In the nucleus of eukaryotic cells, DNA wraps around histone proteins to form nucleosomes, which in turn associate in a compact and dynamic fiber called chromatin. The physical properties of this fiber at different lengthscales, from the DNA double-helix to micrometer-sized chromosomes, are essential to the complex mechanisms of gene expression and its regulation. The present thesis is a contribution to the development of physical models, which are able to link different scales and to interpret and integrate data from a wide range of experimental and computational approaches. In the first part, we use Molecular Dynamics simulations of DNA oligomers to study doublehelical DNA at different temperatures. We estimate the sequence-dependent contribution of entropy to DNA elasticity, in relation with recent experiments on DNA persistence length. In the second part, we model the DNA-histone interactions within the nucleosome core particle,using DNA nanomechanics to extract a force field from a set of crystallographic nucleosome structures and Molecular Dynamics snapshots. In the third part, we consider the softer part of the nucleosome, the linker DNA between coreparticles which transiently associates with the histone H1 to form a "stem".We combine existing structural knowledge with experimental data at two different resolutions (DNA footprints and electro-micrographs) to develop a nanoscale model of the stem.

The soft matter field considers a wide class of objects such as liquids, polymers, gels, colloids, liquid crystals and biological macromolecules, which have complex internal structure and conformational flexibility leading to phenomena and properties having multiple spacial and time scales. Existing computer simulation methods are able to cover these scales, but with different resolutions, and ability to link them together performing a multiscale simulation is highly desirable. The present work addresses systematic multiscaling approach for soft matter studies, using structure-based coarse-graining (CG) methods such as iterative Boltzmann inversion and inverse Monte Carlo. A new software package MagiC implementing these methods is introduced. The software developed for the purpose of effective CG potential derivation is applied for ionic water solution and for water solution of DMPC lipids. A thermodynamic transferability of the obtained potentials is studied. The effective inter-ionic solvent mediated potentials derived for NaCl successfully reproduce structural properties obtained in explicit solvent simulation, which indicates the perspectives of using the structure-based coarse-graining for studies of ion-DNA and other polyelectrolytes systems. The potentials have temperature dependence, dominated mostly by the electrostatic long-range part which can be described by temperature dependent effective dielectric permittivity, leaving the short-range part of the potential thermodynamically transferable. For CG simulations of lipids a 10-bead water-free model of dimyristoylphosphatidylcholine is introduced. Four atomistic reference systems, having different lipid/water ratio are used to derive the effective bead-bead potentials, which are used for subsequent coarse-grained simulations of lipid bilayer. A significant influence of lipid/water ratio in the reference system on the properties of the simulated bilayers is noted, however it can be softened by additional angle-bending interactions. At the same time the obtained bilayers have stable structure with correct density profiles. The model provides acceptable agreement between properties of coarse-grained and atomistic bilayer, liquid crystal - gel phase transition with temperature change, as well as realistic self-aggregation behavior, which results in formation of bilayer, bicell or vesicle from a dispersed lipid solution in a large-scale simulation. / <p>At the time of the doctoral defense, the following paper was unpublished and had a status as follows: Paper 4: Submitted. </p><p> </p>

Many everyday materials, broadly classified as ``particulate media'', are at the heart of many industries and natural phenomena. Examples range from the storage and transport of bulk foods and aggregates such as grains and coal; the processing of pharmaceutical pills and the grinding coffee beans; to the mitigation and cost control of life-threatening events like landslides, earthquakes, and silo failures. The common theme connecting all these phenomena is the mechanical stability of the granular material that arises from interactions at the microscopic level of the grain scale, and how this influences collective properties at the bulk, macroscopic scale. In this dissertation, we present an extensive study of the mechanical properties of a physics-based model of granular particle systems in two dimensions using computer simulations. Specifically, we study the dynamics of an intruder particle that is driven through a dense, disordered packing of particles. This practical technique has the benefit of being amenable to experimental application which we expect will motivate future studies in the area. We find the `microrheology' of the intruder can be traced back to the properties of underlying, original, unperturbed packing, thereby providing a method to characterize the mechanical properties of the material that may otherwise be unavailable. To perform this study, we initially created mechanically stable granular packings of bidisperse discs, for several orders of magnitude of particle friction coefficient $\mu$, over a range in packing densities, or packing fractions $\phi$, in the vicinity of the critical packing fraction $\phi_c$, the density below which the packing is no longer stable. This range in $\phi$ translates to a range in packing pressures $P$, spanning several orders of magnitude down to the $P\rightarrow 0$ limit. For each packing, we apply a driving force to the intruder probe particle and find the critical force $F_{c}$, the minimum force required to induce motion of the probe as it is dragged through the system. We find that $F_{c}(\mu)$ for the different friction packings, scales with the packing pressure $P$ as a power-law according to: $F_{c}(\mu) - F_{c}^{o}(\mu) \sim P^{\beta(\mu)}$. The power-law exponent, $\beta(\mu)$ becomes friction dependent, but approaches the value, $\beta(\mu\to0) = 1.0 \pm 0.1$ in the zero-friction limit. $F_{c}^{o}(\mu)$ is the value of $F_{c}$ in the limit $P \to 0$, that similarly depends on the friction coefficient as, $F_{c}^{o}(\mu) \to 0$, when $\mu \to \infty$. We use this property of $F_{c}^{o}(\mu)$ to characterize the mechanical properties of different frictional packings. Another focus of this study is the `microrheology' of the intruder through force-velocity dependencies in $\mu=0$ systems at different $P$. For this case, the intruder is driven through the packing at a steady-state velocity $$, for driving forces above the critical force $F_D > F_c$. We introduce a scaling function that collapses the force-velocity curves onto a single master curve. This power law scaling of the collapsed curve as $P\rightarrow 0$ is reminiscent of a continuous phase transition, reinforcing the notion that the mechanical state of the system exhibits critical-like features. Furthermore, we also find an alternative scaling collapse of the form: $- \sim (F_{D} - F_{c})^{\alpha}$, where $$ represents a constant velocity term in the limit of small excess forcing, and the critical force $F_{c}$ now appears as fitting parameter that matches our explicit calculations. Thence, we are able to extract $F_{c}$ from a driven probe without a-priori having any knowledge about the state of the system. To further investigate the transition of the system through the different intruder force perturbations, we implemented a coarse graining (CG) technique that transforms our discrete particle interaction force information into continuous stress fields. Through this methodology, we are able to calculate the kinetic and contact stresses as the intruder is driven through the system. We are able to qualify and quantify the directional and distance dependencies of the stress response of the packing due to the driven probe via radial and azimuthal stress calculations. In particular, we find how the stress response not only captures the wake region behind the driven intruder, but also how the stress decays in the forward direction of the intruder, which follows universal behavior.

In soil, where trees and crops grow, heavy vehicles shear and compact the soil, leading to reduced plant growth and diminished nutrient recycling. Computer simulations offer the possibility to improve the understanding of these undesired phenomena. In this thesis, soils were modelled as large collections of contacting spherical particles using the Discrete Element Method (DEM) and the physics engine AGX Dynamics, and these entities were analyzed. In the first part of the thesis, soils, which were considered to be continua, were subjected to various controlled deformations and fields for quantities such as stress and strain were visualized using coarse graining (CG). These fields were then compared against analytical solutions. The main goal of the thesis was to evaluate the usefulness, accuracy, and precision of this plotting technique when applied to DEM-soils. The general behaviour of most fields agreed well with analytical or expected behaviour. Moreover, the fields presented valuable information about phenomena in the soils. Relative errors varied from 1.2 to 27 %. The errors were believed to arise chiefly from non-uniform displacement (due to the inherent granularity in the technique), and unintended uneven particle distribution. The most prominent drawback with the technique was found to be the unreliability of the plots near the boundaries. This is significant, since the behaviour of a soil at the surface where it is in contact with e.g. a vehicle tyre is of interest. In the second part of the thesis, a vehicle traversed a soil and fields were visualized using the same technique. Following a limited analysis, it was found that the stress in the soil can be crudely approximated as the stress in a linear elastic solid.

One of the major goal of the researchers is to reduce energy loss including nanoscale to the structural level. For instance, around 65% of fuel energy is lost during the propulsion of the automobiles, where 11% of the loss happens at tires due to rolling friction. Out of that tire loss, 90 to 95% loss happens due to hysteresis of tire materials. This dissertation focuses on multiscale modeling techniques in order to facilitate the discovery new rubber materials. Enhanced coarse-grained models of elastomers (thermoplastic polyurethane elastomer and natural rubber) are constructed from full-atomic models with reasonable repeat units/beads associated with pressure-correction for non-bonded interactions of the beads using inverse Boltzmann method (IBM). Equivalent continuum modeling is performed with volumetric/isochoric loading to predict macroscopic mechanical properties using molecular mechanics (MM) and molecular dynamics (MD). Glass-transition and rate-dependent mechanical properties along with hysteresis loss under uniaxial deformation is predicted with varying composition of the material. A statistical non-Gaussian treatment of a rubber chain is performed and linked with molecular dynamics in order predict hyperelastic material constants without fitting with any experimental data.

In a celebrated series of experimental observations, starling flocks have been shown to be characterized by scale-free, long-ranged spatial correlations in their velocity fluctuations. While this is expected for velocity orientation correlations on the basis of simple symmetry-breaking arguments, the same scaling-free behaviour for speed (i.e. the absolute value of birds’ velocity) correlations cannot be explained by the same symmetry-based argument. Possible explanations so far put forward required the implicit or explicit fine-tuning of a speed control parameter. In this work we explore a different possibility, investigating the effects of the experimental discrete temporal sampling of individual bird trajectories. We argue that observed velocity may well be a time coarse-grained observable, that is, the sum over many faster course corrections taken by the bird. A simple argument shows such a time coarse-grained speed to be linked with the squared fluctuations of (soft modes) transversal velocities, which may thus acquire a long-range correlation. Our idea is numerically tested by measuring spatial correlations between coarse-grained speeds in the on-lattice equilibrium XY model and the off-lattice out-of-equilibrium Vicsek model in two dimensions. Saturation of the speed correlation length is found in the equilibrium XY model, while in the non-equilibrium Vicsek model ordered symmetry-broken phase shows scale-free behaviour with a correlation length ξ is found to be proportional to system size L. We conclude that in non-equilibrium flocking models, the temporal coarse-graining procedure is able to reproduce scale-free behaviour at system sizes which are relevant to the experimental observations. We believe that this mechanism might find applications beyond the case of starling flocks and perhaps be relevant for other experimental observations of collective motion.

Low-resolution, coarse-grained models are powerful computational tools to investigate the behavior of biological systems over time and length scales that are not accessible to all-atom Molecular Dynamics simulations. While several algorithms exist that aim at constructing accurate coarse-grained potentials, few works focus on the choice of the reduced representation, or mapping, to be employed to describe the high-resolution system with a lower number of degrees of freedom. This thesis proposes a series of approaches to investigate and characterise the representation problem in coarse-grained modelling of proteins. This is achieved by employing a collection of diverse methods, including statistical mechanics, machine learning algorithms and information-theoretical tools. The central mathematical object of this work is the mapping entropy, a Kullback-Leibler divergence that measures the intrinsic quality of a given reduced representation. When this quantity is minimised, we obtain the maximally informative coarse-grained mappings of a biomolecule, which cover the structure with an uneven level of detail. Tests conducted over a set of well-known proteins show that regions preserved with high probability are often related to important functional mechanisms of the molecule. Applications of the mapping entropy outside of the field of structural biology show promising results, leading to the identification of those combinations of features that retain the maximum amount of information about the high-resolution system. Additionally, a purely structural notion of scalar product and distance between coarse-grained mappings is introduced, which allow to analyse the metric and topological properties of the mapping space. The thorough exploration of such space leads to the discovery of qualitatively different reduced representations of the biomolecule of interest.

No description available.

The purpose of this thesis is to improve predictions of irradiation hardening in metals with a focus on coarse-graining via meso-scale simulations. Increasing hardness and decreasing in ductility in nuclear reactor pressure vessel steel is the limiting factor of nuclear reactor life, and accurately predicting reactor life is of the utmost importance for the safe operation of nuclear facilities. This is an inherently multi-scale problem with primary damage occurring at the atomic scale and its effects propagating across ten orders of magnitude in length and time scale to changes in macroscopic material properties, which must be reflected in its methods of prediction. To achieve this goal, this thesis develops two novel approaches to simulate the motion of dislocations in irradiated alpha-iron. First, a dislocation dynamics simulation coarse-graining insight from atomistic dislocation-defect simulations is used to guide the selection of proposed constitutive models. Several studies investigating the effect of size distribution show that the mean defect size can be used with the selected models to predict material hardening without a complex treatment for the defect size distribution. The hardening effect of the commonly observed defect types are found independently and a superposition principle is proposed for materials with both defect types. Second, a link to transition state theory and thermally activated reactions is established using a new method augmenting a discrete dislocation dynamics simulations with the nudged elastic band method to characterise the minimum energy pathways of dislocation reactions. This development enables calculations of activation energy for dislocation events using a continuum method as well as the numerical calculations of dislocation attempt frequency. The thesis concludes with an extension to the analysis of coarse-graining unit events to large scale dislocation-obstacle bypass phenomena.

In general, this dissertation is concerned with modeling of mechanical behavior of protein molecules. In particular, we focus on coarse-grained models, which bridge the gap in time and length scale between the atomistic simulation and biological processes. The dissertation presents three independent studies involving such models. The first study is concerned with a rigorous coarse-graining method for dynamics of linear systems. In this method, as usual, the conformational space of the original atomistic system is divided into master and slave degrees of freedom. Under the assumption that the characteristic timescales of the masters are slower than those of the slaves, the method results in Langevin-type equations of motion governed by an effective potential of mean force. In addition, coarse-graining introduces hydrodynamic-like coupling among the masters as well as non-trivial inertial effects. Application of our method to the long-timescale part of the relaxation spectra of proteins shows that such dynamic coupling is essential for reproducing their relaxation rates and modes. The second study is concerned with calibration of elastic network models based on the so-called B-factors, obtained from x-ray crystallographic measurements. We show that a proper calibration procedure must account for rigid-body motion and constraints imposed by the crystalline environment on the protein. These fundamental aspects of protein dynamics in crystals are often ignored in currently used elastic network models, leading to potentially erroneous network parameters. We develop an elastic network model that properly takes rigid-body motion and crystalline constraints into account. This model reveals that B-factors are dominated by rigid-body motion rather than deformation, and therefore B-factors are poorly suited for identifying elastic properties of protein molecules. Furthermore, it turns out that B-factors for a benchmark set of three hundred and thirty protein molecules can be well approximated by assuming that the protein molecules are rigid. The third study is concerned with the polymer mediated interaction between two planar surfaces. In particular, we consider the case where a thin polymer layer bridges two parallel plates. We consider two models of monodisperse and polydisperse for the polymer layer and obtain an analytical expression for the force-distance relationship of the two plates. / text