DOI: 10.1063/1.1667470. Folding probabilities: A novel approach to folding transitions and the two-dimensional Ising-model

Folding probabilities: A novel approach to folding transitions and the two-dimensional Ising-model

10.1063/1.1667470

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

The theoretical concept of folding probability, pfold, has proven to be a useful means to characterize the kinetics of protein folding. Here, we illustrate the practical importance of pfold and demonstrate how it can be determined theoretically. We derive a general analytical expression for pfold and show how it can be estimated from simulations for systems where the transition rates between the relevant microstates are not known. By analyzing the Ising model we are able to determine the scaling behavior of the numerical error in the pfold estimate as function of the number of analyzed Monte Carlo runs. We apply our method to a simple, newly developed protein folding model for the formation of alpha helices. It is demonstrated that our technique highly parallelizes the calculation of pfold and that it is orders of magnitude more efficient than conventional approaches.

Bibliography

Lenz, P., Zagrovic, B., Shapiro, J., & Pande, V. S. (2004). Folding probabilities: A novel approach to folding transitions and the two-dimensional Ising-model. The Journal of Chemical Physics, 120(14), 6769â6778.

Authors 4

Peter Lenz (first)
Bojan Zagrovic (additional)
Jessica Shapiro (additional)
Vijay S. Pande (additional)

References 30 Referenced 13

10.1103/RevModPhys.72.259 / Rev. Mod. Phys. (2000)
10.1126/science.282.5389.740 / Science (1998)
10.1006/jmbi.2001.5033 / J. Mol. Biol. (2001)
10.1103/PhysRevB.57.R13985 / Phys. Rev. B (1998)
10.1002/(SICI)1097-0134(19980101)30:1<2::AID-PROT2>3.0.CO;2-R / Proteins (1998)
10.1002/bbpc.19910950318 / Ber. Bunsenges. Phys. Chem. (1991)
10.1063/1.475393 / J. Chem. Phys. (1998)
10.1002/prot.1058 / Proteins: Struct., Funct., Genet. (2001)
{'key': '2024021112112757700_r9'}
10.1063/1.1699114 / J. Chem. Phys. (1953)
{'key': '2024021112112757700_r11'}
{'key': '2024021112112757700_r12'}
10.1016/0021-9991(83)90014-1 / J. Comput. Phys. (1983)
10.1021/ja00214a002 / J. Am. Chem. Soc. (1988)
{'key': '2024021112112757700_r15', 'first-page': '3005', 'volume': '101', 'year': '1997', 'journal-title': 'J. Phys. Chem.'} / J. Phys. Chem. (1997)
10.1146/annurev.biophys.29.1.327 / Annu. Rev. Biophys. Biomol. Struct. (2000)
10.1002/bip.360310911 / Biopolymers (1991)
{'key': '2024021112112757700_r18', 'first-page': '1221', 'volume': '223', 'year': '1992', 'journal-title': 'J. Mol. Biol.'} / J. Mol. Biol. (1992)
10.1006/jmbi.1996.0339 / J. Mol. Biol. (1996)
10.1063/1.1730390 / J. Chem. Phys. (1959)
10.1063/1.467320 / J. Chem. Phys. (1994)
10.1021/bi00199a029 / Biochemistry (1994)
10.1016/0301-0104(91)87067-6 / Chem. Phys. (1991)
10.1006/jmbi.2001.4586 / J. Mol. Biol. (2001)
10.1073/pnas.96.25.14258 / Proc. Natl. Acad. Sci. U.S.A. (1999)
{'key': '2024021112112757700_r26'}
{'key': '2024021112112757700_r27'}
{'key': '2024021112112757700_r28'}
{'key': '2024021112112757700_r29', 'first-page': '570', 'volume': '77', 'year': '1997', 'journal-title': 'Phys. Rev. Lett.'} / Phys. Rev. Lett. (1997)
10.1016/S0550-3213(97)00419-7 / Nucl. Phys. B (1997)

Dates

Type	When
Created	21 years, 5 months ago (March 24, 2004, 6:04 p.m.)
Deposited	1 year, 6 months ago (Feb. 11, 2024, 7:11 a.m.)
Indexed	1 year, 6 months ago (Feb. 11, 2024, 7:40 a.m.)
Issued	21 years, 4 months ago (April 8, 2004)
Published	21 years, 4 months ago (April 8, 2004)
Published Print	21 years, 4 months ago (April 8, 2004)

Funders 0

None

BibTeX

@article{Lenz_2004, title={Folding probabilities: A novel approach to folding transitions and the two-dimensional Ising-model}, volume={120}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1667470}, DOI={10.1063/1.1667470}, number={14}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Lenz, Peter and Zagrovic, Bojan and Shapiro, Jessica and Pande, Vijay S.}, year={2004}, month=apr, pages={6769–6778} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2024,
        2,
        11
      ]
    ],
    "date-time": "2024-02-11T12:40:07Z",
    "timestamp": 1707655207722
  },
  "reference-count": 30,
  "publisher": "AIP Publishing",
  "issue": "14",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2004,
        4,
        8
      ]
    ]
  },
  "abstract": "<jats:p>The theoretical concept of folding probability, pfold, has proven to be a useful means to characterize the kinetics of protein folding. Here, we illustrate the practical importance of pfold and demonstrate how it can be determined theoretically. We derive a general analytical expression for pfold and show how it can be estimated from simulations for systems where the transition rates between the relevant microstates are not known. By analyzing the Ising model we are able to determine the scaling behavior of the numerical error in the pfold estimate as function of the number of analyzed Monte Carlo runs. We apply our method to a simple, newly developed protein folding model for the formation of alpha helices. It is demonstrated that our technique highly parallelizes the calculation of pfold and that it is orders of magnitude more efficient than conventional approaches.</jats:p>",
  "DOI": "10.1063/1.1667470",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        3,
        24
      ]
    ],
    "date-time": "2004-03-24T23:04:45Z",
    "timestamp": 1080169485000
  },
  "page": "6769-6778",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 13,
  "title": "Folding probabilities: A novel approach to folding transitions and the two-dimensional Ising-model",
  "prefix": "10.1063",
  "volume": "120",
  "author": [
    {
      "given": "Peter",
      "family": "Lenz",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Lyman Laboratory of Physics, Harvard University, Cambridge, Massachusetts\u200902138"
        },
        {
          "name": "Department of Chemistry, Stanford University, Stanford, California\u200994305"
        }
      ]
    },
    {
      "given": "Bojan",
      "family": "Zagrovic",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Chemistry, Stanford University, Stanford, California\u200994305"
        }
      ]
    },
    {
      "given": "Jessica",
      "family": "Shapiro",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Chemistry, Stanford University, Stanford, California\u200994305"
        }
      ]
    },
    {
      "given": "Vijay S.",
      "family": "Pande",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Department of Chemistry, Stanford University, Stanford, California\u200994305"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024021112112757700_r1",
      "doi-asserted-by": "crossref",
      "first-page": "259",
      "DOI": "10.1103/RevModPhys.72.259",
      "volume": "72",
      "year": "2000",
      "journal-title": "Rev. Mod. Phys."
    },
    {
      "key": "2024021112112757700_r2",
      "doi-asserted-by": "crossref",
      "first-page": "740",
      "DOI": "10.1126/science.282.5389.740",
      "volume": "282",
      "year": "1998",
      "journal-title": "Science"
    },
    {
      "key": "2024021112112757700_r3",
      "doi-asserted-by": "crossref",
      "first-page": "151",
      "DOI": "10.1006/jmbi.2001.5033",
      "volume": "313",
      "year": "2001",
      "journal-title": "J. Mol. Biol."
    },
    {
      "key": "2024021112112757700_r4",
      "doi-asserted-by": "crossref",
      "first-page": "13985",
      "DOI": "10.1103/PhysRevB.57.R13985",
      "volume": "57",
      "year": "1998",
      "journal-title": "Phys. Rev. B"
    },
    {
      "key": "2024021112112757700_r5",
      "doi-asserted-by": "crossref",
      "first-page": "2",
      "DOI": "10.1002/(SICI)1097-0134(19980101)30:1<2::AID-PROT2>3.0.CO;2-R",
      "volume": "30",
      "year": "1998",
      "journal-title": "Proteins"
    },
    {
      "key": "2024021112112757700_r6",
      "doi-asserted-by": "crossref",
      "first-page": "331",
      "DOI": "10.1002/bbpc.19910950318",
      "volume": "95",
      "year": "1991",
      "journal-title": "Ber. Bunsenges. Phys. Chem."
    },
    {
      "key": "2024021112112757700_r7",
      "doi-asserted-by": "crossref",
      "first-page": "334",
      "DOI": "10.1063/1.475393",
      "volume": "108",
      "year": "1998",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021112112757700_r8",
      "doi-asserted-by": "crossref",
      "first-page": "465",
      "DOI": "10.1002/prot.1058",
      "volume": "43",
      "year": "2001",
      "journal-title": "Proteins: Struct., Funct., Genet."
    },
    {
      "key": "2024021112112757700_r9"
    },
    {
      "key": "2024021112112757700_r10",
      "doi-asserted-by": "crossref",
      "first-page": "1087",
      "DOI": "10.1063/1.1699114",
      "volume": "21",
      "year": "1953",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021112112757700_r11"
    },
    {
      "key": "2024021112112757700_r12"
    },
    {
      "key": "2024021112112757700_r13",
      "doi-asserted-by": "crossref",
      "first-page": "24",
      "DOI": "10.1016/0021-9991(83)90014-1",
      "volume": "52",
      "year": "1983",
      "journal-title": "J. Comput. Phys."
    },
    {
      "key": "2024021112112757700_r14",
      "doi-asserted-by": "crossref",
      "first-page": "1666",
      "DOI": "10.1021/ja00214a002",
      "volume": "110",
      "year": "1988",
      "journal-title": "J. Am. Chem. Soc."
    },
    {
      "key": "2024021112112757700_r15",
      "first-page": "3005",
      "volume": "101",
      "year": "1997",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2024021112112757700_r16",
      "doi-asserted-by": "crossref",
      "first-page": "327",
      "DOI": "10.1146/annurev.biophys.29.1.327",
      "volume": "29",
      "year": "2000",
      "journal-title": "Annu. Rev. Biophys. Biomol. Struct."
    },
    {
      "key": "2024021112112757700_r17",
      "doi-asserted-by": "crossref",
      "first-page": "1115",
      "DOI": "10.1002/bip.360310911",
      "volume": "31",
      "year": "1991",
      "journal-title": "Biopolymers"
    },
    {
      "key": "2024021112112757700_r18",
      "first-page": "1221",
      "volume": "223",
      "year": "1992",
      "journal-title": "J. Mol. Biol."
    },
    {
      "key": "2024021112112757700_r19",
      "doi-asserted-by": "crossref",
      "first-page": "560",
      "DOI": "10.1006/jmbi.1996.0339",
      "volume": "259",
      "year": "1996",
      "journal-title": "J. Mol. Biol."
    },
    {
      "key": "2024021112112757700_r20",
      "doi-asserted-by": "crossref",
      "first-page": "526",
      "DOI": "10.1063/1.1730390",
      "volume": "31",
      "year": "1959",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021112112757700_r21",
      "doi-asserted-by": "crossref",
      "first-page": "6052",
      "DOI": "10.1063/1.467320",
      "volume": "101",
      "year": "1994",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024021112112757700_r22",
      "doi-asserted-by": "crossref",
      "first-page": "10026",
      "DOI": "10.1021/bi00199a029",
      "volume": "33",
      "year": "1994",
      "journal-title": "Biochemistry"
    },
    {
      "key": "2024021112112757700_r23",
      "doi-asserted-by": "crossref",
      "first-page": "199",
      "DOI": "10.1016/0301-0104(91)87067-6",
      "volume": "158",
      "year": "1991",
      "journal-title": "Chem. Phys."
    },
    {
      "key": "2024021112112757700_r24",
      "doi-asserted-by": "crossref",
      "first-page": "79",
      "DOI": "10.1006/jmbi.2001.4586",
      "volume": "308",
      "year": "2001",
      "journal-title": "J. Mol. Biol."
    },
    {
      "key": "2024021112112757700_r25",
      "doi-asserted-by": "crossref",
      "first-page": "14258",
      "DOI": "10.1073/pnas.96.25.14258",
      "volume": "96",
      "year": "1999",
      "journal-title": "Proc. Natl. Acad. Sci. U.S.A."
    },
    {
      "key": "2024021112112757700_r26"
    },
    {
      "key": "2024021112112757700_r27"
    },
    {
      "key": "2024021112112757700_r28"
    },
    {
      "key": "2024021112112757700_r29",
      "first-page": "570",
      "volume": "77",
      "year": "1997",
      "journal-title": "Phys. Rev. Lett."
    },
    {
      "key": "2024021112112757700_r29a",
      "doi-asserted-by": "crossref",
      "first-page": "643",
      "DOI": "10.1016/S0550-3213(97)00419-7",
      "volume": "501",
      "year": "1997",
      "journal-title": "Nucl. Phys. B"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/120/14/6769/19122516/6769_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/120/14/6769/19122516/6769_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        11
      ]
    ],
    "date-time": "2024-02-11T12:11:49Z",
    "timestamp": 1707653509000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/120/14/6769/295054/Folding-probabilities-A-novel-approach-to-folding"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2004,
        4,
        8
      ]
    ]
  },
  "references-count": 30,
  "journal-issue": {
    "issue": "14",
    "published-print": {
      "date-parts": [
        [
          2004,
          4,
          8
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1667470",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2004,
        4,
        8
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2004,
        4,
        8
      ]
    ]
  }
}