Skip to main content
SpringerLink
Log in

Sampling Protein Energy Landscapes – The Quest for Efficient Algorithms

  • Chapter
  • First Online:
Multiscale Approaches to Protein Modeling

  • 1156 Accesses

Abstract

Computer simulations aim to become virtual microscopes that can probe the working of cells on a molecular level. One of the remaining obstacles is still poor sampling. This chapter reviews strategies for faster sampling and discusses their limitations. Recent applications to protein folding document the utility of the described techniques.

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 129.00
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 169.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 169.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  • Androulakis IP, Maranas CD, Floudas CA (1997) Prediction of oligopeptide conformations via deterministic global optimization. J Global Optim 11:1–34

    Article  Google Scholar 

  • Anfinsen CB (1973) Principles that govern the folding of protein chains. Science 181:223–230

    Article  PubMed  CAS  Google Scholar 

  • Allen F, Almasi G, Andreoni W, Beece D, Berne BJ, Bright A, Brunheroto J, Cascaval C, Castanos J, Coteus P, Crumley P, Curioni A, Denneau M, Donath W, Eleftheriou W, Fitch B, Fleischer B, Georgiou CJ, Germain R, Giampapa M, Gresh D, Gupta M, Haring R, Ho H, Hochschild P, Hummel S, Jonas T, Lieber D, Martyna G, Maturu K, Moreira J, Newns D, Newton M, Philhower R, Picunko T, Pitera J, Pitman M, Rand R, Royyuru A, Salapura V, Sanomiya A, Shah R, Sham Y, Singh S, Snir M, Suits F, Swetz R, Swope RC, Vishnumurthy B, Ward TJC, Warren H, Zhou R (2001) Blue gene: a vision for protein science using a petaflop supercomputer. IBM Syst J 40:310–327

    Article  Google Scholar 

  • Berg BA, Neuhaus T (1991) Multicanonical algorithms for first order phase transitions. Phys Lett B 267:249–253

    Article  Google Scholar 

  • Berg BA (2003) Metropolis importance sampling for rugged dynamical variables. Phys Rev Lett 90:180601

    Article  PubMed  Google Scholar 

  • Berg BA (2004) Markov chain Monte Carlo simulations and their statistical analysis. World Scientific, Singapore

    Google Scholar 

  • Besold G, Risbo J, Mouritsen OG (1999) Efficient Monte Carlo sampling by direct flattening of free energy barriers. Comp Mater Sci 15:311–340

    Article  CAS  Google Scholar 

  • Brass A, Pendleton BJ, Chen Y, Robson B (1993) Hybrid Monte Carlo simulation theory and initial comparison with molecular dynamics. Biopolymers 33:1307–1315

    Article  CAS  Google Scholar 

  • Curado EMF, Tsallis C (1994) Possible generalization of Boltzmann–Gibbs statistics. J Phys A-Math Gen 27:3663

    Article  Google Scholar 

  • Cvijovic D, Klinowski J (1995) Taboo search: an approach to the multiple minima problem. Science 267:664–666

    Article  CAS  Google Scholar 

  • Daggett V, Fersht AR (2003) Is there a unifying mechanism for protein folding? Trends Biochem Sci 28:18–25

    Article  PubMed  CAS  Google Scholar 

  • Daggett V (2002) Molecular dynamics simulations of the protein unfolding/folding reaction. Acc Chem Res 35:422–429

    Article  PubMed  CAS  Google Scholar 

  • Dantas G, Watters AL, Lunde BM, Eletr ZM, Isern NG, Roseman T, Lipfert J, Doniach S, Tompa M, Kuhlman B, Stoddard BL, Varani G, Baker D (2006) Mis-translation of a computationally designed protein yields an exceptionally stable homodimer: implications for protein engineering and evolution. J Mol Biol 362:1004–1024

    Article  PubMed  CAS  Google Scholar 

  • Duane S, Kennedy AD, Pendleton BJ, Roweth D (1987) Hybrid Monte Carlo. Phys Lett B 195:216–221

    Article  CAS  Google Scholar 

  • Favrin G, Irback A, Sjunnesson F (2001) Monte Carlo update for chain molecules: Biases Gaussian steps in torsional space. J Chem Phys 114:8154–8158

    Article  CAS  Google Scholar 

  • Ferrenberg AM, Swendsen RH (1988) New Monte Carlo technique for studying phase transitions. Phys Rev Lett 61:2635–2638

    Article  PubMed  CAS  Google Scholar 

  • Ferrenberg AM, Swendsen RH (1989) Optimized Monte Carlo data analysis. Phys Rev Lett 63:1195–1198

    Article  PubMed  CAS  Google Scholar 

  • Frenkel D, Smit B (2001) Understanding molecular simulation. From algorithms to applications. In: Computational science series, vol 1, 2nd edn. Academic, New York, NY

    Google Scholar 

  • Geman S, Geman D (1984) Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of images. IEEE T Pattern Anal 6:721–741

    Article  CAS  Google Scholar 

  • Geyer GJ, Thompson EA (1995) Annealing Markov Chain Monte Carlo with applications to ancestral inference. J Am Stat Assoc 90:909–920

    Article  Google Scholar 

  • Gosavi S, Chavez LL, Jennings PA, Onuchic JN (2006) Topological frustration and the folding of interleukin-1 beta. J Mol Biol 357:986–996

    Article  PubMed  CAS  Google Scholar 

  • Gront D, Kolinski A, Hansmann UHE (2005) Exploring protein energy landscape with hierarchical clustering. Int J Quant Chem 105:826

    Article  CAS  Google Scholar 

  • Gō N, Scheraga HA (1970) Ring closure and local conformational deformations of chain molecules. Macromolecules 3:178–187

    Article  Google Scholar 

  • Hansmann UHE, Okamoto Y (1993) Prediction of peptide conformation by multicanonical algorithm: a new approach to the multiple-minima problem. J Comp Chem 14:1333–1338

    Article  CAS  Google Scholar 

  • Hansmann UHE, Okamoto Y (1994) Comparative study of multicanonical and simulated annealing algorithms in the protein folding problem. Physica A 212:415–437

    Article  CAS  Google Scholar 

  • Hansmann UHE, Okamoto Y, Eisenmenger F (1996) Molecular dynamics, Langevin and hybrid Monte Carlo simulations in a multicanonical ensemble. Chem Phys Lett 259:321–330

    Article  CAS  Google Scholar 

  • Hansmann UHE (1997) Parallel tempering algorithm for conformational studies of biological molecules. Chem Phys Lett 281:140–150

    Article  CAS  Google Scholar 

  • Hansmann UHE, Okamoto Y (1998) The generalized-ensemble approach for protein folding simulations. In: Stauffer D (ed) Annual reviews in computational physics, vol. VI. World Scientific, Singapore

    Google Scholar 

  • Hansmann UHE, Okamoto Y (1999a) New Monte Carlo algorithms for protein folding. Curr Opin Struc Biol 9:177–184

    Article  CAS  Google Scholar 

  • Hansmann UHE (1999) Protein folding simulations in a deformed energy landscape. Eur Phys J B 12:607–612

    Article  CAS  Google Scholar 

  • Hansmann UHE, Okamoto Y (1999b) Finite-size scaling of helix–coil transitions in poly-alanine studied by multicanonical simulations. J Chem Phys 110:1267–1276

    Article  CAS  Google Scholar 

  • Hansmann UHE, Wille L (2002) Global optimization by energy landscape paving. Phys Rev Lett 88:068105

    Article  PubMed  Google Scholar 

  • Hansmann UHE (2003) Protein folding in silico – an overview. Comput Sci Eng 5:64–69

    Article  CAS  Google Scholar 

  • Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor, MI

    Google Scholar 

  • Hukushima K, Nemoto K (1996) Exchange Monte Carlo method and applications to spin glass simulations. J Phys Soc (Japan) 65:1604–1608

    Article  CAS  Google Scholar 

  • Kirkpatrick S, Gelatt CP, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  PubMed  CAS  Google Scholar 

  • Kuhlman B, Dantas G, Ireton GC, Varani G, Stoddard BL, Baker D (2003) Design of a novel globular protein fold with atomic level accuracy. Science 302:1364–1368

    Article  PubMed  CAS  Google Scholar 

  • Kumar S, Payne PW, Vásquez M (1996) Method for free-energy calculations using iterative techniques. J Comp Chem 17:1269–1275

    Article  CAS  Google Scholar 

  • Kwak W, Hansmann UHE (2005) Efficient sampling of protein structures by model hopping. Phys Rev Lett 95:138102

    Article  PubMed  Google Scholar 

  • Laio A, Parrinello M (2002) Escaping free-energy minima. Proc Natl Acad Sci USA 99:12562–12566

    Article  PubMed  CAS  Google Scholar 

  • Li Z, Scheraga HA (1987) Monte Carlo-minimization approach to the multiple-minima problem in protein folding. Proc Natl Acad Sci USA 84:6611–6615

    Article  PubMed  CAS  Google Scholar 

  • Lyubartsev AP, Martinovski AA, Shevkunov SV, Vorontsov-Velyaminov PN (1992) New approach to Monte Carlo calculations of the free energy: method of expanded ensembles. J Chem Phys 96:1776–1783

    Article  CAS  Google Scholar 

  • Marinari E, Parisi G (1992) Simulated tempering: a new Monte Carlo scheme. Europhys Lett 19:451–458

    Article  CAS  Google Scholar 

  • Meinke JH, Hansmann UHE (2009) Thermodynamics and free-energy driven folding of the 67-residue protein GS α W – A large-scale Monte Carlo study. J Comp Chem 30:1642–1648

    Article  CAS  Google Scholar 

  • Minor DL Jr, Kim PS (1996) Context-dependent secondary structure formation of a designed protein sequence. Nature 380:730–734

    Article  PubMed  CAS  Google Scholar 

  • Mohanty S, Meinke JH, Zimmermann O, Hansmann UHE (2008) Simulation of Top7-CFr: a transient helix extension guides folding. Proc Natl Acad Sci USA 105:8004–8007

    Article  PubMed  CAS  Google Scholar 

  • Mohanty S, Hansmann UHE (2008) Caching of a Chameleon segment facilitates folding of a protein with end-to-end β-sheet. J Phys Chem B 112:15134

    Article  PubMed  CAS  Google Scholar 

  • Nadler W, Hansmann UHE (2007) Generalized ensemble and tempering simulations: a unified view. Phys Rev E 75:026109

    Article  Google Scholar 

  • Nadler W, Hansmann UHE (2008) Optimized explicit-solvent replica-exchange molecular dynamics from scratch. J Phys Chem B 112:10386

    Article  PubMed  CAS  Google Scholar 

  • Nadler W, Meinke JA, Hansmann UHE (2008) Folding proteins by first-passage-times optimized replica exchange. Phys Rev E 78:061905

    Article  Google Scholar 

  • Schug A, Wenzel W, Hansmann UHE (2005) Energy landscape paving simulations of the trp-cage protein. J Chem Phys 122:194711

    Article  PubMed  Google Scholar 

  • Trebst S, Troyer M, Hansmann UHE (2006) Optimized parallel tempering simulations of proteins. J Chem Phys 124:174903

    Article  PubMed  Google Scholar 

  • Torrie GM, Valleau JP (1977) Nonphysical sampling distributions in Monte Carlo free-energy estimation: umbrella sampling. J Comp Phys 23:187–199

    Article  Google Scholar 

  • Wang FG, Landau DP (2001) Efficient, multiple-range random walk algorithm to calculate the density of states. Phys Rev Lett 86:2050–2053

    Article  PubMed  CAS  Google Scholar 

  • Wenzel W, Hamacher K (1999) Stochastic tunneling approach for global minimization of complex potential energy landscapes. Phys Rev Lett 82:3003

    Article  CAS  Google Scholar 

  • Wu MG, Deem MW (1999) Analytical rebridging Monte Carlo: application to cis/trans isomerization in proline-containing cyclic peptides. J Chem Phys 111:6625–6632

    Article  CAS  Google Scholar 

Download references

Acknowledgments

Support by the National Science Foundation (research grants CHE-998174, 0313618, 0809002) and the National Institutes of Health (GM62838) are acknowledged.

Author information

Authors and Affiliations

  1. Department of Physics, Michigan Technological University, Houghton, MI, USA

    Ulrich H. E. Hansmann

Authors
  1. Ulrich H. E. Hansmann
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ulrich H. E. Hansmann .

Editor information

Editors and Affiliations

  1. Dept. Chemistry, University of Warsaw, ul. Pasteura 1, Warszawa, 02-093, Poland

    Andrzej Kolinski

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer Science+Business Media, LLC

About this chapter

Cite this chapter

Hansmann, U.H.E. (2011). Sampling Protein Energy Landscapes – The Quest for Efficient Algorithms. In: Kolinski, A. (eds) Multiscale Approaches to Protein Modeling. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-6889-0_9

Download citation

Publish with us

Policies and ethics

Search

Navigation