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Vol. 1, No. 1, 2003
Issue release date: 2003
Section title: Original Research Paper
Complexus 2003;1:4–13
(DOI:10.1159/000067638)

Geometry of Compact Tubes and Protein Structures

Banavar J.R.a · Flammini A.b · Marenduzzo D.b · Maritan A.b · Trovato A.c
aDepartment of Physics, Pennsylvania State University, University Park, Pa., USA; bInternational School for Advanced Studies, Trieste, Italy; cNiels Bohr Institutet, Copenhagen, Denmark
email Corresponding Author

Abstract

Proteins form a very important class of polymers. In spite of major advances in the understanding of polymer science, the protein problem has remained largely unsolved. Here, we show that a polymer chain viewed as a tube not only captures the well-known characteristics of polymers and their phases, but also provides a natural explanation for many of the key features of protein behavior. There are two natural length scales associated with a tube subject to compaction – the thickness of the tube and the range of the attractive interactions. For short tubes, when these length scales become comparable, one obtains marginally compact structures, which are relatively few in number compared to those in the generic compact phase of polymers. The motifs associated with the structures in this new phase include helices, hairpins and sheets. We suggest that Nature has selected this phase for the structures of proteins because of its many advantages, including the few candidate structures, the ability to squeeze water out from the hydrophobic core and the flexibility and versatility associated with being marginally compact. Our results provide a framework for understanding the common features of all proteins.

© 2002 S. Karger AG, Basel


  

Key Words

  • Protein
  • Structure
  • Geometry
  • Tube

References

  1. Watson JD, Crick FHC: A structure for deoxyribose nucleic acid. Nature 1953;171:737.
  2. Pauling L: Modern structural chemistry, Nobel Lecture, December 11, 1954. Reprinted in several places, including Science 1956;123:255–258.
  3. Bernal JD: Structure of proteins. Nature 1939;143: 663–667.
  4. Pauling L: Molecular architecture and biological reactions. Chem Eng News 1946;24:1064–1066.
  5. Chaikin PM, Lubensky TC: Principles of condensed matter physics. Cambridge, Cambridge University Press 1995.
  6. Woodward AE: Atlas of polymer morphology. New York, Hanser Publishers, 1988.
  7. Chothia C: One thousand families for the molecular biologist. Nature 1992;357:543–544.
  8. Anfinsen C: Principles that govern the folding of protein chains. Science 1973;181:223-230.
  9. Ramachandran GN, Sasisekharan V: Conformations of polypeptides and proteins. Adv Protein Chem 1968;23:283–438.
  10. Gonzalez O, Maddocks JH: Global curvature, thickness and the ideal shapes of knots. Proc Natl Acad Sci USA 1999;96:4769–4773.
  11. Banavar JR, Gonzalez O, Maddocks JH, Maritan A: Self-interactions of strands and sheets. J Stat Phys, in press.
  12. Pauling L, Corey RB, Branson HR: The structure of proteins: Two hydrogen-bonded helical conformations of the polypeptide chain. Proc Natl Acad Sci USA 1951;37:205–211.
  13. Pauling L, Corey RB: Conformations of polypeptide chains with favored orientations around single bonds: two new pleated sheets. Proc Natl Acad Sci USA 1951;37:729–740
  14. Allain FHT, Yen M, Masse JE, Schultze P, Dieckmann T, Johnson RC, Feigon J: Solution structure of the HMG protein NHP6A and its interaction with DNA reveals the structural determinants for non sequence specific binding. Embo J 1999: 18:2563.
  15. Baumann U, Wu S, Flaherty KM, Mckay DB: Three-dimensional structure of the alkalyne protease of Pseudomonas aeruginosa: A two-domain protein with a calcium binding parallel beta roll motif. Embo J 1993;12:3357.
  16. Chang KY, Tinoco I: The Structure of an RNA ‘kissing hairpin complex of the HIV tar hairpin loop and its complement. J Mol Biol 1997;269:52.
  17. Maritan A, Micheletti C, Trovato A, Banavar JR: Optimal shapes of compact strings. Nature 2000;406:287–290.
  18. Banavar JR, Maritan A, Micheletti C, Trovato A: Geometry and physics of proteins. Proteins 2002;47:315–322.
  19. Tinkham M: Introduction to Superconductivity, New York, McGraw-Hill, 1996.
  20. Pitard E, Garel T, Orland H: Protein folding, anisotropic collapse and blue phases. J Phys I (France) 1997;7:1201.
  21. Dobson CM: Protein misfolding, evolution and disease. Trends Biochem Sci 1999;24:329.
  22. Banavar JR, Maritan A: Computational approach to the protein folding problem. Proteins 2001;42:433–435.
  23. Denton M, Marshall C: Laws of form revisited. Nature 2001;410:417.
  24. Sokal AD: Monte Carlo methods for the self-avoiding walk. Nucl Phys B Suppl. 1996;47:172.
  25. Wang FG, Landau DP: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys Rev Lett 2001;86:2050.

  

Author Contacts

Jayanth R. Banavar
Department of Physics, 104 Davey Laboratory
Pennsylvania State University, University Park, PA 16802 (USA)
Tel +1 814 863 1089, Fax +1 814 865 0978
E-Mail banavar@psu.edu
Amos Maritan
SISSA, Via Beirut 2–4
I–34014 Trieste (Italy)
Tel. + 39 040 2240462, Fax + 39 040 3787528
E-Mail maritan@sissa.it

  

Article Information

Received: March 19, 2002
Accepted after revision: July 15, 2002
Number of Print Pages : 10
Number of Figures : 5, Number of Tables : 0, Number of References : 25

  

Publication Details

Complexus

Vol. 1, No. 1, Year 2003 (Cover Date: 2003)

Journal Editor: Henri Atlan, Paris/Jerusalem
ISSN: 1424–8492 (print), 1424–8506 (Online)

For additional information: http://www.karger.com/cpu


Copyright / Drug Dosage / Disclaimer

Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher or, in the case of photocopying, direct payment of a specified fee to the Copyright Clearance Center.
Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in goverment regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug.
Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.

Abstract

Proteins form a very important class of polymers. In spite of major advances in the understanding of polymer science, the protein problem has remained largely unsolved. Here, we show that a polymer chain viewed as a tube not only captures the well-known characteristics of polymers and their phases, but also provides a natural explanation for many of the key features of protein behavior. There are two natural length scales associated with a tube subject to compaction – the thickness of the tube and the range of the attractive interactions. For short tubes, when these length scales become comparable, one obtains marginally compact structures, which are relatively few in number compared to those in the generic compact phase of polymers. The motifs associated with the structures in this new phase include helices, hairpins and sheets. We suggest that Nature has selected this phase for the structures of proteins because of its many advantages, including the few candidate structures, the ability to squeeze water out from the hydrophobic core and the flexibility and versatility associated with being marginally compact. Our results provide a framework for understanding the common features of all proteins.

© 2002 S. Karger AG, Basel


  

Author Contacts

Jayanth R. Banavar
Department of Physics, 104 Davey Laboratory
Pennsylvania State University, University Park, PA 16802 (USA)
Tel +1 814 863 1089, Fax +1 814 865 0978
E-Mail banavar@psu.edu
Amos Maritan
SISSA, Via Beirut 2–4
I–34014 Trieste (Italy)
Tel. + 39 040 2240462, Fax + 39 040 3787528
E-Mail maritan@sissa.it

  

Article Information

Received: March 19, 2002
Accepted after revision: July 15, 2002
Number of Print Pages : 10
Number of Figures : 5, Number of Tables : 0, Number of References : 25

  

Publication Details

Complexus

Vol. 1, No. 1, Year 2003 (Cover Date: 2003)

Journal Editor: Henri Atlan, Paris/Jerusalem
ISSN: 1424–8492 (print), 1424–8506 (Online)

For additional information: http://www.karger.com/cpu


Article / Publication Details

First-Page Preview
Abstract of Original Research Paper

Received: 7/18/2002
Published online: 12/11/2002
Issue release date: 2003

Number of Print Pages: 10
Number of Figures: 5
Number of Tables: 0

ISSN: 1424-8492 (Print)
eISSN: 1424-8506 (Online)

For additional information: http://www.karger.com/CPU


Copyright / Drug Dosage

Copyright: All rights reserved. No part of this publication may be translated into other languages, reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying, recording, microcopying, or by any information storage and retrieval system, without permission in writing from the publisher or, in the case of photocopying, direct payment of a specified fee to the Copyright Clearance Center.
Drug Dosage: The authors and the publisher have exerted every effort to ensure that drug selection and dosage set forth in this text are in accord with current recommendations and practice at the time of publication. However, in view of ongoing research, changes in goverment regulations, and the constant flow of information relating to drug therapy and drug reactions, the reader is urged to check the package insert for each drug for any changes in indications and dosage and for added warnings and precautions. This is particularly important when the recommended agent is a new and/or infrequently employed drug.
Disclaimer: The statements, opinions and data contained in this publication are solely those of the individual authors and contributors and not of the publishers and the editor(s). The appearance of advertisements or/and product references in the publication is not a warranty, endorsement, or approval of the products or services advertised or of their effectiveness, quality or safety. The publisher and the editor(s) disclaim responsibility for any injury to persons or property resulting from any ideas, methods, instructions or products referred to in the content or advertisements.

References

  1. Watson JD, Crick FHC: A structure for deoxyribose nucleic acid. Nature 1953;171:737.
  2. Pauling L: Modern structural chemistry, Nobel Lecture, December 11, 1954. Reprinted in several places, including Science 1956;123:255–258.
  3. Bernal JD: Structure of proteins. Nature 1939;143: 663–667.
  4. Pauling L: Molecular architecture and biological reactions. Chem Eng News 1946;24:1064–1066.
  5. Chaikin PM, Lubensky TC: Principles of condensed matter physics. Cambridge, Cambridge University Press 1995.
  6. Woodward AE: Atlas of polymer morphology. New York, Hanser Publishers, 1988.
  7. Chothia C: One thousand families for the molecular biologist. Nature 1992;357:543–544.
  8. Anfinsen C: Principles that govern the folding of protein chains. Science 1973;181:223-230.
  9. Ramachandran GN, Sasisekharan V: Conformations of polypeptides and proteins. Adv Protein Chem 1968;23:283–438.
  10. Gonzalez O, Maddocks JH: Global curvature, thickness and the ideal shapes of knots. Proc Natl Acad Sci USA 1999;96:4769–4773.
  11. Banavar JR, Gonzalez O, Maddocks JH, Maritan A: Self-interactions of strands and sheets. J Stat Phys, in press.
  12. Pauling L, Corey RB, Branson HR: The structure of proteins: Two hydrogen-bonded helical conformations of the polypeptide chain. Proc Natl Acad Sci USA 1951;37:205–211.
  13. Pauling L, Corey RB: Conformations of polypeptide chains with favored orientations around single bonds: two new pleated sheets. Proc Natl Acad Sci USA 1951;37:729–740
  14. Allain FHT, Yen M, Masse JE, Schultze P, Dieckmann T, Johnson RC, Feigon J: Solution structure of the HMG protein NHP6A and its interaction with DNA reveals the structural determinants for non sequence specific binding. Embo J 1999: 18:2563.
  15. Baumann U, Wu S, Flaherty KM, Mckay DB: Three-dimensional structure of the alkalyne protease of Pseudomonas aeruginosa: A two-domain protein with a calcium binding parallel beta roll motif. Embo J 1993;12:3357.
  16. Chang KY, Tinoco I: The Structure of an RNA ‘kissing hairpin complex of the HIV tar hairpin loop and its complement. J Mol Biol 1997;269:52.
  17. Maritan A, Micheletti C, Trovato A, Banavar JR: Optimal shapes of compact strings. Nature 2000;406:287–290.
  18. Banavar JR, Maritan A, Micheletti C, Trovato A: Geometry and physics of proteins. Proteins 2002;47:315–322.
  19. Tinkham M: Introduction to Superconductivity, New York, McGraw-Hill, 1996.
  20. Pitard E, Garel T, Orland H: Protein folding, anisotropic collapse and blue phases. J Phys I (France) 1997;7:1201.
  21. Dobson CM: Protein misfolding, evolution and disease. Trends Biochem Sci 1999;24:329.
  22. Banavar JR, Maritan A: Computational approach to the protein folding problem. Proteins 2001;42:433–435.
  23. Denton M, Marshall C: Laws of form revisited. Nature 2001;410:417.
  24. Sokal AD: Monte Carlo methods for the self-avoiding walk. Nucl Phys B Suppl. 1996;47:172.
  25. Wang FG, Landau DP: Efficient, multiple-range random walk algorithm to calculate the density of states. Phys Rev Lett 2001;86:2050.