DOI: 10.1063/1.1810475. Binomial leap methods for simulating stochastic chemical kinetics

Binomial leap methods for simulating stochastic chemical kinetics

10.1063/1.1810475

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the τ-leap and midpoint τ-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches.

Bibliography

Tian, T., & Burrage, K. (2004). Binomial leap methods for simulating stochastic chemical kinetics. The Journal of Chemical Physics, 121(21), 10356â10364.

Authors 2

Tianhai Tian (first)
Kevin Burrage (additional)

References 20 Referenced 232

10.1093/genetics/149.4.1633 / Genetics (1998)
{'key': '2024020702193564700_r2', 'first-page': '633', 'volume': '422', 'year': '2003', 'journal-title': 'Science'} / Science (2003)
10.1038/35053181 / Nature (London) (2001)
10.1073/pnas.022628299 / Proc. Natl. Acad. Sci. U.S.A. (2002)
{'key': '2024020702193564700_r5', 'first-page': '268', 'volume': '2', 'year': '2001', 'journal-title': 'Nat. Rev. Genet.'} / Nat. Rev. Genet. (2001)
10.1021/j100540a008 / J. Phys. Chem. (1977)
10.1063/1.1378322 / J. Chem. Phys. (2001)
10.1063/1.1627296 / J. Chem. Phys. (2003)
{'key': '2024020702193564700_r9'}
10.1063/1.1613254 / J. Chem. Phys. (2003)
10.1063/1.1545446 / J. Chem. Phys. (2003)
10.1063/1.1505860 / J. Chem. Phys. (2002)
10.1016/j.pbiomolbio.2004.01.014 / Prog. Biophys. Mol. Biol. (2004)
10.1021/jp993732q / J. Phys. Chem. A (2000)
10.1063/1.481811 / J. Chem. Phys. (2000)
{'key': '2024020702193564700_r16', 'first-page': '11026', 'volume': '105', 'year': '2001', 'journal-title': 'J. Phys. Chem. B'} / J. Phys. Chem. B (2001)
{'key': '2024020702193564700_r17'}
10.1145/42372.42381 / Commun. ACM (1988)
10.1145/355993.355997 / ACM Trans. Math. Softw. (1982)
10.1093/bioinformatics/18.3.470 / Bioinformatics (2002)

Dates

Type	When
Created	20 years, 9 months ago (Nov. 15, 2004, 7:03 p.m.)
Deposited	1 year, 6 months ago (Feb. 6, 2024, 11:33 p.m.)
Indexed	2 weeks, 5 days ago (Aug. 6, 2025, 9:01 a.m.)
Issued	20 years, 8 months ago (Dec. 1, 2004)
Published	20 years, 8 months ago (Dec. 1, 2004)
Published Print	20 years, 8 months ago (Dec. 1, 2004)

Funders 0

None

BibTeX

@article{Tian_2004, title={Binomial leap methods for simulating stochastic chemical kinetics}, volume={121}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1810475}, DOI={10.1063/1.1810475}, number={21}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Tian, Tianhai and Burrage, Kevin}, year={2004}, month=dec, pages={10356–10364} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        6
      ]
    ],
    "date-time": "2025-08-06T13:01:45Z",
    "timestamp": 1754485305047
  },
  "reference-count": 20,
  "publisher": "AIP Publishing",
  "issue": "21",
  "content-domain": {
    "domain": [
      "pubs.aip.org"
    ],
    "crossmark-restriction": true
  },
  "published-print": {
    "date-parts": [
      [
        2004,
        12,
        1
      ]
    ]
  },
  "abstract": "<jats:p>This paper discusses efficient simulation methods for stochastic chemical kinetics. Based on the \u03c4-leap and midpoint \u03c4-leap methods of Gillespie [D. T. Gillespie, J. Chem. Phys. 115, 1716 (2001)], binomial random variables are used in these leap methods rather than Poisson random variables. The motivation for this approach is to improve the efficiency of the Poisson leap methods by using larger stepsizes. Unlike Poisson random variables whose range of sample values is from zero to infinity, binomial random variables have a finite range of sample values. This probabilistic property has been used to restrict possible reaction numbers and to avoid negative molecular numbers in stochastic simulations when larger stepsize is used. In this approach a binomial random variable is defined for a single reaction channel in order to keep the reaction number of this channel below the numbers of molecules that undergo this reaction channel. A sampling technique is also designed for the total reaction number of a reactant species that undergoes two or more reaction channels. Samples for the total reaction number are not greater than the molecular number of this species. In addition, probability properties of the binomial random variables provide stepsize conditions for restricting reaction numbers in a chosen time interval. These stepsize conditions are important properties of robust leap control strategies. Numerical results indicate that the proposed binomial leap methods can be applied to a wide range of chemical reaction systems with very good accuracy and significant improvement on efficiency over existing approaches.</jats:p>",
  "DOI": "10.1063/1.1810475",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2004,
        11,
        16
      ]
    ],
    "date-time": "2004-11-16T00:03:57Z",
    "timestamp": 1100563437000
  },
  "page": "10356-10364",
  "update-policy": "http://dx.doi.org/10.1063/aip-crossmark-policy-page",
  "source": "Crossref",
  "is-referenced-by-count": 232,
  "title": "Binomial leap methods for simulating stochastic chemical kinetics",
  "prefix": "10.1063",
  "volume": "121",
  "author": [
    {
      "given": "Tianhai",
      "family": "Tian",
      "sequence": "first",
      "affiliation": [
        {
          "name": "Advanced Computational Modelling Centre, University of Queensland, Brisbane\u2009QLD\u20094072, Australia"
        }
      ]
    },
    {
      "given": "Kevin",
      "family": "Burrage",
      "sequence": "additional",
      "affiliation": [
        {
          "name": "Advanced Computational Modelling Centre, University of Queensland, Brisbane\u2009QLD\u20094072, Australia"
        }
      ]
    }
  ],
  "member": "317",
  "reference": [
    {
      "key": "2024020702193564700_r1",
      "doi-asserted-by": "crossref",
      "first-page": "1633",
      "DOI": "10.1093/genetics/149.4.1633",
      "volume": "149",
      "year": "1998",
      "journal-title": "Genetics"
    },
    {
      "key": "2024020702193564700_r2",
      "first-page": "633",
      "volume": "422",
      "year": "2003",
      "journal-title": "Science"
    },
    {
      "key": "2024020702193564700_r3",
      "doi-asserted-by": "crossref",
      "first-page": "391",
      "DOI": "10.1038/35053181",
      "volume": "409",
      "year": "2001",
      "journal-title": "Nature (London)"
    },
    {
      "key": "2024020702193564700_r4",
      "doi-asserted-by": "crossref",
      "first-page": "673",
      "DOI": "10.1073/pnas.022628299",
      "volume": "99",
      "year": "2002",
      "journal-title": "Proc. Natl. Acad. Sci. U.S.A."
    },
    {
      "key": "2024020702193564700_r5",
      "first-page": "268",
      "volume": "2",
      "year": "2001",
      "journal-title": "Nat. Rev. Genet."
    },
    {
      "key": "2024020702193564700_r6",
      "doi-asserted-by": "crossref",
      "first-page": "2340",
      "DOI": "10.1021/j100540a008",
      "volume": "81",
      "year": "1977",
      "journal-title": "J. Phys. Chem."
    },
    {
      "key": "2024020702193564700_r7",
      "doi-asserted-by": "crossref",
      "first-page": "1716",
      "DOI": "10.1063/1.1378322",
      "volume": "115",
      "year": "2001",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020702193564700_r8",
      "doi-asserted-by": "crossref",
      "first-page": "12784",
      "DOI": "10.1063/1.1627296",
      "volume": "119",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020702193564700_r9"
    },
    {
      "key": "2024020702193564700_r10",
      "doi-asserted-by": "crossref",
      "first-page": "8229",
      "DOI": "10.1063/1.1613254",
      "volume": "119",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020702193564700_r11",
      "doi-asserted-by": "crossref",
      "first-page": "4999",
      "DOI": "10.1063/1.1545446",
      "volume": "118",
      "year": "2003",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020702193564700_r12",
      "doi-asserted-by": "crossref",
      "first-page": "6959",
      "DOI": "10.1063/1.1505860",
      "volume": "117",
      "year": "2002",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020702193564700_r13",
      "doi-asserted-by": "crossref",
      "first-page": "217",
      "DOI": "10.1016/j.pbiomolbio.2004.01.014",
      "volume": "85",
      "year": "2004",
      "journal-title": "Prog. Biophys. Mol. Biol."
    },
    {
      "key": "2024020702193564700_r14",
      "doi-asserted-by": "crossref",
      "first-page": "1876",
      "DOI": "10.1021/jp993732q",
      "volume": "104",
      "year": "2000",
      "journal-title": "J. Phys. Chem. A"
    },
    {
      "key": "2024020702193564700_r15",
      "doi-asserted-by": "crossref",
      "first-page": "297",
      "DOI": "10.1063/1.481811",
      "volume": "113",
      "year": "2000",
      "journal-title": "J. Chem. Phys."
    },
    {
      "key": "2024020702193564700_r16",
      "first-page": "11026",
      "volume": "105",
      "year": "2001",
      "journal-title": "J. Phys. Chem. B"
    },
    {
      "key": "2024020702193564700_r17"
    },
    {
      "key": "2024020702193564700_r18",
      "doi-asserted-by": "crossref",
      "first-page": "216",
      "DOI": "10.1145/42372.42381",
      "volume": "31",
      "year": "1988",
      "journal-title": "Commun. ACM"
    },
    {
      "key": "2024020702193564700_r19",
      "doi-asserted-by": "crossref",
      "first-page": "163",
      "DOI": "10.1145/355993.355997",
      "volume": "8",
      "year": "1982",
      "journal-title": "ACM Trans. Math. Softw."
    },
    {
      "key": "2024020702193564700_r20",
      "doi-asserted-by": "crossref",
      "first-page": "470",
      "DOI": "10.1093/bioinformatics/18.3.470",
      "volume": "18",
      "year": "2002",
      "journal-title": "Bioinformatics"
    }
  ],
  "container-title": "The Journal of Chemical Physics",
  "original-title": [],
  "language": "en",
  "link": [
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/121/21/10356/19270965/10356_1_online.pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://pubs.aip.org/aip/jcp/article-pdf/121/21/10356/19270965/10356_1_online.pdf",
      "content-type": "unspecified",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        2,
        7
      ]
    ],
    "date-time": "2024-02-07T04:33:55Z",
    "timestamp": 1707280435000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://pubs.aip.org/jcp/article/121/21/10356/532579/Binomial-leap-methods-for-simulating-stochastic"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2004,
        12,
        1
      ]
    ]
  },
  "references-count": 20,
  "journal-issue": {
    "issue": "21",
    "published-print": {
      "date-parts": [
        [
          2004,
          12,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1063/1.1810475",
  "relation": {},
  "ISSN": [
    "0021-9606",
    "1089-7690"
  ],
  "subject": [],
  "published-other": {
    "date-parts": [
      [
        2004,
        12,
        1
      ]
    ]
  },
  "published": {
    "date-parts": [
      [
        2004,
        12,
        1
      ]
    ]
  }
}