Transition from stochastic to deterministic behavior in calcium oscillations
Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough...
Ausführliche Beschreibung
Gespeichert in:
| Autor*in: |
Kummer, Ursula - 1967- [verfasserIn] Pahle, Jürgen - 1976- [verfasserIn] |
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| Format: |
E-Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
September 2005 |
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| Anmerkung: |
Gesehen am 23.05.2017 |
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| Umfang: |
9 |
| Übergeordnetes Werk: |
Enthalten in: Biophysical journal - Cambridge, Mass. : Cell Press, 1960, 89(2005), 3, Seite 1603-1611 |
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| Übergeordnetes Werk: |
volume:89 ; year:2005 ; number:3 ; pages:1603-1611 ; extent:9 |
| Links: |
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| DOI / URN: |
10.1529/biophysj.104.057216 |
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| Katalog-ID: |
1558932976 |
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| 520 | |a Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism. | ||
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10.1529/biophysj.104.057216 doi (DE-627)1558932976 (DE-576)488932971 (DE-599)BSZ488932971 (OCoLC)1340975714 DE-627 ger DE-627 rda eng Kummer, Ursula 1967- verfasserin (DE-588)115411682 (DE-627)691297975 (DE-576)176480897 aut Transition from stochastic to deterministic behavior in calcium oscillations Ursula Kummer, Borut Krajnc, Jürgen Pahle, Anne K. Green, C. Jane Dixon, Marko Marhl September 2005 9 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Gesehen am 23.05.2017 Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism. Pahle, Jürgen 1976- verfasserin (DE-588)136080243 (DE-627)577146467 (DE-576)300819382 aut Enthalten in Biophysical journal Cambridge, Mass. : Cell Press, 1960 89(2005), 3, Seite 1603-1611 Online-Ressource (DE-627)270425357 (DE-600)1477214-0 (DE-576)091017602 1542-0086 nnns volume:89 year:2005 number:3 pages:1603-1611 extent:9 http://dx.doi.org/10.1529/biophysj.104.057216 Verlag Resolving-System kostenfrei Volltext http://www.sciencedirect.com/science/article/pii/S000634950572806X Verlag kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_2013 ISIL_DE-16-250 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 89 2005 3 1603-1611 9 2013 01 DE-16-250 2970149052 00 --%%-- --%%-- --%%-- --%%-- l01 23-05-17 2403 01 DE-LFER 2971464326 00 --%%-- --%%-- n --%%-- l01 08-06-17 2403 01 DE-LFER http://dx.doi.org/10.1529/biophysj.104.057216 2013 01 DE-16-250 00 s hd2005 2013 01 DE-16-250 01 s (DE-627)1410508463 wissenschaftlicher Artikel (Zeitschrift) 2013 01 DE-16-250 02 s per_6 2013 01 DE-16-250 03 s s_9 2013 01 DE-16-250 04 p (DE-627)1497999472 Kummer, Ursula 2013 01 DE-16-250 04 k (DE-627)1416822720 Extern 2013 01 DE-16-250 04 s (DE-627)1410501914 Verfasser 2013 01 DE-16-250 04 s pos_1 2013 01 DE-16-250 05 p (DE-627)1558617299 Pahle, Jürgen 2013 01 DE-16-250 05 k (DE-627)1416822720 Extern 2013 01 DE-16-250 05 s (DE-627)1410501914 Verfasser 2013 01 DE-16-250 05 s pos_3 |
| spelling |
10.1529/biophysj.104.057216 doi (DE-627)1558932976 (DE-576)488932971 (DE-599)BSZ488932971 (OCoLC)1340975714 DE-627 ger DE-627 rda eng Kummer, Ursula 1967- verfasserin (DE-588)115411682 (DE-627)691297975 (DE-576)176480897 aut Transition from stochastic to deterministic behavior in calcium oscillations Ursula Kummer, Borut Krajnc, Jürgen Pahle, Anne K. Green, C. Jane Dixon, Marko Marhl September 2005 9 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Gesehen am 23.05.2017 Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism. Pahle, Jürgen 1976- verfasserin (DE-588)136080243 (DE-627)577146467 (DE-576)300819382 aut Enthalten in Biophysical journal Cambridge, Mass. : Cell Press, 1960 89(2005), 3, Seite 1603-1611 Online-Ressource (DE-627)270425357 (DE-600)1477214-0 (DE-576)091017602 1542-0086 nnns volume:89 year:2005 number:3 pages:1603-1611 extent:9 http://dx.doi.org/10.1529/biophysj.104.057216 Verlag Resolving-System kostenfrei Volltext http://www.sciencedirect.com/science/article/pii/S000634950572806X Verlag kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_2013 ISIL_DE-16-250 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 89 2005 3 1603-1611 9 2013 01 DE-16-250 2970149052 00 --%%-- --%%-- --%%-- --%%-- l01 23-05-17 2403 01 DE-LFER 2971464326 00 --%%-- --%%-- n --%%-- l01 08-06-17 2403 01 DE-LFER http://dx.doi.org/10.1529/biophysj.104.057216 2013 01 DE-16-250 00 s hd2005 2013 01 DE-16-250 01 s (DE-627)1410508463 wissenschaftlicher Artikel (Zeitschrift) 2013 01 DE-16-250 02 s per_6 2013 01 DE-16-250 03 s s_9 2013 01 DE-16-250 04 p (DE-627)1497999472 Kummer, Ursula 2013 01 DE-16-250 04 k (DE-627)1416822720 Extern 2013 01 DE-16-250 04 s (DE-627)1410501914 Verfasser 2013 01 DE-16-250 04 s pos_1 2013 01 DE-16-250 05 p (DE-627)1558617299 Pahle, Jürgen 2013 01 DE-16-250 05 k (DE-627)1416822720 Extern 2013 01 DE-16-250 05 s (DE-627)1410501914 Verfasser 2013 01 DE-16-250 05 s pos_3 |
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10.1529/biophysj.104.057216 doi (DE-627)1558932976 (DE-576)488932971 (DE-599)BSZ488932971 (OCoLC)1340975714 DE-627 ger DE-627 rda eng Kummer, Ursula 1967- verfasserin (DE-588)115411682 (DE-627)691297975 (DE-576)176480897 aut Transition from stochastic to deterministic behavior in calcium oscillations Ursula Kummer, Borut Krajnc, Jürgen Pahle, Anne K. Green, C. Jane Dixon, Marko Marhl September 2005 9 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Gesehen am 23.05.2017 Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism. Pahle, Jürgen 1976- verfasserin (DE-588)136080243 (DE-627)577146467 (DE-576)300819382 aut Enthalten in Biophysical journal Cambridge, Mass. : Cell Press, 1960 89(2005), 3, Seite 1603-1611 Online-Ressource (DE-627)270425357 (DE-600)1477214-0 (DE-576)091017602 1542-0086 nnns volume:89 year:2005 number:3 pages:1603-1611 extent:9 http://dx.doi.org/10.1529/biophysj.104.057216 Verlag Resolving-System kostenfrei Volltext http://www.sciencedirect.com/science/article/pii/S000634950572806X Verlag kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_2013 ISIL_DE-16-250 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 89 2005 3 1603-1611 9 2013 01 DE-16-250 2970149052 00 --%%-- --%%-- --%%-- --%%-- l01 23-05-17 2403 01 DE-LFER 2971464326 00 --%%-- --%%-- n --%%-- l01 08-06-17 2403 01 DE-LFER http://dx.doi.org/10.1529/biophysj.104.057216 2013 01 DE-16-250 00 s hd2005 2013 01 DE-16-250 01 s (DE-627)1410508463 wissenschaftlicher Artikel (Zeitschrift) 2013 01 DE-16-250 02 s per_6 2013 01 DE-16-250 03 s s_9 2013 01 DE-16-250 04 p (DE-627)1497999472 Kummer, Ursula 2013 01 DE-16-250 04 k (DE-627)1416822720 Extern 2013 01 DE-16-250 04 s (DE-627)1410501914 Verfasser 2013 01 DE-16-250 04 s pos_1 2013 01 DE-16-250 05 p (DE-627)1558617299 Pahle, Jürgen 2013 01 DE-16-250 05 k (DE-627)1416822720 Extern 2013 01 DE-16-250 05 s (DE-627)1410501914 Verfasser 2013 01 DE-16-250 05 s pos_3 |
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10.1529/biophysj.104.057216 doi (DE-627)1558932976 (DE-576)488932971 (DE-599)BSZ488932971 (OCoLC)1340975714 DE-627 ger DE-627 rda eng Kummer, Ursula 1967- verfasserin (DE-588)115411682 (DE-627)691297975 (DE-576)176480897 aut Transition from stochastic to deterministic behavior in calcium oscillations Ursula Kummer, Borut Krajnc, Jürgen Pahle, Anne K. Green, C. Jane Dixon, Marko Marhl September 2005 9 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Gesehen am 23.05.2017 Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism. Pahle, Jürgen 1976- verfasserin (DE-588)136080243 (DE-627)577146467 (DE-576)300819382 aut Enthalten in Biophysical journal Cambridge, Mass. : Cell Press, 1960 89(2005), 3, Seite 1603-1611 Online-Ressource (DE-627)270425357 (DE-600)1477214-0 (DE-576)091017602 1542-0086 nnns volume:89 year:2005 number:3 pages:1603-1611 extent:9 http://dx.doi.org/10.1529/biophysj.104.057216 Verlag Resolving-System kostenfrei Volltext http://www.sciencedirect.com/science/article/pii/S000634950572806X Verlag kostenfrei Volltext GBV_USEFLAG_U GBV_ILN_2013 ISIL_DE-16-250 SYSFLAG_1 GBV_KXP GBV_ILN_20 GBV_ILN_22 GBV_ILN_23 GBV_ILN_24 GBV_ILN_31 GBV_ILN_32 GBV_ILN_39 GBV_ILN_40 GBV_ILN_60 GBV_ILN_62 GBV_ILN_63 GBV_ILN_69 GBV_ILN_70 GBV_ILN_73 GBV_ILN_74 GBV_ILN_90 GBV_ILN_95 GBV_ILN_100 GBV_ILN_101 GBV_ILN_105 GBV_ILN_110 GBV_ILN_151 GBV_ILN_161 GBV_ILN_170 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 GBV_ILN_2008 GBV_ILN_2009 GBV_ILN_2010 GBV_ILN_2011 GBV_ILN_2014 GBV_ILN_2015 GBV_ILN_2020 GBV_ILN_2021 GBV_ILN_2025 GBV_ILN_2026 GBV_ILN_2027 GBV_ILN_2034 GBV_ILN_2038 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2056 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2088 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2118 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2190 GBV_ILN_2336 GBV_ILN_2470 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4249 GBV_ILN_4251 GBV_ILN_4305 GBV_ILN_4306 GBV_ILN_4307 GBV_ILN_4313 GBV_ILN_4322 GBV_ILN_4323 GBV_ILN_4324 GBV_ILN_4325 GBV_ILN_4326 GBV_ILN_4333 GBV_ILN_4334 GBV_ILN_4335 GBV_ILN_4338 GBV_ILN_4367 GBV_ILN_4393 GBV_ILN_4700 GBV_ILN_2403 GBV_ILN_2403 ISIL_DE-LFER AR 89 2005 3 1603-1611 9 2013 01 DE-16-250 2970149052 00 --%%-- --%%-- --%%-- --%%-- l01 23-05-17 2403 01 DE-LFER 2971464326 00 --%%-- --%%-- n --%%-- l01 08-06-17 2403 01 DE-LFER http://dx.doi.org/10.1529/biophysj.104.057216 2013 01 DE-16-250 00 s hd2005 2013 01 DE-16-250 01 s (DE-627)1410508463 wissenschaftlicher Artikel (Zeitschrift) 2013 01 DE-16-250 02 s per_6 2013 01 DE-16-250 03 s s_9 2013 01 DE-16-250 04 p (DE-627)1497999472 Kummer, Ursula 2013 01 DE-16-250 04 k (DE-627)1416822720 Extern 2013 01 DE-16-250 04 s (DE-627)1410501914 Verfasser 2013 01 DE-16-250 04 s pos_1 2013 01 DE-16-250 05 p (DE-627)1558617299 Pahle, Jürgen 2013 01 DE-16-250 05 k (DE-627)1416822720 Extern 2013 01 DE-16-250 05 s (DE-627)1410501914 Verfasser 2013 01 DE-16-250 05 s pos_3 |
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Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. 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Transition from stochastic to deterministic behavior in calcium oscillations Ursula Kummer, Borut Krajnc, Jürgen Pahle, Anne K. Green, C. Jane Dixon, Marko Marhl |
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transition from stochastic to deterministic behavior in calcium oscillations |
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Transition from stochastic to deterministic behavior in calcium oscillations |
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Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism. Gesehen am 23.05.2017 |
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Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism. Gesehen am 23.05.2017 |
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Simulation and modeling is becoming more and more important when studying complex biochemical systems. Most often, ordinary differential equations are employed for this purpose. However, these are only applicable when the numbers of participating molecules in the biochemical systems are large enough to be treated as concentrations. For smaller systems, stochastic simulations on discrete particle basis are more accurate. Unfortunately, there are no general rules for determining which method should be employed for exactly which problem to get the most realistic result. Therefore, we study the transition from stochastic to deterministic behavior in a widely studied system, namely the signal transduction via calcium, especially calcium oscillations. We observe that the transition occurs within a range of particle numbers, which roughly corresponds to the number of receptors and channels in the cell, and depends heavily on the attractive properties of the phase space of the respective systems dynamics. We conclude that the attractive properties of a system, expressed, e.g., by the divergence of the system, are a good measure for determining which simulation algorithm is appropriate in terms of speed and realism. Gesehen am 23.05.2017 |
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