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Solving methods of systems of linear equations
Šotolová, Petra ; Jančařík, Antonín (advisor) ; Novotná, Jarmila (referee)
My bachelor's thesis is focused on methods for solving systems of linear equations. Its aim is to explain the application of these methods for solving systems of linear equations and to assign advantages and the type of system for which each method is advantageous. The thesis should be suitable for elementary and secondary school students, university students, as well as individuals not studying mathematics. It describes substitution method, addition method, comparison method, graphical method, Gaussian elimination, Gauss-Jordan elimination, inverse matrix and Cramer's rule and their application in solving systems of two or more linear equations with two or more unknowns. It includes a general explanation and a specific procedure with examples, advantages and disadvantages of each method, and types of systems for which the method would be used. The thesis examines the number of solutions of systems of equations depending on the form of the system. It also explains basic concepts and provides simplified definitions of the terms used.
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Methods for prediction of secondary structure in proteins
Hoštáková, Nina ; Provazník, Ivo (referee) ; Maděránková, Denisa (advisor)
The examination of protein structure is crucial in determining protein function in organism. This work deals with the issue of 1D, 2D and 3D structures, into which are proteins organized in space. Emphasis is placed on secondary structure, which can be predicted directly from the amino acid sequences and then used for the estimation of spatial structure. On this procedure are focused computational methods, using algorithms that convert the order of amino acids into the order of preferences for secondary structures. To direct determination of the structure by creating structural models is devoted chapter Experimental Methods (NMR spectroscopy, RTG crystallography). The main aim of this work is practical realization of protein secondary structure prediction method. The created program is supplemented by graphical user interface. In the final part the results of the program based on Chou- Fasman method are compared to the outputs of freely available softwares from the Internet.
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Interactions of Proteins with Nucleic Acids: from Structure to Specificity
Jakubec, Dávid ; Vondrášek, Jiří (advisor) ; Šponer, Jiří (referee) ; Zagrovic, Bojan (referee)
Sequence-specific interactions between proteins and nucleic acids play an essential role in the cell biology. While several molecular mechanisms contributing to the binding speci- ficity have been identified empirically, no general protein-DNA recognition code has been described to date. In this thesis, I explore selected characteristics of protein-DNA inter- actions using computational methods. First, the pairwise interactions between the basic biomolecular building blocks-amino acids and nucleotides-are investigated. It is shown that several statistically enriched, biologically relevant interaction motifs correspond to the most energetically favorable configurations of the respective binding partners. In ad- dition, a relationship between the physico-chemical properties of the amino acid residues found at the protein-DNA interface and the local geometric features of the DNA helix is presented. Next, the applicability of molecular dynamics-based setups to the description of binding equilibria in protein-DNA systems is investigated. Discrepancies are observed between the description offered by the computer simulations and experimental results, as well as between the results obtained using two molecular mechanical force fields. Finally, the more general evolutionary aspects of protein organization...
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Computational study of short peptides and miniproteins in different environments
Vymětal, Jiří ; Vondrášek, Jiří (advisor) ; Svozil, Daniel (referee) ; Berka, Karel (referee)
Apart from biological functions, peptides are of uttermost importance as models for un- folded, denatured or disordered state of the proteins. Similarly, miniproteins such as Trp-cage have proven their role as simple models of both experimental and theoretical studies of protein folding. Molecular dynamics and computer simulations can provide an unique insight on processes at atomic level. However, simulations of peptides and minipro- teins face two cardinal problems-inaccuracy of force fields and inadequate conformation sampling. Both principal issues were tackled in this theses. Firstly, the differences in several force field for peptides and proteins were questioned. We demonstrated the inability of the used force fields to predict consistently intrinsic conformational preferences of individual amino acids in the form of dipeptides and the source of the discrepancies was traced. In order to shed light on the nature of conformational ensembles under various denatur- ing conditions, we studied host-guest AAXAA peptides. The simulations revealed that thermal and chemical denaturation by urea produces qualitatively different ensembles and shift propensities of individual amino acids to particular conformers. The problem of insufficient conformation sampling was dealt by introducing gyration- and...
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Methods for prediction of secondary structure in proteins
Hoštáková, Nina ; Provazník, Ivo (referee) ; Maděránková, Denisa (advisor)
The examination of protein structure is crucial in determining protein function in organism. This work deals with the issue of 1D, 2D and 3D structures, into which are proteins organized in space. Emphasis is placed on secondary structure, which can be predicted directly from the amino acid sequences and then used for the estimation of spatial structure. On this procedure are focused computational methods, using algorithms that convert the order of amino acids into the order of preferences for secondary structures. To direct determination of the structure by creating structural models is devoted chapter Experimental Methods (NMR spectroscopy, RTG crystallography). The main aim of this work is practical realization of protein secondary structure prediction method. The created program is supplemented by graphical user interface. In the final part the results of the program based on Chou- Fasman method are compared to the outputs of freely available softwares from the Internet.
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