In this study, we consider electrostatics contributed from the molecules in the ionic solution. It plays a significant role in determining the binding affinity of molecules and drugs. We develop the overall framework of computing electrostatic properties for three-dimensional molecular structures, including potential, energy, and forces. These properties are derived from Poisson-Boltzmann equation, a partial differential equation that describes the electrostatic behavior of molecules in ionic solutions. In order to compute these properties, we derived new boundary integral equations and designed a boundary element algorithm based on the linear time fast multipole method for solving the linearized Poisson-Boltzmann equation. Meanwhile, a higher-order parametric formulation called algebraic spline model is used for accurate approximation of the unknown solution of the linearized Poisson-Boltzmann equation. Based on algebraic spline model, we represent the normal derivative of electrostatic potential by surrounding electrostatic potential. This representation guarantees the consistent relation between electrostatic potential and its normal derivative. In addition, accurate numerical solution and fast computation for electrostatic energy and forces are also discussed. In addition, we described our hierarchical modeling and parameter optimization of molecular structures. Based on this technique, we can control the scalability of molecular models for electrostatic computation. The numerical test and experimental results show that the proposed techniques offer an efficient and accurate solution for solving the electrostatic problem of molecules. / text

An understanding of the mechanical properties of viral capsids (protein assemblies forming shell containers) has become necessary as their perceived use as nano-materials for targeted drug delivery. In this thesis, a heterogeneous, spatially detailed model of the viral capsid is considered. This model takes into account the increased degrees of freedom between the capsomers (capsid sub-structures) and the interactions between them to better reflect their deformation properties. A spatially realistic finite element multi-domain decomposition of viral capsid shells is also generated from atomistic PDB (Protein Data Bank) information, and non-linear continuum elastic simulations are performed. These results are compared to homogeneous shell simulation re- sults to bring out the importance of non-homogenous material properties in determining the deformation of the capsid. Finally, multiscale methods in structural analysis are reviewed to study their potential application to the study of nanoindentation of viral capsids. / text

<p>This thesis consists of two papers considering different aspects of stochastic process modelling and the minimisation of computational cost.</p><p>In the first paper, we analyse statistical signal properties and develop a Gaussian pro- cess model for scenarios with a moving receiver in a scattering environment, as in Clarke’s model, with the generalisation that noise is introduced through scatterers randomly flip- ping on and off as a function of time. The Gaussian process model is developed by extracting mean and covariance properties from the Multipath Fading Channel model (MFC) through coarse graining. That is, we verify that under certain assumptions, signal realisations of the MFC model converge to a Gaussian process and thereafter compute the Gaussian process’ covariance matrix, which is needed to construct Gaussian process signal realisations. The obtained Gaussian process model is under certain assumptions less computationally costly, containing more channel information and having very similar signal properties to its corresponding MFC model. We also study the problem of fitting our model’s flip rate and scatterer density to measured signal data.</p><p>The second paper generalises a multilevel Forward Euler Monte Carlo method intro- duced by Giles [1] for the approximation of expected values depending on the solution to an Ito stochastic differential equation. Giles work [1] proposed and analysed a Forward Euler Multilevel Monte Carlo method based on realsiations on a hierarchy of uniform time discretisations and a coarse graining based control variates idea to reduce the computa- tional effort required by a standard single level Forward Euler Monte Carlo method. This work introduces an adaptive hierarchy of non uniform time discretisations generated by adaptive algorithms developed by Moon et al. [3, 2]. These adaptive algorithms apply either deterministic time steps or stochastic time steps and are based on a posteriori error expansions first developed by Szepessy et al. [4]. Under sufficient regularity conditions, our numerical results, which include one case with singular drift and one with stopped dif- fusion, exhibit savings in the computational cost to achieve an accuracy of O(T ol), from O(T ol−3 ) to O (log (T ol) /T ol)2 . We also include an analysis of a simplified version of the adaptive algorithm for which we prove similar accuracy and computational cost results.</p><p> </p>

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The aim of this work is to provide a mathematical and numerical analysis of the static quasicontinuum (QC) method. The QC method is, in essence, a finite element method for atomistic material models. By restricting the set of admissible deformations to linear splines with respect to a finite element mesh, the computational complexity of atomistic material models is reduced considerably. We begin with a general review of atomistic material models and the QC method and, most importantly, a thorough discussion of the correct concept of static equilibrium. For example, it is shown that, in contrast to global energy minimization, a ‘dynamic’ selection procedure based on gradient flows models the physically correct behaviour. Next, an atomistic model with long-range Lennard–Jones type interactions is analyzed in one dimension. A rigorous demonstration is given for the existence and stability of elastic as well as fractured steady states, and it is shown that they can be approximated by a QC method if the mesh is sufficiently well adapted to the exact solution; this can be measured by the interpolation error. While the a priori error analysis is an important theoretical step for understanding the approximation properties of the QC method, it is in general unclear how to compute the QC deformation whose existence is guaranteed by the a priori analysis. An a posteriori analysis is therefore performed as well. It is shown that, if a computed QC deformation is stable and has a sufficiently small residual, then there exists a nearby exact solution and the error is estimated. This a posteriori existence idea is also analyzed in an abstract setting. Finally, extensions of the ideas to higher dimensions are investigated in detail.

Membrane active peptides with the ability to cross the plasma membrane represent a promising class of therapeutic compounds. However, translocation efficacy and membrane toxicity of these peptides appear correlated and a better understanding of their mechanisms of action is needed to achieve the desired effect. Here, a range of coarse grain molecular dynamics simulations have been performed to systematically investigate the interactions of such cell-penetrating peptides (CPPs) with biologically relevant membranes. Challenges associated to the development of a suitable asymmetric mammalian membrane model demonstrated the importance of lipid species distribution on the bilayer mechanical properties, as well as the effect of coarse graining on its electrostatic properties. However, simulations successfully discriminated between two CPPs, penetratin and transportan, and were consistent with the experimental data available for these. The results obtained suggest that the ability of transportan peptides to aggregate into flexible, dynamic, transmembrane bundles is responsible for their relative membrane toxicity. The stability and structure of these aggregates, as well as the extent of the bilayer perturbations they induced, were shown to depend on the membrane composition and asymmetry, thus providing a molecular basis to explain how the toxicity of CPPs is modulated by membranes. In particular, bilayer destabilisation was enhanced by the presence of anionic lipids and hampered by that of cholesterol. Transportan aggregates were also observed to trigger lipid flip-flops above a certain size and a new pathway for such events, not relying on the formation of water defects, was characterised.

Landscapes are comprised of multiple ecosystems shaped by disturbances varying in severity and source. Moderate disturbance from weather, pathogens, insects, and age-related senescence, in contrast to severe disturbances that fell trees, may increase standing woody debris and alter the contribution of coarse woody debris (CWD) to total ecosystem respiration (RE). However, woody debris dynamics are rarely examined following moderate disturbances that substantially increase standing dead wood stocks. We used an experimental manipulation of moderate disturbance in an upper Great Lakes forest to: 1) examine decadal changes in CWD stocks through a moderate disturbance; 2) quantify in situ CWD respiration during different stages of decay for downed and standing woody debris and; 3) estimate the annual contribution of CWD respiration to the ecosystem C balance through comparison with RE and net ecosystem production (NEP). We found that the standing dead wood mass of 24.5 Mg C ha-1 was an order of magnitude greater than downed woody debris stocks and a large source of ecosystem C flux six years following disturbance. Instantaneous in situ respiration rates from standing and downed woody debris in the earliest stages of decay were not significantly different from one another. Independently derived estimates of ecosystem CWD respiration of 1.1to 2.1 Mg C ha-1 yr-1 six years following disturbance were comparable in magnitude to NEP and 12.5 % to 23.8 % of RE, representing a substantial increase relative to pre-disturbance levels. Ecosystem respiration and NEP were stable following moderate disturbance even though ecosystem CWD respiration increased substantially, suggesting a reduction in the respiratory C contribution from other sources. We conclude that CWD is an essential component of the ecosystem C balance following a moderate forest disturbance.

This master thesis was tasked to find out how the parameter of interior atmosphere changes at student's club "Mrtvá Ryba", that means atmospheric aerosols sized from 0,524 to 20 micrometers. This work tries to show indoor aerosols before and after the smoking ban and its comparison. This work describes concentrations PM1 and PM10, and their behavior per day. Concentrations was measured by APS (Aerodynamic particle sizer). The measurement was the first step in the non-smoking club, then processing with retrieved informations in CoPlot, CoStat and Excel, where the statistical method has done, and comparison with previous values. T-tests was used for statistics and linear regresion. The result confirms, what was it supposed to, so concentracion values are significantly different. The average concentration of all measured days (six) of smoking campaign was at PM1 13,28 µg.m-3 and at PM10 23,38 µg.m-3. The average concentration of all measured days (thirty six) of non-smoking campaign was at PM1 4,88 µg.m-3 and at PM10 24,61 µg.m-3. Resulting concentration of aerosol particles was explicity lower at non-smoking period than at smoking period. Contamination of interior enviroment is influenced by many factors. The most important factor is presence of persons and their number, concentration of outdoor...

Structure and mechanical properties of DNA play a key role in its biological functioning. A lot of well-established conclusions about the DNA structure and its sequence-dependent variabil- ity came from various experimental and computational studies of the Dickerson-Drew dodecamer (DD), a prototypic B-DNA molecule of the sequence (5')CGCGAATTCGCG(3'). In this study we present a detailed analysis of structural and mechan- ical properties of DD based on extensive atomistic molecular dynamics (MD) simulations with explicit representation of wa- ter and ionic environment. We analyze three simulated systems covering different ionic conditions and water models. Two MD trajectories are reported for the first time, one of them being 2.4 µs long. An extensive comparsion with one recent NMR struc- ture and four recent X-ray structures is made. It is found that the end basepairs can adopt two different pairing motifs dur- ing the simulation: the canonical Watson-Crick pair or a non- canonical trans Watson-Crick/Sugar Edge pair. These states can significantly influence the structure of DD even at the third step from the end. A clear relationship is found between the BI/BII backbone substates and the basepair step conformation. A model of rigid bases is used to study mechanical properties of the DNA. The non-local...

Structural and mechanical properties of nucleic acids play a key role in a wide range of biological processes, as well as in the field of nucleic acid nanotechnology. The thesis presents results of several studies focused on modelling these properties. Extensive unrestrained atomic-resolution molecular dynamics (MD) simulations are used to investigate structural dynamics of nucleic acids, and to parametrize their mechanical models. The deformation energy is assumed to be a general quadratic function of suitably chosen internal coordinates. Two types of models are employed which differ in the level of coarse- graining. The first one is based on the description of conformation at the level of individual bases and the second, coarser one is used to study global bending and twisting flexibility. The models are applied to explain mechanical properties of A-tracts in the context of DNA looping and nucleosome positioning, to characterize twist-stretch cou- pled deformations in DNA and RNA, and to predict changes in the properties of damaged DNA that are likely to be relevant for damage recognition and repair. Besides that, we propose a general model of DNA allostery, applied to study the effect of minor groove binding of small ligands and the allosteric coupling between proteins mediated by the DNA. A careful...