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.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Literature
Anfinsen, C. B. 1973. Principles that govern the folding of protein chains.Science 181, 223–230.
Barahona, f. 1982. On the computational complexity of ising spin glass models.J. Phys. A: Math. Gen. 15, 3241–3253.
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.
Baxter, R. J. 1982.Exactly Solved Models in Statistical Mechanics London: Academic Press.
Bennett, C. H., F. Bessette, G. Brassard, L. Salvail and J. Smolin. 1992a. Experimental quantum cryptographys.J. Crypt. 5, 3–28.
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.
Bennett, C. H., G. Brassard C. Crépeau and M.-H. Skubiszewska. 1992b. Practical quantum oblivious transfer.Proc. Crypt. 91, 351–366.
Bennett, C. H., G. Brassard and N. D. Mermin. 1992. Quantum cryptography without Bell's theorem.Phys. Rev. Lett. 68. 557–559.
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.
Brassard, G. 1988.Modern Cryptology, Lecture Notes in Computer Science, Vol. 325. New York: Springer-Verlag.
Brassard, G. and C. Crépeau. 1990. Quantum bit commitment and coin tossing protocols.Proc. Crypt. 90, 49–61.
Deutsch, D. 1985. Quantum theory, the Church-Turing principle and the universal quantum computer.Proc. R. Soc. London A 400, 97–117.
Deutsch, D. 1989. Quantum computational networks.Proc. R. Soc. London A 425, 73–90.
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.
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.
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.
Levitt, M. and S. Lifson. 1969. Refinement of protein conformations using a macromolecular energy minimization procedure.J. molec. Biol. 46, 269–279.
Levitt, M. and R. Sharon. 1988. Accurate simulation of protei dynamics in solution.Proc. natn. Acad. Sci. U.S.A. 85, 7557–7561.
Privalov, P. L. 1979. Stability of proteins.Adv. Protein Chem. 33, 167–241.
Privalov, P. L. 1982. Stability of proteins: proteins which do not present a single cooperative system.Adv. Protein Chem. 35, 1–104.
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.
Wasserman, S. A. and N. R. Cozzarelli. 1986. Biochemical topology: applications to DNA recombination and replication.Science 232, 951–960.
Welsh, D. J. A. 1993. The complexity of knots.Ann. Disc. Math. 55, 159–171.
Wiesner, S. 1983. Conjugate coding.Assoc. comput. mach. SIGACT News 15 (1), 78–88 (manuscript written about 1970).
Author information
Authors and Affiliations
Rights 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
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF02460704