Advertisement

Formation of Secondary and Supersecondary Structure of Proteins as a Result of Coupling Between Local and Backbone-Electrostatic Interactions: A View Through Cluster-Cumulant Scope

  • Adam LiwoEmail author
  • Adam K. Sieradzan
  • Cezary Czaplewski
Protocol
Part of the Methods in Molecular Biology book series (MIMB, volume 1958)

Abstract

The secondary structure of proteins results from both local and long-range interactions, the latter being primarily backbone hydrogen bonding. In this chapter, based on our recent work, we suggest that the striking regularity of secondary structure can be described, in a semi-analytical manner, in terms of Kubo cluster cumulants (corresponding to the expansion of the protein’s potential of mean force) that originate from the coupling between the backbone-local and backbone-electrostatic interactions. This finding is illustrated by the analysis of the Protein Data Bank statistics. Examples demonstrating the importance of the coupling terms in coarse-grained treatment of proteins are also presented.

Key words

Coarse graining Potential of mean force Kubo cluster cumulants Local and electrostatic interactions Coupling terms UNRES force field 

Notes

Acknowledgments

This work was supported by grants UMO-2017/25/B/ST4/01026, UMO-2015/17/D/ST4/00509 and UMO-2017/26/M/ST4/00044 from the National Science Center of Poland (Narodowe Centrum Nauki). Calculations were carried out using the computational resources provided by (a) the supercomputer resources at the Informatics Center of the Metropolitan Academic Network (CI TASK) in Gdańsk, (b) the supercomputer resources at the Interdisciplinary Center of Mathematical and Computer Modeling (ICM), University of Warsaw (grant GA71-23), (c) the Polish Grid Infrastructure (PL-GRID), and (d) our 488-processor Beowulf cluster at the Faculty of Chemistry, University of Gdańsk.

References

  1. 1.
    Ramachandran GN, Sasisekharan V (1968) Conformation of polypeptides and proteins. Adv Protein Chem 23:283–437CrossRefGoogle Scholar
  2. 2.
    Pauling L, Corey RB (1951) Configuration of polypeptide chains. Nature 168:550–551CrossRefGoogle Scholar
  3. 3.
    Pauling L, Corey RB (1953) Stable configurations of polypeptide chains. Proc R Soc B 141:21–33Google Scholar
  4. 4.
    Hoang TX, Trovato A, Seno F, Banavar JR, Maritan A (2004) Geometry and symmetry presculpt the free-energy landscape of proteins. Proc Natl Acad Sci U S A 101:7960–7964CrossRefGoogle Scholar
  5. 5.
    Molkenthin N, Hu S, Niemi JA (2011) Discrete nonlinear Schrödinger equation and polygonal solitons with applications to collapsed proteins. Phys Rev. Lett 106:078102CrossRefGoogle Scholar
  6. 6.
    Krokhotin A, Liwo A, Maisuradze GG, Niemi AJ, Scheraga HA (2014) Kinks, loops, and protein folding, with protein a as an example. J Chem Phys 140:4855735Google Scholar
  7. 7.
    Peng XB, Sieradzan AK, Niemi AJ (2016) Thermal unfolding of myoglobin in the Landau-Ginzburg-Wilson approach. Phys Rev. E 92:062405CrossRefGoogle Scholar
  8. 8.
    Maier JA, Martinez C, Kasavajhala K, Wickstrom L, Hauser KE, Simmerling C (2015) ff14sb: Improving the accuracy of protein side chain and backbone parameters from ff99sb. J Chem Theory Comput 11:3696–3713CrossRefGoogle Scholar
  9. 9.
    Kmiecik S, Gront D, Kolinski M, Wieteska L, Dawid AE, Kolinski A (2016) Coarse-grained protein models and their applications. Chem Rev 116:7898–7936CrossRefGoogle Scholar
  10. 10.
    Liwo A, Czaplewski C, Pillardy J, Scheraga HA (2001) Cumulant-based expressions for the multibody terms for the correlation between local and electrostatic interactions in the united-residue force field. J Chem Phys 115:2323–2347CrossRefGoogle Scholar
  11. 11.
    Liwo A, Czaplewski C, Ołdziej S, Rojas AV, Kaźmierkiewicz R, Makowski M, Murarka RK, Scheraga HA (2008) Simulation of protein structure and dynamics with the coarse-grained UNRES force field. In: Voth G (ed) Coarse-graining of condensed phase and biomolecular systems. Taylor & Francic Group, LLC, Boca Raton, pp 1391–1411Google Scholar
  12. 12.
    Liwo A, Baranowski M, Czaplewski C, Gołaś E, He Y, Jagieła D, Krupa P, Maciejczyk M, Makowski M, Mozolewska MA, Niadzvedtski A, Ołdziej S, Scheraga HA, Sieradzan AK, Ślusarz R, Wirecki T, Yin Y, Zaborowski B (2014) A unified coarse-grained model of biological macromolecules based on mean-field multipole.multipole interactions. J Mol Model 20:2306CrossRefGoogle Scholar
  13. 13.
    Sieradzan AK, Makowski M, Augustynowicz A, Liwo A (2017) A general method for the derivation of the functional forms of the effective energy terms in coarse-grained energy functions of polymers. I. Backbone potentials of coarse-grained polypeptide chains. J Chem Phys 146:124106CrossRefGoogle Scholar
  14. 14.
    Ayton GS, Noid WG, Voth GA (2007) Multiscale modeling of biomolecular systems: in serial and in parallel. Curr Opin Struct Biol 17:192–198CrossRefGoogle Scholar
  15. 15.
    Nishikawa K, Momany FA, Scheraga HA (1974) Low-energy structures of two dipeptides and their relationship to bend conformations. Macromolecules 7:797–806CrossRefGoogle Scholar
  16. 16.
    Berman HM, Westbrook J, Feng Z, Gilliland G, Bhat TN, Weissig H, Shindyalov IN, Bourne PE (2000) The protein data bank. Nucl Acid Res 28:235–242CrossRefGoogle Scholar
  17. 17.
    Kubo R (1962) Generalized cumulant expansion method. J Phys Soc Japan 17:1100–1120CrossRefGoogle Scholar
  18. 18.
    Liwo A, Khalili M, Czaplewski C, Kalinowski S, Ołdziej S, Wachucik K, Scheraga HA (2007) Modification and optimization of the united-residue (UNRES) potential energy function for canonical simulations. I. Temperature dependence of the effective energy function and tests of the optimization method with single training proteins. J Phys Chem B 111:260–285CrossRefGoogle Scholar
  19. 19.
    Ołdziej S, Łągiewka J, Liwo A, Czaplewski C, Chinchio M, Nanias M, Scheraga HA (2004) Optimization of the UNRES force field by hierarchical design of the potential-energy landscape. 3. Use of many proteins in optimization. J Phys Chem B 108, 16950–16959Google Scholar
  20. 20.
    Kortemme T, Ramirez-Alvarado M, Serrano L (1998) Design of a 20-amino acid, three-stranded β-sheet protein. Science 282:253–256.Google Scholar
  21. 21.
    Zhou R, Maisuradze GG, Sunol D, Todorovski T, Macias MJ, Xiao Y, Scheraga HA, Czaplewski C, Liwo A (2014) Folding kinetics of ww domains with the united residue force field for bridging microscopic motions and experimental measurements. Proc Natl Acad Sci U S A 111:18243–18248CrossRefGoogle Scholar
  22. 22.
    Krupa P, Hałis A, Żmudzińska W, Ołdziej S, Scheraga HA, Liwo A (2017) Maximum likelihood calibration of the UNRES force field for simulation of protein structure and dynamics. J Chem Inf Model 57:2364–2377Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  • Adam Liwo
    • 1
    Email author
  • Adam K. Sieradzan
    • 1
  • Cezary Czaplewski
    • 1
  1. 1.Faculty of ChemistryUniversity of GdańskGdańskPoland

Personalised recommendations