Computational design with flexible backbone sampling for protein remodeling and scaffolding of complex binding sites

Dissertation presented to obtain the Doutoramento (Ph.D.) degree in Biochemistry at the Instituto de Tecnologia Qu mica e Biol ogica da Universidade Nova de Lisboa

Optimizing Computational Frameworks to Study the Influence of the Protein Environment on the Individual Site Energies of Chromophores in Photosystem II of Photosynthesis

Photosynthesis is a process in which electromagnetic radiation is converted into chemical energy. Photosystems capture photons with chromophores and transfer their energy to reaction centers using chromophores as a medium. In the reaction center, the excitation energy is used to perform chemical reactions. Knowledge of chromophore site energies is crucial to the understanding of excitation energy transfer pathways in photosystems and the ability to compute the site energies in a fast and accurate manner is mandatory for investigating how protein dynamics ef-fect the site energies and ultimately energy pathways with time. In this work we developed two software frameworks designed to optimize the calculations of chro-mophore site energies within a protein environment. The first is for performing quantum mechanical energy optimizations on molecules and the second is for com-puting site energies of chromophores in a fast and accurate manner using the polar-izability embedding method. The two frameworks allow for the fast and accurate calculation of chromophore site energies within proteins, ultimately allowing for the effect of protein dynamics on energy pathways to be studied. We use these frame-works to compute the site energies of the eight chromophores in the reaction center of photosystem II (PSII) using a 1.9 Å resolution x-ray structure of photosystem II. We compare our results to conflicting experimental data obtained from both isolat-ed intact PSII core preparations and the minimal reaction center preparation of PSII, and find our work more supportive of the former.

Reliability Estimation of Open Source Software based Computational Systems

Software systems are progressively being deployed in many facets of human life. The implication of the failure of such systems, has an assorted impact on its customers. The fundamental aspect that supports a software system, is focus on quality. Reliability describes the ability of the system to function under specified environment for a specified period of time and is used to objectively measure the quality. Evaluation of reliability of a computing system involves computation of hardware and software reliability. Most of the earlier works were given focus on software reliability with no consideration for hardware parts or vice versa. However, a complete estimation of reliability of a computing system requires these two elements to be considered together, and thus demands a combined approach. The present work focuses on this and presents a model for evaluating the reliability of a computing system. The method involves identifying the failure data for hardware components, software components and building a model based on it, to predict the reliability. To develop such a model, focus is given to the systems based on Open Source Software, since there is an increasing trend towards its use and only a few studies were reported on the modeling and measurement of the reliability of such products. The present work includes a thorough study on the role of Free and Open Source Software, evaluation of reliability growth models, and is trying to present an integrated model for the prediction of reliability of a computational system. The developed model has been compared with existing models and its usefulness of is being discussed.

Estimation of the probability of congestion using Monte Carlo method in OPS networks

In networks with small buffers, such as optical packet switching based networks, the convolution approach is presented as one of the most accurate method used for the connection admission control. Admission control and resource management have been addressed in other works oriented to bursty traffic and ATM. This paper focuses on heterogeneous traffic in OPS based networks. Using heterogeneous traffic and bufferless networks the enhanced convolution approach is a good solution. However, both methods (CA and ECA) present a high computational cost for high number of connections. Two new mechanisms (UMCA and ISCA) based on Monte Carlo method are proposed to overcome this drawback. Simulation results show that our proposals achieve lower computational cost compared to enhanced convolution approach with an small stochastic error in the probability estimation

A collocation method for high frequency scattering by convex polygons

We consider the problem of scattering of a time-harmonic acoustic incident plane wave by a sound soft convex polygon. For standard boundary or finite element methods, with a piecewise polynomial approximation space, the computational cost required to achieve a prescribed level of accuracy grows linearly with respect to the frequency of the incident wave. Recently Chandler–Wilde and Langdon proposed a novel Galerkin boundary element method for this problem for which, by incorporating the products of plane wave basis functions with piecewise polynomials supported on a graded mesh into the approximation space, they were able to demonstrate that the number of degrees of freedom required to achieve a prescribed level of accuracy grows only logarithmically with respect to the frequency. Here we propose a related collocation method, using the same approximation space, for which we demonstrate via numerical experiments a convergence rate identical to that achieved with the Galerkin scheme, but with a substantially reduced computational cost.

A Galerkin boundary element method for high frequency scattering by convex polygons

In this paper we consider the problem of time-harmonic acoustic scattering in two dimensions by convex polygons. Standard boundary or finite element methods for acoustic scattering problems have a computational cost that grows at least linearly as a function of the frequency of the incident wave. Here we present a novel Galerkin boundary element method, which uses an approximation space consisting of the products of plane waves with piecewise polynomials supported on a graded mesh, with smaller elements closer to the corners of the polygon. We prove that the best approximation from the approximation space requires a number of degrees of freedom to achieve a prescribed level of accuracy that grows only logarithmically as a function of the frequency. Numerical results demonstrate the same logarithmic dependence on the frequency for the Galerkin method solution. Our boundary element method is a discretization of a well-known second kind combined-layer-potential integral equation. We provide a proof that this equation and its adjoint are well-posed and equivalent to the boundary value problem in a Sobolev space setting for general Lipschitz domains.

A Nyström method for a boundary value problem arising in unsteady water wave problems

This paper is concerned with solving numerically the Dirichlet boundary value problem for Laplace’s equation in a nonlocally perturbed half-plane. This problem arises in the simulation of classical unsteady water wave problems. The starting point for the numerical scheme is the boundary integral equation reformulation of this problem as an integral equation of the second kind on the real line in Preston et al. (2008, J. Int. Equ. Appl., 20, 121–152). We present a Nystr¨om method for numerical solution of this integral equation and show stability and convergence, and we present and analyse a numerical scheme for computing the Dirichlet-to-Neumann map, i.e., for deducing the instantaneous fluid surface velocity from the velocity potential on the surface, a key computational step in unsteady water wave simulations. In particular, we show that our numerical schemes are superalgebraically convergent if the fluid surface is infinitely smooth. The theoretical results are illustrated by numerical experiments.

Finding the smallest eigenvalue by the inverse Monte Carlo method with refinement

Finding the smallest eigenvalue of a given square matrix A of order n is computationally very intensive problem. The most popular method for this problem is the Inverse Power Method which uses LU-decomposition and forward and backward solving of the factored system at every iteration step. An alternative to this method is the Resolvent Monte Carlo method which uses representation of the resolvent matrix [I -qA](-m) as a series and then performs Monte Carlo iterations (random walks) on the elements of the matrix. This leads to great savings in computations, but the method has many restrictions and a very slow convergence. In this paper we propose a method that includes fast Monte Carlo procedure for finding the inverse matrix, refinement procedure to improve approximation of the inverse if necessary, and Monte Carlo power iterations to compute the smallest eigenvalue. We provide not only theoretical estimations about accuracy and convergence but also results from numerical tests performed on a number of test matrices.

A swarm intelligence method for feature tracking in AMV derivation

Feature tracking is a key step in the derivation of Atmospheric Motion Vectors (AMV). Most operational derivation processes use some template matching technique, such as Euclidean distance or cross-correlation, for the tracking step. As this step is very expensive computationally, often shortrange forecasts generated by Numerical Weather Prediction (NWP) systems are used to reduce the search area. Alternatives, such as optical flow methods, have been explored, with the aim of improving the number and quality of the vectors generated and the computational efficiency of the process. This paper will present the research carried out to apply Stochastic Diffusion Search, a generic search technique in the Swarm Intelligence family, to feature tracking in the context of AMV derivation. The method will be described, and we will present initial results, with Euclidean distance as reference.

Comparison of the computational cost of a Monte Carlo and deterministic algorithm for computing bilinear forms of matrix powers

In this paper we consider bilinear forms of matrix polynomials and show that these polynomials can be used to construct solutions for the problems of solving systems of linear algebraic equations, matrix inversion and finding extremal eigenvalues. An almost Optimal Monte Carlo (MAO) algorithm for computing bilinear forms of matrix polynomials is presented. Results for the computational costs of a balanced algorithm for computing the bilinear form of a matrix power is presented, i.e., an algorithm for which probability and systematic errors are of the same order, and this is compared with the computational cost for a corresponding deterministic method.

An efficient numerical method for compressible flows of a real gas using arithmetic averaging

An efficient numerical method is presented for the solution of the Euler equations governing the compressible flow of a real gas. The scheme is based on the approximate solution of a specially constructed set of linearised Riemann problems. An average of the flow variables across the interface between cells is required, and this is chosen to be the arithmetic mean for computational efficiency, which is in contrast to the usual square root averaging. The scheme is applied to a test problem for five different equations of state.

Fast and accurate SCFT calculations for periodic block-copolymer morphologies using the spectral method with Anderson mixing

We study the numerical efficiency of solving the self-consistent field theory (SCFT) for periodic block-copolymer morphologies by combining the spectral method with Anderson mixing. Using AB diblock-copolymer melts as an example, we demonstrate that this approach can be orders of magnitude faster than competing methods, permitting precise calculations with relatively little computational cost. Moreover, our results raise significant doubts that the gyroid (G) phase extends to infinite $\chi N$. With the increased precision, we are also able to resolve subtle free-energy differences, allowing us to investigate the layer stacking in the perforated-lamellar (PL) phase and the lattice arrangement of the close-packed spherical (S$_{cp}$) phase. Furthermore, our study sheds light on the existence of the newly discovered Fddd (O$^{70}$) morphology, showing that conformational asymmetry has a significant effect on its stability.