Computational studies of proteins and nucleic acid (Dissertation)

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On pKa Calculations in RNA and the Use of Structure to Improve Sequence Alignments

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Computational studies of proteins and nucleic acid (Dissertation)

  1. 1. Computational Studies of Proteins and Nucleic Acids:<br />On pKa Calculations in RNA and the<br />Use of Structure to Improve Sequence Alignments<br />Christopher Lung Kong Tang<br />Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences <br />Columbia University2008<br />© 2008Christopher Lung Kong TangAll rights reserved<br />ABSTRACT<br />Computational Studies of Proteins and Nucleic Acids: On pKa Calculations in RNA and the Use of Structure to Improve Sequence AlignmentsChristopher Lung Kong Tang<br />Proteins with similar sequences fold into similar structures. This observation has been used extensively in homology modeling, a method used to predict the structure of a protein target by aligning its amino acid sequence to that of a related protein template whose structure is known. A homology model is constructed by transferring the coordinates of the structure from the template to the target using the alignment of their sequences as a guide. However, even proteins with very little sequence similarity may have similar structures, or share common substructures. Recognizing these relationships (a process called fold recognition), and providing accurate alignments once they are found, are two important problems that continue to be a challenge. <br />Structural alignments can reveal similarities in proteins even where no significant sequence similarity exists. Prior work has shown that structural alignments can also capture important sequence signals even between very distantly related proteins. Exactly how this is applied to fold recognition and the sequence alignment problem has been the subject of much active research. Often, some of the most accurate methods for fold recognition and sequence alignment combine several different types of sequence and structural information. These include information such as actual or predicted secondary structure, amino acid preferences for different structural environments, and the lengths and distributions of gaps.<br />Sequence profiles describe positions in a protein by the frequency they can be replaced by each of the twenty amino acids. This thesis describes the creation of sequence profiles based on structural alignments called HMAP (hybrid multi-dimensional alignment of profiles). In particular, they are called “hybrid” because they combine and use several kinds of information, including amino acid preferences, and actual or predicted secondary structure. Profiles can be merged based on alignments derived from the structural superposition of related templates. In this thesis, these profiles are tested for their ability to detect structurally-related proteins in comprehensive benchmarks based on: (1) the protein classification database: SCOP, and (2) a quantitative measure of protein structural distance (PSD) to define true structural relationships. We find that the use of actual and predicted secondary structure greatly improves fold recognition and alignment quality, and the level of alignment accuracy achieved compares favorably to some of the top-performing methods in blind structure prediction experiments such as CASP. Profiles merged based on structural alignments also perform well, suggesting that weak sequence signals may be captured by these profiles.<br />Structural relationships, such as those detected by using HMAP in fold recognition, can be used to make functional inferences for proteins with unknown biological function. Indeed, it is sometimes possible to transfer functional information such as the ligand binding sites or active site residues once an alignment has been made between two proteins. This is made possible in part by the growing number of protein structures being contributed to the RCSB. There is now also an increasing number of functional RNA molecules whose structures have been solved. These RNA structures can similarly provide answers to questions about the functions of different kinds of RNA molecules, ranging from riboswitches to ribozymes. <br />Ribozymes are RNA molecules that catalyze specific chemical reactions. The mechanism by which RNA can do this has been the subject of much scientific study as well as human curiosity. Recently, it has been found that hepatitis delta virus (HDV) and other ribozymes do not require chemical groups other than those normally found in RNA for catalysis, and in fact, some nucleobase (base) groups need to be protonated in order to function effectively. This has implied that RNA is capable of stabilizing protonated nucleotides at physiological pH, and in so doing, shift the pKas of one or more of its own bases. Protonated nucleotides are found in the structures of a wide variety of RNAs, and can be shown to play structural as well as functional roles. <br />Methods based on the Poisson-Boltzmann equation have been quite successful in calculating amino acid pKa shifts in proteins. Solutions of the Poisson-Boltzmann equation describe the electrostatic potential around charged and polar molecules immersed in an aqueous solvent with mobile counterions. The focus of the research presented here was to establish whether methods based on this equation could be successfully applied to RNA molecules. In particular, we started with MCCE, a method for calculating pKa shifts in proteins, and added the capability to apply it to RNA molecules. This work has required addressing several issues: (1) the nonlinear behavior of electrostatic potentials in the presence of highly charged molecules, for example in RNA, has not usually been treated in protein pKa calculations, (2) the lack of atomic charge parameters for protonated nucleotides has required their development and testing, and (3) a set of experimental results from the literature was needed to test the validity of the calculations. The work presented in this thesis now shows that the method: (1) can reproduce pKa shifts that have been measured experimentally, though some appear to be overestimated, (2) reproduces changes in the pKa shifts due to changes in salt concentration, (3) predicts the locations of nucleotides that may be functionally important due to their unusual pKa shifts, and (4) can help explain how structural features contribute to the pKa shifts of nucleotides in ribozymes and other RNAs. Applied to several RNAs including the HDV and hairpin ribozymes, the results support the idea that RNA structure can stabilize protonated nucleotides where they may be critical for structure or function. The structural features that help stabilize these shifts are also discussed.<br />With the development of our method, the structural information obtained from RNA molecules can now be used for calculating the pKa shifts of nucleotides in RNA. Calculations of pKa shifts in RNA can also be used as they are in proteins. Like in proteins, the identification of chemical groups that have abnormally shifted pKas or titration curves can lead to the identification of active site residues in RNA. With the development of a pKa calculation for RNA molecules, this kind of analysis, when used in a database-wide search, may also provide much needed information about the functions of many more RNA molecules. As the number of RNA structures continues to grow, such information can become even more valuable when methods for aligning RNA sequences to their homologs are applied, and the information from one RNA structure is leveraged by applying the information to RNA molecules of similar structures.<br />Table of Contents<br /> TOC o " 1-3" h z u <br />1Introduction PAGEREF _Toc198541888 h 1<br />1.1The Thermodynamic Hypothesis PAGEREF _Toc198541889 h 1<br />2On the Sequence Alignment Problem In Protein Homology Modeling PAGEREF _Toc198541890 h 6<br />2.1 The Protein Structure Prediction Problem PAGEREF _Toc198541891 h 6<br />2.2Homology Modeling PAGEREF _Toc198541892 h 10<br />2.3Sequence Alignments: Toward Improving Accuracy PAGEREF _Toc198541893 h 14<br />3On the Role of Structural Information in Remote Homology Detection and Sequence Alignment: New Methods in Using Hybrid Sequence Profiles PAGEREF _Toc198541894 h 20<br />3.1 Research Paper I PAGEREF _Toc198541895 h 20<br />4On the Suboptimal Alignment of Protein Sequences PAGEREF _Toc198541896 h 41<br />4.1Introduction PAGEREF _Toc198541897 h 41<br />4.2 Alignment Sampling: Background and Current Methods PAGEREF _Toc198541898 h 42<br />4.3Theory: Dynamic Programming and Suboptimal Alignments PAGEREF _Toc198541899 h 47<br />4.4 Future Directions PAGEREF _Toc198541900 h 54<br />5On the Protonation of Nucleotides in RNA Structures PAGEREF _Toc198541901 h 57<br />5.1Introduction PAGEREF _Toc198541902 h 57<br />5.2Classical Electrostatics and the Calculation of pKa Shifts PAGEREF _Toc198541903 h 58<br />5.3The Hepatitis Delta Virus Ribozyme: A Curious RNA PAGEREF _Toc198541904 h 67<br />6Calculation of pKas in RNA: On the Structural Origins and Functional Roles of Protonated Nucleotides PAGEREF _Toc198541905 h 74<br />6.1Research Paper II PAGEREF _Toc198541906 h 74<br />6.2Supplementary Materials to Paper II PAGEREF _Toc198541907 h 97<br />6.3Software availability PAGEREF _Toc198541908 h 112<br />7 Implications and Future Work on the Calculation of pKa shifts in RNA PAGEREF _Toc198541909 h 115<br />Bibliography PAGEREF _Toc198541910 h 116<br />List of Figures<br />Figure 2.1The Homology Modeling Process11<br />Figure 4.1Redundant and Non-redundant Suboptimal Alignments46<br />Figure 4.2A Dynamic Programming Matrix Containing a Path49<br />Figure 4.3A Step in the Dynamic Programming Algorithm51<br />Figure 4.4A Traceback Step in Waterman’s Near Optimal Alignment Algorithm53<br />Figure 6.1Relationship of the Nonlinear Correction Term to Net Charge97<br />Figure 6.2Comparison of pKa Calculations with and without the Nonlinear Correction Term99<br />Figure 6.3Structures of the Nucleotides and Model Compounds100<br />List of Tables<br />Table 2.1Methods of Sequence Alignment and Selected Examples16<br />Table 6.1Atomic Radii Parameters for Nucleotides101<br />Table 6.2Partial Atomic Charges for Nucleotides104<br />Table 6.3Calculated Transfer Free Energies for Model Nucleic Acid Compounds107<br />Table 6.4Dependence of Calculated Transfer Free Energies on Atomic Radii109<br />Table 6.5Parameters for MCCE and qnifft 110<br />Table 6.6pKas of Nucleotides in Leadzyme at 0.1 M Salt113<br />Table 6.7pKas of Nucleotides in Leadzyme at 0.5 M Salt114<br />Acknowledgements<br />I am deeply indebted to Prof. Barry Honig for the opportunity to work in his lab. Barry has been many things to me: a thoughtful advisor, an insightful teacher, a diligent colleague and a caring friend. Much that I have learned and accomplished could not have been done without Barry, who has, over the years, helped me without hesitation in many professional and personal capacities. Barry’s comments, guidance, and concern for my development, have supported, encouraged, enlightened and cheered me throughout my time in his lab.<br />I owe a great debt of gratitude to Prof. Emil Alexov, who has contributed much to my learning. It is in part through our frequent discussions and his direct contributions that much of my own work was possible. I thank Prof. Marilyn Gunner here for her permission to develop MCCE, a program that Emil and I have added to and used extensively. I am very grateful to Prof. Anna Pyle for her enthusiasm and comments, both of which were encouraging and enlightening throughout our work together.<br />I would like to thank Profs. Burkhard Rost, Larry Shapiro, Diana Murray, and An-Suei Yang for their participation in my academic development and their valuable role in advising me. Prof. Ron Liem has played an important role in encouraging and supporting me, and both he and Fred Loweff have assisted me in as many capacities the graduate school could provide. <br />I thank Shana Posy, Markus Fischer, Remo Rohs for their comments on the (last minute distributions of) drafts of my manuscript. Including them, my life has been greatly enriched by the many kind and talented scientists and students I have been fortunate to work with. I have greatly enjoyed collaborating with Lucy Forrest, Donald Petrey, Lei Xie, Rachel Kolodny, Kely Norel, Andrew Kuziemko, and Jiang Zhu. Conversations with Jeromie Vendome, Sean West, Peng Liu, Brian Chen and certainly many others have frequently brought joy. I much appreciate Katie Rosa and Zaia Sivo for their encouragement in addition to their help in administrative capacities. They have made my life easier. I thank Charles Williams, Juli, Val, Anna, Yung, Jimmy, Christina and Utpal for their enduring friendships, who, each in their own way, have kept me sane for many years.<br />I cannot end without mentioning my brother Howard, or my parents Tohping and Yong Ying Tang. Without the sacrifices of my parents, or the support of my brother, there would not be this acknowledgement to write.<br />Dedicated in loving memory to my father, <br />John Tohping Tang, who instilled in me a great curiosity.<br />1Introduction<br />1.1The Thermodynamic Hypothesis<br />In 1963, J.C. Kendrew wrote: <br />In the very long run, it should only be necessary to determine the amino acid sequence of a protein in order to predict its three-dimensional structure. In my view this day will not come soon, but when it does come the x-ray crystallographer can go out of business, perhaps with a certain sense of relief… ADDIN EN.CITE <EndNote><Cite><Author>Kendrew</Author><Year>1963</Year><RecNum>1</RecNum><record><rec-number>1</rec-number><foreign-keys><key app=" EN" db-id=" prff505fgxdxzyeepxavvpdl0ptwtszzdpdz" >1</key></foreign-keys><ref-type name=" Journal Article" >17</ref-type><contributors><authors><author>Kendrew, J. C.</author></authors></contributors><titles><title>Myoglobin and the structure of proteins</title><secondary-title>Science</secondary-title></titles><periodical><full-title>Science</full-title></periodical><pages>1259-66</pages><volume>139</volume><keywords><keyword>*Myoglobin</keyword></keywords><dates><year>1963</year><pub-dates><date>Mar 29</date></pub-dates></dates><accession-num>14031909</accession-num><urls><related-urls><url>http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=14031909 </url></related-urls></urls></record></Cite></EndNote>(Kendrew, 1963)<br />Indeed, the protein-making machinery of a living organism needs only to link amino acid residues into the proper sequence and the process of folding into the correct three-dimensional structure happens spontaneously, requiring no further information other than sequence. This observation was first reported by C.B. Anfinsen in his classical refolding experiments concerning the protein bovine pancreatic ribonuclease ADDIN EN.CITE <EndNote><Cite><Author>Anfinsen</Author><Year>1961</Year><RecNum>2</RecNum><record><rec-number>2</rec-number><foreign-keys><key app=" EN" db-id=" prff505fgxdxzyeepxavvpdl0ptwtszzdpdz" >2</key></foreign-keys><ref-type name=" Journal Article" >17</ref-type><contributors><authors><author>Anfinsen, C. B.</author><author>Haber, E.</author><author>Sela, M.</author><author>White, F. H., Jr.</author></authors></contributors><titles><title>The kinetics of formation of native ribonuclease during oxidation of the reduced polypeptide chain</title><secondary-title>Proc Natl Acad Sci U S A</secondary-title></titles><periodical><full-title>Proc Natl Acad Sci U S A</full-title></periodical><pages>1309-14</pages><volume>47</volume><keywords><keyword>Ribonucleases/*chemistry</keyword></keywords><dates><year>1961</year><pub-dates><date>Sep 15</date></pub-dates></dates><accession-num>13683522</accession-num><urls><related-urls><url>http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=13683522 </url></related-urls></urls></record></Cite></EndNote>(Anfinsen, 1961). In these experiments, proteins were unfolded using reducing and denaturing conditions, creating a mixture of inactive proteins with scrambled disulfide bonds. When the inactive proteins were later allowed to refold, it was found that they could do so spontaneously, completely reverting to their native, active form without the addition of any other cellular factors. This key observation was interpreted to mean that the correct native conformation of a protein is encoded entirely within its amino acid sequence, and independent of external information. From this, C.B. Anfinsen proposed the “thermodynamic hypothesis” ADDIN EN.CITE <EndNote><Cite><Author>Anfinsen</Author><Year>1973</Year><RecNum>3</RecNum><record><rec-number>3</rec-number><foreign-keys><key app=" EN" db-id=" prff505fgxdxzyeepxavvpdl0ptwtszzdpdz" >3</key></foreign-keys><ref-type name=" Journal Article" >17</ref-type><contributors><authors><author>Anfinsen, C. B.</author></authors></contributors><titles><title>Principles that govern the folding of protein chains</title><secondary-title>Science</secondary-title></titles><periodical><full-title>Science</full-title></periodical><pages>223-30</pages><volume>181</volume><number>96</number><keywords><keyword>Amino Acid Sequence</keyword><keyword>Animals</keyword><keyword>Antigen-Antibody Reactions</keyword><keyword>Cattle</keyword><keyword>Epitopes</keyword><keyword>Exonucleases</keyword><keyword>Goats/immunology</keyword><keyword>Models, Structural</keyword><keyword>Pancreas/enzymology</keyword><keyword>Peptides</keyword><keyword>Proinsulin</keyword><keyword>*Protein Conformation</keyword><keyword>Protein Denaturation</keyword><keyword>*Ribonucleases</keyword><keyword>Spectrometry, Fluorescence</keyword><keyword>Staphylococcus/enzymology</keyword><keyword>Swine</keyword><keyword>Viscosity</keyword></keywords><dates><year>1973</year><pub-dates><date>Jul 20</date></pub-dates></dates><accession-num>4124164</accession-num><urls><related-urls><url>http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=4124164 </url></related-urls></urls></record></Cite></EndNote>(Anfinsen, 1973) – that the native conformation is the one such conformation wherein no further net decrease in conformational free energy can occur. Thus, the proper folding and structure of a protein is achieved solely by minimizing the conformational free energy of its residue sequence. To take this reasoning further: if the components of a protein’s conformational free energy could be well-described and calculated, then, in theory, it would also be possible to calculate and thereby predict its three-dimensional conformation solely from its primary sequence. Today, we are only partially successful – in many ways, it is possible to accurately describe the conformational free energies of proteins PEVuZE5vdGU+PENpdGU+PEF1dGhvcj5MYXphcmlkaXM8L0F1dGhvcj48WWVhcj4xOTk5PC9ZZWFy PjxSZWNOdW0+Mzc8L1JlY051bT48cmVjb3JkPjxyZWMtbnVtYmVyPjM3PC9yZWMtbnVtYmVyPjxm b3JlaWduLWtleXM+PGtleSBhcHA9IkVOIiBkYi1pZD0icHJmZjUwNWZneGR4enllZXB4YXZ2cGRs MHB0d3RzenpkcGR6Ij4zNzwva2V5PjwvZm9yZWlnbi1rZXlzPjxyZWYtdHlwZSBuYW1lPSJKb3Vy bmFsIEFydGljbGUiPjE3PC9yZWYtdHlwZT48Y29udHJpYnV0b3JzPjxhdXRob3JzPjxhdXRob3I+ TGF6YXJpZGlzLCBULjwvYXV0aG9yPjxhdXRob3I+S2FycGx1cywgTS48L2F1dGhvcj48L2F1dGhv cnM+PC9jb250cmlidXRvcnM+PGF1dGgtYWRkcmVzcz5EZXBhcnRtZW50IG9mIENoZW1pc3RyeSBh bmQgQ2hlbWljYWwgQmlvbG9neSwgSGFydmFyZCBVbml2ZXJzaXR5LCAxMiBPeGZvcmQgU3QsIENh bWJyaWRnZSwgTUEsIDAyMTM4LCBVU0EuPC9hdXRoLWFkZHJlc3M+PHRpdGxlcz48dGl0bGU+RGlz Y3JpbWluYXRpb24gb2YgdGhlIG5hdGl2ZSBmcm9tIG1pc2ZvbGRlZCBwcm90ZWluIG1vZGVscyB3 aXRoIGFuIGVuZXJneSBmdW5jdGlvbiBpbmNsdWRpbmcgaW1wbGljaXQgc29sdmF0aW9uPC90aXRs 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However, the number of available conformations, the so-called conformational space, for typical molecules is very large, and it remains difficult to sample conformations from within this space without use of heavy computational resources ADDIN EN.CITE <EndNote><Cite><Author>Das</Author><Year>2007</Year><RecNum>25</RecNum><record><rec-number>25</rec-number><foreign-keys><key app=" EN" db-id=" prff505fgxdxzyeepxavvpdl0ptwtszzdpdz" >25</key></foreign-keys><ref-type name=" Journal Article" >17</ref-type><contributors><authors><author>Das, R.</author><author>Qian, B.</author><author>Raman, S.</author><author>Vernon, R.</author><author>Thompson, J.</author><author>Bradley, P.</author><author>Khare, S.</author><author>Tyka, M. D.</author><author>Bhat, D.</author><author>Chivian, D.</author><author>Kim, D. E.</author><author>Sheffler, W. H.</author><author>Malmstrom, L.</author><author>Wollacott, A. M.</author><author>Wang, C.</author><author>Andre, I.</author><author>Baker, D.</author></authors></contributors><auth-address>Department of Biochemistry, University of Washington, Seattle, Washington 98195.</auth-address><titles><title>Structure prediction for CASP7 targets using extensive all-atom refinement with Rosetta@home</title><secondary-title>Proteins</secondary-title></titles><periodical><full-title>Proteins</full-title></periodical><pages>118-28</pages><edition>2007/09/27</edition><dates><year>2007</year><pub-dates><date>Sep 25</date></pub-dates></dates><isbn>1097-0134 (Electronic)</isbn><accession-num>17894356</accession-num><urls><related-urls><url>http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=17894356</url></related-urls></urls><electronic-resource-num>10.1002/prot.21636</electronic-resource-num><language>Eng</language></record></Cite></EndNote>(Das, 2007). 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accurate energetic description of biological molecules is fundamental to understanding the nature of their structure and function. 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Indeed, the electrostatic description of molecules can supply visual intuition that leads to an understanding of how electrostatics properties (which is the consequence of structure) contribute to the function of a biological molecule. A classic example includes the use of the PBE to compute the electrostatic potentials surrounding the protein superoxide dismutase ADDIN EN.CITE <EndNote><Cite><Author>Klapper</Author><Year>1986</Year><RecNum>15</RecNum><record><rec-number>15</rec-number><foreign-keys><key app=" EN" db-id=" prff505fgxdxzyeepxavvpdl0ptwtszzdpdz" >15</key></foreign-keys><ref-type name=" Journal Article" >17</ref-type><contributors><authors><author>Klapper, I.</author><author>Hagstrom, R.</author><author>Fine, R.</author><author>Sharp, K.</author><author>Honig, B.</author></authors></contributors><auth-address>High Energy Physics Division, Argonne National Laboratory, Illinois 60439.</auth-address><titles><title>Focusing of electric fields in the active site of Cu-Zn superoxide dismutase: effects of ionic strength and amino-acid modification</title><secondary-title>Proteins</secondary-title></titles><periodical><full-title>Proteins</full-title></periodical><pages>47-59</pages><volume>1</volume><number>1</number><edition>1986/09/01</edition><keywords><keyword>Amino Acids</keyword><keyword>Binding Sites</keyword><keyword>Electrochemistry</keyword><keyword>Models, Chemical</keyword><keyword>Osmolar Concentration</keyword><keyword>Superoxide Dismutase/*metabolism</keyword></keywords><dates><year>1986</year><pub-dates><date>Sep</date></pub-dates></dates><isbn>0887-3585 (Print)</isbn><accession-num>3449851</accession-num><urls><related-urls><url>http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=3449851</url></related-urls></urls><electronic-resource-num>10.1002/prot.340010109</electronic-resource-num><language>eng</language></record></Cite></EndNote>(Klapper, 1986). Calculations using the PBE reveal a highly-charged positive center on the surface of the protein near the active site, which functions to draw the negatively charged substrate into the active site center ADDIN EN.CITE <EndNote><Cite><Author>Sharp</Author><Year>1987</Year><RecNum>14</RecNum><record><rec-number>14</rec-number><foreign-keys><key app=" EN" db-id=" prff505fgxdxzyeepxavvpdl0ptwtszzdpdz" >14</key></foreign-keys><ref-type name=" Journal Article" >17</ref-type><contributors><authors><author>Sharp, K.</author><author>Fine, R.</author><author>Honig, B.</author></authors></contributors><titles><title>Computer simulations of the diffusion of a substrate to an active site of an enzyme</title><secondary-title>Science</secondary-title></titles><periodical><full-title>Science</full-title></periodical><pages>1460-3</pages><volume>236</volume><number>4807</number><edition>1987/06/12</edition><keywords><keyword>*Binding Sites</keyword><keyword>*Computer Simulation</keyword><keyword>Diffusion</keyword><keyword>Enzymes/*metabolism</keyword><keyword>Kinetics</keyword><keyword>Mathematics</keyword><keyword>Mutation</keyword><keyword>Superoxide Dismutase/metabolism</keyword></keywords><dates><year>1987</year><pub-dates><date>Jun 12</date></pub-dates></dates><isbn>0036-8075 (Print)</isbn><accession-num>3589666</accession-num><urls><related-urls><url>http://www.ncbi.nlm.nih.gov/entrez/query.fcgi?cmd=Retrieve&db=PubMed&dopt=Citation&list_uids=3589666</url></related-urls></urls><language>eng</language></record></Cite></EndNote>(Sharp, 1987). 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