Inverse bifurcation analysis: application to simple gene systems
<p>Abstract</p> <p>Background</p> <p>Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional <it>forward problem </it>of determining the mapping from...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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BMC
2006-07-01
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| Series: | Algorithms for Molecular Biology |
| Online Access: | http://www.almob.org/content/1/1/11 |
| _version_ | 1831601121212235776 |
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| author | Schuster Peter Engl Heinz W Lu James |
| author_facet | Schuster Peter Engl Heinz W Lu James |
| author_sort | Schuster Peter |
| collection | DOAJ |
| description | <p>Abstract</p> <p>Background</p> <p>Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional <it>forward problem </it>of determining the mapping from parameter space to the space of model behavior, the <it>inverse problem </it>of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties.</p> <p>Results</p> <p>We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved.</p> |
| first_indexed | 2024-12-18T14:56:53Z |
| format | Article |
| id | doaj.art-2cb36077d3b641889bea3a88db86aaab |
| institution | Directory Open Access Journal |
| issn | 1748-7188 |
| language | English |
| last_indexed | 2024-12-18T14:56:53Z |
| publishDate | 2006-07-01 |
| publisher | BMC |
| record_format | Article |
| series | Algorithms for Molecular Biology |
| spelling | doaj.art-2cb36077d3b641889bea3a88db86aaab2022-12-21T21:04:02ZengBMCAlgorithms for Molecular Biology1748-71882006-07-01111110.1186/1748-7188-1-11Inverse bifurcation analysis: application to simple gene systemsSchuster PeterEngl Heinz WLu James<p>Abstract</p> <p>Background</p> <p>Bifurcation analysis has proven to be a powerful method for understanding the qualitative behavior of gene regulatory networks. In addition to the more traditional <it>forward problem </it>of determining the mapping from parameter space to the space of model behavior, the <it>inverse problem </it>of determining model parameters to result in certain desired properties of the bifurcation diagram provides an attractive methodology for addressing important biological problems. These include understanding how the robustness of qualitative behavior arises from system design as well as providing a way to engineer biological networks with qualitative properties.</p> <p>Results</p> <p>We demonstrate that certain inverse bifurcation problems of biological interest may be cast as optimization problems involving minimal distances of reference parameter sets to bifurcation manifolds. This formulation allows for an iterative solution procedure based on performing a sequence of eigen-system computations and one-parameter continuations of solutions, the latter being a standard capability in existing numerical bifurcation software. As applications of the proposed method, we show that the problem of maximizing regions of a given qualitative behavior as well as the reverse engineering of bistable gene switches can be modelled and efficiently solved.</p>http://www.almob.org/content/1/1/11 |
| spellingShingle | Schuster Peter Engl Heinz W Lu James Inverse bifurcation analysis: application to simple gene systems Algorithms for Molecular Biology |
| title | Inverse bifurcation analysis: application to simple gene systems |
| title_full | Inverse bifurcation analysis: application to simple gene systems |
| title_fullStr | Inverse bifurcation analysis: application to simple gene systems |
| title_full_unstemmed | Inverse bifurcation analysis: application to simple gene systems |
| title_short | Inverse bifurcation analysis: application to simple gene systems |
| title_sort | inverse bifurcation analysis application to simple gene systems |
| url | http://www.almob.org/content/1/1/11 |
| work_keys_str_mv | AT schusterpeter inversebifurcationanalysisapplicationtosimplegenesystems AT englheinzw inversebifurcationanalysisapplicationtosimplegenesystems AT lujames inversebifurcationanalysisapplicationtosimplegenesystems |