Physique des polymères | EPFL Graph Search

La physique des polymères s'intéresse aux propriétés des matériaux formés de longues molécules, assemblages en chaînes de dizaines de molécules élémentaires : les polymères. Ces molécules peuvent être observées à l'état solide, liquide, en solution, à l'état colloïdal ou confinées à une interface. Leurs propriétés physiques très particulières ont conduit au développement d'outils théoriques spécifiques et à l'apparition de cette nouvelle branche de la physique aux applications nombreuses. La physique des polymères et la chimie des polymères font partie de la science des polymères. Polymère en solution Les premiers éclairages théoriques importants concernant les polymères fondus ou en solution ont été fournis par la physique statistique. Du fait de la géométrie particulière des molécules, on comprend aujourd'hui mieux leurs propriétés que celle de certains liquides "simples" comme l'eau. C'est le modèle physique décrivant les polymères le plus simple. On considère que chaque monomère a une longueur fixée a et est orienté de manière aléatoire, toutes les directions étant équiprobables (matériau isotrope). Ainsi, la géométrie d'une chaîne est équivalente à celle d'une marche aléatoire simple à 3 dimensions. Dans ce cas, on peut montrer que pour un grand nombre de pas, la distance entre les deux extrémités de la chaîne suit une loi gaussienne, d'où le nom du modèle. Ce modèle néglige toutefois toutes les interactions entre monomères pouvant induire des corrélations entre les orientations. L'organisation spatiale d'un polymère est très étendue. Comme dans une structure comme la tour Eiffel, une grande partie de l'espace est cependant vide (ou contient de l'air pour la tour Eiffel et du solvant pour un polymère). On peut malgré tout définir fonctionnellement et mathématiquement l'étendue spatiale occupée par un polymère à travers son rayon de giration. Mathématiquement, il s'agit de la distance moyenne entre une extrémité de la chaîne et le centre de masse de la structure.

From polymers to gene regulation

Aleksandre Japaridze

DNA molecule is the fundamental component of every living organism, since it encodes the hereditary information. Although the genetic code of almost 200 species has been sequenced, the direct connection between gene sequence, DNA structure and biological function remains poorly understood. The aim of this thesis was to investigate the connection between DNA function and structure. Throughout the thesis we will discuss experiments testing the link between different physical properties of DNA with its biological function. For this purpose we used atomic force microscopy (AFM), a high resolution imaging technique. The first chapter is devoted to explain the basic concepts of AFM technique, as well as the composition and structure of DNA molecules. We also describe some of the polymer physics models of DNA, defining basic quantities like the persistence and the critical exponent. In chapter 2 we discuss experiments, in which we studied changes in the physical properties of DNA molecules, when bound to the substrate surface with various methods. We show that, when DNA is strongly bound to the surface, it retains its physiological B-form. On contrary, when weakly bound, a conformational B-to-A-form transition takes place. We also discuss a novel experimental method, combining nanometer sized PDMS slits with AFM, for studying DNA in geometrical confinement. When DNA is weakly confined, DNA persistence length increases, molecules elongate and adopt more anisotropic shapes. Under stronger confinement, DNA hairpins form. In chapter 3 we study binding of staining dyes, proteins and RNA polymerase (RNAP) to DNA molecules. First we show that DNA physical properties are significantly affected when stained with dyes. Depending on the dye binding mode, either the contour length, or the persistence length or both simultaneously change. We move further and investigate the role of protein amino acids and DNA sequence in the formation of nucleoprotein complexes. On the example of EspR protein, a key virulence regulator in Mycobacterium tuberculosis (MTB), we show that single amino acid mutations, lead to lower DNA binding affinity. These mutations also impair the formation of higher order protein-DNA complexes, silencing the MTB virulence. Afterwards, on the examples of RNAP and H-NS protein, we show the importance of DNA sequence for the binding and higher order oligomerization. By introducing DNA mutations disrupting the helical phasing between RNAP binding sites in the fis promoter sequence, we significantly lower the RNAP binding affinity. The helical phasing of the binding sites somehow coordinates the cooperative binding of RNAP to the promoter. Finally on the model of H-NS protein, we show how different spatial arrangements of strong binding sites for an architectural protein in the DNA, determine the final 3D structure of the assembled nucleoprotein complex. The final chapter, is fully devoted to the study of a completely new type of DNA organisation, which we call Hyperplectonemes. Hyperplectonemes are very ordered DNA structures, formed by large supercoiled molecules, in the presence of attractive DNA-DNA potential. First, we describe their structure and its dependence on various environmental factors, than their binding to nucleoid associated proteins. We argue that this emerging DNA organisation is the basic structure of the bacterial chromatin, which is further modulated by numerous DNA binding and condensing proteins in vivo.

EPFL2015

Looping probabilities of elastic chains: A path integral approach

John Maddocks, Ludovica Cotta-Ramusino

We consider an elastic chain at thermodynamic equilibrium with a heat bath, and derive an approximation to the probability density function, or pdf, governing the relative location and orientation of the two ends of the chain. Our motivation is to exploit continuum mechanics models for the computation of DNA looping probabilities, but here we focus on explaining the novel analytical aspects in the derivation of our approximation formula. Accordingly, and for simplicity, the current presentation is limited to the illustrative case of planar configurations. A path integral formalism is adopted, and, in the standard way, the first approximation to the looping pdf is obtained from a minimal energy configuration satisfying prescribed end conditions. Then we compute an additional factor in the pdf which encompasses the contributions of quadratic fluctuations about the minimum energy configuration along with a simultaneous evaluation of the partition function. The original aspects of our analysis are twofold. First, the quadratic Lagrangian describing the fluctuations has cross-terms that are linear in first derivatives. This, seemingly small, deviation from the structure of standard path integral examples complicates the necessary analysis significantly. Nevertheless, after a nonlinear change of variable of Riccati type, we show that the correction factor to the pdf can still be evaluated in terms of the solution to an initial value problem for the linear system of Jacobi ordinary differential equations associated with the second variation. The second novel aspect of our analysis is that we show that the Hamiltonian form of these linear Jacobi equations still provides the appropriate correction term in the inextensible, unshearable limit that is commonly adopted in polymer physics models of, e. g. DNA. Prior analyses of the inextensible case have had to introduce nonlinear and nonlocal integral constraints to express conditions on the relative displacement of the end points. Our approximation formula for the looping pdf is of quite general applicability as, in contrast to most prior approaches, no assumption is made of either uniformity of the elastic chain, nor of a straight intrinsic shape. If the chain is uniform the Jacobi system evaluated at certain minimum energy configurations has constant coefficients. In such cases our approximate pdf can be evaluated in an entirely explicit, closed form. We illustrate our analysis with a planar example of this type and compute an approximate probability of cyclization, i.e., of forming a closed loop, from a uniform elastic chain whose intrinsic shape is an open circular arc.

2010

On The Stochastic Modeling Of Rigid Body Systems With Application To Polymer Dynamics

John Maddocks

The stochastic equations of motion for a system of interacting rigid bodies in a solvent are formulated and studied. Three-dimensional bodies of arbitrary shape, with arbitrary couplings between translational and rotational degrees of freedom, as arise in coarse-grained models of polymers, are considered. Beginning from an Euler-Langevin form of the equations, two different, properly invariant, Hamilton-Langevin forms are derived and studied together with various associated measures. Under different conditions depending on the choice of rotational coordinates, the canonical measure is shown to be a stationary solution of an associated Fokker-Planck equation and to always factorize into independent measures on configuration and velocity spaces. Explicit expressions are given for these measures, along with a certain Jacobian factor associated with the three-dimensional rotation group. When specialized to a fully coupled, quadratic model of a stiff polymer such as DNA, our results yield an explicit characterization of the complete set of model parameters.

2010

Looping probabilities of elastic chains: A path integral approach

John Maddocks, Ludovica Cotta-Ramusino

2010

From polymers to gene regulation

Aleksandre Japaridze

EPFL2015