DNA Topology | EPFL Graph Search

This thesis explores different aspects of DNA topology through experimental and numerical techniques. Topology is a vast mathematical field, that deals with the spatial properties of objects undergoing continuous deformations, but here it is restricted to the description of closed space curves such as rings, knots and catenanes. Topology is connected to practical problems in different domains including polymer physics, because a polymer chain is a type of space curve, whose statistical properties are affected by the closure of its ends; and biology, because the double-helical interwinding of the two strands formingDNA is described by topological concepts, and also because a closed DNA molecule can adopt complex topologies like knotted or catenated conformations in vivo. Both physical and biological aspects of topology are investigated in the three chapters of this thesis. Chapter 1 introduces on a general level the experimental techniques, numerical methods and topology concepts that are at the core of the presented research. Chapter 2 is an experimental study of the statistical properties of DNA rings adsorbed on surfaces, and imaged by atomic force microscopy (AFM). DNA rings of different sizes are first studied in a dilute state, allowing us to investigate the consequences of the circular topology on polymer physics of two-dimensional chains. We confirm certain theoretical results, e.g. the topological invariance of the scaling exponent in two dimensions; but we also propose new models taking into account the specificities of the problem, in particular the interplay between excluded volume effects and topology, for the description of standard polymer physics measures like the asphericity or the bond correlation function. In addition to isolated DNA rings, we study DNA rings in a semi-dilute state. Comparing the statistical properties of the DNA rings imaged by AFM with a numerical model, we formulate a simplified description of this system in terms of two dimensional pressurized vesicles. Finally, we study a last case, in which DNA rings are confined within circular boundaries in two dimensions. We show how confinement strongly affects the statistical properties of the DNA chains, and verify that our experimental system is a good model for polymer confinement by comparing the data with numerical simulations. In chapter 3, we use numerical simulations to study two other topological forms taken by closed DNA in vivo: catenanes and knots. In both cases, we analyze the conformations of these objects, in particular as a function of their torsional state, and find complex behaviors proper to these topologies: for example, the large scale supercoiling of toroidal catenanes, or the different response of left- and right-handed knots to torsion. We then focus on the activity of a class of enzymes called topoisomerases, that are able to change the topology of DNA molecules (e.g. by unknotting a DNA knot). In particular, we try to deduce how the structural properties of DNA knots and catenanes affect the activity of one of these enzymes called topo IV, and also simulate its activity. We show that our numerical model provides results that compare well with experimental data, and could therefore provide a basis for the design of new experiments. Finally, we present a new model for the simulation of the activity of another topoisomerase called gyrase, that is responsible for introducing supercoiling into DNA. This model includes a few essential features of the interaction between gyrase and DNA, which permit to efficiently reproduce experimental measurements.

Statistical Study of the Unfolding of Multimodular Proteins and their Energy Landscape by Atomic Force Microscopy

Fabrizio Benedetti

The aim of the present thesis is to investigate several aspects of: the proteins mechanics, interprotein interactions and to study also new techniques, theoretical and technical, to obtain and analyze the force spectroscopy experiments. The first section is dedicated to the statistical properties of the unfolding forces in a chain of homomeric multimodular proteins. The basic idea of this kind of statistic is to divide the peaks observed in a force extension curve in separate groups and then analyze these groups considering their position in the force curves. In fact in a multimodular homomeric protein the unfolding force is related to the number of not yet unfolded modules (we call it "N"). Such effect yields to a linear dependence of the most probable unfolding force of a peak on ln(N). We demonstrate how such dependence can be used to extract the kinetic parameters and how, ignoring it, could lead to significant errors. Following this topic we continue with non kinetic methods that, using the resampling from the rupture forces of any peak, could reconstruct the rupture forces for all the other peaks in a chain. Then a discussion about the Monte Carlo simulation for protein pulling is present. In fact a theoretical framework for such methodology has to be introduced to understand the various simulations done. In this chapter we also introduce a methodology to study the ligand receptor interactions when we directly functionalize the AFM tip and the substrate. In fact, in many of our experiments, we see a "cloud of points" in the force vs loading rate graph. We have modeled a system composed by "N" parallel springs, and studying the distribution of forces obtained in the force vs loading rate graph we have establish a procedure to restore the kinetic parameters used. Such procedure has then been used to discuss real experiments similar to biotin-avidin interaction. In the following chapter we discuss a first order approximation of the Bell-Evans model where a more explicit form of the potential is considered. In particular the dependence of the curvature of the potential on the applied force at the minimum and at the metastable state is considered. In the well known Bell-Evans model the prefactors of the transition rate are fixed at any force, however this is not what happen in nature, where the prefactors (that are the second local derivative of the interacting energy with respect to the reaction coordinate in its minimum and maximum) depend on the force applied. The results obtained with the force spectroscopy of the Laminin-binding-protein are discussed, in particular this protein showed a phase transition when the pH was changed. The behavior of this protein changes, from a normal WLC behavior to a plateau behavior. The analysis of the force spectroscopy curves shows a distribution of length where the maximum of the first prominent peak correspond to the full length of the protein. However, length that could be associated with dimers and trymers are also present in this distribution. Later a new approach to study the lock and key mechanism, using "handles" with a specific force extension pattern, is introduced. In particular handles of (I27)3 and (I27–SNase)3 were biochemically attached to: strept-actin molecules, biotin molecules, RNase and Angiogenin. The main idea is to have a system composed by "handle-(molecule A)-(molecule B)-handle" where the handles are covalently attached to the respective molecules and the two molecules "A and B" are attached by secondary bonds. This approach allows a better recognition of the protein-protein interaction enabling us to filter out spurious events. Doing a statistic on the rupture forces and comparing this with the statistic of the detachments of the system of the bare handles, we are able to extract the information of the interaction between the molecule A and B. The two last chapters are of more preliminary character that the previous part of the thesis. A section is dedicated to the estimation of effective mass and viscous drag of the cantilevers studied by autocorrelation and noise power spectrum. Usually the noise power spectrum method is the most used, however the autocorrelation should give approximately the same information. The parameters obtained are important in high frequency modulation techniques. In fact, they are needed to interpret the results. The results of these two methods show a good agreement in the estimation of the mass and the viscous drag of the various cantilever used. Afterwards a chapter is dedicated to the discussion of the force spectroscopy experiments using a low frequency modulation of the cantilever base. Such experiments allow us to record the phase and the amplitude shift of the modulation signal used. Using the amplitude channel we managed to restore the static force signal with a lower level of noise. Moreover these signals give us direct information about the dynamic stiffness and the lose of energy in the system, information that, using the standard technique would be difficult (or even impossible) to obtain.

EPFL2012

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

Scaling properties of DNA knots studied by atomic force microscopy

Erika Ercolini

The main subject of the present thesis is the experimental study of the scaling properties of DNA knots of different complexities by tapping mode atomic force microscopy (AFM) in air. Homo- or heterogeneous mixture of DNA knot types were deposited onto mica in regimes of (i) strong adsorption, which induces a kinetic trapping of the molecules, and of (ii) weak adsorption, which permits relaxation on the surface. The contour of each knotted molecule was analyzed by a box counting algorithm, giving the number of boxes containing a part of the molecule, N(L), as a function of the box size, L, allowing to recover the relation N(L) ≈ L-df, where df is the fractal dimension and ν = 1/df is the scaling exponent. This relationship is complicated by the presence of a persistence length of DNA (about 50 nm) which introduces a crossover from a rigid rod behavior to a self-avoiding walk behavior. In (i) the radius of gyration of the adsorbed DNA knot scales with the 3D Flory exponent ν ≈ 0.58 within error. In (ii), the value ν ≈ 0.66, intermediate between the 3D and 2D (ν = 3/4) exponents, was found, indicating an incomplete 2D relaxation or a different polymer universality class. A different analysis, where the fractal dimension was determined by a customized box counting algorithm giving the knot mass as a function of the box size, yielded compatible results. In the case of weak binding conditions, AFM images show evidence of the localization of knot crossings, which is an effect theoretically predicted for knotted polymers confined in two dimensions (flat knots). Part of this thesis is dedicated to a fascinating application of AFM: the imaging of biomolecules in an aqueous buffer. In particular, images of plasmids adsorbed to mica strong enough to be visualized and loosely enough to see them moving in consecutive scans will be shown. The possibility of imaging under buffer molecules loosely anchored to the substrate opens the way to the investigation of biological processes near physiological conditions. The first step of the study of homologous recombination will be presented. We will also show images concerning our study of the activity of topoisomerase I on supercoiled plasmids. Clusters of DNA molecules and proteins were found when imaging in presence of magnesium, in agreement with recent findings by AFM in air. The research on topoisomerases and their interactions with inhibitors or poisons is a hot topic, being these enzymes targets of anti-cancer drugs. Our study paves the way to the investigation of the activity of topoisomerase II, the enzyme which removes knots from DNA. Finally, the principles of static and dynamic light scattering, and the results of dynamic light scattering on latex beads of known size will be presented. Particular emphasis will be given to the discussion of the contribution of light scattering techniques for future experiments on the study of the static and dynamic properties of DNA knotted molecules in solution. These experiments would contribute to shed light on the possible dependence of the gyration radius of knotted polymers on the knot type, and would allow testing theoretical predictions about their relaxation time.

EPFL2008