Abstract
The conformational space of two protein structures has been examined using a stochastic search method in an effort to locate the global minimum conformation. In order to reduce this optimization problem to a tractable level, we have implemented a simplified force field representation of the protein structure that drastically reduces the degrees of freedom. The model replaces each ammo acid (containing many atoms) with a single sphere centered on the Cα position. These spheres are connected by virtual bonds, producing a “string of beads” model of the peptide chain. This model has been coupled with our stochastic search method to globally optimize the conformation of two common structural motifs found in proteins, a 22-residue α-helical hairpin and a 46-residue β-barrel. The search method described further reduces the optimization problem by taking advantage of the rotational isomerisms associated with molecular conformations and stochastically explores the energy surface using internal, torsional degrees of freedom. The approach proved to be highly efficient for globally optimizing the conformation of the α-helical hairpin and β-barrel structure on a moderately powered workstation. The results were further verified by applying variations in the search strategy that probed the low energy regions of conformational space near the suspected global minimum. Since this method also provides information regarding the low energy conformers, we have presented an analysis of the structures populated, and brief comparisons with other work. Finally, we applied the method to globally optimize the conformation of a 9-residue peptide fragment using a popular all-atom representation and successfully located the global minimum consistent with results from previous work.
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References
AMBER 3.0 Revision A: G. Seibel, U. C. Singh, P. K. Weiner, J. W. Caldwell, and P. A. Kollman, Regents of the University of California (1989).
T. L. Blundell and L. N. Johnson,Protein Crystallography, Academic Press, New York (1976).
U. Burkert and N. L. Allinger,Molecular Mechanics, ACS Monograph No. 177, American Chemical Society, Washington, D. C. (1982).
T. E. Creighton, Stability of Folded Conformations,Curr. Opin. Struct. Biol,1, (1991) 5–16.
G. Crippen and M. E. Snow, A 1.8 AResolution Potential Function for Protein Folding,Biopolymers,29 (1990) 1479–89.
W. G. Dauben and K. S. Pitzer,Steric Effects in Organic Chemistry, ed. by M. S. Newman, Wiley, New York, 1956.
K. A. Dill, Dominant Forces in Protein Folding,Biochemistry,29 (1990) 7133–55.
G. D. Fasman,Prediction of Protein Structure and the Principles of Protein Conformation, Plenum Press, New York (1989).
David M. Ferguson and Peter A. Kollman, Can the Lennard-Jones 6–12 Function Replace the 10–12 Form in Molecular Mechanics Calculations?,J. Comput. Chem.,5 (1991) 620–6.
David M. Ferguson, William A. Glauser and Douglas J. Raber, Molecular Mechanics Conformational Analysis of Cyclononane Using the RIPS Method and Comparison with Quantum Mechanical Calculations,J. Comput Chem.,10 (1989) 903–910.
D.M. Ferguson and D. J. Raber, A new approach to probing conformational space with molecular mechanics: random incremental pulse search,J. Am. Chem. Soc,111 (1989) 4371–8.
D. M. Ferguson and D. J. Raber, Molecular Mechanics Calculations of Several Lanthanides: An Application of the Random Incremental Pulse Search,J. Comput. Chem.,11 (1990) 1061–71.
P. Flory,Conformations of Biopolymers, ed. by G. N. Ramachandran, Vol. 1, Academic Press, New York (1967).
David Garrett, Keith Kastella, and David M. Ferguson, New Results on Protein Folding from Simulated Annealing,J. Am. Ghem. Soc, in press.
C. Ghelis and J. Yan,Protein Folding, Academic Press, New York (1982).
W. C. Guida, G. Chang, and W. C. Still, An Internal Coordinate Monte Carlo Method for Searching Confonnational Space,J. Am. Chem. Soc,111 (1989) 4379.
A. T. Hagler and B. Honig, On the Formation of Protein Tertiary Structure on a Computer,Proc. Natl. Acad. Sci. USA,75 (1978) 554–8.
M.R. Hoare, Structure and Dynamics of Simple Microclusters,Advances in Chemical Physics,40 (1979) 49–135.
J. D. Honeycutt and D. Thirumalai, The Nature of Folded States of Globular Proteins,Biopolymers,32 (1992) 695–709.
S. Kirkpatrick, C. D. Gelatt, Jr., and M. D. Vecchi, Optimization by Simulated Annealing,Science,220 (1983) 671–80.
I. D. Kuntz, G. M. Crippen, and P. A. Kollman, Calculation of Protein Tertiary Structure,J. Mol. Biol,106 (1976) 983–94.
M. Levitt and A. Warshel, Computer Simulation of Protein Folding,Nature (London),253 (1975) 694–8.
Z. Li and H. A. Scheraga, Monte Carlo-minimization Approach to the Multiple Minima Problem in Protein Folding,Proc. Natl. Acad. Sci. USA, 84 (1987) 6611.
S. Lifson and A. Warshel, Consistent Force Field for Calculations of Conformations, Vibrational Spectra, and Enthalpies of Cycloalkane and n-Alkane Molecules,J. Ghem. Phys.,49 (1968) 5116–29.
R.S. Maier, J.B. Rosen, G.L. Xue, A Discrete-Continuous Algorithm for Molecular Energy Minimization, in Proceedings ofIEEE/ACM Supercomputing'91, pp. 778–786, IEEE Computer Society Press 1992.
S. R. Niketic and K. Rasmussen,The Consistent Force Field, ed. by G. Berthier and others, Springer-Verlag, New York (1977).
E. B. Wilson, Jr., J. C. Decius, and P. C. Cross,Molecular Vibrations, McGraw-Hill, New York (1955).
In unpublished work we found the original algorithm of ref. 26 to be inefficient for large, linear hydrocarbons and di- and tri-peptide molecules. Our results indicated that the use of external coordinates was a limiting factor.
P. L. Privalov, Stability of Proteins,Adv. Protein Chem.,33 (1979) 167–241.
A. Rey and J. Skolnick, Comparison of Lattice Monte Carlo Dynamics and Brownian Dynamics of Folding Pathways of α-helical Hairpins,Chemical Physics,158 (1991) 199–219.
F. M. Richards, The Protein Folding Problem,Scientific American,264 (1991) 54–63.
J. S. Richardson, The Anatomy and Taxonomy of Protein Structure,Adv. Protein Chem.,34 (1981) 167–339.
M. Saunders, K. N. Houk, Y. Wu, W. C. Still, M. Lipton, G. Chang, and W. C. Guida, Conformations of Cycloheptadecane. A Comparison of Methods for Conformational Searching,J. Am. Chem. Soc,112 (1990) 1419–27.
J. Skolnick and A. Kolinski, Computer Simulations of Globular Protein Folding and Tertiary Structure,Annu. Rev. Phys. Chem.,40 (1989) 207–35.
SPASMS is a new molecular dynamics and mechanics program package authored by David Spellmeyer, William Swope, Erik-Robert Evensen, Dave Ferguson, and Peter Kollman. The FORTRAN source code and operations manual are available from the University of California, San Francisco.
William C. Swope and David M. Ferguson, Alternative Expressions for Energies and Forces Due to Angle Bending and Torsional Energy,J. Comput. Chem.,13 (1992) 585–94.
J. M. Troyer and F. E. Cohen, Simplified Models for Understanding and Predicting Protein Structure, inReviews in Computational Chemistry, Vol. 2, ed. by K. B. Lipkowitz and D. B. Boyd, VCH Publishers, New York, 1991.
S. J. Weiner, P. A. Kollman, D. T. Nguyen, and D. A. Case, An All Atom Force Field for Simulations of Proteins and Nucleic Acids,J. Comput. Chem.,7 (1986) 230–52.
S. Wilson and W. L. Cui, Applications of Simulated Annealing to Peptides,Biopolymers,29 (1990) 225–35.
C. Wilson and S. Doniach, A Computer Model to Dynamically Simulate Protein Folding: Studies with Crambin,Prot. Struct. Func. Gen.,6 (1989) 193–209.
K. Wuthrich,NMR of Proteins and Nucleic Acids, Wiley, New York (1986).
G.L. Xue, R.S. Maier, J.B. Rosen, Minimizing the Lennard-Jones Potential Function on a Massively Parallel Computer, in Proceedings of1992 ACM International Conference on Supercomputing, pp. 409–416, ACM Press, 1992.
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Ferguson, D.M., Marsh, A., Metzger, T. et al. Conformational searches for the global minimum of protein models. J Glob Optim 4, 209–227 (1994). https://doi.org/10.1007/BF01096723
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DOI: https://doi.org/10.1007/BF01096723