{"title":"E-optimal solutions to distance geometry problems via global continuation","authors":"J. J. Moré, Zhi-jun Wu","doi":"10.1090/dimacs/023/10","DOIUrl":"https://doi.org/10.1090/dimacs/023/10","url":null,"abstract":"","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121866805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding, Proceedings of a DIMACS Workshop, USA, March 20-21, 1995","authors":"P. Pardalos, D. Shalloway, G. Xue","doi":"10.1090/DIMACS/023","DOIUrl":"https://doi.org/10.1090/DIMACS/023","url":null,"abstract":"","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"78 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1995-11-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129364767","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Byrd, E. Eskow, A. Hoek, Bobby Schnabel, Chung-Shang Shao, Zhihong Zou
The problem of nding the naturally occurring structure of a pro tein is believed to correspond to minimizing the free or potential energy of the protein This is generally a very di cult global optimizationproblem with a large number of parameters and a huge number of local minimizers includ ing many with function values near that of the global minimizer This paper presents a new global optimization method for such problems The method consists of an initial phase that locates some reasonably low local minimizers of the energy function followed by the main phase that progresses from the best current local minimizers to even lower local minimizers The method combines portions that work on small subsets of the parameters including small scale global optimizations using stochastic methods with local minimizations in volving all the parameters In computational tests on the protein polyalanine with up to amino acids internal parameters the method appears to be very successful in nding the lowest energy structures The largest case is particularly signi cant because the lowest energy structures that are found include ones that exhibit interesting tertiary as opposed to just secondary
{"title":"Global optimization methods for protein folding problems","authors":"R. Byrd, E. Eskow, A. Hoek, Bobby Schnabel, Chung-Shang Shao, Zhihong Zou","doi":"10.1090/dimacs/023/03","DOIUrl":"https://doi.org/10.1090/dimacs/023/03","url":null,"abstract":"The problem of nding the naturally occurring structure of a pro tein is believed to correspond to minimizing the free or potential energy of the protein This is generally a very di cult global optimizationproblem with a large number of parameters and a huge number of local minimizers includ ing many with function values near that of the global minimizer This paper presents a new global optimization method for such problems The method consists of an initial phase that locates some reasonably low local minimizers of the energy function followed by the main phase that progresses from the best current local minimizers to even lower local minimizers The method combines portions that work on small subsets of the parameters including small scale global optimizations using stochastic methods with local minimizations in volving all the parameters In computational tests on the protein polyalanine with up to amino acids internal parameters the method appears to be very successful in nding the lowest energy structures The largest case is particularly signi cant because the lowest energy structures that are found include ones that exhibit interesting tertiary as opposed to just secondary","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122146053","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"A minimal principle in the phase problem of X-ray crystallography","authors":"H. Hauptman","doi":"10.1090/dimacs/023/06","DOIUrl":"https://doi.org/10.1090/dimacs/023/06","url":null,"abstract":"","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122730920","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Thermodynamics and kinetics of protein folding","authors":"A. Sali, E. Shakhnovich, M. Karplus","doi":"10.1090/dimacs/023/13","DOIUrl":"https://doi.org/10.1090/dimacs/023/13","url":null,"abstract":"","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"83 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114624922","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Global minimization on rugged energy landscapes","authors":"P. Amara, Jianpeng Ma, J. Straub","doi":"10.1090/dimacs/023/01","DOIUrl":"https://doi.org/10.1090/dimacs/023/01","url":null,"abstract":"","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130390343","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The determination of a stable molecular structure can often be formulated in terms of calculating the global (or approximate global) minimum of a potential energy function. Computing the global minimum of this function is very difficult because it typically has a very large number of local minima which may grow exponentially with molecule size. The optimization method presented involves collecting a large number of conformers, each attained by finding a local minimum of the potential energy function from a random starting point. The information from these conformers is then used to form a convex quadratic global underestimating function for the potential energy of all known conformers. This underestimator is an L 1 approximation to all known local minima, and is obtained by a linear programming formulation and solution. The minimum of this underestimator is used to predict the global minimum for the function, allowing a localized conformer search to be performed based on the predicted minimum. The new set of conformers generated by the localized search serves as the basis for another quadratic underestimation step in an iterative algorithm. This algorithm has been used to determine the structures of homopolymers of lengthn ≤ 30 with no sidechains. While it is estimated that there areO(3n) local minima for a chain of length n, this method requires O(n4) computing time on average. It is also shown that the global minimum potential energy values lie on a concave quadratic curve for n ≤ 30. This important property permits estimation of the minimum energy for larger molecules, and also can be used to accelerate the global minimization algorithm.
{"title":"Molecular structure determination by convex, global underestimation of local energy minima","authors":"A. Phillips, J. B. Rosen, V. H. Walke","doi":"10.1090/dimacs/023/12","DOIUrl":"https://doi.org/10.1090/dimacs/023/12","url":null,"abstract":"The determination of a stable molecular structure can often be formulated in terms of calculating the global (or approximate global) minimum of a potential energy function. Computing the global minimum of this function is very difficult because it typically has a very large number of local minima which may grow exponentially with molecule size. The optimization method presented involves collecting a large number of conformers, each attained by finding a local minimum of the potential energy function from a random starting point. The information from these conformers is then used to form a convex quadratic global underestimating function for the potential energy of all known conformers. This underestimator is an L 1 approximation to all known local minima, and is obtained by a linear programming formulation and solution. The minimum of this underestimator is used to predict the global minimum for the function, allowing a localized conformer search to be performed based on the predicted minimum. The new set of conformers generated by the localized search serves as the basis for another quadratic underestimation step in an iterative algorithm. This algorithm has been used to determine the structures of homopolymers of lengthn ≤ 30 with no sidechains. While it is estimated that there areO(3n) local minima for a chain of length n, this method requires O(n4) computing time on average. It is also shown that the global minimum potential energy values lie on a concave quadratic curve for n ≤ 30. This important property permits estimation of the minimum energy for larger molecules, and also can be used to accelerate the global minimization algorithm.","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114187147","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
R. Pachter, Zhiqiang Wang, J. A. Lupo, S. Fairchild, Brian Sennett
{"title":"The design of chromophore containing biomolecules","authors":"R. Pachter, Zhiqiang Wang, J. A. Lupo, S. Fairchild, Brian Sennett","doi":"10.1090/dimacs/023/11","DOIUrl":"https://doi.org/10.1090/dimacs/023/11","url":null,"abstract":"","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126395037","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Energy directed conformational search of protein loops and segments","authors":"R. Bruccoleri","doi":"10.1090/dimacs/023/02","DOIUrl":"https://doi.org/10.1090/dimacs/023/02","url":null,"abstract":"","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125613160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Xiche Hu, Dong Xu, K. Hamer, K. Schulten, J. Koepke, H. Michel
We illustrate in this article how one proceeds to predict the structure of integral membrane proteins using a combined approach in which molecular dynamics simulations and energy minimization are performed based on structural information from conventional structure prediction methods and experimental constraints derived from biochemical and spectroscopical data. We focus here on the prediction of the structure of the light-harvesting complex II (LH–II) of Rhodospirillum molischianum, an integral membrane protein of 16 polypeptides aggregating and binding to 24 bacteriochlorophyll a’s and 12 lycopenes. Hydropathy analysis was performed to identify the putative transmembrane segments. Multiple sequence alignment propensity analyses further pinpointed the exact sites of the 20 residue long transmembrane segment and the four residue long terminal sequence at both ends, which were independently verified and improved by homology modeling. A consensus assignment for secondary structure was derived from a combination of all the prediction methods used. The three-dimensional structures for the αand the β-apoprotein were built by comparative modeling. The resulting tertiary structures were combined into an αβ dimer pair with bacteriochlorophyll a’s attached under constraints provided by site directed mutagenesis and FT Resonance Raman spectra, as well as by conservation of residues. The αβ dimer pairs were then aggregated into a quaternary structure through molecular dynamics simulations and energy minimization. The structure of LH–II, so determined, was an octamer of αβ heterodimers forming a ring with a diameter of 70 Å. We discuss how the resulting structure may be used to solve the phase problem in X-ray crystallography in a procedure called molecular replacement.
{"title":"Knowledge based structure prediction of the light-harvesting complex II of Rhodospirillum molishianum","authors":"Xiche Hu, Dong Xu, K. Hamer, K. Schulten, J. Koepke, H. Michel","doi":"10.1090/dimacs/023/07","DOIUrl":"https://doi.org/10.1090/dimacs/023/07","url":null,"abstract":"We illustrate in this article how one proceeds to predict the structure of integral membrane proteins using a combined approach in which molecular dynamics simulations and energy minimization are performed based on structural information from conventional structure prediction methods and experimental constraints derived from biochemical and spectroscopical data. We focus here on the prediction of the structure of the light-harvesting complex II (LH–II) of Rhodospirillum molischianum, an integral membrane protein of 16 polypeptides aggregating and binding to 24 bacteriochlorophyll a’s and 12 lycopenes. Hydropathy analysis was performed to identify the putative transmembrane segments. Multiple sequence alignment propensity analyses further pinpointed the exact sites of the 20 residue long transmembrane segment and the four residue long terminal sequence at both ends, which were independently verified and improved by homology modeling. A consensus assignment for secondary structure was derived from a combination of all the prediction methods used. The three-dimensional structures for the αand the β-apoprotein were built by comparative modeling. The resulting tertiary structures were combined into an αβ dimer pair with bacteriochlorophyll a’s attached under constraints provided by site directed mutagenesis and FT Resonance Raman spectra, as well as by conservation of residues. The αβ dimer pairs were then aggregated into a quaternary structure through molecular dynamics simulations and energy minimization. The structure of LH–II, so determined, was an octamer of αβ heterodimers forming a ring with a diameter of 70 Å. We discuss how the resulting structure may be used to solve the phase problem in X-ray crystallography in a procedure called molecular replacement.","PeriodicalId":347710,"journal":{"name":"Global Minimization of Nonconvex Energy Functions: Molecular Conformation and Protein Folding","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131432190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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