Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach

Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enz...
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Autor*in:	Kram, Sebastian [verfasserIn] Schäfer, Maximilian [verfasserIn] Rabenstein, Rudolf [verfasserIn]

Format:	E-Artikel
Sprache:	Englisch

Erschienen:	2017

Schlagwörter:	Enzyme kinetics Perturbation approach Nonlinear ordinary differential equations

Übergeordnetes Werk:	Enthalten in: Journal of mathematical chemistry - Dordrecht [u.a.] : Springer Science + Business Media B.V., 1987, 56(2017), 4 vom: 11. Dez., Seite 1153-1183
Übergeordnetes Werk:	volume:56 ; year:2017 ; number:4 ; day:11 ; month:12 ; pages:1153-1183

Links:	Volltext

DOI / URN:	10.1007/s10910-017-0848-3

Katalog-ID:	SPR014557207

Internformat


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245	1	0	\|a Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach
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520			\|a Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy.
650		4	\|a Enzyme kinetics \|7 (dpeaa)DE-He213
650		4	\|a Perturbation approach \|7 (dpeaa)DE-He213
650		4	\|a Nonlinear ordinary differential equations \|7 (dpeaa)DE-He213
700	1		\|a Schäfer, Maximilian \|e verfasserin \|4 aut
700	1		\|a Rabenstein, Rudolf \|e verfasserin \|4 aut
773	0	8	\|i Enthalten in \|t Journal of mathematical chemistry \|d Dordrecht [u.a.] : Springer Science + Business Media B.V., 1987 \|g 56(2017), 4 vom: 11. Dez., Seite 1153-1183 \|w (DE-627)30246879X \|w (DE-600)1491406-2 \|x 1572-8897 \|7 nnns
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912			\|a GBV_ILN_138
912			\|a GBV_ILN_150
912			\|a GBV_ILN_151
912			\|a GBV_ILN_152
912			\|a GBV_ILN_161
912			\|a GBV_ILN_170
912			\|a GBV_ILN_171
912			\|a GBV_ILN_187
912			\|a GBV_ILN_206
912			\|a GBV_ILN_213
912			\|a GBV_ILN_224
912			\|a GBV_ILN_230
912			\|a GBV_ILN_250
912			\|a GBV_ILN_281
912			\|a GBV_ILN_285
912			\|a GBV_ILN_293
912			\|a GBV_ILN_370
912			\|a GBV_ILN_602
912			\|a GBV_ILN_636
912			\|a GBV_ILN_702
912			\|a GBV_ILN_2001
912			\|a GBV_ILN_2003
912			\|a GBV_ILN_2004
912			\|a GBV_ILN_2005
912			\|a GBV_ILN_2006
912			\|a GBV_ILN_2007
912			\|a GBV_ILN_2009
912			\|a GBV_ILN_2010
912			\|a GBV_ILN_2011
912			\|a GBV_ILN_2014
912			\|a GBV_ILN_2015
912			\|a GBV_ILN_2020
912			\|a GBV_ILN_2021
912			\|a GBV_ILN_2025
912			\|a GBV_ILN_2026
912			\|a GBV_ILN_2027
912			\|a GBV_ILN_2031
912			\|a GBV_ILN_2034
912			\|a GBV_ILN_2037
912			\|a GBV_ILN_2038
912			\|a GBV_ILN_2039
912			\|a GBV_ILN_2044
912			\|a GBV_ILN_2048
912			\|a GBV_ILN_2049
912			\|a GBV_ILN_2050
912			\|a GBV_ILN_2055
912			\|a GBV_ILN_2057
912			\|a GBV_ILN_2059
912			\|a GBV_ILN_2061
912			\|a GBV_ILN_2064
912			\|a GBV_ILN_2065
912			\|a GBV_ILN_2068
912			\|a GBV_ILN_2070
912			\|a GBV_ILN_2086
912			\|a GBV_ILN_2088
912			\|a GBV_ILN_2093
912			\|a GBV_ILN_2106
912			\|a GBV_ILN_2107
912			\|a GBV_ILN_2108
912			\|a GBV_ILN_2110
912			\|a GBV_ILN_2111
912			\|a GBV_ILN_2112
912			\|a GBV_ILN_2113
912			\|a GBV_ILN_2116
912			\|a GBV_ILN_2118
912			\|a GBV_ILN_2119
912			\|a GBV_ILN_2122
912			\|a GBV_ILN_2129
912			\|a GBV_ILN_2143
912			\|a GBV_ILN_2144
912			\|a GBV_ILN_2147
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912			\|a GBV_ILN_2152
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912			\|a GBV_ILN_2446
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912			\|a GBV_ILN_2472
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allfields	10.1007/s10910-017-0848-3 doi (DE-627)SPR014557207 (SPR)s10910-017-0848-3-e DE-627 ger DE-627 rakwb eng 540 510 ASE 35.05 bkl Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy. Enzyme kinetics (dpeaa)DE-He213 Perturbation approach (dpeaa)DE-He213 Nonlinear ordinary differential equations (dpeaa)DE-He213 Schäfer, Maximilian verfasserin aut Rabenstein, Rudolf verfasserin aut Enthalten in Journal of mathematical chemistry Dordrecht [u.a.] : Springer Science + Business Media B.V., 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)30246879X (DE-600)1491406-2 1572-8897 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://dx.doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 35.05 ASE AR 56 2017 4 11 12 1153-1183
spelling	10.1007/s10910-017-0848-3 doi (DE-627)SPR014557207 (SPR)s10910-017-0848-3-e DE-627 ger DE-627 rakwb eng 540 510 ASE 35.05 bkl Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy. Enzyme kinetics (dpeaa)DE-He213 Perturbation approach (dpeaa)DE-He213 Nonlinear ordinary differential equations (dpeaa)DE-He213 Schäfer, Maximilian verfasserin aut Rabenstein, Rudolf verfasserin aut Enthalten in Journal of mathematical chemistry Dordrecht [u.a.] : Springer Science + Business Media B.V., 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)30246879X (DE-600)1491406-2 1572-8897 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://dx.doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 35.05 ASE AR 56 2017 4 11 12 1153-1183
allfields_unstemmed	10.1007/s10910-017-0848-3 doi (DE-627)SPR014557207 (SPR)s10910-017-0848-3-e DE-627 ger DE-627 rakwb eng 540 510 ASE 35.05 bkl Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy. Enzyme kinetics (dpeaa)DE-He213 Perturbation approach (dpeaa)DE-He213 Nonlinear ordinary differential equations (dpeaa)DE-He213 Schäfer, Maximilian verfasserin aut Rabenstein, Rudolf verfasserin aut Enthalten in Journal of mathematical chemistry Dordrecht [u.a.] : Springer Science + Business Media B.V., 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)30246879X (DE-600)1491406-2 1572-8897 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://dx.doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 35.05 ASE AR 56 2017 4 11 12 1153-1183
allfieldsGer	10.1007/s10910-017-0848-3 doi (DE-627)SPR014557207 (SPR)s10910-017-0848-3-e DE-627 ger DE-627 rakwb eng 540 510 ASE 35.05 bkl Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy. Enzyme kinetics (dpeaa)DE-He213 Perturbation approach (dpeaa)DE-He213 Nonlinear ordinary differential equations (dpeaa)DE-He213 Schäfer, Maximilian verfasserin aut Rabenstein, Rudolf verfasserin aut Enthalten in Journal of mathematical chemistry Dordrecht [u.a.] : Springer Science + Business Media B.V., 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)30246879X (DE-600)1491406-2 1572-8897 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://dx.doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 35.05 ASE AR 56 2017 4 11 12 1153-1183
allfieldsSound	10.1007/s10910-017-0848-3 doi (DE-627)SPR014557207 (SPR)s10910-017-0848-3-e DE-627 ger DE-627 rakwb eng 540 510 ASE 35.05 bkl Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent Computermedien c rdamedia Online-Ressource cr rdacarrier Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy. Enzyme kinetics (dpeaa)DE-He213 Perturbation approach (dpeaa)DE-He213 Nonlinear ordinary differential equations (dpeaa)DE-He213 Schäfer, Maximilian verfasserin aut Rabenstein, Rudolf verfasserin aut Enthalten in Journal of mathematical chemistry Dordrecht [u.a.] : Springer Science + Business Media B.V., 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)30246879X (DE-600)1491406-2 1572-8897 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://dx.doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_SPRINGER SSG-OLC-PHA SSG-OPC-MAT SSG-OPC-ASE GBV_ILN_11 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_120 GBV_ILN_138 GBV_ILN_150 GBV_ILN_151 GBV_ILN_152 GBV_ILN_161 GBV_ILN_170 GBV_ILN_171 GBV_ILN_187 GBV_ILN_206 GBV_ILN_213 GBV_ILN_224 GBV_ILN_230 GBV_ILN_250 GBV_ILN_281 GBV_ILN_285 GBV_ILN_293 GBV_ILN_370 GBV_ILN_602 GBV_ILN_636 GBV_ILN_702 GBV_ILN_2001 GBV_ILN_2003 GBV_ILN_2004 GBV_ILN_2005 GBV_ILN_2006 GBV_ILN_2007 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_2031 GBV_ILN_2034 GBV_ILN_2037 GBV_ILN_2038 GBV_ILN_2039 GBV_ILN_2044 GBV_ILN_2048 GBV_ILN_2049 GBV_ILN_2050 GBV_ILN_2055 GBV_ILN_2057 GBV_ILN_2059 GBV_ILN_2061 GBV_ILN_2064 GBV_ILN_2065 GBV_ILN_2068 GBV_ILN_2070 GBV_ILN_2086 GBV_ILN_2088 GBV_ILN_2093 GBV_ILN_2106 GBV_ILN_2107 GBV_ILN_2108 GBV_ILN_2110 GBV_ILN_2111 GBV_ILN_2112 GBV_ILN_2113 GBV_ILN_2116 GBV_ILN_2118 GBV_ILN_2119 GBV_ILN_2122 GBV_ILN_2129 GBV_ILN_2143 GBV_ILN_2144 GBV_ILN_2147 GBV_ILN_2148 GBV_ILN_2152 GBV_ILN_2153 GBV_ILN_2188 GBV_ILN_2190 GBV_ILN_2232 GBV_ILN_2336 GBV_ILN_2446 GBV_ILN_2470 GBV_ILN_2472 GBV_ILN_2507 GBV_ILN_2522 GBV_ILN_2548 GBV_ILN_4012 GBV_ILN_4035 GBV_ILN_4037 GBV_ILN_4046 GBV_ILN_4112 GBV_ILN_4125 GBV_ILN_4126 GBV_ILN_4242 GBV_ILN_4246 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_4336 GBV_ILN_4338 GBV_ILN_4393 GBV_ILN_4700 35.05 ASE AR 56 2017 4 11 12 1153-1183
language	English
source	Enthalten in Journal of mathematical chemistry 56(2017), 4 vom: 11. Dez., Seite 1153-1183 volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183
sourceStr	Enthalten in Journal of mathematical chemistry 56(2017), 4 vom: 11. Dez., Seite 1153-1183 volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183
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institution	findex.gbv.de
topic_facet	Enzyme kinetics Perturbation approach Nonlinear ordinary differential equations
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container_title	Journal of mathematical chemistry
authorswithroles_txt_mv	Kram, Sebastian @@aut@@ Schäfer, Maximilian @@aut@@ Rabenstein, Rudolf @@aut@@
publishDateDaySort_date	2017-12-11T00:00:00Z
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A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. 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author	Kram, Sebastian
spellingShingle	Kram, Sebastian ddc 540 bkl 35.05 misc Enzyme kinetics misc Perturbation approach misc Nonlinear ordinary differential equations Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach
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topic_title	540 510 ASE 35.05 bkl Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach Enzyme kinetics (dpeaa)DE-He213 Perturbation approach (dpeaa)DE-He213 Nonlinear ordinary differential equations (dpeaa)DE-He213
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title_full	Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach
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title_sort	approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach
title_auth	Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach
abstract	Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy.
abstractGer	Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy.
abstract_unstemmed	Abstract This contribution presents an approximate solution of the enzyme kinetics problem for the case of excess of an enzyme over the substrate. A first order perturbation approach is adopted where the perturbation parameter is the relation of the substrate concentration to the total amount of enzyme. As a generalization over existing solutions for the same problem, the presented approximation allows for nonzero initial conditions for the substrate and the enzyme concentrations as well as for nonzero initial complex concentration. Nevertheless, the approximate solution is obtained in analytical form involving only elementary functions like exponentials and logarithms. The presentation discusses all steps of the procedure, starting from amplitude and time scaling for a non-dimensional representation and for the identification of the perturbation parameter. Suitable time constants lead to the short term and long term behaviour, also known as the inner and outer solution. Special attention is paid to the matching process by the definition of a suitable intermediate layer. The results are presented in concise form as a summary of the required calculations. An extended example compares the zero order and first order perturbation approximations for the short term and long term solution as well as the uniform solution. A comparison to the numerical solution of the initial set of nonlinear ordinary differential equations demonstrates the achievable accuracy.
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container_issue	4
title_short	Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach
url	https://dx.doi.org/10.1007/s10910-017-0848-3
remote_bool	true
author2	Schäfer, Maximilian Rabenstein, Rudolf
author2Str	Schäfer, Maximilian Rabenstein, Rudolf
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doi_str	10.1007/s10910-017-0848-3
up_date	2024-07-04T02:14:48.545Z
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Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach

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