Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process
Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially g...
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Gespeichert in:
| Autor*in: |
Kessler, David A. [verfasserIn] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2014 |
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| Schlagwörter: |
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| Anmerkung: |
© Springer Science+Business Media New York 2014 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of statistical physics - Springer US, 1969, 158(2014), 4 vom: 15. Nov., Seite 783-805 |
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| Übergeordnetes Werk: |
volume:158 ; year:2014 ; number:4 ; day:15 ; month:11 ; pages:783-805 |
| Links: |
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| DOI / URN: |
10.1007/s10955-014-1143-3 |
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OLC2046625390 |
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| 520 | |a Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. | ||
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10.1007/s10955-014-1143-3 doi (DE-627)OLC2046625390 (DE-He213)s10955-014-1143-3-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kessler, David A. verfasserin aut Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. Luria–Delbrück Mutants Growth Alpha-stable distribution Levine, Herbert aut Enthalten in Journal of statistical physics Springer US, 1969 158(2014), 4 vom: 15. Nov., Seite 783-805 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:158 year:2014 number:4 day:15 month:11 pages:783-805 https://doi.org/10.1007/s10955-014-1143-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_4323 33.00 VZ AR 158 2014 4 15 11 783-805 |
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10.1007/s10955-014-1143-3 doi (DE-627)OLC2046625390 (DE-He213)s10955-014-1143-3-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kessler, David A. verfasserin aut Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. Luria–Delbrück Mutants Growth Alpha-stable distribution Levine, Herbert aut Enthalten in Journal of statistical physics Springer US, 1969 158(2014), 4 vom: 15. Nov., Seite 783-805 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:158 year:2014 number:4 day:15 month:11 pages:783-805 https://doi.org/10.1007/s10955-014-1143-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_4323 33.00 VZ AR 158 2014 4 15 11 783-805 |
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10.1007/s10955-014-1143-3 doi (DE-627)OLC2046625390 (DE-He213)s10955-014-1143-3-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kessler, David A. verfasserin aut Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. Luria–Delbrück Mutants Growth Alpha-stable distribution Levine, Herbert aut Enthalten in Journal of statistical physics Springer US, 1969 158(2014), 4 vom: 15. Nov., Seite 783-805 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:158 year:2014 number:4 day:15 month:11 pages:783-805 https://doi.org/10.1007/s10955-014-1143-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_4323 33.00 VZ AR 158 2014 4 15 11 783-805 |
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10.1007/s10955-014-1143-3 doi (DE-627)OLC2046625390 (DE-He213)s10955-014-1143-3-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kessler, David A. verfasserin aut Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. Luria–Delbrück Mutants Growth Alpha-stable distribution Levine, Herbert aut Enthalten in Journal of statistical physics Springer US, 1969 158(2014), 4 vom: 15. Nov., Seite 783-805 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:158 year:2014 number:4 day:15 month:11 pages:783-805 https://doi.org/10.1007/s10955-014-1143-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_4323 33.00 VZ AR 158 2014 4 15 11 783-805 |
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10.1007/s10955-014-1143-3 doi (DE-627)OLC2046625390 (DE-He213)s10955-014-1143-3-p DE-627 ger DE-627 rakwb eng 530 VZ 33.00 bkl Kessler, David A. verfasserin aut Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process 2014 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer Science+Business Media New York 2014 Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. Luria–Delbrück Mutants Growth Alpha-stable distribution Levine, Herbert aut Enthalten in Journal of statistical physics Springer US, 1969 158(2014), 4 vom: 15. Nov., Seite 783-805 (DE-627)129549711 (DE-600)219136-2 (DE-576)015002918 0022-4715 nnns volume:158 year:2014 number:4 day:15 month:11 pages:783-805 https://doi.org/10.1007/s10955-014-1143-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-PHY GBV_ILN_20 GBV_ILN_70 GBV_ILN_2002 GBV_ILN_4323 33.00 VZ AR 158 2014 4 15 11 783-805 |
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Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. © Springer Science+Business Media New York 2014 |
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Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. © Springer Science+Business Media New York 2014 |
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Abstract One of the most popular models for quantitatively understanding the emergence of drug resistance both in bacterial colonies and in malignant tumors was introduced long ago by Luria and Delbrück. Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. Some of our results have been presented previously in abbreviated form [12]. © Springer Science+Business Media New York 2014 |
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Scaling Solution in the Large Population Limit of the General Asymmetric Stochastic Luria–Delbrück Evolution Process |
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https://doi.org/10.1007/s10955-014-1143-3 |
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Levine, Herbert |
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Levine, Herbert |
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129549711 |
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| doi_str |
10.1007/s10955-014-1143-3 |
| up_date |
2024-07-04T05:31:48.572Z |
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1803625282730459136 |
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Here, individual resistant mutants emerge randomly during the birth events of an exponentially growing sensitive population. A most interesting limit of this process occurs when the population size $$N$$ is large and mutation rates are low, but not necessarily small compared to $$1/N$$. Here we provide a scaling solution valid in this limit, making contact with the theory of Levy $$\alpha $$-stable distributions, in particular one discussed long ago by Landau. One consequence of this association is that moments of the distribution are highly misleading as far as characterizing typical behavior. A key insight that enables our solution is that working in the fixed population size ensemble is not the same as working in a fixed time ensemble. 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