Conductivity of Concentrated Electrolytes.

The conductivity of ionic solutions is arguably their most important trait, being widely used in electrochemical, biochemical, and environmental applications. The Debye-Hückel-Onsager theory successfully predicts the conductivity at very low ionic concentrations of up to a few millimolars, but there is no well-established theory applicable at higher concentrations. We study the conductivity of ionic solutions using a stochastic density functional theory, paired with a modified Coulomb interaction that accounts for the hard-core repulsion between the ions. The modified potential suppresses unphysical, short-range electrostatic interactions, which are present in the Debye-Hückel-Onsager theory. Our results for the conductivity show very good agreement with experimental data up to 3 molars, without any fit parameters. We provide a compact expression for the conductivity, accompanied by a simple analytical approximation.

Sampling constrained stochastic trajectories using Brownian bridges.

We present a new method to sample conditioned trajectories of a system evolving under Langevin dynamics based on Brownian bridges. The trajectories are conditioned to end at a certain point (or in a certain region) in space. The bridge equations can be recast exactly in the form of a non-linear stochastic integro-differential equation. This equation can be very well approximated when the trajectories are closely bundled together in space, i.e., at low temperature, or for transition paths. The approximate equation can be solved iteratively using a fixed point method. We discuss how to choose the initial trajectories and show some examples of the performance of this method on some simple problems. This method allows us to generate conditioned trajectories with a high accuracy.

Conductance of concentrated electrolytes: Multivalency and the Wien effect.

The electric conductivity of ionic solutions is well understood at low ionic concentrations of up to a few millimolar but becomes difficult to unravel at higher concentrations that are still common in nature and technological applications. A model for the conductivity at high concentrations was recently put forth for monovalent electrolytes at low electric fields. The model relies on applying a stochastic density-functional theory and using a modified electrostatic pair-potential that suppresses unphysical, short-range electrostatic interactions. Here, we extend the theory to multivalent ions as well as to high electric fields where a deviation from Ohm's law known as the Wien effect occurs. Our results are in good agreement with experiments and recent simulations.

Parameterizing elastic network models to capture the dynamics of proteins.

Coarse-grained normal mode analyses of protein dynamics rely on the idea that the geometry of a protein structure contains enough information for computing its fluctuations around its equilibrium conformation. This geometry is captured in the form of an elastic network (EN), namely a network of edges between its residues. The normal modes of a protein are then identified with the normal modes of its EN. Different approaches have been proposed to construct ENs, focusing on the choice of the edges that they are comprised of, and on their parameterizations by the force constants associated with those edges. Here we propose new tools to guide choices on these two facets of EN. We study first different geometric models for ENs. We compare cutoff-based ENs, whose edges have lengths that are smaller than a cutoff distance, with Delaunay-based ENs and find that the latter provide better representations of the geometry of protein structures. We then derive an analytical method for the parameterization of the EN such that its dynamics leads to atomic fluctuations that agree with experimental B-factors. To limit overfitting, we attach a parameter referred to as flexibility constant to each atom instead of to each edge in the EN. The parameterization is expressed as a non-linear optimization problem whose parameters describe both rigid-body and internal motions. We show that this parameterization leads to improved ENs, whose dynamics mimic MD simulations better than ENs with uniform force constants, and reduces the number of normal modes needed to reproduce functional conformational changes.

Numerical Simulation of Finite-Temperature Field Theory for Interacting Bosons.

We report a stable and efficient complex Langevin sampling scheme for performing approximation-free numerical simulations directly on the path-integral coherent-states field theory for an assembly of interacting bosons. We apply the method to generate the λ line of critical phase transitions associated with Bose-Einstein condensation in a model ϕ^{4} scalar field theory. The new approach enjoys near-linear scaling in the resolved (d+1) spatial and imaginary-time dimensions and should be particularly efficient for the study of dense systems at low temperature.

Statistical Physics Approach to the Optimal Transport Problem.

Originally defined for the optimal allocation of resources, optimal transport (OT) has found many theoretical and practical applications in multiple domains of science and physics. In this Letter we develop a new method for solving the discrete version of this problem using techniques derived from statistical physics. We derive a strongly concave free energy function that captures the constraints of the OT problem at a finite temperature. Its maximum defines an optimal transport plan, or registration between the two discrete probability measures that are compared, as well as a pseudodistance between those measures that satisfies the triangular inequalities. The computation of this pseudodistance is fast and numerically stable. The temperature dependent OT pseudodistance is shown to decrease monotonically with respect to the inverse of the temperature and to converge to the standard OT distance at zero temperature, providing a robust framework for temperature annealing. We illustrate applications of this framework to the problem of image comparison.

A Polymer Model for the Quantitative Reconstruction of Chromosome Architecture from HiC and GAM Data.

It is widely believed that the folding of the chromosome in the nucleus has a major effect on genetic expression. For example, coregulated genes in several species have been shown to colocalize in space despite being far away on the DNA sequence. In this manuscript, we present a new, to our knowledge, method to model the three-dimensional structure of the chromosome in live cells based on DNA-DNA interactions measured in high-throughput chromosome conformation capture experiments and genome architecture mapping. Our approach incorporates a polymer model and directly uses the contact probabilities measured in high-throughput chromosome conformation capture experiments and genome architecture mapping experiments rather than estimates of average distances between genomic loci. Specifically, we model the chromosome as a Gaussian polymer with harmonic interactions and extract the coupling coefficients best reproducing the experimental contact probabilities. In contrast to existing methods, we give an exact expression of the contact probabilities at thermodynamic equilibrium. The Gaussian effective model reconstructed with our method reproduces experimental contacts with high accuracy. We also show how Brownian dynamics simulations of our reconstructed Gaussian effective model can be used to study chromatin organization and possibly give some clue about its dynamics.

Dielectric constant of ionic solutions: Combined effects of correlations and excluded volume.

The dielectric constant of ionic solutions is known to reduce with increasing ionic concentrations. However, the origin of this effect has not been thoroughly explored. In this paper, we study two such possible sources: long-range Coulombic correlations and solvent excluded-volume. Correlations originate from fluctuations of the electrostatic potential beyond the mean-field Poisson-Boltzmann theory, evaluated by employing a field-theoretical loop expansion of the free energy. The solvent excluded-volume, on the other hand, stems from the finite ion size, accounted for via a lattice-gas model. We show that both correlations and excluded volume are required in order to capture the important features of the dielectric behavior. For highly polar solvents, such as water, the dielectric constant is given by the product of the solvent volume fraction and a concentration-dependent susceptibility per volume fraction. The available solvent volume decreases as a function of ionic strength due the increasing volume fraction of ions. A similar decrease occurs for the susceptibility due to the correlations between the ions and solvent, reducing the dielectric response even further. Our predictions for the dielectric constant fit well with experiments for a wide range of concentrations for different salts in different temperatures, using a single fit parameter related to the ion size.

Absence of knots in known RNA structures.

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, however, have not yet been systematically screened for the occurrence of physical knots. We have accordingly undertaken the systematic profiling of the several thousand RNA structures present in the Protein Data Bank (PDB). The search identified no more than three deeply knotted RNA molecules. These entries are rRNAs of about 3,000 nt solved by cryo-EM. Their genuine knotted state is, however, doubtful based on the detailed structural comparison with homologs of higher resolution, which are all unknotted. Compared with the case of proteins and viral DNA, the observed incidence of knots in available RNA structures is, therefore, practically negligible. This fact suggests that either evolutionary selection or thermodynamic and kinetic folding mechanisms act toward minimizing the entanglement of RNA to an extent that is unparalleled by other types of biomolecules. A possible general strategy for designing synthetic RNA sequences capable of self-tying in a twist-knot fold is finally proposed.

Numerical Encodings of Amino Acids in Multivariate Gaussian Modeling of Protein Multiple Sequence Alignments.

Residues in proteins that are in close spatial proximity are more prone to covariate as their interactions are likely to be preserved due to structural and evolutionary constraints. If we can detect and quantify such covariation, physical contacts may then be predicted in the structure of a protein solely from the sequences that decorate it. To carry out such predictions, and following the work of others, we have implemented a multivariate Gaussian model to analyze correlation in multiple sequence alignments. We have explored and tested several numerical encodings of amino acids within this model. We have shown that 1D encodings based on amino acid biochemical and biophysical properties, as well as higher dimensional encodings computed from the principal components of experimentally derived mutation/substitution matrices, do not perform as well as a simple twenty dimensional encoding with each amino acid represented with a vector of one along its own dimension and zero elsewhere. The optimum obtained from representations based on substitution matrices is reached by using 10 to 12 principal components; the corresponding performance is less than the performance obtained with the 20-dimensional binary encoding. We highlight also the importance of the prior when constructing the multivariate Gaussian model of a multiple sequence alignment.

RNA Base Pairing Determines the Conformations of RNA Inside Spherical Viruses.

Many simple RNA viruses enclose their genetic material by a protein shell called the capsid. While the capsid structures are well characterized for most viruses, the structure of RNA inside the shells and the factors contributing to it remain poorly understood. We study the impact of base pairing on the conformations of RNA and find that it undergoes a swollen coil to globule continuous transition as a function of the strength of the pairing interaction. We also observe a first order transition and kink profile as a function of RNA length. All these transitions could explain the different RNA profiles observed inside viral shells.

Ab initio sampling of transition paths by conditioned Langevin dynamics.

We propose a novel stochastic method to generate Brownian paths conditioned to start at an initial point and end at a given final point during a fixed time tf under a given potential U(x). These paths are sampled with a probability given by the overdamped Langevin dynamics. We show that these paths can be exactly generated by a local stochastic partial differential equation. This equation cannot be solved in general but we present several approximations that are valid either in the low temperature regime or in the presence of barrier crossing. We show that this method warrants the generation of statistically independent transition paths. It is computationally very efficient. We illustrate the method first on two simple potentials, the two-dimensional Mueller potential and the Mexican hat potential, and then on the multi-dimensional problem of conformational transitions in proteins using the "Mixed Elastic Network Model" as a benchmark.

Phase Behavior of DNA in the Presence of DNA-Binding Proteins.

To characterize the thermodynamical equilibrium of DNA chains interacting with a solution of nonspecific binding proteins, we implemented a Flory-Huggins free energy model. We explored the dependence on DNA and protein concentrations of the DNA collapse. For physiologically relevant values of the DNA-protein affinity, this collapse gives rise to a biphasic regime with a dense and a dilute phase; the corresponding phase diagram was computed. Using an approach based on Hamiltonian paths, we show that the dense phase has either a molten globule or a crystalline structure, depending on the DNA bending rigidity, which is influenced by the ionic strength. These results are valid at the thermodynamical equilibrium and therefore should be consistent with many biological processes, whose characteristic timescales range typically from 1 ms to 10 s. Our model may thus be applied to biological phenomena that involve DNA-binding proteins, such as DNA condensation with crystalline order, which occurs in some bacteria to protect their chromosome from detrimental factors; or transcription initiation, which occurs in clusters called transcription factories that are reminiscent of the dense phase characterized in this study.

Probing the binding affinity of amyloids to reduce toxicity of oligomers in diabetes.

MOTIVATION: Amyloids play a role in the degradation of ß-cells in diabetes patients. In particular, short amyloid oligomers inject themselves into the membranes of these cells and create pores that disrupt the strictly controlled flow of ions through the membranes. This leads to cell death. Getting rid of the short oligomers either by a deconstruction process or by elongating them into longer fibrils will reduce this toxicity and allow the ß-cells to live longer. RESULTS: We develop a computational method to probe the binding affinity of amyloid structures and produce an amylin analog that binds to oligomers and extends their length. The binding and extension lower toxicity and ß-cell death. The amylin analog is designed through a parsimonious selection of mutations and is to be administered with the pramlintide drug, but not to interact with it. The mutations (T9K L12K S28H T30K) produce a stable native structure, strong binding affinity to oligomers, and long fibrils. We present an extended mathematical model for the insulin-glucose relationship and demonstrate how affecting the concentration of oligomers with such analog is strictly coupled with insulin release and ß-cell fitness. AVAILABILITY AND IMPLEMENTATION: SEMBA, the tool to probe the binding affinity of amyloid proteins and generate the binding affinity scoring matrices and R-scores is available at: http://amyloid.cs.mcgill.ca

The elusive quest for RNA knots.

Physical entanglement, and particularly knots arise spontaneously in equilibrated polymers that are sufficiently long and densely packed. Biopolymers are no exceptions: knots have long been known to occur in proteins as well as in encapsidated viral DNA. The rapidly growing number of RNA structures has recently made it possible to investigate the incidence of physical knots in this type of biomolecule, too. Strikingly, no knots have been found to date in the known RNA structures. In this Point of View Article we discuss the absence of knots in currently available RNAs and consider the reasons why knots in RNA have not yet been found, despite the expectation that they should exist in Nature. We conclude by singling out a number of RNA sequences that, based on the properties of their predicted secondary structures, are good candidates for knotted RNAs.

Ionic profiles close to dielectric discontinuities: Specific ion-surface interactions.

We study, by incorporating short-range ion-surface interactions, ionic profiles of electrolyte solutions close to a non-charged interface between two dielectric media. In order to account for important correlation effects close to the interface, the ionic profiles are calculated beyond mean-field theory, using the loop expansion of the free energy. We show that how it is possible to overcome the well-known deficiency of the regular loop expansion close to the dielectric jump and treat the non-linear boundary conditions within the framework of field theory. The ionic profiles are obtained analytically to one-loop order in the free energy, and their dependence on different ion-surface interactions is investigated. The Gibbs adsorption isotherm as well as the ionic profiles is used to calculate the surface tension, in agreement with the reverse Hofmeister series. Consequently, from the experimentally measured surface tension, one can extract a single adhesivity parameter, which can be used within our model to quantitatively predict hard to measure ionic profiles.

McGenus: a Monte Carlo algorithm to predict RNA secondary structures with pseudoknots.

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.

Dynamics of polymers: a mean-field theory.

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.

Coherent states formulation of polymer field theory.

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.