Skip to main content
Log in

Complexity of protein folding

  • Published:
Bulletin of Mathematical Biology Aims and scope Submit manuscript

Abstract

It is believed that the native folded three-dimensional conformation of a protein is its lowest free energy state, or one of its lowest. It is shown here that both a two-and three-dimensional mathematical model describing the folding process as a free energy minimization problems is NP-hard. This means that the problem belongs to a large set of computational problems, assumed to be very hard (“conditionally intractable”). Some of the possible ramifications of this results are speculated upon.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

Literature

  • Anfinsen, C. B. 1973. Principles that govern the folding of protein chains.Science 181, 223–230.

    Google Scholar 

  • Barahona, f. 1982. On the computational complexity of ising spin glass models.J. Phys. A: Math. Gen. 15, 3241–3253.

    Article  MathSciNet  Google Scholar 

  • Barahona, F., R. Maynard, R. Rammal and J. P. Uhry. 1982. Morphology of ground states of two-dimensional frustration model.J. Phys. A: Math. Gen. 15, 673–699.

    Article  MathSciNet  Google Scholar 

  • Baxter, R. J. 1982.Exactly Solved Models in Statistical Mechanics London: Academic Press.

    MATH  Google Scholar 

  • Bennett, C. H., F. Bessette, G. Brassard, L. Salvail and J. Smolin. 1992a. Experimental quantum cryptographys.J. Crypt. 5, 3–28.

    MATH  Google Scholar 

  • Bennett, C. H. and G. Brassard. 1989. The dawn of a new era for quantum cryptography: the experimental prototype is working!,Assoc. comput. mach SIGACT News 20 (4), 78–82.

    Article  Google Scholar 

  • Bennett, C. H., G. Brassard C. Crépeau and M.-H. Skubiszewska. 1992b. Practical quantum oblivious transfer.Proc. Crypt. 91, 351–366.

    Google Scholar 

  • Bennett, C. H., G. Brassard and N. D. Mermin. 1992. Quantum cryptography without Bell's theorem.Phys. Rev. Lett. 68. 557–559.

    Article  MATH  MathSciNet  Google Scholar 

  • Bieche, I., R. Maynard, R. Rammal and J. P. Uhry. 1980. On the ground states of the frustration model of a spin glass by a matching method of graph theory.J. Phys. A. Math. Gen. 13, 2553–2567.

    Article  MathSciNet  Google Scholar 

  • Brassard, G. 1988.Modern Cryptology, Lecture Notes in Computer Science, Vol. 325. New York: Springer-Verlag.

    MATH  Google Scholar 

  • Brassard, G. and C. Crépeau. 1990. Quantum bit commitment and coin tossing protocols.Proc. Crypt. 90, 49–61.

    Google Scholar 

  • Deutsch, D. 1985. Quantum theory, the Church-Turing principle and the universal quantum computer.Proc. R. Soc. London A 400, 97–117.

    MATH  MathSciNet  Google Scholar 

  • Deutsch, D. 1989. Quantum computational networks.Proc. R. Soc. London A 425, 73–90.

    Article  MATH  MathSciNet  Google Scholar 

  • Fraenkel, A. S. 1990. Deexponentializing complex computational mathematical problems using physical or biological systems. Technical Report CS90-30. Department of Applied mathematics and Computer Science. Weizman Institute of Science.

  • Garey, M. R. and D. S. Johnson. 1979.Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco, CA: Freeman.

    MATH  Google Scholar 

  • Gierasch, L. M. and J. King (Eds.) 1990.Protein folding: Deciphering the Second Half of the Genetic Code. Washington, D.C.: American Association for the Advacement of Science.

    Google Scholar 

  • Janin, J. and S. J. Wodak. 1983. Structural domains in proteins and their role in the dynamics of protein function.Prog. Biophys molec. Biol. 42, 21–78.

    Article  Google Scholar 

  • Levitt, M. and S. Lifson. 1969. Refinement of protein conformations using a macromolecular energy minimization procedure.J. molec. Biol. 46, 269–279.

    Article  Google Scholar 

  • Levitt, M. and R. Sharon. 1988. Accurate simulation of protei dynamics in solution.Proc. natn. Acad. Sci. U.S.A. 85, 7557–7561.

    Article  Google Scholar 

  • Privalov, P. L. 1979. Stability of proteins.Adv. Protein Chem. 33, 167–241.

    Google Scholar 

  • Privalov, P. L. 1982. Stability of proteins: proteins which do not present a single cooperative system.Adv. Protein Chem. 35, 1–104.

    Article  Google Scholar 

  • Robertson, N. and P. D. Seymour. 1988. Graph minors XV, Wagner's conjecture, manuscript.

  • Unger, R. and J. Moult. 1993. Finding the lowest free energy conformation of a protein is a NP-complete problem: proof and implications.Bull. math. Biol. 55, 1183–1198.

    Article  MATH  Google Scholar 

  • Wasserman, S. A. and N. R. Cozzarelli. 1986. Biochemical topology: applications to DNA recombination and replication.Science 232, 951–960.

    Google Scholar 

  • Welsh, D. J. A. 1993. The complexity of knots.Ann. Disc. Math. 55, 159–171.

    Article  MATH  MathSciNet  Google Scholar 

  • Wiesner, S. 1983. Conjugate coding.Assoc. comput. mach. SIGACT News 15 (1), 78–88 (manuscript written about 1970).

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Fraenkel, A.S. Complexity of protein folding. Bltn Mathcal Biology 55, 1199–1210 (1993). https://doi.org/10.1007/BF02460704

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02460704

Keywords

Navigation