdx1 homeodomain bound to DNA (PDB 2H1K) obtained previously in our lab shows two complexes with differences in the conformation of the N-terminal arm, major groove contacts, and backbone contacts, raising new questions about the DNA recognition process by homeodomains. Here, we carry out fully atomistic Molecular Dynamics simulations both in crystal and aqueous environments in order to elucidate the nature of the difference in binding contacts. The crystal simulations reproduce the X-ray experimental structures well. In the absence of crystal packing constraints, the differences between the two complexes increase during the solution simulations. Thus, the conformational differences are not an artifact of crystal packing. In solution, the homeodomain with a disordered N-terminal arm repositions to a partially specific orientation. Both the crystal and aqueous simulations support the existence of different stable binding conformers identified in the original crystallographic data with different degrees of specificity. We propose that protein-protein and protein-DNA interactions favor a subset of the possible conformations. This flexibility in DNA binding may facilitate multiple functions for the same transcription factor.

Recipes for free energy calculations in biomolecular systems.

During the last decade, several methods for sampling phase space and calculating various free energies in biomolecular systems have been devised or refined for molecular dynamics (MD) simulations. Thus, state-of-the-art methodology and the ever increasing computer power allow calculations that were forbidden a decade ago. These calculations, however, are not trivial as they require knowledge of the methods, insight into the system under study, and, quite often, an artful combination of different methodologies in order to avoid the various traps inherent in an unknown free energy landscape. In this chapter, we illustrate some of these concepts with two relatively simple systems, a sugar ring and proline oligopeptides, whose free energy landscapes still offer considerable challenges. In order to explore the configurational space of these systems, and to surmount the various free energy barriers, we combine three complementary methods: a nonequilibrium umbrella sampling method (adaptively biased MD, or ABMD), replica-exchange molecular dynamics (REMD), and steered molecular dynamics (SMD). In particular, ABMD is used to compute the free energy surface of a set of collective variables; REMD is used to improve the performance of ABMD, to carry out sampling in space complementary to the collective variables, and to sample equilibrium configurations directly; and SMD is used to study different transition mechanisms.