arXiv subjects

Henri Orland

Publications and source records attributed to Henri Orland.

At least 55 records · Page 3Linked to original sources

arXiv2009

Dominant Folding Pathways of a Beta-Hairpin

We use the Dominant Reaction Pathway (DRP) approach to study the dynamics of the folding of a beta-hairpin, within a model which accounts for both native and non-native interactions. We compare the most probable folding pathways calculated with the DRP method with those obtained directly from molecular dynamics (MD) simulations. We find that the two approaches give completely consistent results. We investigate the effects of the non-native hydrophobic interactions on the folding dynamics found them to be small.

q-bio.BM↗

arXiv2009

Accelerated Sampling of Boltzmann distributions

The sampling of Boltzmann distributions by stochastic Markov processes, can be strongly limited by the crossing time of high (free) energy barriers. As a result, the system may stay trapped in metastable states, and the relaxation time to the equilibrium Boltzmann distribution may be very large compared to the available computational time. In this paper, we show how, by a simple modification of the Hamiltonian, one can dramatically decrease the relaxation time of the system, while retaining the same equilibrium distribution. The method is illustrated on the case of the one-dimensional double-well potential.

cond-mat.stat-mech↗

arXiv2009

Mechanism of thermal renaturation and hybridization of nucleic acids: Kramers process and universality in Watson-Crick base pairing

Renaturation and hybridization reactions lead to the pairing of complementary single-stranded nucleic acids. We present here a theoretical investigation of the mechanism of these reactions in vitro under thermal conditions (dilute solutions of single-stranded chains, in the presence of molar concentrations of monovalent salts and at elevated temperatures). The mechanism follows a Kramers' process, whereby the complementary chains overcome a potential barrier through Brownian motion. The barrier originates from a single rate-limiting nucleation event in which the first complementary base pairs are formed. The reaction then proceeds through a fast growth of the double helix. For the DNA of bacteriophages T7, T4 and $ϕ$X174 as well as for Escherichia coli DNA, the bimolecular rate $k_2$ of the reaction increases as a power law of the average degree of polymerization $ $ of the reacting single- strands: $k_2 \prop ^α$. This relationship holds for $100 \leq \leq 50 000$ with an experimentally determined exponent $α= 0.51 \pm 0.01$. The length dependence results from a thermodynamic excluded-volume effect. The reacting single-stranded chains are predicted to be in universal good solvent conditions, and the scaling law is determined by the relevant equilibrium monomer contact probability. The value theoretically predicted for the exponent is $α= 1-νθ_2$, where $ν$ is Flory's swelling exponent ($nu approx 0.588$) and $θ_2$ is a critical exponent introduced by des Cloizeaux ($θ_2 \approx 0.82$), yielding $α= 0.52 \pm 0.01$, in agreement with the experimental results.

q-bio.BM↗

arXiv2008

Kramers Theory for Conformational Transitions of Macromolecules

We consider the application of Kramers theory to the microscopic calculation of rates of conformational transitions of macromolecules. The main difficulty in such an approach is to locate the transition state in a huge configuration space. We present a method which identifies the transition state along the most probable reaction pathway. It is then possible to microscopically compute the activation energy, the damping coefficient, the eigenfrequencies at the transition state and obtain the rate, without any a-priori choice of a reaction coordinate. Our theoretical results are tested against the results of Molecular Dynamics simulations for transitions in a 2-dimensional double well and for the cis-trans isomerization of a linear molecule.

q-bio.BM↗

arXiv2008

Impact of loop statistics on the thermodynamics of RNA folding

Loops are abundant in native RNA structures and proliferate close to the unfolding transition. By including a statistical weight ~ l^{-c} for loops of length l in the recursion relation for the partition function, we show that the calculated heat capacity depends sensitively on the presence and value of the exponent c, even of short t-RNA. For homo-RNA we analytically calculate the critical temperature and critical exponents which exhibit a non-universal dependence on c.

cond-mat.soft↗

arXiv2008

Supersymmetry and Nonequilibrium Work Relations

We give a field-theoretic proof of the nonequilibrium work relations for a space dependent field with stochastic dynamics. The path integral representation and its symmetries allow us to derive Jarzynski's equality. In addition, we derive a set of exact identities that generalize the fluctuation-dissipation relations to far-from equilibrium situations. These identities are prone to experimental verification. Furthermore, we show that supersymmetry invariance of the Langevin equation, which is broken when the external potential is time-dependent, is partially restored by adding to the action a term which is precisely Jarzynski's work. Jarzynski's equality can also be deduced from this supersymmetry

cond-mat.stat-mech↗

arXiv2007

Dipolar Poisson-Boltzmann Equation: Ions and Dipoles Close to Charged Surfaces

We present an extension to the Poisson-Boltzmann model where the dipolar features of solvent molecules are taken explicitly into account. The formulation is derived at mean-field level and can be extended to any order in a systematic expansion. It is applied to a two-plate system with oppositely charged surfaces. The ion distribution and profiles in the dipolar order parameter are calculated and can result in a large correction to the inter-plate pressure.

cond-mat.soft↗

arXiv2006

Topological classification of RNA structures

We present a novel topological classification of RNA secondary structures with pseudoknots. It is based on the topological genus of the circular diagram associated to the RNA base-pair structure. The genus is a positive integer number, whose value quantifies the topological complexity of the folded RNA structure. In such a representation, planar diagrams correspond to pure RNA secondary structures and have zero genus, whereas non planar diagrams correspond to pseudoknotted structures and have higher genus. We analyze real RNA structures from the databases wwPDB and Pseudobase, and classify them according to their topological genus. We compare the results of our statistical survey with existing theoretical and numerical models. We also discuss possible applications of this classification and show how it can be used for identifying new RNA structural motifs.

q-bio.BM↗

arXiv2006

Real symmetric random matrices and replicas

Various ensembles of random matrices with independent entries are analyzed by the replica formalism in the large-N limit. A result on the Laplacian random matrix with Wigner-rescaling is generalized to arbitrary probability distribution.

cond-mat.stat-mech↗

arXiv2006

Are better conducting molecules more rigid?

We investigate the electronic origin of the bending stiffness of conducting molecules. It is found that the bending stiffness associated with electronic motion, which we refer to as electro-stiffness, $κ_{e}$, is governed by the molecular orbital overlap $t$ and the gap width $u$ between HOMO and LUMO levels, and behaves as $κ_{e}\sim t^{2}/\sqrt{u^2+t^{2}}$. To study the effect of doping, we analyze the electron filling-fraction dependence on $κ_{e}$ and show that doped molecules are more flexible. In addition, to estimate the contribution of $κ_{e}$ to the total stiffness, we consider molecules under a voltage bias, and study the length contraction ratio as a function of the voltage. The molecules are shown to be contracted or dilated, with $κ_{e}$ increasing nonlinearly with the applied bias.

cond-mat.soft↗

arXiv2005

Manning condensation in two dimensions

We consider a macroion confined to a cylindrical cell and neutralized by oppositely charged counterions. Exact results are obtained for the two-dimensional version of this problem, in which ion-ion and ion-macroion interactions are logarithmic. In particular, the threshold for counterion condensation is found to be the same as predicted by mean-field theory. With further increase of the macroion charge, a series of single-ion condensation transitions takes place. Our analytical results are expected to be exact in the vicinity of these transitions and are in very good agreement with recent Monte-Carlo simulation data.

cond-mat.soft↗

arXiv2005

Checking for optimal solutions in some $NP$-complete problems

For some weighted $NP$-complete problems, checking whether a proposed solution is optimal is a non-trivial task. Such is the case for the celebrated traveling salesman problem, or the spin-glass problem in 3 dimensions. In this letter, we consider the weighted tripartite matching problem, a well known $NP$-complete problem. We write mean-field finite temperature equations for this model, and show that they become exact at zero temperature. As a consequence, given a possible solution, we propose an algorithm which allows to check in a polynomial time if the solution is indeed optimal. This algorithm is generalized to a class of variants of the multiple traveling salesmen problem.

cond-mat.stat-mech↗

arXiv2004

Generalized Poland-Scheraga model for DNA hybridization

The Poland-Scheraga (PS) model for the helix-coil transition of DNA considers the statistical mechanics of the binding (or hybridization) of two complementary strands of DNA of equal length, with the restriction that only bases with the same index along the strands are allowed to bind. In this paper, we extend this model by relaxing these constraints: We propose a generalization of the PS model which allows for the binding of two strands of unequal lengths $N_{1}$ and $N_{2}$ with unrelated sequences. We study in particular (i) the effect of mismatches on the hybridization of complementary strands (ii) the hybridization of non complementary strands (as resulting from point mutations) of unequal lengths $N_{1}$ and $N_{2}$. The use of a Fixman-Freire scheme scales down the computational complexity of our algorithm from $O(N_{1}^{2}N_{2}^{2})$ to $O(N_{1}N_{2})$.The simulation of complementary strands of a few kbps yields results almost identical to the PS model. For short strands of equal or unequal lengths, the binding displays a strong sensitivity to mutations. This model may be relevant to the experimental protocol in DNA microarrays, and more generally to the molecular recognition of DNA fragments. It also provides a physical implementation of sequence alignments.

q-bio.BM↗

arXiv2004

Electric response of DNA hairpins to magnetic fields

We study the electric properties of single-stranded DNA molecules with hairpin-like shapes in the presence of a magnetic flux. It is shown that the current amplitude can be modulated by the applied field. The details of the electric response strongly depend on the twist angles. The current exhibits periodicity for geometries where the flux through the plaquettes of the ladder can be cancelled pairwise (commensurate twist). Further twisting the geometry and changing its length causes complex aperiodic oscillations. We also study persistent currents: They reduce to simple harmonic oscillations if the system is commensurate, otherwise deviations occur due to the existence of closed paths leading to a washboard shape.

cond-mat.mes-hall↗

arXiv2004

Generalized Poland-Scheraga model for supercoiled DNA

The Poland-Scheraga (PS) model for the helix-coil transition of DNA considers the statistical mechanics of the thermally induced binding of two complementary strands of DNA. In this paper, we show how to modify the PS model when a torque is applied to the extremities of DNA: We propose a simple model for the energy of twisted DNA and compute the entropy of a loop, subject to angular constraints (supercoiling). The denaturation curves are shifted towards lower or higher temperatures depending on the sign of the torque, and the UV absorption peaks are softened. The properties of supercoiled DNA can be deduced through the use of a numerical Legendre transform. In the homogeneous case, we find that for weak supercoiling, the phenomenological quadratic law relating the torsional energy to the number of unpaired bases is recovered.

q-bio.BM↗

arXiv2003

Field Theory of Polymers: Escaping the Sign Problem

We examine statistical field theories of polymeric fluids in view of performing numerical simulations. The partition function of these systems can be expressed as a functional integral over real density fields. The introduction of density field variables serves to decouple interactions among non-bonded monomers, and renders the resulting effective Hamiltonian H for the field theory real and the Boltzmann factor $\exp (-H)$ positive definite. This is in contrast with conventional (Edwards) field-theories expressed in terms of chemical potentials that have complex H. The density field theory involves the calculation of an intermediate functional integral, which provides the entropy of the polymer fluid at a fixed density profile. This functional integral is positive definite and we show that in the thermodynamic limit of large systems, it is dominated by saddle points of the integrand. This procedure side-steps the "sign problem" in the chemical potential field formulation. The formalism is illustrated in the context of models of flexible polymers. We discuss the implications for field-theoretic computer simulations of polymeric fluids.

cond-mat.stat-mech↗

arXiv2002

Variational charge renormalization in charged systems

We apply general variational techniques to the problem of the counterion distribution around highly charged objects where strong condensation of counterions takes place. Within a field-theoretic formulation using a fluctuating electrostatic potential, the concept of surface-charge renormalization is recovered within a simple one-parameter variational procedure. As a test, we reproduce the Poisson-Boltzmann surface potential for a single charge planar surface both in the weak-charge and strong-charge regime. We then apply our techniques to non-planar geometries where closed-form solutions of the non-linear Poisson-Boltzmann equation are not available. In the cylindrical case, the Manning charge renormalization result is obtained in the limit of vanishing salt concentration. However, for intermediate salt concentrations a slow crossover to the non-charge-renormalized regime (at high salt) is found with a quasi-power-law behavior which helps to understand conflicting experimental and theoretical results for the electrostatic persistence length of polyelectrolytes. In the spherical geometry charge renormalization is only found at intermediate salt concentrations.

cond-mat.soft↗

arXiv2002

On the Remarkable Spectrum of a Non-Hermitean Random Matrix Model

A non-Hermitean random matrix model proposed a few years ago has a remarkably intricate spectrum. Various attempts have been made to understand the spectrum, but even its dimension is not known. Using the Dyson-Schmidt equation, we show that the spectrum consists of a non-denumerable set of lines in the complex plane. Each line is the support of the spectrum of a periodic Hamiltonian, obtained by the infinite repetition of any finite sequence of the disorder variables. Our approach is based on the ``theory of words.'' We make a complete study of all 4-letter words. The spectrum is complicated because our matrix contains everything that will ever be written in the history of the universe, including this particular paper.

math-ph↗