[Show abstract][Hide abstract] ABSTRACT: The ongoing effort to detect and characterize physical entanglement in
biopolymers has so far established that knots are present in many globular
proteins and also abound in viral DNA packaged inside bacteriophages. RNA
molecules, on the other hand, have not yet been systematically screened for the
occurrence of physical knots. We have accordingly undertaken the systematic
profiling of the ~6,000 RNA structures present in the protein data bank. The
search identified no more than three deeply-knotted RNA molecules. These are
ribosomal RNAs solved by cryo-em and consist of about 3,000 nucleotides.
Compared to the case of proteins and viral DNA, the observed incidence of RNA
knots is therefore practically negligible. This suggests that either
evolutionary selection, or thermodynamic and kinetic folding mechanisms act
towards minimizing the entanglement of RNA to an extent that is unparalleled by
other types of biomolecules. The properties of the three observed RNA knotting
patterns provide valuable clues for designing RNA sequences capable of
self-tying in a twist-knot fold.
[Show abstract][Hide abstract] ABSTRACT: Methods for computing electrostatic interactions often account implicitly for the solvent, due to the much smaller number of degrees of freedom involved. In the Poisson–Boltzmann (PB) approach the electrostatic potential is obtained by solving the Poisson–Boltzmann equation (PBE), where the solvent region is modeled as a homogeneous medium with a high dielectric constant. PB however is not exempt of problems. It does not take into account for example the sizes of the ions in the atmosphere surrounding the solute, nor does it take into account the inhomogeneous dielectric response of water due to the presence of a highly charged surface. In this paper we review two major modifications of PB that circumvent these problems, namely the size-modified PB (SMPB) equation and the Dipolar Poisson–Boltzmann Langevin (DPBL) model. In SMPB, steric effects between ions are accounted for with a lattice gas model. In DPBL, the solvent region is no longer modeled as a homogeneous dielectric media but rather as an assembly of self-orienting interacting dipoles of variable density. This model results in a dielectric profile that transits smoothly from the solute to the solvent region as well as in a variable solvent density that depends on the charges of the solute. We show successful applications of the DPBL formalism to computing the solvation free energies of isolated ions in water. Further developments of more accurately modified PB models are discussed.
Journal of Theoretical and Computational Chemistry 05/2014; 13(03). · 0.52 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We derive a general mean-field theory of inhomogeneous polymer dynamics; a theory whose form has been speculated and widely applied, but not heretofore derived. Our approach involves a functional integral representation of a Martin-Siggia-Rose (MSR) type description of the exact many-chain dynamics. A saddle point approximation to the generating functional, involving conditions where the MSR action is stationary with respect to a collective density field ρ and a conjugate MSR response field ϕ, produces the desired dynamical mean-field theory. Besides clarifying the proper structure of mean-field theory out of equilibrium, our results have implications for numerical studies of polymer dynamics involving hybrid particle-field simulation techniques such as the single-chain in mean-field method.
The Journal of Chemical Physics 02/2014; 140(8):084902. · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We introduce a stable and efficient complex Langevin (CL) scheme to enable the first direct numerical simulations of the coherent-states (CS) formulation of polymer field theory. In contrast with Edwards' well-known auxiliary-field (AF) framework, the CS formulation does not contain an embedded nonlinear, non-local, implicit functional of the auxiliary fields, and the action of the field theory has a fully explicit, semi-local, and finite-order polynomial character. In the context of a polymer solution model, we demonstrate that the new CS-CL dynamical scheme for sampling fluctuations in the space of coherent states yields results in good agreement with now-standard AF-CL simulations. The formalism is potentially applicable to a broad range of polymer architectures and may facilitate systematic generation of trial actions for use in coarse-graining and numerical renormalization-group studies.
The Journal of Chemical Physics 01/2014; 140(2):024905. · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We study the variation of the dielectric response of ionic aqueous solutions as function of their ionic strength. The effect of salt on the dielectric constant appears through the coupling between ions and dipolar water molecules. On a mean-field level, we account for any internal charge distribution of particles. The dipolar degrees of freedom are added to the ionic ones and result in a generalization of the Poisson-Boltzmann (PB) equation called the Dipolar PB (DPB). By looking at the DPB equation around a fixed point-like ion, a closed-form formula for the dielectric constant is obtained. We express the dielectric constant using the "hydration length" that characterizes the hydration shell of dipoles around ions, and thus the strength of the dielectric decrement. The DPB equation is then examined for three additional cases: mixture of solvents, polarizable medium, and ions of finite size. Employing field-theoretical methods, we expand the Gibbs free-energy to first order in a loop expansion and calculate self-consistently the dielectric constant. For pure water, the dipolar fluctuations represent an important correction to the mean-field value and good agreement with the water dielectric constant is obtained. For ionic solutions we predict analytically the dielectric decrement that depends on the ionic strength in a nonlinear way. Our prediction fits rather well a large range of concentrations for different salts using only one fit parameter related to the size of ions and dipoles. A linear dependence of the dielectric constant on the salt concentration is observed at low salinity, and a noticeable deviation from linearity can be seen for ionic strength above 1 M, in agreement with experiments.
The Journal of Chemical Physics 10/2013; 139(16):164909. · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: In 1969, Edwards and Freed adapted the ``coherent state'' methods
employed in the second quantization formalism of quantum many-body
theory to study polymer networks. Since its introduction into polymer
science, this formalism has been largely neglected and to our knowledge,
has never been applied as a basis for numerical simulations, even for
linear polymers. However, in contrast to the Edwards auxiliary-field
framework, this alternative polymer field theory has several attractive
features, including an action or effective Hamiltonian with an explicit,
finite-order, and semi-local polynomial character. We thus revisited the
CS formalism and show that these characteristics have advantages both
for analytical and numerical studies of linear polymers at equilibrium.
For this purpose, we developed a new Complex Langevin sampling scheme
that allows for simulations within the CS formalism with stable and
efficient numerical characteristics. We anticipate that this methodology
will facilitate efficient simulations of a wide range of systems,
including complicated branched and networked polymers and liquid
[Show abstract][Hide abstract] ABSTRACT: Amyloid proteins aggregate into polymorphic fibrils that damage tissues of the brain, nerves, and heart. Experimental and computational studies have examined the structural basis and the nucleation of short fibrils, but the ability to predict and precisely quantify the stability of larger aggregates has remained elusive. We established a complete classification of fibril shapes and developed a tool called CreateFibril to build such complex, polymorphic, modular structures automatically. We applied stability landscapes, a technique we developed to reveal reliable fibril structural parameters, to assess fibril stability. CreateFibril constructed HET-s, Aβ, and amylin fibrils up to 17 nm in length, and utilized a novel dipolar solvent model that captured the effect of dipole-dipole interactions between water and very large molecular systems to assess their aqueous stability. Our results validate experimental data for HET-s and Aβ, and suggest novel (to our knowledge) findings for amylin. In particular, we predicted the correct structural parameters (rotation angles, packing distances, hydrogen bond lengths, and helical pitches) for the one and three predominant HET-s protofilaments. We reveal and structurally characterize all known Aβ polymorphic fibrils, including structures recently classified as wrapped fibrils. Finally, we elucidate the predominant amylin fibrils and assert that native amylin is more stable than its amyloid form. CreateFibril and a database of all stable polymorphic fibril models we tested, along with their structural energy landscapes, are available at http://amyloid.cs.mcgill.ca.
[Show abstract][Hide abstract] ABSTRACT: We present McGenus, an algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. McGenus can treat sequences of up to 1000 bases and performs an advanced stochastic search of their minimum free energy structure allowing for non-trivial pseudoknot topologies. Specifically, McGenus uses a Monte Carlo algorithm with replica exchange for minimizing a general scoring function which includes not only free energy contributions for pair stacking, loop penalties, etc. but also a phenomenological penalty for the genus of the pairing graph. The good performance of the stochastic search strategy was successfully validated against TT2NE which uses the same free energy parametrization and performs exhaustive or partially exhaustive structure search, albeit for much shorter sequences (up to 200 bases). Next, the method was applied to other RNA sets, including an extensive tmRNA database, yielding results that are competitive with existing algorithms. Finally, it is shown that McGenus highlights possible limitations in the free energy scoring function. The algorithm is available as a web server at http://ipht.cea.fr/rna/mcgenus.php.
Nucleic Acids Research 12/2012; · 8.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The generation of defect-free polymer nanostructures by nanoimprinting methods is described. Long-range nanorheology and shorter-range surface energy effects can be efficiently combined to provide alignment of copolymer lamellae over several micrometers. As an example, a perpendicular organization with respect to circular tracks is shown, demonstrating the possibility of writing ordered radial nanostructures over large distances.
[Show abstract][Hide abstract] ABSTRACT: We study the variation of the dielectric response of a dielectric liquid
(e.g. water) when a salt is added to the solution. Employing field-theoretical
methods we expand the Gibbs free-energy to first order in a loop expansion and
calculate self-consistently the dielectric constant. We predict analytically
the dielectric decrement which depends on the ionic strength in a complex way.
Furthermore, a qualitative description of the hydration shell is found and is
characterized by a single length scale. Our prediction fits rather well a large
range of concentrations for different salts using only one fit parameter
related to the size of ions and dipoles.
[Show abstract][Hide abstract] ABSTRACT: We study block copolymers (BCP) on patterned substrates, where the top
polymer film surface is not constrained but is a free interface that adapts its
shape self-consistently. In particular, we investigate the combined effect of
the free interface undulations with the wetting of the BCP film as induced by
nano-patterned substrates. For a finite volume of BCP material, we find
equilibrium droplets composed of coexisting perpendicular and parallel lamellar
domains. The self-assembly of BCP on topographic patterned substrates was also
investigated and it was found that the free interface induces mixed
morphologies of parallel and perpendicular domains coupled with a non-flat free
interface. In both cases, the free interface relaxes the strong constraints
that would otherwise be imposed by a fixed top boundary (which is commonly used
in simulations), and affects strongly the BCP ordering. Our study has some
interesting consequences for experimental setups of graphoepitaxy and
Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics 09/2011; · 2.33 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present an extension of the self-consistent mean field theory for protein side-chain modeling in which solvation effects are included based on the Poisson-Boltzmann (PB) theory. In this approach, the protein is represented with multiple copies of its side chains. Each copy is assigned a weight that is refined iteratively based on the mean field energy generated by the rest of the protein, until self-consistency is reached. At each cycle, the variational free energy of the multi-copy system is computed; this free energy includes the internal energy of the protein that accounts for vdW and electrostatics interactions and a solvation free energy term that is computed using the PB equation. The method converges in only a few cycles and takes only minutes of central processing unit time on a commodity personal computer. The predicted conformation of each residue is then set to be its copy with the highest weight after convergence. We have tested this method on a database of hundred highly refined NMR structures to circumvent the problems of crystal packing inherent to x-ray structures. The use of the PB-derived solvation free energy significantly improves prediction accuracy for surface side chains. For example, the prediction accuracies for χ(1) for surface cysteine, serine, and threonine residues improve from 68%, 35%, and 43% to 80%, 53%, and 57%, respectively. A comparison with other side-chain prediction algorithms demonstrates that our approach is consistently better in predicting the conformations of exposed side chains.
The Journal of Chemical Physics 08/2011; 135(5):055104. · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Small Angle X-ray Scattering (SAXS) techniques are becoming more and more useful for structural biologists and biochemists, thanks to better access to dedicated synchrotron beamlines, better detectors and the relative easiness of sample preparation. The ability to compute the theoretical SAXS profile of a given structural model, and to compare this profile with the measured scattering intensity, yields crucial structural informations about the macromolecule under study and/or its complexes in solution. An important contribution to the profile, besides the macromolecule itself and its solvent-excluded volume, is the excess density due to the hydration layer. AquaSAXS takes advantage of recently developed methods, such as AquaSol, that give the equilibrium solvent density map around macromolecules, to compute an accurate SAXS/WAXS profile of a given structure and to compare it to the experimental one. Here, we describe the interface architecture and capabilities of the AquaSAXS web server (http://lorentz.dynstr.pasteur.fr/aquasaxs.php).
Nucleic Acids Research 06/2011; 39(Web Server issue):W184-9. · 8.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Loops are essential secondary structure elements in folded DNA and RNA molecules and proliferate close to the melting transition. Using a theory for nucleic acid secondary structures that accounts for the logarithmic entropy -c ln m for a loop of length m, we study homopolymeric single-stranded nucleic acid chains under external force and varying temperature. In the thermodynamic limit of a long strand, the chain displays a phase transition between a low-temperature/low-force compact (folded) structure and a high-temperature/high-force molten (unfolded) structure. The influence of c on phase diagrams, critical exponents, melting, and force extension curves is derived analytically. For vanishing pulling force, only for the limited range of loop exponents 2 < c ≲ 2.479 a melting transition is possible; for c ≤ 2 the chain is always in the folded phase and for 2.479 ≲ c always in the unfolded phase. A force-induced melting transition with singular behavior is possible for all loop exponents c < 2.479 and can be observed experimentally by single-molecule force spectroscopy. These findings have implications for the hybridization or denaturation of double-stranded nucleic acids. The Poland-Scheraga model for nucleic acid duplex melting does not allow base pairing between nucleotides on the same strand in denatured regions of the double strand. If the sequence allows these intra-strand base pairs, we show that for a realistic loop exponent c ≈ 2.1 pronounced secondary structures appear inside the single strands. This leads to a lower melting temperature of the duplex than predicted by the Poland-Scheraga model. Further, these secondary structures renormalize the effective loop exponent [Formula: see text], which characterizes the weight of a denatured region of the double strand, and thus affect universal aspects of the duplex melting transition.
The European Physical Journal E 06/2011; 34(6):1-15. · 2.18 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present TT2NE, a new algorithm to predict RNA secondary structures with pseudoknots. The method is based on a classification of RNA structures according to their topological genus. TT2NE is guaranteed to find the minimum free energy structure regardless of pseudoknot topology. This unique proficiency is obtained at the expense of the maximum length of sequences that can be treated, but comparison with state-of-the-art algorithms shows that TT2NE significantly improves the quality of predictions. Analysis of TT2NE's incorrect predictions sheds light on the need to study how sterical constraints limit the range of pseudoknotted structures that can be formed from a given sequence. An implementation of TT2NE on a public server can be found at http://ipht.cea.fr/rna/tt2ne.php.
Nucleic Acids Research 05/2011; 39(14):e93. · 8.81 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We propose a novel stochastic method to generate paths conditioned to start in an initial state and end in a given final state during a certain time t(f). These paths are weighted with a probability given by the overdamped Langevin dynamics. We show that these paths can be exactly generated by a non-local stochastic differential equation. In the limit of short times, we show that this complicated non-solvable equation can be simplified into an approximate local stochastic differential equation. For longer times, the paths generated by this approximate equation do not satisfy the correct statistics, but this can be corrected by an adequate reweighting of the trajectories. In all cases, the paths are statistically independent and provide a representative sample of transition paths. The method is illustrated on the one-dimensional quartic oscillator.
The Journal of Chemical Physics 05/2011; 134(17):174114. · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: The dominant reaction pathway is a rigorous framework to microscopically compute the most probable trajectories, in nonequilibrium transitions. In the low-temperature regime, such dominant pathways encode the information about the reaction mechanism and can be used to estimate nonequilibrium averages of arbitrary observables. On the other hand, at sufficiently high temperatures, the stochastic fluctuations around the dominant paths become important and have to be taken into account. In this work, we develop a technique to systematically include the effects of such stochastic fluctuations, to order k(B)T. This method is used to compute the probability for a transition to take place through a specific reaction channel and to evaluate the reaction rate.
The Journal of Chemical Physics 04/2011; 134(16):164109. · 3.12 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: We present NanoImprint lithography experiments and modeling of thin films of block copolymers (BCP). The NanoImprint technique is found to be an efficient tool not only to align lamellar phases perpendicularly to the substrate but also to get rid of in-plane defects over distances much larger than the natural lamellar periodicity. The modeling relies on self-consistent field calculations done in two- and three-dimensions and is found to be in good agreement with the experiments. It also offers some insight on the NanoImprint lithography setup and on the conditions required to perfectly ordered BCP lamellae.
[Show abstract][Hide abstract] ABSTRACT: We study non-equilibrium work relations for a space-dependent field with stochastic dynamics (model A). Jarzynski's equality is obtained through symmetries of the dynamical action in the path-integral representation. We derive a set of exact identities that generalize the fluctuation–dissipation relations to non-stationary and far-from-equilibrium situations. These identities are prone to experimental verification. Furthermore, we show that a well-studied invariance of the Langevin equation under supersymmetry, which is known to be broken when the external potential is time dependent, can be partially restored by adding to the action a term which is precisely Jarzynski's work. The work identities can then be retrieved as consequences of the associated Ward–Takahashi identities.
Journal of Physics A Mathematical and Theoretical 02/2011; 44(9):095002. · 1.77 Impact Factor