Contributions of topological polar-polar contacts to achieve better folding stability of 2D/3D HP lattice proteins: An <i>in silico</i> approach

Salomón J. Alas-Guardado; Pedro Pablo González-Pérez; Hiram Isaac Beltrán; Salomón J. Alas-Guardado; Pedro Pablo González-Pérez; Hiram Isaac Beltrán

doi:10.3934/biophy.2021023

AIMS Biophysics

2021, Volume 8, Issue 3: 291-306. doi: 10.3934/biophy.2021023

Previous Article Next Article

Research article Special Issues

Contributions of topological polar-polar contacts to achieve better folding stability of 2D/3D HP lattice proteins: An in silico approach

1.
Departamento de Ciencias Naturales, Universidad Autónoma Metropolitana Unidad Cuajimalpa, CDMX 05300, México. orcid.org/0000-0001-8903-8766
2.
Departamento de Matemáticas Aplicadas y Sistemas, Universidad Autónoma Metropolitana, Unidad Cuajimalpa, CDMX 05300, México. orcid.org/0000-0001-7223-9035
3.
Departamento de Ciencias Básicas, Universidad Autónoma Metropolitana, Unidad Azcapotzalco, CDMX 02200, México. orcid.org/0000-0002-1097-455X

Received: 27 April 2021 Accepted: 12 July 2021 Published: 23 July 2021

Many of the simplistic hydrophobic-polar lattice models, such as Dill's model (called Model 1 herein), are aimed to fold structures through hydrophobic-hydrophobic interactions mimicking the well-known hydrophobic collapse present in protein structures. In this work, we studied 11 designed hydrophobic-polar sequences, S₁-S₈ folded in 2D-square lattice, and S₉-S₁₁ folded in 3D-cubic lattice. And to better fold these structures we have developed Model 2 as an approximation to convex function aimed to weight hydrophobic-hydrophobic but also polar-polar contacts as an augmented version of Model 1. In this partitioned approach hydrophobic-hydrophobic ponderation was tuned as α-1 and polar-polar ponderation as α. This model is centered in preserving required hydrophobic substructure, and at the same time including polar-polar interactions, otherwise absent, to reach a better folding score now also acquiring the polar-polar substructure. In all tested cases the folding trials were better achieved with Model 2, using α values of 0.05, 0.1, 0.2 and 0.3 depending of sequence size, even finding optimal scores not reached with Model 1. An important result is that the better folding score, required the lower α weighting. And when α values above 0.3 are employed, no matter the nature of the hydrophobic-polar sequence, banning of hydrophobic-hydrophobic contacts started, thus yielding misfolding of sequences. Therefore, the value of α to correctly fold structures is the result of a careful weighting among hydrophobic-hydrophobic and polar-polar contacts.
- HP model,
- protein folding/structure,
- polar contacts,
- genetic algorithm,
- convex function
Citation: Salomón J. Alas-Guardado, Pedro Pablo González-Pérez, Hiram Isaac Beltrán. Contributions of topological polar-polar contacts to achieve better folding stability of 2D/3D HP lattice proteins: An in silico approach[J]. AIMS Biophysics, 2021, 8(3): 291-306. doi: 10.3934/biophy.2021023

Related Papers:

Abstract

Many of the simplistic hydrophobic-polar lattice models, such as Dill's model (called Model 1 herein), are aimed to fold structures through hydrophobic-hydrophobic interactions mimicking the well-known hydrophobic collapse present in protein structures. In this work, we studied 11 designed hydrophobic-polar sequences, S₁-S₈ folded in 2D-square lattice, and S₉-S₁₁ folded in 3D-cubic lattice. And to better fold these structures we have developed Model 2 as an approximation to convex function aimed to weight hydrophobic-hydrophobic but also polar-polar contacts as an augmented version of Model 1. In this partitioned approach hydrophobic-hydrophobic ponderation was tuned as α-1 and polar-polar ponderation as α. This model is centered in preserving required hydrophobic substructure, and at the same time including polar-polar interactions, otherwise absent, to reach a better folding score now also acquiring the polar-polar substructure. In all tested cases the folding trials were better achieved with Model 2, using α values of 0.05, 0.1, 0.2 and 0.3 depending of sequence size, even finding optimal scores not reached with Model 1. An important result is that the better folding score, required the lower α weighting. And when α values above 0.3 are employed, no matter the nature of the hydrophobic-polar sequence, banning of hydrophobic-hydrophobic contacts started, thus yielding misfolding of sequences. Therefore, the value of α to correctly fold structures is the result of a careful weighting among hydrophobic-hydrophobic and polar-polar contacts.

Acknowledgments

Authors would like to thank the support provided by Oscar Sánchez Cortés, in the improvements of the Evolution bioinformatics platform. This research was supported by CONACyT (project 0222872 HIB and project A1-S-46202 SJAG) and by Universidad Autónoma Metropolitana.

Conflict of interest

The authors declare no conflict of interest.

References

[1]	Goodman CM, Choi S, Shandler S, et al. (2007) Foldamers as versatile frameworks for the design and evolution of function. Nat Chem Biol 3: 252-262. doi: 10.1038/nchembio876
[2]	Hill DJ, Mio MJ, Prince RB, et al. (2001) A field guide to foldamers. Chem Rev 101: 3893-4012. doi: 10.1021/cr990120t
[3]	Anfinsen CB (1973) Principles that govern the folding of protein chains. Science 181: 223-230. doi: 10.1126/science.181.4096.223
[4]	Dill KA, Ozkan SB, Shell MS, et al. (2008) The protein folding problem. Annu Rev Biophys 37: 289-316. doi: 10.1146/annurev.biophys.37.092707.153558
[5]	Dill KA, MacCallum JL (2012) The protein-folding problem, 50 years on. Science 338: 1042-1046. doi: 10.1126/science.1219021
[6]	Rose GD, Fleming PJ, Banavar JR, et al. (2006) A backbone-based theory of protein folding. Proc Natl Acad Sci U S A 103: 16623-16633. doi: 10.1073/pnas.0606843103
[7]	Hu J, Chen T, Wang M, et al. (2017) A critical comparison of coarse-grained structure-based approaches and atomic models of protein folding. Phys Chem Chem Phys 19: 13629-13639. doi: 10.1039/C7CP01532A
[8]	Berger B, Leighton TOM (1998) Protein folding in the hydrophobic-hydrophilic (HP) model is NP-complete. J Comput Biol 5: 27-40. doi: 10.1089/cmb.1998.5.27
[9]	Shatabda S, Newton MAH, Rashid MA, et al. (2014) How good are simplified models for protein structure prediction? Adv Bioinf 2014: 867179. doi: 10.1155/2014/867179
[10]	Madain A, Dalhoum ALA, Sleit A (2018) Computational modeling of proteins based on cellular automata: A method of HP folding approximation. Protein J 37: 248-260. doi: 10.1007/s10930-018-9771-0
[11]	Backofen R, Will S, Bornberg-Bauer E (1999) Application of constraint programming techniques for structure prediction of lattice proteins with extended alphabets. Bioinformatics 15: 234-242. doi: 10.1093/bioinformatics/15.3.234
[12]	Onuchic JN, Luthey-Schulten Z, Wolynes PG (1997) Theory of protein folding: the energy landscape perspective. Annu Rev Phys Chem 48: 545-600. doi: 10.1146/annurev.physchem.48.1.545
[13]	Gupta A, Maňuch J, Stacho L (2005) Structure-approximating inverse protein folding problem in the 2D HP model. J Comput Biol 12: 1328-1345. doi: 10.1089/cmb.2005.12.1328
[14]	Hoque T, Chetty M, Sattar A (2009) Extended HP model for protein structure prediction. J Comput Biol 16: 85-103. doi: 10.1089/cmb.2008.0082
[15]	Shmygelska A, Hoos HH (2005) An ant colony optimisation algorithm for the 2D and 3D hydrophobic polar protein folding problem. BMC Bioinf 6: 30. doi: 10.1186/1471-2105-6-30
[16]	Bechini A (2013) On the characterization and software implementation of general protein lattice models. PLoS One 8: e59504. doi: 10.1371/journal.pone.0059504
[17]	Abeln S, Vendruscolo M, Dobson CM, et al. (2014) A simple lattice model that captures protein folding, aggregation and amyloid formation. PLoS One 9: e85185. doi: 10.1371/journal.pone.0085185
[18]	Adcock SA, McCammon JA (2006) Molecular dynamics: survey of methods for simulating the activity of proteins. Chem Rev 106: 1589-1615. doi: 10.1021/cr040426m
[19]	Ferina J, Daggett V (2019) Visualizing protein folding and unfolding. J Mol Biol 431: 1540-1564. doi: 10.1016/j.jmb.2019.02.026
[20]	Compiani M, Capriotti E (2013) Computational and theoretical methods for protein folding. Biochemistry 52: 8601-8624. doi: 10.1021/bi4001529
[21]	Beck DAC, Daggett V (2004) Methods for molecular dynamics simulations of protein folding/unfolding in solution. Methods 34: 112-120. doi: 10.1016/j.ymeth.2004.03.008
[22]	Piana S, Klepeis JL, Shaw DE (2014) Assessing the accuracy of physical models used in protein-folding simulations: quantitative evidence from long molecular dynamics simulations. Curr Opin Struct Biol 24: 98-105. doi: 10.1016/j.sbi.2013.12.006
[23]	Dill KA, Bromberg S, Yue K, et al. (1995) Principles of protein folding—a perspective from simple exact models. Protein Sci 4: 561-602. doi: 10.1002/pro.5560040401
[24]	Newberry RW, Raines RT (2019) Secondary forces in protein folding. ACS Chem Biol 14: 1677-1686. doi: 10.1021/acschembio.9b00339
[25]	Pace CN, Fu H, Fryar KL, et al. (2011) Contribution of hydrophobic interactions to protein stability. J Mol Biol 408: 514-528. doi: 10.1016/j.jmb.2011.02.053
[26]	Pace CN, Scholtz JM, Grimsley GR (2014) Forces stabilizing proteins. FEBS Lett 588: 2177-2184. doi: 10.1016/j.febslet.2014.05.006
[27]	Leonhard K, Prausnitz JM, Radke CJ (2003) Solvent–amino acid interaction energies in 3-D-lattice MC simulations of model proteins. Aggregation thermodynamics and kinetics. Phys Chem Chem Phys 5: 5291-5299. doi: 10.1039/B305414D
[28]	Zhou HX, Pang X (2018) Electrostatic interactions in protein structure, folding, binding, and condensation. Chem Rev 118: 1691-1741. doi: 10.1021/acs.chemrev.7b00305
[29]	Kumar S, Nussinov R (2002) Close-range electrostatic interactions in proteins. Chem Bio Chem 3: 604-617. doi: 10.1002/1439-7633(20020703)3:7<604::AID-CBIC604>3.0.CO;2-X
[30]	Moreno-Hernández S, Levitt M (2012) Comparative modeling and protein-like features of hydrophobic-polar models on a two-dimensional lattice. Proteins 80: 1683-1693. doi: 10.1002/prot.24067
[31]	Alas SJ, González-Pérez PP (2016) Simulating the folding of HP-sequences with a minimalist model in an inhomogeneous medium. Biosystems 142: 52-67. doi: 10.1016/j.biosystems.2016.03.010
[32]	Gonzalez-Perez PP, Orta DJ, Peña I, et al. (2017) A computational approach to studying protein folding problems considering the crucial role of the intracellular environment. J Comput Biol 24: 995-1013. doi: 10.1089/cmb.2016.0115
[33]	de Jesús Alas S, González-Pérez PP, Beltrán HI (2019) In silico minimalist approach to study 2D HP protein folding into an inhomogeneous space mimicking osmolyte effect: First trial in the search of foldameric backbones. Biosystems 181: 31-43. doi: 10.1016/j.biosystems.2019.04.005
[34]	Dill KA (1990) Dominant forces in protein folding. Biochemistry 29: 7133-7155. doi: 10.1021/bi00483a001
[35]	Beltrán HI, Rojo-Domínguez A, Gutiérrez MES, et al. (2009) Exploring dimensionality, systematic mutations and number of contacts in simple HP ab-initio protein folding using a blackboard-based agent platform. Int J Phys Math Sci 3: 256-265.
[36]	Pérez PPG, Beltrán HI, Rojo-Domínguez A, et al. (2009) Multi-agent systems applied in the modeling and simulation of biological problems: A case study in protein folding. World Acad Sci, Eng Technol 58: 128.

biophy-08-03-019-s001.pdf

Reader Comments

Your name:*

Email:*
© 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)