By calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and... Show moreBy calculating the linear response of packings of soft frictionless disks to quasistatic external perturbations, we investigate the critical scaling behavior of their elastic properties and nonaffine deformations as a function of the distance to jamming. Averaged over an ensemble of similar packings, these systems are well described by elasticity, while in single packings we determine a diverging length scale ℓ∗ up to which the response of the system is dominated by the local packing disorder. This length scale, which we observe directly, diverges as 1/Δz, where Δz is the difference between contact number and its isostatic value, and appears to scale identically to the length scale which had been introduced earlier in the interpretation of the spectrum of vibrational modes. It governs the crossover from isostatic behavior at the small scale to continuum behavior at the large scale; indeed we identify this length scale with the coarse graining length needed to obtain a smooth stress field. We characterize the nonaffine displacements of the particles using the displacement angle distribution, a local measure for the amount of relative sliding, and analyze the connection between local relative displacements and the elastic moduli. Show less
Chemotaxis, the process in which cells detect a concentration gradient of a specific substance, interpret that information, and subsequently initiate movement towards the source is an essential... Show moreChemotaxis, the process in which cells detect a concentration gradient of a specific substance, interpret that information, and subsequently initiate movement towards the source is an essential part of many biological phenomena. It___s central to the processes in wound healing, in immune defense and in the formation of a viable embryo. In this thesis I used the well characterized social amoeba Dictyostelium discoideum to investigate, in depth, the dynamics that govern the first steps in the detection of a chemical gradient. D. discoideum detects cyclic adenosine mono-phosphate (cAMP) by a special receptor protein, cAMP receptor 1 (cAR1). Inside the cell this receptor activates a G protein which subsequently initiates a complex signaling cascade. Using fluorescence single-molecule microscopy I investigated the movements of both cAR1 and its associated G protein. During chemotaxis both proteins show striking differences in mobility between the leading and trailing edge of the cell. Those differences are presumably key to our understanding of gradient sensing by cells that have been ignored in models so far. Show less
Amorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can jam into a rigid, disordered state where they withstand finite shear stresses before yielding. Here... Show moreAmorphous materials as diverse as foams, emulsions, colloidal suspensions and granular media can jam into a rigid, disordered state where they withstand finite shear stresses before yielding. Here we review the current understanding of the transition to jamming and the nature of the jammed state for disordered packings of particles that act through repulsive contact interactions and are at zero temperature and zero shear stress. We first discuss the breakdown of affine assumptions that underlies the rich mechanics near jamming. We then extensively discuss jamming of frictionless soft spheres. At the jamming point, these systems are marginally stable (isostatic) in the sense of constraint counting, and many geometric and mechanical properties scale with distance to this jamming point. Finally, we discuss current explorations of jamming of frictional and non-spherical (ellipsoidal) particles. Both friction and asphericity tune the contact number at jamming away from the isostatic limit, but in opposite directions. This allows one to disentangle the distance to jamming and the distance to isostaticity. The picture that emerges is that most quantities are governed by the contact number and scale with the distance to isostaticity, while the contact number itself scales with the distance to jamming. Show less
This thesis is about weakly driven granular flows and suspensions. Chapter 1 is an overview of the current knowledge of slow granular flows in so-called split-bottom geometries, which in essence... Show moreThis thesis is about weakly driven granular flows and suspensions. Chapter 1 is an overview of the current knowledge of slow granular flows in so-called split-bottom geometries, which in essence consist of a disk rotating at the bottom of a container. In chapter 2 we study dry granular flows in this split-bottom geometry, both in the frictional, slow, rate-independent regime, and in the liquid-like, rate dependent regime which is reached for faster flows. Chapters 3-5 deal with the flow of suspensions in the same geometry. We improve the so-called index matched scanning technique, that allows 3D imaging of the suspensions. Also for the suspension we study both the slow, rate independent and the faster, rate dependent regime. In all cases we combine 2D and 3D imaging of the flow with rheological measurements. Chapter 6 is devoted to the rheology of dry, weakly vibrated granular media. In chapter 7 we revisit a classic experiment on the compaction of granular media. Show less
Cells use membranes as their boundary, shielding their inside from the outside world, and to create internal structure. The different membranes in a cell have large variations in chemical... Show moreCells use membranes as their boundary, shielding their inside from the outside world, and to create internal structure. The different membranes in a cell have large variations in chemical composition, elasticity, shape and function. In contrast with the standard static picture often shown in cartoons, membranes are moreover one of the most dynamic components of the cell. Based on a detailed study of the structure and shape of various membranes we have developed techniques to measure the relevant physical parameters. Using these, we can directly couple the structure and shape to the function of the membrane. Combining these studies with studies of the membrane dynamics we find that membranes can spontaneously demix in different domains, which can interact with each other by forces mediated by the membrane itself. This interaction results in a sorting of the domains by size. Introducing an active element, molecular motors, into the system, we find that new structures are formed. An example of such a structure is a long membrane tube. These tubes also exhibit rich dynamics, and oscillating growth and shrink patters, which makes them suitable length and shape regulators in living cells. Show less
Membrane heterogeneity on the micro- and nanometer scale plays an important role for a large number of biological processes. In parallel to the conception of refined membrane models, new... Show moreMembrane heterogeneity on the micro- and nanometer scale plays an important role for a large number of biological processes. In parallel to the conception of refined membrane models, new experimental techniques to determine membrane microstructure were developed in recent years. Single molecule fluorescence has emerged as one of the leading technologies since it delivers the required spatial resolution and can be employed in living cells. In a complementary approach artificial model systems are used to study specific biophysical aspects of membranes in isolation and in a controllable way. In this thesis we show how phase separated artificial membranes can be used to gain fundamental insight into lipid composition based heterogeneity (Chap. 2) and membrane mediated interactions (Chap. 3). We demonstrate that those interactions can lead to lipid domain sorting (Chap. 4). Experiments with artificial membranes are complemented with live cell studies. We develop a robust analysis method for single molecule position data (Chap. 5) and use it to study the role of heterogeneity in cell signaling (Chap. 6). Finally, we show how protein cluster formation can be measured by counting single molecules in live cells (Chap. 7). Show less
Proteins and enzymes play a key role in all biological systems. Understanding the mechanism of biological functions and reactions in which proteins and enzymes are involved requires a detailed... Show moreProteins and enzymes play a key role in all biological systems. Understanding the mechanism of biological functions and reactions in which proteins and enzymes are involved requires a detailed characterization of protein structure and dynamics. Structure refers to geometrical structure, as a result of the local arrangement of amino-acid side chains, and electronic structure, in particular at the active site of proteins and enzymes. Dynamics refers to structural changes that proteins undergo to perform their function. The work reported in this thesis concerns both methodological developments and the application of electron paramagnetic resonance (EPR) to study protein structure and dynamics. To this end, both continuous wave (cw) and pulsed microwave excitation have been applied. In the research described in this thesis transition-metal ions, such as Cu(II) and Fe(III), and nitroxide spin labels have been used as paramagnetic probes. Show less
Animals and plants are build from a large number of cells. These cells continuously respond to signals from outside and inside the cell by producing various kinds of proteins. The blueprints of... Show moreAnimals and plants are build from a large number of cells. These cells continuously respond to signals from outside and inside the cell by producing various kinds of proteins. The blueprints of these proteins are stored in genes. The genes, in cells with a nucleus, are carried in chromosomes: threadlike structures in the nucleus of a cell that become visible when the cell, upon dividing, condenses these structures. Chromosomes consist of roughly two parts: proteins, that take care of the condensation and DNA, carrying the genetic information of the cell. Without this condensation, the DNA in a human cell would never fit into the nucleus. During a cell division, DNA is compacted even more. The condensation has to be done in an orderly fashion so that the chromosomes can be replicated correctly at each cell division. Besides the compaction, the DNA still needs to be accessible for the expression of genes. The activity of genes can even be controlled by regulation of the DNA compaction. For a complete understanding of the regulation of DNA compaction, we need to understand, at molecular detail, not only the structure but also the dynamics of the compaction of DNA. At the first level of compaction, DNA winds around specific proteins, called histones. The DNA-histon complex is called a nucleosome. Another species of histone proteins, called linker histones are known to constrict the DNA exiting the nucleosome, thereby stabilizing the structure of the nucleosome. Under physiological conditions, arrays of nucleosomes fold into compact fibers called chromatin fibers. The transient structure of nucleosomes and the interaction between nucleosomes in a chromatin fiber, plays an important role in the compaction of DNA. We chose to use force spectroscopy, because this technique makes it possible to study the structure and dynamics of nucleosomes at the level of single molecules. In chapter 2 we introduced a simple method for dynamic force spectroscopy using magnetic tweezers. This method allows application of sub-piconewton force on single molecules, by calibration of the applied force from the distance between a pair of magnets and a magnetic sphere, which is used to apply a force to a molecule. Initial dynamic force spectroscopy experiments on DNA molecules revealed a large hysteresis in the force-extension curve. This hysteresis was caused by viscous drag on the magnetic bead making it impossible to measure the weak interactions between DNA and nucleosomes. Smaller beads decreased this hysteresis sufficiently to reveal intra-molecular interactions at sub-piconewton forces. Compared to typical quasi-static force spectroscopy our method is significantly faster, allowing the real time study of transient structures and reaction intermediates. As a proof of principle nucleosome-nucleosome interactions on a sub-saturated chromatin fiber were analyzed. In chapter 3 we investigated the Brownian fluctuations of the magnetic sphere in a magnetic tweezers experiment. We measured the force induced unwrapping of DNA from a single nucleosome. We showed that hidden Markov analysis, adopted for the non-linear force-extension of DNA, can readily resolve unwrapping events that are significantly smaller than the Brownian fluctuations. The probability distribution of the height of the magnetic bead was used to accurately resolve small changes in contour length and persistence length of a DNA molecule containing a nucleosome. The latter is shown to be directly related to the DNA bending angle of the complex. The adapted hidden Markov analysis can be used for any transient DNA-protein complex and provides a robust method for the investigation of these transient events. In chapter 4 we used magnetic tweezers to probe the mechanical properties of a single, well-defined array of 25 nucleosomes folded into a chromatin fiber. We found that the fiber stretched linearly like a Hookian spring to more than three times its starting length at forces up to 4\mbox{ pN}. This unexpected large extension points to a solenoid as the underlying topology of the chromatin fiber. Surprisingly, linker histones do not affect the length or stiffness of the fibers. They do stabilize the fiber at forces up to 7\mbox{ pN}. Fibers with a nucleosome repeat length of 167 basepairs instead of 197 basepairs are significantly stiffer, consistent with a two-start helical arrangement. The extensive thermal breathing of the chromatin fiber that is a consequence of the observed high compliance provides a structural basis for understanding the balance between compaction of DNA to fit into the cell core and the transparency of DNA to allow proteins to access the genetic information of the cell. In chapter 5 we investigated the unexpected difference in the force needed for the unwrapping of the first turn and unwrapping of the second turn of nucleosomes in experiments on single nucleosomes and nucleosomes in a fiber. The forces needed to unwrap a single nucleosome were much smaller, 3 pN for the first turn and 6 pN for the second turn, than those for a nucleosome in a fiber, 6 pN and 18 pN respectively. We modeled a nucleosome-DNA-bead system, used in force spectroscopy experiments, as spheres and springs. We found that the thermal fluctuations of neighbouring nucleosomes stabilized the nucleosome thereby increasing the unwrapping force for a nucleosome in a fiber. This effect shows that results obtained for single nucleosomes cannot simply be extrapolated to a system containing multiple nucleosomes. Show less
Many proteins that interact with DNA perform or enhance their specific functions by binding simultaneously to multiple target sites, thereby inducing a loop in the DNA. The dynamics and energies... Show moreMany proteins that interact with DNA perform or enhance their specific functions by binding simultaneously to multiple target sites, thereby inducing a loop in the DNA. The dynamics and energies involved in this loop formation influence the reaction mechanism. Tethered particle motion has proven a powerful technique to study in real time protein-induced DNA looping dynamics while minimally perturbing the DNA–protein interactions. In addition, it permits many single-molecule experiments to be performed in parallel. Using as a model system the tetrameric Type II restriction enzyme SfiI, that binds two copies of its recognition site, we show here that we can determine the DNA–protein association and dissociation steps as well as the actual process of protein-induced loop capture and release on a single DNA molecule. The result of these experiments is a quantitative reaction scheme for DNA looping by SfiI that is rigorously compared to detailed biochemical studies of SfiI looping dynamics. We also present novel methods for data analysis and compare and discuss these with existing methods. The general applicability of the introduced techniques will further enhance tethered particle motion as a tool to follow DNA–protein dynamics in real time. Show less
This thesis describes coupling of light to periodic structures. A material is patterned with a regular pattern on a length scale comparable to the wavelength of light. With these structures, light... Show moreThis thesis describes coupling of light to periodic structures. A material is patterned with a regular pattern on a length scale comparable to the wavelength of light. With these structures, light can be manipulated very precisely. The structures find applications in semiconductor lasers, light emitting diodes (LEDs), photovoltaic cells, and detectors of light. A periodic array of holes in a layer of semiconductor or in a thin metal film causes a coupling between the incident light and light that is trapped inside the layer. This coupling can be studied by measuring the reflection and transmission. The environment has an important role here; e.g. placing glass antennas in the holes can increase the coupling between light and plasmons. A thin, superconducting wire can be used as a detector of light. To increase the surface area, the wire is folded into a meander. The optical properties of this detector are very dependent on the polarization, due to the regular periodic structure of the meander. Moreover, we found that the absorption of a very thin absorbing layer can be almost 100%, when it is illuminated under the right angle, from the substrate. This can be used to increase the efficiency of the detectors. Show less
In this thesis we consider several effects of a Dirac spectrum in photonic crystals on the scattering and propagation of light. We calculate the effect of a Dirac point (a conical singularity in... Show moreIn this thesis we consider several effects of a Dirac spectrum in photonic crystals on the scattering and propagation of light. We calculate the effect of a Dirac point (a conical singularity in the band structure) on the transmission of radiation through a photonic crystal. We find that the transmission at the Dirac point is inversely proportional to the longitudinal dimension of the crystal. Further we propose a method to detect the pseudospin-1/2 Berry phase produced by the Dirac-type band structure of a triangular-lattice photonic crystal. In addition we show that the half-integer spin and the associated Berry phase remain observable in the presence of disorder in the crystal: the destructive interference caused by the Berry phase suppresses the reflected intensity at an angle which is related to the angle of incidence by time-reversal symmetry causing extinction of coherent backscattering. We test all our predictions numerically by solving the full Maxwell equations. We also demonstrate that the Goos-Hanchen effect, which has been observed for the first time in optics and has applications in particular in photonic crystals, is of high importance for graphene. We show that the Goos-Hanchen effect in an n-doped channel with p-doped boundaries doubles the degeneracy of the lowest propagating mode, introducing a two-fold degeneracy on top of the usual spin and valley degeneracies. This can be observed as a stepwise increase by 8e^2/h of the conductance with increasing channel width. Show less
