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Peptide Folding in Cellular Environments: A Monte Carlo and Markov Modeling Approach

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Computational Methods to Study the Structure and Dynamics of Biomolecules and Biomolecular Processes

Part of the book series: Springer Series on Bio- and Neurosystems ((SSBN,volume 8))

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Abstract

Steric interactions with surrounding macromolecules tend to favor the compact native state of a globular protein over its unfolded state. However, in experiments conducted in cells and concentrated protein solutions, both stabilization and destabilization of proteins have been observed, compared to dilute-solution conditions. Therefore, in order to understand the effects of surrounding macromolecules on protein properties such as stability, there is a need for computational modeling beyond the level of hard-sphere crowders. Here, we discuss some recent exploratory studies of peptide folding in the presence of explicit protein crowders, carried out by us using an all-atom Monte Carlo-based approach along with an implicit solvent force field. For interpreting the simulation data, time-lagged independent component analysis and Markov state modeling are used.

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References

  1. Zimmerman, S.B., Trach, S.O.: Estimation of macromolecule concentrations and excluded volume effects for the cytoplasm of escherichia coli. J. Mol. Biol. 222, 599 (1991)

    Article  Google Scholar 

  2. Theillet, F.X., Binolfi, A., Frembgen-Kesner, T., Hingorani, K., Sarkar, M., Kyne, C., Li, C., Crowley, P.B., Gierasch, L., Pielak, G.J., Elcock, A.H., Gershenson, A., Selenko, P.: Physicochemical properties of cells and their effects on intrinsically disordered proteins (IDPs). Chem. Rev. 114, 6661 (2014)

    Article  Google Scholar 

  3. Smith, A.E., Zhang, Z., Pielak, G.J., Li, C.: NMR studies of protein folding and binding in cells and cell-like environments. Curr. Opin. Struct. Biol. 30, 7 (2015)

    Article  Google Scholar 

  4. Zhou, H.X.: Influence of crowded cellular environments on protein folding, binding, and oligomerization: biological consequences and potentials of atomistic modeling. FEBS Lett. 587, 1053 (2013)

    Article  Google Scholar 

  5. Feig, M., Sugita, Y.: Reaching new levels of realism in modeling biological macromolecules in cellular environments. J. Mol. Graph. Model. 45, 144 (2013)

    Article  Google Scholar 

  6. Ellis, R.J.: Macromolecular crowding: obvious but underappreciated. Trends Biochem. Sci. 26, 597 (2001)

    Article  Google Scholar 

  7. Zhou, H.X., Rivas, G., Minton, A.P.: Macromolecular crowding and confinement: biochemical, biophysical, and potential physiological consequences. Annu. Rev. Biophys. 37, 375 (2008)

    Article  Google Scholar 

  8. Cheung, M.S., Klimov, D., Thirumalai, D.: Molecular crowding enhances native state stability and refolding rates of globular proteins. Proc. Natl. Acad. Sci. USA 102, 4753 (2005)

    Article  Google Scholar 

  9. Minh, D.D.L., Chang, C.E., Trylska, J., Tozzini, V., McCammon, J.A.: The influence of macromolecular crowding on HIV-1 protease internal dynamics. J. Am. Chem. Soc. 128, 6006 (2006)

    Article  Google Scholar 

  10. Stagg, L., Zhang, S.Q., Cheung, M.S., Wittung-Stafshede, P.: Molecular crowding enhances native structure and stability of \(\alpha \)/\(\beta \) protein flavodoxin. Proc. Natl. Acad. Sci. USA 104, 18976 (2007)

    Article  Google Scholar 

  11. Qin, S., Zhou, H.X.: Atomistic modeling of macromolecular crowding predicts modest increases in protein folding and binding stability. Biophys. J. 97, 12 (2009)

    Article  Google Scholar 

  12. Jefferys, B.R., Kelley, L.A., Sternberg, M.J.E.: Protein folding requires crowd control in a simulated cell. J. Mol. Biol. 397, 1329 (2010)

    Article  Google Scholar 

  13. Tsao, D., Dokholyan, N.V.: Macromolecular crowding induces polypeptide compaction and decreases folding cooperativity. Phys. Chem. Chem. Phys. 12, 3491 (2010)

    Article  Google Scholar 

  14. Mittal, J., Best, R.B.: Dependence of protein folding stability and dynamics on the density and composition of macromolecular crowders. Biophys. J. 98, 315 (2010)

    Article  Google Scholar 

  15. Samiotakis, A., Cheung, M.S.: Folding dynamics of trp-cage in the presence of chemical interference and macromolecular crowding. i. J. Chem. Phys. 135(17), 175101 (2011)

    Article  Google Scholar 

  16. Qin, S., Zhou, H.X.: Effects of macromolecular crowding on the conformational ensembles of disordered proteins. J. Phys. Chem. Lett. 4, 3429 (2013)

    Article  Google Scholar 

  17. Kang, H., Pincus, P.A., Hyeon, C., Thirumalai, D.: Effects of macromolecular crowding on the collapse of biopolymers. Phys. Rev. Lett. 114, 068303 (2015)

    Article  Google Scholar 

  18. Latshaw II, D.C., Hall, C.K.: Effects of hydrophobic macromolecular crowders on amyloid \(\beta \) (16–22) aggregation. Biophys. J. 109, 124 (2015)

    Article  Google Scholar 

  19. Miller, C.M., Kim, Y.C., Mittal, J.: Protein composition determines the effect of crowding on the properties of disordered proteins. Biophys. J. 111, 28 (2016)

    Article  Google Scholar 

  20. Miklos, A.C., Sarkar, M., Wang, Y., Pielak, G.J.: Protein crowding tunes protein stability. J. Am. Chem. Soc. 133, 7116 (2011)

    Article  Google Scholar 

  21. Guzman, I., Gelman, H., Tai, J., Gruebele, M.: The extracellular protein VlsE is destabilized inside cells. J. Mol. Biol. 426, 11 (2014)

    Article  Google Scholar 

  22. Feig, M., Yu, I., Wang, P.H., Nawrocki, G., Sugita, Y.: Crowding in cellular environments at an atomistic level from computer simulations. J. Phys. Chem. B 121, 8009 (2017)

    Article  Google Scholar 

  23. Qin, S., Zhou, H.X.: Protein folding, binding, and droplet formation in cell-like conditions. Curr. Opin. Struct. Biol. 43, 28 (2017)

    Article  Google Scholar 

  24. McGuffee, S.R., Elcock, A.H.: Diffusion, crowding & protein stability in a dynamic molecular model of the bacterial cytoplasm. PLOS Comput. Biol. 6, e1000694 (2010)

    Article  Google Scholar 

  25. Yu, I., Mori, T., Ando, T., Harada, R., Jung, J., Sugita, Y., Feig, M.: Biomolecular interactions modulate macromolecular structure and dynamics in atomistic model of a bacterial cytoplasm. eLife 5, 18457 (2016)

    Google Scholar 

  26. Feig, M., Sugita, Y.: Variable interactions between protein crowders and biomolecular solutes are important in understanding cellular crowding. J. Phys. Chem. B 116, 599 (2012)

    Article  Google Scholar 

  27. Predeus, A.V., Gul, S., Gopal, S.M., Feig, M.: Conformational sampling of peptides in the presence of protein crowders from AA/CG-multiscale simulations. J. Phys. Chem. B 116, 8610 (2012)

    Article  Google Scholar 

  28. Macdonald, B., McCarley, S., Noeen, S., van Giessen, A.E.: Protein–protein interactions affect alpha helix stability in crowded environments. J. Phys. Chem. B 119, 2956 (2015)

    Article  Google Scholar 

  29. Bille, A., Linse, B., Mohanty, S., Irbäck, A.: Equilibrium simulation of trp-cage in the presence of protein crowders. J. Chem. Phys. 143, 175102 (2015)

    Article  Google Scholar 

  30. Bille, A., Mohanty, S., Irbäck, A.: Peptide folding in the presence of interacting protein crowders. J. Chem. Phys. 144, 175105 (2016)

    Article  Google Scholar 

  31. Irbäck, A., Mohanty, S.: Protein folding/unfolding in the presence of interacting macromolecular crowders. Eur. Phys. J. - Spec. Top. 226, 627 (2017)

    Article  Google Scholar 

  32. Nilsson, D., Mohanty, S., Irbäck, A.: Markov modeling of peptide folding in the presence of protein crowders. J. Chem. Phys. 148, 055101 (2018)

    Article  Google Scholar 

  33. Neidigh, J.W., Fesinmeyer, R.M., Andersen, N.H.: Designing a 20-residue protein. Nat. Struct. Biol. 9, 425 (2002)

    Article  Google Scholar 

  34. Fesinmeyer, R.M., Hudson, F.M., Andersen, N.H.: Enhanced hairpin stability through loop design: the case of the protein g b1 domain hairpin. J. Am. Chem. Soc. 126, 7238 (2004)

    Article  Google Scholar 

  35. Moses, E., Hinz, H.J.: Basic pancreatic trypsin inhibitor has unusual thermodynamic stability parameters. J. Mol. Biol. 170, 765 (1983)

    Article  Google Scholar 

  36. Gronenborn, A.M., Filpula, D.R., Essig, N.Z., Achari, A., Whitlow, M., Wingfield, P.T., Clore, G.M.: A novel, highly stable fold of the immunoglobulin binding domain of streptococcal protein G. Science 253, 657 (1991)

    Article  Google Scholar 

  37. Molgedey, L., Schuster, H.G.: Separation of a mixture of independent signals using time delayed correlations. Phys. Rev. Lett. 72, 3634 (1994)

    Article  Google Scholar 

  38. Naritomi, Y., Fuchigami, S.: Slow dynamics of a protein backbone in molecular dynamics simulation revealed by time-structure based independent component analysis. J. Chem. Phys. 139, 215102 (2013)

    Article  Google Scholar 

  39. Schwantes, C.R., Pande, V.S.: Improvements in Markov state model construction reveal many non-native interactions in the folding of NTL9. J. Chem. Theor. Comput. 9, 2000 (2013)

    Article  Google Scholar 

  40. Pérez-Hernández, G., Paul, F., Giorgino, T., De Fabritiis, G., Noé, F.: Identification of slow molecular order parameters for Markov model construction. J. Chem. Phys. 139, 015102 (2013)

    Article  Google Scholar 

  41. Schütte, C., Fischer, A., Huisinga, W., Deuflhard, P.: A direct approach to conformational dynamics based on Hybrid Monte Carlo. J. Comput. Phys. 151, 146 (1999)

    Article  MathSciNet  Google Scholar 

  42. Chodera, J.D., Singhal, N., Pande, V.S., Dill, K.A., Swope, W.C.: Automatic discovery of metastable states for the construction of markov models of macromolecular conformational dynamics. J. Chem. Phys. 126, 155101 (2007)

    Article  Google Scholar 

  43. Buchete, N.V., Hummer, G.: Coarse master equations for peptide folding dynamics. J. Phys. Chem. B 112, 6057 (2008)

    Article  Google Scholar 

  44. Bowman, G.R., Beauchamp, K.A., Boxer, G., Pande, V.S.: Progress and challenges in the automated construction of Markov state models for full protein systems. J. Chem. Phys. 131, 124101 (2009)

    Article  Google Scholar 

  45. Prinz, J.H., Wu, H., Sarich, M., Keller, B., Senne, M., Held, M., Chodera, J.D., Schütte, C., Noé, F.: Markov models of molecular kinetics: generation and validation. J. Chem. Phys. 134, 174105 (2011)

    Article  Google Scholar 

  46. Chodera, J.D., Noé, F.: Markov state models of biomolecular conformational dynamics. Curr. Opin. Struct. Biol. 25, 135 (2014)

    Article  Google Scholar 

  47. Noé, F., Clementi, C.: Collective variables for the study of long-time kinetics from molecular trajectories: theory and methods. Curr. Opin. Struct. Biol. 43, 141 (2017)

    Article  Google Scholar 

  48. Irbäck, A., Mitternacht, S., Mohanty, S.: An effective all-atom potential for proteins. BMC Biophys. 2, 2 (2009)

    Article  Google Scholar 

  49. Irbäck, A., Mohanty, S.: Folding thermodynamics of peptides. Biophys. J. 88, 1560 (2005)

    Article  Google Scholar 

  50. Mitternacht, S., Luccioli, S., Torcini, A., Imparato, A., Irbäck, A.: Changing the mechanical unfolding pathway of FnIII10 by tuning the pulling strength. Biophys. J. 96, 429 (2009)

    Article  Google Scholar 

  51. Jónsson, S.Æ., Mohanty, S., Irbäck, A.: Distinct phases of free \(\alpha \)-synuclein – a Monte Carlo study. Proteins 80, 2169 (2012)

    Article  Google Scholar 

  52. Mohanty, S., Meinke, J.H., Zimmermann, O.: Folding of Top7 in unbiased all-atom Monte Carlo simulations. Proteins 81, 1446 (2013)

    Article  Google Scholar 

  53. Bille, A., Jónsson, S.Æ., Akke, M., Irbäck, A.: Local unfolding and aggregation mechanisms of SOD1 – a Monte Carlo exploration. J. Phys. Chem. B 117, 9194 (2013)

    Article  Google Scholar 

  54. Jónsson, S.Æ., Mitternacht, S., Irbäck, A.: Mechanical resistance in unstructured proteins. Biophys. J. 104, 2725 (2013)

    Article  Google Scholar 

  55. Petrlova, J., Bhattacherjee, A., Boomsma, W., Wallin, S., Lagerstedt, J.O., Irbäck, A.: Conformational and aggregation properties of the 1–93 fragment of apolipoprotein A-I. Protein Sci. 23, 1559 (2014)

    Article  Google Scholar 

  56. Favrin, G., Irbäck, A., Mohanty, S.: Oligomerization of amyloid A\(\beta _{16-22}\) peptides using hydrogen bonds and hydrophobicity forces. Biophys. J. 87, 3657 (2004)

    Article  Google Scholar 

  57. Cheon, M., Chang, I., Mohanty, S., Luheshi, L.M., Dobson, C.M., Vendruscolo, M., Favrin, G.: Structural reorganisation and potential toxicity of oligomeric species formed during the assembly of amyloid fibrils. PLOS Comput. Biol. 3, e173 (2007)

    Article  Google Scholar 

  58. Irbäck, A., Mitternacht, S.: Spontaneous \(\beta \)-barrel formation: an all-atom Monte Carlo study of A\(\beta \)(16–22) oligomerization. Proteins 71, 207 (2008)

    Article  Google Scholar 

  59. Li, D., Mohanty, S., Irbäck, A., Huo, S.: Formation and growth of oligomers: a Monte Carlo study of an amyloid tau fragment. PLOS Comput. Biol. 4, e1000238 (2008)

    Article  Google Scholar 

  60. Mitternacht, S., Staneva, I., Härd, T., Irbäck, A.: Monte Carlo study of the formation and conformational properties of dimers of a\(\beta \)42 variants. J. Mol. Biol. 410, 357 (2011)

    Article  Google Scholar 

  61. Irbäck, A., Mohanty, S.: PROFASI: a Monte Carlo simulation package for protein folding and aggregation. J. Comput. Chem. 27, 1548 (2006)

    Article  Google Scholar 

  62. Favrin, G., Irbäck, A., Sjunnesson, F.: Monte Carlo update for chain molecules: biased Gaussian steps in torsional space. J. Chem. Phys. 114, 8154 (2001)

    Article  Google Scholar 

  63. Dodd, L.R., Boone, T.D., Theodorou, D.N.: A concerted rotation algorithm for atomistic Monte Carlo simulation of polymer melts and glasses. Mol. Phys. 78, 961 (1993)

    Article  Google Scholar 

  64. Zamuner, S., Rodriguez, A., Seno, F., Trovato, A.: An efficient algorithm to perform local concerted movements of a chain molecule. PLOS One 10, e0118342 (2015)

    Article  Google Scholar 

  65. Irbäck, A., Jónsson, S.Æ., Linnemann, N., Linse, B., Wallin, S.: Aggregate geometry in amyloid fibril nucleation. Phys. Rev. Lett. 110, 058101 (2013)

    Article  Google Scholar 

  66. Irbäck, A., Wessén, J.: Thermodynamics of amyloid formation and the role of intersheet interactions. J. Chem. Phys. 143, 105104 (2015)

    Article  Google Scholar 

  67. Swendsen, R.H., Wang, J.S.: Replica Monte Carlo simulation of spin glasses. Phys. Rev. Lett. 57, 2607 (1986)

    Article  MathSciNet  Google Scholar 

  68. Neuhaus, T., Hager, J.S.: Free-energy calculations with multiple Gaussian modified ensembles. Phys. Rev. E 74, 036702 (2006)

    Article  Google Scholar 

  69. Kim, J., Straub, J.E.: Generalized simulated tempering for exploring strong phase transitions. J. Chem. Phys. 133, 154101 (2010)

    Article  Google Scholar 

  70. Lindahl, V., Lidmar, J., Hess, B.: Accelerated weight histogram method for exploring free energy landscapes. J. Chem. Phys. 141, 044110 (2014)

    Article  Google Scholar 

  71. Scherer, M.K., Trendelkamp-Schroer, B., Paul, F., Pérez-Hernández, G., Hoffmann, M., Plattner, N., Wehmeyer, C., Prinz, J.H., Noé, F.: PyEMMA 2: a software package for estimation, validation, and analysis of Markov models. J. Chem. Theor. Comput. 11, 5525 (2015)

    Article  Google Scholar 

  72. Seeber, M., Felline, A., Raimondi, F., Muff, S., Friedman, R., Rao, F., Caflisch, A., Fanelli, F.: Wordom: A user-friendly program for the analysis of molecular structures, trajectories, and free energy surfaces. J. Comput. Chem. 32, 1183 (2010)

    Article  Google Scholar 

  73. Biarnés, X., Pietrucci, F., Marinelli, F., Laio, A.: METAGUI. A VMD interface for analyzing metadynamics and molecular dynamics simulations. Comput. Phys. Commun. 183, 203 (2012)

    Article  Google Scholar 

  74. Harrigan, M.P., Sultan, M.M., Hernández, C.X., Husic, B.E., Eastman, P., Schwantes, C.R., Beauchamp, K.A., McGibbon, R.T., Pande, V.S.: MSMBuilder: statistical models for biomolecular dynamics. Biophys. J. 112, 10 (2017)

    Article  Google Scholar 

  75. Lloyd, S., Trans, I.E.E.E.: Least squares quantization in PCM. Inf. Theor. 28, 129 (1982)

    Article  MathSciNet  Google Scholar 

  76. Kube, S., Weber, M.: A coarse graining method for the identification of transition rates between molecular conformations. J. Chem. Phys. 126, 024103 (2007)

    Article  Google Scholar 

  77. Djurdjevac, N., Sarich, M., Schütte, C.: Estimating the eigenvalue error of Markov state models. Multiscale Model. Simul. 10, 61 (2012)

    Article  MathSciNet  Google Scholar 

  78. Prinz, J.H., Chodera, J.D., Noé, F.: Spectral rate theory for two-state kinetics. Phys. Rev. X 4, 011020 (2014)

    Google Scholar 

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Acknowledgements

The work discussed in this article was in part supported by the Swedish Research Council (Grant no. 621-2014-4522) and the Swedish strategic research program eSSENCE. The simulations were performed on resources provided by the Swedish National Infrastructure for Computing (SNIC) at LUNARC, Lund University, Sweden, and Jülich Supercomputing Centre, Forschungszentrum Jülich, Germany.

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Correspondence to Anders Irbäck .

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Nilsson, D., Mohanty, S., Irbäck, A. (2019). Peptide Folding in Cellular Environments: A Monte Carlo and Markov Modeling Approach. In: Liwo, A. (eds) Computational Methods to Study the Structure and Dynamics of Biomolecules and Biomolecular Processes. Springer Series on Bio- and Neurosystems, vol 8. Springer, Cham. https://doi.org/10.1007/978-3-319-95843-9_13

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