Opposite effect of counterions on the persistence length of nicked and non-nicked DNA.

Using cryo-electron microscopy we reconstructed the three-dimensional trajectories adopted in cryovitrified solutions by double-stranded DNA molecules in which the backbone of one strand lacked a phosphate at regular intervals of 20 nucleotides. The shape of such nicked DNA molecules was compared with that of DNA molecules with exactly the same sequence but without any single-stranded scissions. Upon changing the salt concentration we observed opposite effects of charge neutralization on nicked and non-nicked DNA. In low salt solutions (10 mM Tris-HCl, 10 mM NaCl) the applied dense nicking caused ca 3.5-fold reduction of the DNA persistence length as compared with non-nicked DNA. Upon increasing the salt concentration (to 150 mM NaCl and 10 mM MgCl2) the persistence length of non-nicked DNA appreciably decreased while that of nicked DNA molecules increased by a factor of 2.

Vertebrate conserved non coding DNA regions have a high persistence length and a short persistence time.

BACKGROUND: The comparison of complete genomes has revealed surprisingly large numbers of conserved non-protein-coding (CNC) DNA regions. However, the biological function of CNC remains elusive. CNC differ in two aspects from conserved protein-coding regions. They are not conserved across phylum boundaries, and they do not contain readily detectable sub-domains. Here we characterize the persistence length and time of CNC and conserved protein-coding regions in the vertebrate and insect lineages. RESULTS: The persistence length is the length of a genome region over which a certain level of sequence identity is consistently maintained. The persistence time is the evolutionary period during which a conserved region evolves under the same selective constraints.Our main findings are: (i) Insect genomes contain 1.60 times less conserved information than vertebrates; (ii) Vertebrate CNC have a higher persistence length than conserved coding regions or insect CNC; (iii) CNC have shorter persistence times as compared to conserved coding regions in both lineages. CONCLUSION: Higher persistence length of vertebrate CNC indicates that the conserved information in vertebrates and insects is organized in functional elements of different lengths. These findings might be related to the higher morphological complexity of vertebrates and give clues about the structure of active CNC elements.Shorter persistence time might explain the previously puzzling observations of highly conserved CNC within each phylum, and of a lack of conservation between phyla. It suggests that CNC divergence might be a key factor in vertebrate evolution. Further evolutionary studies will help to relate individual CNC to specific developmental processes.

Determination of DNA persistence length by cryo-electron microscopy. Separation of the static and dynamic contributions to the apparent persistence length of DNA.

Axial deflection of DNA molecules in solution results from thermal motion and intrinsic curvature related to the DNA sequence. In order to measure directly the contribution of thermal motion we constructed intrinsically straight DNA molecules and measured their persistence length by cryo-electron microscopy. The persistence length of such intrinsically straight DNA molecules suspended in thin layers of cryo-vitrified solutions is about 80 nm. In order to test our experimental approach, we measured the apparent persistence length of DNA molecules with natural "random" sequences. The result of about 45 nm is consistent with the generally accepted value of the apparent persistence length of natural DNA sequences. By comparing the apparent persistence length to intrinsically straight DNA with that of natural DNA, it is possible to determine both the dynamic and the static contributions to the apparent persistence length.

Persistence Length, Mass Fractal, and Branching in the Aggregating of Vinyltriethoxysilane-Derived Organic/Silica Hybrids

Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)

Spatial visualization of DNA in solution.

An image analysis method is presented which allows for the reconstruction of the three-dimensional path of filamentous objects from two of their projections. Starting with stereo pairs, this method is used to trace the trajectory of DNA molecules embedded in vitreous ice and leads to a faithful representation of their three-dimensional shape in solution. This computer-aided reconstruction is superior to the subjective three-dimensional impression generated by observation of stereo pairs of micrographs because it enables one to look at the reconstructed molecules from any chosen direction and distance and allows quantitative analysis such as determination of distances, curvature, persistence length, and writhe of DNA molecules in solution.

Elastic properties and secondary structure formation of single-stranded DNA at monovalent and divalent salt conditions

Single-stranded DNA (ssDNA) plays a major role in several biological processes. It is therefore of fundamental interest to understand how the elastic response and the formation of secondary structures are modulated by the interplay between base pairing and electrostatic interactions. Here we measure force-extension curves (FECs) of ssDNA molecules in optical tweezers set up over two orders of magnitude of monovalent and divalent salt conditions, and obtain its elastic parameters by fitting the FECs to semiflexible models of polymers. For both monovalent and divalent salts, we find that the electrostatic contribution to the persistence length is proportional to the Debye screening length, varying as the inverse of the square root of cation concentration. The intrinsic persistence length is equal to 0.7 nm for both types of salts, and the effectivity of divalent cations in screening electrostatic interactions appears to be 100-fold as compared with monovalent salt, in line with what has been recently reported for single-stranded RNA. Finally, we propose an analysis of the FECs using a model that accounts for the effective thickness of the filament at low salt condition and a simple phenomenological description that quantifies the formation of non-specific secondary structure at low forces.

Force Spectroscopy with Dual-Trap Optical Tweezers: Molecular Stiffness Measurements and Coupled Fluctuations Analysis

ABSTRACT Dual-trap optical tweezers are often used in high-resolution measurements in single-molecule biophysics. Such measurements can be hindered by the presence of extraneous noise sources, the most prominent of which is the coupling of fluctuations along different spatial directions, which may affect any optical tweezers setup. In this article, we analyze, both from the theoretical and the experimental points of view, the most common source for these couplings in dual-trap optical-tweezers setups: the misalignment of traps and tether. We give criteria to distinguish different kinds of misalignment, to estimate their quantitative relevance and to include them in the data analysis. The experimental data is obtained in a, to our knowledge, novel dual-trap optical-tweezers setup that directly measures forces. In the case in which misalignment is negligible, we provide a method to measure the stiffness of traps and tether based on variance analysis. This method can be seen as a calibration technique valid beyond the linear trap region. Our analysis is then employed to measure the persistence length of dsDNA tethers of three different lengths spanning two orders of magnitude. The effective persistence length of such tethers is shown to decrease with the contour length, in accordance with previous studies.

Elastic properties and secondary structure formation of single-stranded DNA at monovalent and divalent salt conditions

Single-stranded DNA (ssDNA) plays a major role in several biological processes. It is therefore of fundamental interest to understand how the elastic response and the formation of secondary structures are modulated by the interplay between base pairing and electrostatic interactions. Here we measure force-extension curves (FECs) of ssDNA molecules in optical tweezers set up over two orders of magnitude of monovalent and divalent salt conditions, and obtain its elastic parameters by fitting the FECs to semiflexible models of polymers. For both monovalent and divalent salts, we find that the electrostatic contribution to the persistence length is proportional to the Debye screening length, varying as the inverse of the square root of cation concentration. The intrinsic persistence length is equal to 0.7 nm for both types of salts, and the effectivity of divalent cations in screening electrostatic interactions appears to be 100-fold as compared with monovalent salt, in line with what has been recently reported for single-stranded RNA. Finally, we propose an analysis of the FECs using a model that accounts for the effective thickness of the filament at low salt condition and a simple phenomenological description that quantifies the formation of non-specific secondary structure at low forces.

The aggregation process in tetraethoxysilane-derived sonogels as an analogy to the critical phenomenon

The structural evolution in silica sols prepared from tetraethoxysilane (TEOS) sonohydrolysis was studied 'in situ' using small-angle x-ray scattering (SAXS). The structure of the gelling system can be reasonably well described by a correlation function given by gamma(r) similar to (1/R(2))(1/r) exp(- r/xi), where xi is the structure correlation length and R is a chain persistence length, as an analogy to the Ornstein-Zernike theory in describing critical phenomenon. This approach is also expected for the scattering from some linear and branched molecules as polydisperse coils of linear chains and random f-functional branched polycondensates. The characteristic length. grows following an approximate power law with time t as xi similar to t(1) (with the exponent quite close to 1) while R remains undetermined but with a constant value, except at the beginning of the process in which the growth of. is slower and R increases by only about 15% with respect to the value of the initial sol. The structural evolution with time is compatible with an aggregation process by a phase separation by coarsening. The mechanism of growth seems to be faster than those typically observed for pure diffusion controlled cluster-cluster aggregation. This suggests that physical forces (hydrothermal forces) could be actuating together with diffusion in the gelling process of this system. The data apparently do not support a spinodal decomposition mechanism, at least when starting from the initial stable acid sol studied here.

Visualization, manipulation and force spectroscopy of cylindrical polymer brushes

The Ph.D. thesis deals with the conformational study of individual cylindrical polymer brush molecules using atomic force microscopy (AFM). Imaging combined with single molecule manipulation has been used to unravel questions concerning conformational changes, desorption behavior and mechanical properties of individual macromolecules and supramolecular structures. In the first part of the thesis (chapter 5) molecular conformations of cylindrical polymer brushes with poly-(N-isopropylacrylamide) (PNIPAM) side chains were studied in various environmental conditions. Also micelle formation of cylindrical brush-coil blockcopolymers with polyacrylic acid side chains and polystyrene coil have been visualized. In chapter 6 the mechanical properties of single cylindrical polymer brushes with (PNIPAM) side chains were investigated. Assuming that the brushes adopt equilibrium conformation on the surface, an average persistence length of lp= (29 ± 3) nm was determined by the end-to-end distance vs. contour length analysis in terms of the wormlike chain (WLC) model. Stretching experiments suggest that an exact determination of the persistence length using force extension curves is impeded by the contribution of the side chains. Modeling the stretching of the bottle brush molecule as extension of a dual spring (side chain and main chain) explains the frequently observed very low persistence length arising from a dominant contribution of the side chain elasticity at small overall contour lengths. It has been shown that it is possible to estimate the “true” persistence length of the bottle brush molecule from the intercept of a linear extrapolation of the inverse square root of the apparent persistence length vs. the inverse contour length plot. By virtue of this procedure a “true” persistence length of 140 nm for the PNIPAM brush molecules is predicted. Chapter 7 and 8 deal with the force-extension behavior of PNIPAM cylindrical brushes studied in poor solvent conditions. The behavior is shown to be qualitatively different from that in a good solvent. Force induced globule-cylinder conformational changes are monitored using “molecule specific force spectroscopy” which is a combined AFM imaging and SMFS technique. An interesting behavior of the unfolding-folding transitions of single collapsed PNIPAM brush molecules has been observed by force spectroscopy using the so called “fly-fishing” mode. A plateau force is observed upon unfolding the collapsed molecule, which is attributed to a phase transition from a collapsed brush to a stretched conformation. Chapter 9 describes the desorption behavior of single cylindrical polyelectrolyte brushes with poly-L-lysine side chains deposited on a mica surface using the “molecule specific force spectroscopy” technique to resolve statistical discrepancies usually observed in SMFS experiments. Imaging of the brushes and inferring the persistence length from a end-to-end distance vs. contour length analysis results in an average persistence length of lp = (25 ± 5) nm assuming that the chains adopt their equilibrium conformation on the surface. Stretching experiments carried out on individual poly-L-lysine brush molecules by force spectroscopy using the “fly-fishing” mode provide a persistence length in the range of 7-23 nm in reasonable accordance with the imaging results. In chapter 10 the conformational behavior of cylindrical poly-L-lysine brush-sodium dodecyl sulfate complexes was studied using AFM imaging. Surfactant induced cylinder to helix like to globule conformational transitions were observed.

Statistical mechanics of protein complexed and condensed DNA

In this thesis I treat various biophysical questions arising in the context of complexed / ”protein-packed” DNA and DNA in confined geometries (like in viruses or toroidal DNA condensates). Using diverse theoretical methods I consider the statistical mechanics as well as the dynamics of DNA under these conditions. In the first part of the thesis (chapter 2) I derive for the first time the single molecule ”equation of state”, i.e. the force-extension relation of a looped DNA (Eq. 2.94) by using the path integral formalism. Generalizing these results I show that the presence of elastic substructures like loops or deflections caused by anchoring boundary conditions (e.g. at the AFM tip or the mica substrate) gives rise to a significant renormalization of the apparent persistence length as extracted from single molecule experiments (Eqs. 2.39 and 2.98). As I show the experimentally observed apparent persistence length reduction by a factor of 10 or more is naturally explained by this theory. In chapter 3 I theoretically consider the thermal motion of nucleosomes along a DNA template. After an extensive analysis of available experimental data and theoretical modelling of two possible mechanisms I conclude that the ”corkscrew-motion” mechanism most consistently explains this biologically important process. In chapter 4 I demonstrate that DNA-spools (architectures in which DNA circumferentially winds on a cylindrical surface, or onto itself) show a remarkable ”kinetic inertness” that protects them from tension-induced disruption on experimentally and biologically relevant timescales (cf. Fig. 4.1 and Eq. 4.18). I show that the underlying model establishes a connection between the seemingly unrelated and previously unexplained force peaks in single molecule nucleosome and DNA-toroid stretching experiments. Finally in chapter 5 I show that toroidally confined DNA (found in viruses, DNAcondensates or sperm chromatin) undergoes a transition to a twisted, highly entangled state provided that the aspect ratio of the underlying torus crosses a certain critical value (cf. Eq. 5.6 and the phase diagram in Fig. 5.4). The presented mechanism could rationalize several experimental mysteries, ranging from entangled and supercoiled toroids released from virus capsids to the unexpectedly short cholesteric pitch in the (toroidaly wound) sperm chromatin. I propose that the ”topological encapsulation” resulting from our model may have some practical implications for the gene-therapeutic DNA delivery process.

Eigenschaften von thermoresponsiven Bürstenpolymeren

In dieser Doktorarbeit werden die Eigenschaften von thermoresponsiven Bürstenpolymeren untersucht. Hierbei konnten erstmalig thermische Konformationsübergänge von zylindrischen Bürstenmolekülen auf Oberflächen beobachtet werden. Der Einfluss der Oberfläche auf die Umkehrbarkeit und die Kinetik der Übergänge wurde untersucht. Die dabei erhaltenen Erkenntnisse konnten verwendet werden, um das Verhalten der Polymere auf anderen Oberflächen vorherzusagen. Im zweiten Projekt wurde gezeigt, dass Einzelmolekül-Kraftspektroskopie eine gute Methode für die Untersuchung der mechanischen Eigenschaften von Bürstenpolymeren in guten Lösungsmitteln ist. Mit kleinen Substanzmengen kann die Persistenzlänge der Polymere bestimmt werden. Es ist möglich zu zeigen, dass die Persistenzlänge der Polymerbürsten von ihrer Seitenkettenlänge abhängt. Überraschenderweise funktioniert das Experiment nicht, wenn man die Bürsten aus einem Polymerfilm zieht anstatt ein Einzelmolekülexperiment durchzuführen. In diesem Fall zeigen die Kraft-Abstands-Kurven zu lange Kontur- und Persistenzlängen. Diese Beobachtung ist für lineare Polymere nicht gültig. Im dritten Teil der Doktorarbeit werden Kraft-Abstands-Experimente an einzelnen kollabierten Polymeren untersucht. In schlechten Lösungsmitteln zeigen die Bürsten ein moleküllängenabhängiges Kraft-Plateau, welches theoretisch vorausgesagt wurde und einen Phasenübergang von einem kollabierten zu einem entspannten Zustand der Polymerkette anzeigt. In Fly-Fishing-Experimenten kann man eine Hysterese zwischen den beiden Messkurven beobachten, welche bei mehrfachem Ziehen kleiner wird. Alle Experimente in schlechten Lösungsmitteln wurden mit linearen Polymeren reproduziert, um den Einfluss der Molekülarchitektur von den generellen Eigenschaften von Polymeren in schlechten Lösungsmitteln unterscheiden zu können. Zum Abschluss wird die Abhängigkeit der Polymerentfaltung von der Laderate des Experiments gemessen.

Force-mediated kinetics of single P-selectin/ligand complexes observed by atomic force microscopy

Leukocytes roll along the endothelium of postcapillary venules in response to inflammatory signals. Rolling under the hydrodynamic drag forces of blood flow is mediated by the interaction between selectins and their ligands across the leukocyte and endothelial cell surfaces. Here we present force-spectroscopy experiments on single complexes of P-selectin and P-selectin glycoprotein ligand-1 by atomic force microscopy to determine the intrinsic molecular properties of this dynamic adhesion process. By modeling intermolecular and intramolecular forces as well as the adhesion probability in atomic force microscopy experiments we gain information on rupture forces, elasticity, and kinetics of the P-selectin/P-selectin glycoprotein ligand-1 interaction. The complexes are able to withstand forces up to 165 pN and show a chain-like elasticity with a molecular spring constant of 5.3 pN nm−1 and a persistence length of 0.35 nm. The dissociation constant (off-rate) varies over three orders of magnitude from 0.02 s−1 under zero force up to 15 s−1 under external applied forces. Rupture force and lifetime of the complexes are not constant, but directly depend on the applied force per unit time, which is a product of the intrinsic molecular elasticity and the external pulling velocity. The high strength of binding combined with force-dependent rate constants and high molecular elasticity are tailored to support physiological leukocyte rolling.

Pulling a single chromatin fiber reveals the forces that maintain its higher-order structure

Single chicken erythrocyte chromatin fibers were stretched and released at room temperature with force-measuring laser tweezers. In low ionic strength, the stretch-release curves reveal a process of continuous deformation with little or no internucleosomal attraction. A persistence length of 30 nm and a stretch modulus of ≈5 pN is determined for the fibers. At forces of 20 pN and higher, the fibers are modified irreversibly, probably through the mechanical removal of the histone cores from native chromatin. In 40–150 mM NaCl, a distinctive condensation-decondensation transition appears between 5 and 6 pN, corresponding to an internucleosomal attraction energy of ≈2.0 kcal/mol per nucleosome. Thus, in physiological ionic strength the fibers possess a dynamic structure in which the fiber locally interconverting between “open” and “closed” states because of thermal fluctuations.

Direct observation of extension and retraction of type IV pili

Type IV pili are thin filaments that extend from the poles of a diverse group of bacteria, enabling them to move at speeds of a few tenths of a micrometer per second. They are required for twitching motility, e.g., in Pseudomonas aeruginosa and Neisseria gonorrhoeae, and for social gliding motility in Myxococcus xanthus. Here we report direct observation of extension and retraction of type IV pili in P. aeruginosa. Cells without flagellar filaments were labeled with an amino-specific Cy3 fluorescent dye and were visualized on a quartz slide by total internal reflection microscopy. When pili were attached to a cell and their distal ends were free, they extended or retracted at rates of about 0.5 μm s−1 (29°C). They also flexed by Brownian motion, exhibiting a persistence length of about 5 μm. Frequently, the distal tip of a filament adsorbed to the substratum and the filament was pulled taut. From the absence of lateral deflections of such filaments, we estimate tensions of at least 10 pN. Occasionally, cell bodies came free and were pulled forward by pilus retraction. Thus, type IV pili are linear actuators that extend, attach at their distal tips, exert substantial force, and retract.