Lipschitzian Pattern Search and Immunological Algorithm with Quasi-Newton Method for the Protein Folding Problem: An Innovative Multistage Approach

1. Levitt, M.: Protein folding by restrained energy minimization and molecular dynamics. J. Mol. Biol. 170, 723–764 (1983)

   Article  Google Scholar 

2. Simons, K.T., Kooperberg, C., Huang, E., Baker, D.: Assembly of protein tertiary structures from fragments with similar local sequences using simulated annealing and bayesian scoring function. J. Mol. Biol. 306, 1191–1199 (1997)

   Article  Google Scholar 

3. Hansmann, U.H., Okamoto, Y.: Numerical comparisons of three recently proposed algorithms in the protein folding problem. J. Comp. Chem. 18, 920–933 (1997)

   Article  Google Scholar 

4. Bowie, J.U., Eisemberg, D.: An evolutionary approach to folding small alpha-helical proteins that uses sequence information and an empirical guiding fitness function. Proc. Natl. Acad. Sci. USA 91, 4436–4440 (1994)

   Article  Google Scholar 

5. Huang, S.E., Samudrala, R., Ponder, J.W.: Ab initio folding prediction of small helical proteins using distance geometry and knowledge-based scoring functions. J. Mol. Biol. 290, 267–281 (1999)

   Article  Google Scholar 

6. Jones, D.R., Perttunen, C.D., Stuckman, B.E.: Lipschitzian optimization without the lipschitz constant. J. of Optimization Theory and Application 79, 157–181 (1993)

   Article  MathSciNet  MATH  Google Scholar 

7. Finkel, D.E.: DIRECT Optimization Algorithm User Guide. Technical Report, CRSC N.C. State University (March 2003), ftp://ftp.ncsu.edu/pub/ncsu/crsc/pdf/crsc-tr03-11.pdf

8. Nicosia, G., Cutello, V., Bentley, P., Timmis, J. (eds.): ICARIS 2004. LNCS, vol. 3239. Springer, Heidelberg (2004)

   Google Scholar 

9. Cutello, V., Nicosia, G., Pavone, M.: Exploring the capability of immune algorithms: A characterization of hypermutation operators. In: Nicosia, G., Cutello, V., Bentley, P.J., Timmis, J. (eds.) ICARIS 2004. LNCS, vol. 3239, pp. 263–276. Springer, Heidelberg (2004)

   Chapter  Google Scholar 

10. Dunbrack Jr., R.L., Cohen, F.E.: Bayesian statistical analysis of protein sidechain rotamer preferences. Protein Science 6, 1661–1681 (1997)

    Article  Google Scholar 

11. Purisima, E.O., Scheraga, H.A.: An approach to the multiple-minima problem in protein folding by relaxing dimensionality. test on enkephalin. J. Mol. Biol. 196, 697–709 (1987)

    Article  Google Scholar 

12. Li, Z., Scheraga, H.A.: Structure and free energy of complex thermodynamics systems. J. Mol. Stru. 179, 333–352 (1988)

    Article  Google Scholar 

13. Kaiser Jr., C.E., Lamont, G.B., Merkle, L.D., Gates Jr., G.H., Patcher, R.: Polypeptide structure prediction: Real-valued versus binary hybrid genetic algorithms. In: Proc. of the ACM Symposium on Applied Computing (SAC), San Jose, CA, March 1997, pp. 279–286 (1997)

    Google Scholar 

14. Bindewald, E., Hesser, J., Männer, R.: Implementing genetic algorithms with sterical constraints for protein structure prediction. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 959–967. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

15. Rabow, A.A., Scheraga, H.A.: Improved genetic algorithm for the protein folding problem by use of cartesian combination operators. Protein Science 5, 1800–1815 (1996)

    Article  Google Scholar 

16. Baldi, P., Pollastri, G.: The Principled Design of Large-Scale Recursive Neural Network Architectures-DAG-RNNs and the Protein Structure Prediction Problem. Journal of Machine Learning Research 4, 575–603 (2003)

    MATH  Google Scholar 

17. Dennis, J.E., Schnabel, R.B.: Numerical Methods for Unconstrained Optimization and Nonlinear Equations. Prentice- Hall, Englewood Cliffs (1983)

    MATH  Google Scholar 

18. Byrd, R.H., Nocedal, J., Schnabel, R.B.: Representation of quasi Newton matrices and their use in limited memory methods. Mathematical Programming 63(4), 129–156 (1994)

    Article  MathSciNet  MATH  Google Scholar 

19. McLachlan, A.D.: Rapid Comparison of Protein Structures. Acta Cryst. A38, 871–873 (1982)

    Article  Google Scholar 

20. Huang, C.C., Couch, G.S., Pettersen, E.F., Ferrin, T.E.: Chimera: An Extensible Molecular Modeling Application Constructed Using Standard Components. In: Pacific Symposium on Biocomputing, vol. 1, p. 724 (1996)

    Google Scholar 

21. Hiroyasu, T., Miki, M., Iwahashi, T., Okamoto, Y.: Dual Individual Distributed Genetic Algorithm for Minimizing the Energy of Protein Tertiary Structure, BioGEC 2003. In: Biological Applications of Genetic and Evolutionary Computation, Genetic and Evolutionary Computation Conference 2003 (GECCO 2003), Chicago, Illinois, USA, July 12-16 (2003)

    Google Scholar 

22. Hansmann, U.H.E., Okamoto, Y.: Prediction of Peptide Conformation by the Multicanonical Algorithm. In: Landau, D.P., Mon, K.K., Schttler, H.B. (eds.) Computer Simulation Studies in Condensed Matter Physics VI, p. 168. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

23. Foloppe, N., MacKerell Jr., A.D.: All-Atom Empirical Force Field for Nucleic Acids: I. Parameter Optimization Based on Small Molecule and Condensed Phase Macromolecular Target Data. J. Comput. Chem. 21, 86–104 (2000)

    Article  Google Scholar 

Download references