Exact analytical loop closure in proteins using polynomial equations

✍ Scribed by Wedemeyer, William J.; Scheraga, Harold A.

• Publisher: John Wiley and Sons
• Year: 1999
• Tongue: English
• Weight: 438 KB
• Volume: 20
• Category: Article
• ISSN: 0192-8651
• DOI: 10.1002/(sici)1096-987x(199906)20:8<819::aid-jcc8>3.0.co;2-y

✦ Synopsis

Loop closure in proteins has been studied actively for over 25 years. Using spherical geometry and polynomial equations, several loop-closure problems in proteins are solved exactly by reducing them to the determination of the real roots of a polynomial. Loops of seven, eight, and nine atoms are treated explicitly, including the tripeptide and disulfide-bonded loop-closure problems. The number of valid loop closures can be evaluated by the method of Sturm chains, which counts the number of real roots of a polynomial. Longer loops can be treated by three methods: by sampling enough dihedral angles to reduce the problem to a soluble loop-closure problem; by applying the loopclosure algorithm hierarchically; or by decimating the chain into independently moving rigid elements that can be reconnected using loop-closure algorithms. Applications of the methods to docking, homology modeling and NMR problems are discussed.