Mathematically modeling PCR: An asymptotic approximation with potential for optimization
A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action and simplifying assumptions regarding the structure of the reactions. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being...
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| Format: | Article |
| Language: | English |
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AIMS Press
2010-03-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.363 |
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| author | Martha Garlick James Powell David Eyre Thomas Robbins |
| author_facet | Martha Garlick James Powell David Eyre Thomas Robbins |
| author_sort | Martha Garlick |
| collection | DOAJ |
| description | A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action and simplifying assumptions regarding the structure of the reactions. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one base pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage, and a map is developed from the solutions to simulate PCR. The map recreates observed PCR well, and gives us the ability to optimize the PCR process. Our results suggest that dynamically optimizing the extension and annealing stages of individual samples may significantly reduce the total time for a PCR run. Moreover, we present a nearly optimal design that functions almost as well and does not depend on the specifics of a single reaction, and so would work for multi sample and multiplex applications. |
| format | Article |
| id | doaj-art-534359fd80ab454e953794b6b35f6504 |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2010-03-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-534359fd80ab454e953794b6b35f65042025-01-24T02:00:28ZengAIMS PressMathematical Biosciences and Engineering1551-00182010-03-017236338410.3934/mbe.2010.7.363Mathematically modeling PCR: An asymptotic approximation with potential for optimizationMartha Garlick0James Powell1David Eyre2Thomas Robbins3Department of Mathematics and Statistics, Utah State University, Logan UT 84322Department of Mathematics and Statistics, Utah State University, Logan UT 84322Department of Mathematics and Statistics, Utah State University, Logan UT 84322Department of Mathematics and Statistics, Utah State University, Logan UT 84322A mathematical model for PCR (Polymerase Chain Reaction) is developed using the law of mass action and simplifying assumptions regarding the structure of the reactions. Differential equations are written from the chemical equations, preserving the detail of the complementary DNA single strand being extended one base pair at a time. The equations for the annealing stage are solved analytically. The method of multiple scales is used to approximate solutions for the extension stage, and a map is developed from the solutions to simulate PCR. The map recreates observed PCR well, and gives us the ability to optimize the PCR process. Our results suggest that dynamically optimizing the extension and annealing stages of individual samples may significantly reduce the total time for a PCR run. Moreover, we present a nearly optimal design that functions almost as well and does not depend on the specifics of a single reaction, and so would work for multi sample and multiplex applications.https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.363mathematical modelpolymerase chain reactionpcroptimization.method of multiple scalesdynamical systems |
| spellingShingle | Martha Garlick James Powell David Eyre Thomas Robbins Mathematically modeling PCR: An asymptotic approximation with potential for optimization Mathematical Biosciences and Engineering mathematical model polymerase chain reaction pcr optimization. method of multiple scales dynamical systems |
| title | Mathematically modeling PCR: An asymptotic approximation with potential for optimization |
| title_full | Mathematically modeling PCR: An asymptotic approximation with potential for optimization |
| title_fullStr | Mathematically modeling PCR: An asymptotic approximation with potential for optimization |
| title_full_unstemmed | Mathematically modeling PCR: An asymptotic approximation with potential for optimization |
| title_short | Mathematically modeling PCR: An asymptotic approximation with potential for optimization |
| title_sort | mathematically modeling pcr an asymptotic approximation with potential for optimization |
| topic | mathematical model polymerase chain reaction pcr optimization. method of multiple scales dynamical systems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2010.7.363 |
| work_keys_str_mv | AT marthagarlick mathematicallymodelingpcranasymptoticapproximationwithpotentialforoptimization AT jamespowell mathematicallymodelingpcranasymptoticapproximationwithpotentialforoptimization AT davideyre mathematicallymodelingpcranasymptoticapproximationwithpotentialforoptimization AT thomasrobbins mathematicallymodelingpcranasymptoticapproximationwithpotentialforoptimization |