The graduation of secondary structure elements |
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| Affiliation: | 1. Adnan Menderes University, Faculty of Medicine, Department of Internal Medicine, Aydin, Turkey;2. Ege University, Faculty of Medicine, Division of Hematology, Izmir, Turkey;3. Gazi University, Faculty of Medicine, Division of Hematology, Ankara, Turkey;4. Bozyaka Training and Research Hospital, Izmir, Turkey;5. Mersin University, Faculty of Medicine, Division of Hematology, Mersin, Turkey;6. Bülent Ecevit University, Faculty of Medicine, Division of Hematology, Zonguldak, Turkey;7. Dicle University, Faculty of Medicine, Division of Hematology, Diyarbakir, Turkey;8. Karadeniz University, Faculty of Medicine, Division of Hematology, Trabzon, Turkey;9. Bezmialem University, Faculty of Medicine, Division of Hematology, Istanbul, Turkey;1. MARBEC, Univ Montpellier, CNRS, Ifremer, IRD, Sète, France;2. Ifremer, UMR 6308 Amure, Plouzané, France;3. CEE-M, Univ Montpellier, CNRS, INRAE, Institut Agro, Montpellier, France;4. UMR Fromage, INRAE, Université Clermont Auvergne, VetAgro-Sup, Aurillac, France;1. Department of Psychiatry, University of California San Diego, United States;2. Geriatric Research Clinical and Education Center, Veterans Affairs Puget Sound Health Care System and Division of Gerontology and Geriatric Medicine, Department of Medicine, University of Washington School of Medicine, United States;1. Department of Pharmacy, Shengjing Hospital of China Medical University, Shenyang 110004, China;2. Wuya College of Innovation, School of Pharmacy, Key Laboratory of Structure-Based Drug Design & Discovery, Ministry of Education, Shenyang Pharmaceutical University, Shenyang 110016, China;3. Hubei Key Laboratory of Natural Medicinal Chemistry and Resource Evaluation, School of Pharmacy, Tongji Medical College, Huazhong University of Science and Technology, Wuhan 430030, China |
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| Abstract: | A method of graduating (i.e., least-squares fitting) a smooth polynomial curve through long elements of protein secondary structure is described. It uses the Chebyshev polynomials of a discrete (integer) variable with several restraints to prevent artifactual curvatures. A new recursion formula is given which allows the evaluation of the polynomials on rational-number points as well as on the integer points. High-order splines suitable for interpolation between integer points are also discussed. The new method finds applications in graphics and in structural analysis. |
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