The fractal nature of folds and the Walsh copolymers

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• 作者：Vladimir R. Rosenfeld
• 关键词：Fractal ; Energy minimum ; Fold ; Nucleotide and amino ; acid distribution ; (Complementary) codonic palindrome ; Semigroup ; Idempotent ; Hadamard matrix ; (Discrete) Walsh function ; Walsh copolymer ; (Molecular) zipper
• 刊名：Journal of Mathematical Chemistry
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：54
• 期：2
• 页码：559-571
• 全文大小：428 KB
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• 作者单位：Vladimir R. Rosenfeld (1) (2)
  
  1. Mathematical Chemistry Group, Department of Marine Sciences, Texas A&M University at Galveston, Galveston, TX, 77553–1675, USA
  2. Department of Computer Science and Mathematics, Ariel University, 40700, Ariel, Israel
  
• 刊物类别：Chemistry and Materials Science
• 刊物主题：Chemistry
  Physical Chemistry
  Theoretical and Computational Chemistry
  Mathematical Applications in Chemistry
  
• 出版者：Springer Netherlands
• ISSN：1572-8897

文摘

We discuss the fractal nature of protein folds and some mathematical apparatus to describe them. In particular, the scaling symmetry of such selfsimilar objects is described using semigroup theory. As is also shown, purely mathematical considerations may open the way toward a possible rational design of a wide class of synthetic folds of diverse chemical nature (for potential nanotechnological applications). In this regard, a special role is given to the Walsh functions and associated with them molecular constructions called Walsh copolymers.