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] |
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| Format: |
Artikel |
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| Sprache: |
Englisch |
| Erschienen: |
2017 |
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| Anmerkung: |
© Springer International Publishing AG, part of Springer Nature 2017 |
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| Übergeordnetes Werk: |
Enthalten in: Journal of mathematical chemistry - Springer International Publishing, 1987, 56(2017), 4 vom: 11. Dez., Seite 1153-1183 |
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| Übergeordnetes Werk: |
volume:56 ; year:2017 ; number:4 ; day:11 ; month:12 ; pages:1153-1183 |
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| DOI / URN: |
10.1007/s10910-017-0848-3 |
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OLC2060424526 |
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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 | |
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| 700 | 1 | |a Rabenstein, Rudolf |0 (orcid)0000-0002-4348-1225 |4 aut | |
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10.1007/s10910-017-0848-3 doi (DE-627)OLC2060424526 (DE-He213)s10910-017-0848-3-p DE-627 ger DE-627 rakwb eng 510 540 VZ Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing AG, part of Springer Nature 2017 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 Perturbation approach Nonlinear ordinary differential equations Schäfer, Maximilian (orcid)0000-0002-3332-4701 aut Rabenstein, Rudolf (orcid)0000-0002-4348-1225 aut Enthalten in Journal of mathematical chemistry Springer International Publishing, 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 AR 56 2017 4 11 12 1153-1183 |
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10.1007/s10910-017-0848-3 doi (DE-627)OLC2060424526 (DE-He213)s10910-017-0848-3-p DE-627 ger DE-627 rakwb eng 510 540 VZ Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing AG, part of Springer Nature 2017 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 Perturbation approach Nonlinear ordinary differential equations Schäfer, Maximilian (orcid)0000-0002-3332-4701 aut Rabenstein, Rudolf (orcid)0000-0002-4348-1225 aut Enthalten in Journal of mathematical chemistry Springer International Publishing, 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 AR 56 2017 4 11 12 1153-1183 |
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10.1007/s10910-017-0848-3 doi (DE-627)OLC2060424526 (DE-He213)s10910-017-0848-3-p DE-627 ger DE-627 rakwb eng 510 540 VZ Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing AG, part of Springer Nature 2017 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 Perturbation approach Nonlinear ordinary differential equations Schäfer, Maximilian (orcid)0000-0002-3332-4701 aut Rabenstein, Rudolf (orcid)0000-0002-4348-1225 aut Enthalten in Journal of mathematical chemistry Springer International Publishing, 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 AR 56 2017 4 11 12 1153-1183 |
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10.1007/s10910-017-0848-3 doi (DE-627)OLC2060424526 (DE-He213)s10910-017-0848-3-p DE-627 ger DE-627 rakwb eng 510 540 VZ Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing AG, part of Springer Nature 2017 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 Perturbation approach Nonlinear ordinary differential equations Schäfer, Maximilian (orcid)0000-0002-3332-4701 aut Rabenstein, Rudolf (orcid)0000-0002-4348-1225 aut Enthalten in Journal of mathematical chemistry Springer International Publishing, 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 AR 56 2017 4 11 12 1153-1183 |
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10.1007/s10910-017-0848-3 doi (DE-627)OLC2060424526 (DE-He213)s10910-017-0848-3-p DE-627 ger DE-627 rakwb eng 510 540 VZ Kram, Sebastian verfasserin aut Approximation of enzyme kinetics for high enzyme concentration by a first order perturbation approach 2017 Text txt rdacontent ohne Hilfsmittel zu benutzen n rdamedia Band nc rdacarrier © Springer International Publishing AG, part of Springer Nature 2017 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 Perturbation approach Nonlinear ordinary differential equations Schäfer, Maximilian (orcid)0000-0002-3332-4701 aut Rabenstein, Rudolf (orcid)0000-0002-4348-1225 aut Enthalten in Journal of mathematical chemistry Springer International Publishing, 1987 56(2017), 4 vom: 11. Dez., Seite 1153-1183 (DE-627)129246441 (DE-600)59132-4 (DE-576)27906036X 0259-9791 nnns volume:56 year:2017 number:4 day:11 month:12 pages:1153-1183 https://doi.org/10.1007/s10910-017-0848-3 lizenzpflichtig Volltext GBV_USEFLAG_A SYSFLAG_A GBV_OLC SSG-OLC-CHE SSG-OLC-MAT SSG-OLC-PHA SSG-OLC-DE-84 SSG-OPC-MAT GBV_ILN_70 GBV_ILN_4012 AR 56 2017 4 11 12 1153-1183 |
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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. © Springer International Publishing AG, part of Springer Nature 2017 |
| 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. © Springer International Publishing AG, part of Springer Nature 2017 |
| 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. © Springer International Publishing AG, part of Springer Nature 2017 |
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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://doi.org/10.1007/s10910-017-0848-3 |
| remote_bool |
false |
| author2 |
Schäfer, Maximilian Rabenstein, Rudolf |
| author2Str |
Schäfer, Maximilian Rabenstein, Rudolf |
| ppnlink |
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| doi_str |
10.1007/s10910-017-0848-3 |
| up_date |
2024-07-04T01:18:41.615Z |
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