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Abstract
Proteins are the main active elements of life whose chemical activities regulate cellular activities. A protein is characterized by having a sequence of amino acids and a three dimensional structure. The threedimensional structure has only been determined experimentally for 50000 of the seven million sequences that are known. Determining the protein structure from its sequence of amino acids is therefore a major problem in computational structural biology and is referred to as the protein folding problem. The folding problem is solved using de novo methods or comparative methods depending on whether the threedimensional structure of a homologous sequence is known. Whether or not a protein model can be used for industrial purposes depends on the quality of the predicted structure. A model can be used to design a drug when the quality is high.
The overall goal of this project is to assess and improve the quality of a predicted structure. The starting point of this work is a technique called metric training where a knowledgebased protein potential, for a fixed set of native protein structures and a set of deformed decoys for each native structure, is designed to have nativedecoy energy gabs that correlates maximally to a nativedecoy distance. The main contribution of this thesis is methods developed for analyzing the performance of metrically trained knowledgebased potentials and for optimizing their performance while making them less dependent on the decoy set used to define them. We focus on using the gradient and the Hessian in the analysis and present a novel smooth solvation potential but otherwise the studied potential is kept close to standard coarse grained potentials.
We analyze the importance of the choice of metric both when used in metric training and when used in the evaluation of the performance of the resulting potential and find a significant improvement by using a metric based on intrinsic geometry. It is wellknown that energy minimization of a potential that is efficient in ordering a fixed set of decoys need not bring the decoys closer to the native state. The next part of the work is focused on improving the convergence of decoy structures and we present a method that significantly improves the results of shorter energy minimizations of a metrically trained potential and discuss its limitations. In an ideal potential all nearnative decoys will converge toward the native structure being atleast a local minimum of the potential. To address how far the current functional form of the potential is from an ideal potential we present two methods for finding the optimal metrically trained potential that simultaneous has a number of native structures as a local minimum. Our results generally indicate that a more finegrained potential is needed to meet desired model accuracies but even with our coarsegrained model we obtain good results and there is an unexplored possibility to combine it with comparative modeling.
To allow fast energy minimization in Matlab a new set of more sparse formulas to calculate the first and second derivatives of a molecular potential is derived and implemented.
The overall goal of this project is to assess and improve the quality of a predicted structure. The starting point of this work is a technique called metric training where a knowledgebased protein potential, for a fixed set of native protein structures and a set of deformed decoys for each native structure, is designed to have nativedecoy energy gabs that correlates maximally to a nativedecoy distance. The main contribution of this thesis is methods developed for analyzing the performance of metrically trained knowledgebased potentials and for optimizing their performance while making them less dependent on the decoy set used to define them. We focus on using the gradient and the Hessian in the analysis and present a novel smooth solvation potential but otherwise the studied potential is kept close to standard coarse grained potentials.
We analyze the importance of the choice of metric both when used in metric training and when used in the evaluation of the performance of the resulting potential and find a significant improvement by using a metric based on intrinsic geometry. It is wellknown that energy minimization of a potential that is efficient in ordering a fixed set of decoys need not bring the decoys closer to the native state. The next part of the work is focused on improving the convergence of decoy structures and we present a method that significantly improves the results of shorter energy minimizations of a metrically trained potential and discuss its limitations. In an ideal potential all nearnative decoys will converge toward the native structure being atleast a local minimum of the potential. To address how far the current functional form of the potential is from an ideal potential we present two methods for finding the optimal metrically trained potential that simultaneous has a number of native structures as a local minimum. Our results generally indicate that a more finegrained potential is needed to meet desired model accuracies but even with our coarsegrained model we obtain good results and there is an unexplored possibility to combine it with comparative modeling.
To allow fast energy minimization in Matlab a new set of more sparse formulas to calculate the first and second derivatives of a molecular potential is derived and implemented.
Original language  English 

Place of Publication  Kgs. Lyngby 

Publisher  Technical University of Denmark 
Number of pages  118 
Publication status  Published  2016 
Series  DTU Compute PHD2015 

Number  376 
ISSN  09093192 
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Projects
 1 Finished

Protein structure refinement by optimization
Carlsen, M., Røgen, P., Stolpe, M., Jørgensen, J. B., Keasar, C. & Hamelryck, T.
Technical University of Denmark
01/08/2011 → 30/09/2015
Project: PhD