A topological measurement of protein compressibility

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• 作者：Marcio Gameiro (1)
  Yasuaki Hiraoka (2)
  Shunsuke Izumi (3)
  Miroslav Kramar (4)
  Konstantin Mischaikow (5)
  Vidit Nanda (6)
  
  1. Instituto de Ci锚ncias Matem谩ticas e de Computa莽茫o ; Universidade de S茫o Paulo ; Caixa Postal 668 ; S茫o Carlos ; SP ; 13560-970 ; Brazil
  2. Institute of Mathematics for Industry ; Kyushu University ; 744 ; Motooka ; Nishi-ku ; Fukuoka ; 819-0395 ; Japan
  3. Department of Mathematical and Life Sciences ; Hiroshima University ; 1-3-1 ; Kagamiyama ; Higashi-Hiroshima ; 739-8526 ; Japan
  4. Department of Mathematics ; Hill Center-Busch Campus Rutgers ; The State University of New Jersey ; 110 Frelinghusen Rd ; Piscataway ; NJ ; 08854-8019 ; USA
  5. Department of Mathematics and BioMaPS ; Hill Center-Busch Campus Rutgers ; The State University of New Jersey ; 110 Frelinghusen Rd ; Piscataway ; NJ ; 08854-8019 ; USA
  6. Department of Mathematics ; The University of Pennsylvania ; DRL ; 209 South 33rd Street ; Philadelphia ; PA ; 19104 ; USA
  
• 关键词：Protein compressibility ; Computational topology ; Persistence diagram ; Stability ; 55N99
• 刊名：Japan Journal of Industrial and Applied Mathematics
• 出版年：2015
• 出版时间：March 2015
• 年：2015
• 卷：32
• 期：1
• 页码：1-17
• 全文大小：1,293 KB
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• 刊物类别：Mathematics and Statistics
• 刊物主题：Applications of Mathematics
  Computational Mathematics and Numerical Analysis
  
• 出版者：Springer Japan
• ISSN：1868-937X

文摘

In this paper we partially clarify the relation between the compressibility of a protein and its molecular geometric structure. To identify and understand the relevant topological features within a given protein, we model its molecule as an alpha filtration and hence obtain multi-scale insight into the structure of its tunnels and cavities. The persistence diagrams of this alpha filtration capture the sizes and robustness of such tunnels and cavities in a compact and meaningful manner. From these persistence diagrams, we extract a measure of compressibility derived from those topological features whose relevance is suggested by physical and chemical properties. Due to recent advances in combinatorial topology, this measure is efficiently and directly computable from information found in the Protein Data Bank (PDB). Our main result establishes a clear linear correlation between the topological measure and the experimentally-determined compressibility of most proteins for which both PDB information and experimental compressibility data are available. Finally, we establish that both the topological measurement and the linear correlation are stable with respect to small perturbations in the input data, such as those arising from experimental errors in compressibility and X-ray crystallography experiments.