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 non-equilibrium 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.Comment: Revised version to appear in Journal of Chemical Physic

Pathologic polyglutamine aggregation begins with a self-poisoning polymer crystal

A long-standing goal of amyloid research has been to characterize the structural basis of the rate-determining nucleating event. However, the ephemeral nature of nucleation has made this goal unachievable with existing biochemistry, structural biology, and computational approaches. Here, we addressed that limitation for polyglutamine (polyQ), a polypeptide sequence that causes Huntington’s and other amyloid-associated neurodegenerative diseases when its length exceeds a characteristic threshold. To identify essential features of the polyQ amyloid nucleus, we used a direct intracellular reporter of self-association to quantify frequencies of amyloid appearance as a function of concentration, conformational templates, and rational polyQ sequence permutations. We found that nucleation of pathologically expanded polyQ involves segments of three glutamine (Q) residues at every other position. We demonstrate using molecular simulations that this pattern encodes a four-stranded steric zipper with interdigitated Q side chains. Once formed, the zipper poisoned its own growth by engaging naive polypeptides on orthogonal faces, in a fashion characteristic of polymer crystals with intramolecular nuclei. We further show that self-poisoning can be exploited to block amyloid formation, by genetically oligomerizing polyQ prior to nucleation. By uncovering the physical nature of the rate-limiting event for polyQ aggregation in cells, our findings elucidate the molecular etiology of polyQ diseases

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 Huntington's 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

Theory of nucleation and growth during phase separation

We present a new model for the entire process of phase-separation that combines steady-state homogeneous nucleation theory with the classical Lifshitz-Slyozov mechanism of ripening, modified to account for the substantial correlations among the droplets. A set of self-consistent interface equations describes the decay of metastable states, incorporating naturally the crossover from early-stage nucleation to the late-stage scaling regime without ad hoc assumptions. We present simulation results for both two and three dimensions. We also present a mean-field, Thomas-Fermi approximation that provides an approximate solution to the many-body problem

Elastic effects in the foaming of thermoplastics

We have investigated shear and bulk elastic stresses in non-Newtonian fluids in which bubble formation due to a blowing agent is taking place. In the absence of shear, these elastic fields manifest themselves strongly during the formation of bubbles, and during coalescence events. At later times, their activity is confined to the surface of the bubbles. These effects cause a significant slow-down in radial growth. In the presence of steady shear, elasticity tends to stabilize bubble shapes, as the maximum number of droplets decreases with shear rate, while their growth rate increases

Nucleation and growth: Decay of a metastable state

We present a self-consistent model that describes the entire process of phase separation from the initial nucleation to the late stage Ostwald ripening regime. The model, formulated in terms of a set of interface equations, naturally incorporates the correlations which originate in the overlapping of the diffusional fields corresponding to the different precipitates

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

Structure and Dynamics of DNA and RNA Double Helices Obtained from the GGGGCC and CCCCGG Hexanucleotide Repeats That Are the Hallmark of C9FTD/ALS Diseases

A (GGGGCC) hexanucleotide repeat (HR) expansion in the C9ORF72 gene, and its associated antisense (CCCCGG) expansion, are considered the major cause behind frontotemporal dementia and amyotrophic lateral sclerosis. We have performed molecular dynamics simulations to characterize the conformation and dynamics of the 12 duplexes that result from the three different reading frames in sense and antisense HRs for both DNA and RNA. These duplexes display atypical structures relevant not only for a molecular level understanding of these diseases but also for enlarging the repertoire of nucleic-acid structural motifs. G-rich helices share common features. The inner G-G mismatches stay inside the helix in G_<i>syn</i>-G_<i>anti</i> conformations and form two hydrogen bonds (HBs) between the Watson–Crick edge of G_<i>anti</i> and the Hoogsteen edge of G_<i>syn</i>. In addition, G_<i>syn</i> in RNA forms a base-phosphate HB. Inner G-G mismatches cause local unwinding of the helix. G-rich double helices are more stable than C-rich helices due to better stacking and HBs of G-G mismatches. C-rich helix conformations vary wildly. C mismatches flip out of the helix in DNA but not in RNA. Least (most) stable C-rich RNA and DNA helices have single (double) mismatches separated by two (four) Watson–Crick basepairs. The most stable DNA structure displays an “e-motif” where mismatched bases flip toward the minor groove and point in the 5′ direction. There are two RNA conformations, where the orientation and HB pattern of the mismatches is coupled to bending of the helix

Structural and Dynamical Characterization of DNA and RNA Quadruplexes Obtained from the GGGGCC and GGGCCT Hexanucleotide Repeats Associated with C9FTD/ALS and SCA36 Diseases

A (GGGGCC) hexanucleotide repeat (HR) expansion in the C9ORF72 gene has been considered the major cause behind both frontotemporal dementia and amyotrophic lateral sclerosis, while a (GGGCCT) is associated with spinocerebellar ataxia 36. Recent experiments involving NMR, CD, optical melting and 1D ¹H NMR spectroscopy, suggest that the r­(GGGGCC) HR can adopt a hairpin structure with G-G mismatches in equilibrium with a G-quadruplex structure. G-Quadruplexes have also been identified for d­(GGGGCC). As these experiments lack molecular resolution, we have used molecular dynamics microsecond simulations to obtain a structural characterization of the G-quadruplexes associated with both HRs. All DNA G-quadruplexes, parallel or antiparallel, with or without loops are stable, while only parallel and one antiparallel (stabilized by diagonal loops) RNA G-quadruplexes are stable. It is known that antiparallel G-quadruplexes require alternating guanines to be in a syn conformation that is hindered by the C3′-endo pucker preferred by RNA. Initial RNA antiparallel quadruplexes built with C2′-endo sugars evolve such that the transition (C2′-endo)-to-(C3′-endo) triggers unwinding and buckling of the flat G-tetrads, resulting in the unfolding of the RNA antiparallel quadruplex. Finally, a parallel G-quadruplex stabilizes an adjacent C-tetrad in both DNA and RNA (thus effectively becoming a mixed quadruplex of 5 layers). The C-tetrad is stabilized by the stacking interactions with the preceding G-tetrad, by cyclical hydrogen bonds C­(N4)-(O2), and by an ion between the G-tetrad and the C-tetrad. In addition, antiparallel DNA G-quadruplexes also stabilize flat C-layers at the ends of the quadruplexes