arXiv subjects

Nicolas Destainville

Publications and source records attributed to Nicolas Destainville.

At least 37 records · Page 2Linked to original sources

arXiv2014

Estimating the asymptotics of solid partitions

We study the asymptotic behavior of solid partitions using transition matrix Monte Carlo simulations. If $p_3(n)$ denotes the number of solid partitions of an integer $n$, we show that $\lim_{n\rightarrow\infty} n^{-3/4} \log p_3(n)\sim 1.822\pm 0.001$. This shows clear deviation from the value $1.7898$, attained by MacMahon numbers $m_3(n)$, that was conjectured to hold for solid partitions as well. In addition, we find estimates for other sub-leading terms in $\log p_3(n)$. In a pattern deviating from the asymptotics of line and plane partitions, we need to add an oscillatory term in addition to the obvious sub-leading terms. The period of the oscillatory term is proportional to $n^{1/4}$, the natural scale in the problem. This new oscillatory term might shed some insight into why partitions in dimensions greater than two do not admit a simple generating function.

cond-mat.stat-mech↗

arXiv2013

Attractive asymmetric inclusions in elastic membranes under tension: cluster phases and membrane invaginations

Up-down asymmetric inclusions impose a local, spontaneous curvature to an elastic membrane. When several of them are inserted in a same membrane, they feel effective forces mediated by the membrane, both of elastic and entropic nature. Following an approach initiated by Dommersnes and Fournier in the vanishing tension case [Eur. Phys. J. B 12, 9 (1999)], and also using a pseudo-analytical micellization theory, we derive the statistical mechanics of asymmetric inclusion assemblies when they are also subject to an additional short-range, attractive interaction. Our main conclusion is that generically, when the membrane is under tension, these inclusions live in small clusters at equilibrium, leading to local membrane invaginations. We also propose a novel curvature-induced demixing mechanism: when inclusions imposing local curvatures of opposite sign coexist, they tend to demix in distinct clusters under realistic conditions. This work has potential implications in the context of the thermodynamics of proteins embedded in biological lipid bilayers.

cond-mat.soft↗

arXiv2013

Slow closure of denaturation bubbles in DNA: twist matters

The closure of long equilibrated denaturation bubbles in DNA is studied using Brownian dynamics simulations. A minimal mesoscopic model is used where the double-helix is made of two interacting bead-spring freely rotating strands, with a non-zero torsional modulus in the duplex state, $κ_ϕ=$200 to 300 kT. For DNAs of lengths N=40 to 100 base-pairs (bps) with a large initial bubble in their middle, long closure times of 0.1 to 100 microseconds are found. The bubble starts winding from both ends until it reaches a 10 bp metastable state. The final closure is limited by three competing mechanisms depending on $κ_ϕ$ and N: arms diffusion until their alignment, bubble diffusion along the DNA until one end is reached, or local Kramers process (crossing over a torsional energy barrier). For clamped ends or long DNAs, the closure occurs via this latter temperature activated mechanism, yielding for the first time a good quantitative agreement with experiments.

cond-mat.soft↗

arXiv2012

Mesoscopic models for DNA stretching under force: new results and comparison to experiments

Single molecule experiments on B-DNA stretching have revealed one or two structural transitions, when increasing the external force. They are characterized by a sudden increase of DNA contour length and a decrease of the bending rigidity. It has been proposed that the first transition, at forces of 60--80 pN, is a transition from B to S-DNA, viewed as a stretched duplex DNA, while the second one, at stronger forces, is a strand peeling resulting in single stranded DNAs (ssDNA), similar to thermal denaturation. But due to experimental conditions these two transitions can overlap, for instance for poly(dA-dT). We derive analytical formula using a coupled discrete worm like chain-Ising model. Our model takes into account bending rigidity, discreteness of the chain, linear and non-linear (for ssDNA) bond stretching. In the limit of zero force, this model simplifies into a coupled model already developed by us for studying thermal DNA melting, establishing a connexion with previous fitting parameter values for denaturation profiles. We find that: (i) ssDNA is fitted, using an analytical formula, over a nanoNewton range with only three free parameters, the contour length, the bending modulus and the monomer size; (ii) a surprisingly good fit on this force range is possible only by choosing a monomer size of 0.2 nm, almost 4 times smaller than the ssDNA nucleobase length; (iii) mesoscopic models are not able to fit B to ssDNA (or S to ss) transitions; (iv) an analytical formula for fitting B to S transitions is derived in the strong force approximation and for long DNAs, which is in excellent agreement with exact transfer matrix calculations; (v) this formula fits perfectly well poly(dG-dC) and $λ$-DNA force-extension curves with consistent parameter values; (vi) a coherent picture, where S to ssDNA transitions are much more sensitive to base-pair sequence than the B to S one, emerges.

cond-mat.soft↗

arXiv2012

Strand diffusion-limited closure of denaturation bubbles in DNA

The closure dynamics of a pre-equilibrated DNA denaturation bubble is studied using both Brownian dynamics simulations and an analytical approach. The numerical model consists of two semi-flexible interacting single strands (ssDNA) and a bending modulus which depends on the base-pair state, with double-strand DNA (dsDNA) segments being 50 times stiffer than ssDNA ones. For DNA lengths from N=20 to 100 base-pairs (bp) and initial bubble sizes of N-6 bp, long closure times of 0.1 to 4 microseconds are found, following a scaling law in N^2.4. The bubble starts to close by a fast zipping which stops when the bubble reaches a highly bent metastable state of length around 10 bp. The limiting final step to complete closure is controlled by the dsDNA "arms" rotational diffusion, with closure occurring once they are nearly aligned. The central role of chain bending, which cannot be accounted for in one-dimensional models, is thus illuminated.

cond-mat.soft↗

arXiv2011

Clusters of proteins in bio-membranes: insights into the roles of interaction potential shapes and of protein diversity

It has recently been proposed that proteins embedded in lipidic bio-membranes can spontaneously self-organize into stable small clusters, or membrane nano-domains, due to the competition between short-range attractive and longer-range repulsive forces between proteins, specific to these systems. In this paper, we carry on our investigation, by Monte Carlo simulations, of different aspects of cluster phases of proteins in bio-membranes. First, we compare different long-range potentials (including notably three-body terms) to demonstrate that the existence of cluster phases should be quite generic. Furthermore, a real membrane contains hundreds of different protein species that are far from being randomly distributed in these nano-domains. We take this protein diversity into account by modulating protein-protein interaction potentials both at short and longer range. We confirm theoretical predictions in terms of biological cluster specialization by deciphering how clusters recruit only a few protein species. In this respect, we highlight that cluster phases can turn out to be an advantage at the biological level, for example by enhancing the cell response to external stimuli.

cond-mat.soft↗

arXiv2010

Probing DNA conformational changes with high temporal resolution by Tethered Particle Motion

The Tethered Particle Motion (TPM) technique informs about conformational changes of DNA molecules, e.g. upon looping or interaction with proteins, by tracking the Brownian motion of a particle probe tethered to a surface by a single DNA molecule and detecting changes of its amplitude of movement. We discuss in this context the time resolution of TPM, which strongly depends on the particle-DNA complex relaxation time, i.e. the characteristic time it takes to explore its configuration space by diffusion. By comparing theory, simulations and experiments, we propose a calibration of TPM at the dynamical level: we analyze how the relaxation time grows with both DNA contour length (from 401 to 2080 base pairs) and particle radius (from 20 to 150~nm). Notably we demonstrate that, for a particle of radius 20~nm or less, the hydrodynamic friction induced by the particle and the surface does not significantly slow down the DNA. This enables us to determine the optimal time resolution of TPM in distinct experimental contexts which can be as short as 20~ms.

cond-mat.soft↗

arXiv2010

An alternative scenario for the formation of specialized protein nano-domains (cluster phases) in biomembranes

We discuss a realistic scenario, accounting for the existence of sub-micrometric protein domains in cell membranes. At the biological level, such membrane domains have been shown to be specialized, in order to perform a determined biological task, in the sense that they gather one or a few protein species out of the hundreds of different ones that a cell membrane may contain. By analyzing the balance between mixing entropy and protein affinities, we propose that such protein sorting in distinct domains can be explained without appealing to pre-existing lipidic micro-phase separations, as in the lipid raft scenario. We show that the proposed scenario is compatible with known physical interactions between membrane proteins, even if thousands of different species coexist.

cond-mat.soft↗

arXiv2010

Quantum algorithm for exact Monte Carlo sampling

We build a quantum algorithm which uses the Grover quantum search procedure in order to sample the exact equilibrium distribution of a wide range of classical statistical mechanics systems. The algorithm is based on recently developed exact Monte Carlo sampling methods, and yields a polynomial gain compared to classical procedures.

quant-ph↗

arXiv2010

Statistical mechanics and dynamics of two supported stacked lipid bilayers

The statistical physics and dynamics of double supported bilayers are studied theoretically. The main goal in designing double supported lipid bilayers is to obtain model systems of biomembranes: the upper bilayer is meant to be almost freely floating, the substrate being screened by the lower bilayer. The fluctuation-induced repulsion between membranes and between the lower membrane and the wall are explicitly taken into account using a Gaussian variational approach. It is shown that the variational parameters, the "effective" adsorption strength and the average distance to the substrate, depend strongly on temperature and membrane elastic moduli, the bending rigidity and the microscopic surface tension, which is a signature of the crucial role played by membrane fluctuations. The range of stability of these supported membranes is studied, showing a complex dependence on bare adsorption strengths. In particular, the experimental conditions to have an upper membrane slightly perturbed by the lower one and still bound to the surface are found. Included in the theoretical calculation of the damping rates associated with membrane normal modes are hydrodynamic friction by the wall and hydrodynamic interactions between both membranes.

cond-mat.soft↗

arXiv2009

Microscopic mechanism for experimentally observed anomalous elasticity of DNA in 2D

By exploring a recent model [Palmeri, J., M. Manghi, and N. Destainville. 2007. Phys. Rev. Lett. 99:088103] where DNA bending elasticity, described by the wormlike chain model, is coupled to base-pair denaturation, we demonstrate that small denaturation bubbles lead to anomalies in the flexibility of DNA at the nanometric scale, when confined in two dimensions (2D), as reported in atomic force microscopy (AFM) experiments [Wiggins, P. A., et al. 2006. Nature Nanotech. 1:137-141]. Our model yields very good fits to experimental data and quantitative predictions that can be tested experimentally. Although such anomalies exist when DNA fluctuates freely in three dimensions (3D), they are too weak to be detected. Interactions between bases in the helical double-stranded DNA are modified by electrostatic adsorption on a 2D substrate, which facilitates local denaturation. This work reconciles the apparent discrepancy between observed 2D and 3D DNA elastic properties and points out that conclusions about the 3D properties of DNA (and its companion proteins and enzymes) do not directly follow from 2D experiments by AFM.

cond-mat.stat-mech↗

arXiv2008

Coupling between denaturation and chain conformations in DNA: stretching, bending, torsion and finite size effects

We develop further a statistical model coupling denaturation and chain conformations in DNA (Palmeri J, Manghi M and Destainville N 2007 Phys. Rev. Lett. 99 088103). Our Discrete Helical Wormlike Chain model takes explicitly into account the three elastic degrees of freedom, namely stretching, bending and torsion of the polymer. By integrating out these external variables, the conformational entropy contributes to bubble nucleation (opening of base-pairs), which sheds light on the DNA melting mechanism. Because the values of monomer length, bending and torsional moduli differ significantly in dsDNA and ssDNA, these effects are important. Moreover, we explore in this context the role of an additional loop entropy and analyze finite-size effects in an experimental context where polydA-polydT is clamped by two G-C strands, as well as for free polymers.

cond-mat.soft↗

arXiv2008

Comment to the Paper of Michael J. Saxton: "A Biological Interpretation of Transient Anomalous Subdiffusion. I. Qualitative Model"

In a recent paper, Michael J. Saxton proposes to interpret as anomalous diffusion the occurrence of apparent transient sub-diffusive regimes in mean-squared displacements (MSD) plots, calculated from experimental trajectories of molecules diffusing in living cells, acquired by Single Particle (or Molecule) Tracking techniques (SPT or SMT). In this Comment, without questioning the existence of sub-diffusive behaviors, which certainly play a key role in numbers of mechanisms in living systems, we point out that the data used by J.M. Saxton can as well be fitted by a simple law, resulting from confined diffusion at short times, with a slower free diffusion superimposed at larger times. When visualizing MSD plots, the transition from short-term diffusion confined in domains of size L, to slower, longer-term free diffusion, can be confused with anomalous diffusion over several orders of magnitude of time.

q-bio.SC↗

arXiv2008

Thermodynamics of nano-cluster phases: a unifying theory

We propose a unifying, analytical theory accounting for the self-organization of colloidal systems in nano- or micro-cluster phases. We predict the distribution of cluter sizes with respect to interaction parameters and colloid concentration. In particular, we anticipate a proportionality regime where the mean cluster size grows proportionally to the concentration, as observed in several experiments. We emphasize the interest of a predictive theory in soft matter, nano-technologies and biophysics.

cond-mat.soft↗

arXiv2007

Theory of fluorescence correlation spectroscopy at variable observation area for two-dimensional diffusion on a meshgrid

It has recently been proposed, with the help of numerical investigations, that fluorescence correlation spectroscopy at variable observation area can reveal the existence of a meshgrid of semi-permeable barriers hindering the two-dimensional diffusion of tagged particles, such as plasmic membrane constituents. We present a complete theory confirming and accounting for these findings. It enables a reliable, quantitative exploitation of experimental data from which the sub-wavelength mesh size can be extracted. Time scales at which fluorescence correlation spectroscopy must be performed experimentally are discussed in detail.

cond-mat.stat-mech↗

arXiv2007

Cluster phases of membrane proteins

A physical scenario accounting for the existence of size-limited submicrometric domains in cell membranes is proposed. It is based on the numerical investigation of the counterpart, in lipidic membranes where proteins are diffusing, of the recently discovered cluster phases in colloidal suspensions. I demonstrate that the interactions between proteins, namely short-range attraction and longer-range repulsion, make possible the existence of stable small clusters. The consequences are explored in terms of membrane organization and diffusion properties. The connection with lipid rafts is discussed and the apparent protein diffusion coefficient as a function of their concentration is analyzed.

cond-mat.soft↗

arXiv2007

Thermal denaturation of fluctuating finite DNA chains: the role of bending rigidity in bubble nucleation

Statistical DNA models available in the literature are often effective models where the base-pair state only (unbroken or broken) is considered. Because of a decrease by a factor of 30 of the effective bending rigidity of a sequence of broken bonds, or bubble, compared to the double stranded state, the inclusion of the molecular conformational degrees of freedom in a more general mesoscopic model is needed. In this paper we do so by presenting a 1D Ising model, which describes the internal base pair states, coupled to a discrete worm like chain model describing the chain configurations [J. Palmeri, M. Manghi, and N. Destainville, Phys. Rev. Lett. 99, 088103 (2007)]. This coupled model is exactly solved using a transfer matrix technique that presents an analogy with the path integral treatment of a quantum two-state diatomic molecule. When the chain fluctuations are integrated out, the denaturation transition temperature and width emerge naturally as an explicit function of the model parameters of a well defined Hamiltonian, revealing that the transition is driven by the difference in bending (entropy dominated) free energy between bubble and double-stranded segments. The calculated melting curve (fraction of open base pairs) is in good agreement with the experimental melting profile of polydA-polydT. The predicted variation of the mean-square-radius as a function of temperature leads to a coherent novel explanation for the experimentally observed thermal viscosity transition. Finally, the influence of the DNA strand length is studied in detail, underlining the importance of finite size effects, even for DNA made of several thousand base pairs.

cond-mat.soft↗

arXiv2006

Numerical entropy and phason elastic constants of plane random tilings with any 2D-fold symmetry

We perform Transition matrix Monte Carlo simulations to evaluate the entropy of rhombus tilings with fixed polygonal boundaries and 2D-fold rotational symmetry. We estimate the large-size limit of this entropy for D=4 to 10. We confirm analytic predictions of N. Destainville et al., J. Stat. Phys. 120, 799 (2005) and M. Widom et al., J. Stat. Phys. 120, 837 (2005), in particular that the large size and large D limits commute, and that entropy becomes insensible to size, phason strain and boundary conditions at large D. We are able to infer finite D and finite size scalings of entropy. We also show that phason elastic constants can be estimated for any D by measuring the relevant perpendicular space fluctuations.

cond-mat.stat-mech↗