Birhythmicity and Hard Excitation from Coupled Synthetic Feedback Loops
Synthetic biology opens up the possibility of creating circuits that would not survive in the natural world and studying their behaviors in living cells, expanding our notion of biology. Based on this, we analyze on a synthetic biological system the effect of coupling between two instability-generat...
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| Format: | Article |
| Language: | English |
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Wiley
2014-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/694854 |
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| author | Aimin Chen Caixia Liu Junwei Wang |
| author_facet | Aimin Chen Caixia Liu Junwei Wang |
| author_sort | Aimin Chen |
| collection | DOAJ |
| description | Synthetic biology opens up the possibility of creating circuits that would not survive in the natural world and studying their behaviors in living cells, expanding our notion of biology. Based on this, we analyze on a synthetic biological system the effect of coupling between two instability-generating mechanisms. The systems considered are two topologically equivalent synthetic networks. In addition to simple periodic oscillations and stable steady state, the system can exhibit a variety of new modes of dynamic behavior: coexistence between two stable periodic regimes (birhythmicity) and coexistence of a stable periodic regime with a stable steady state (hard excitation). Birhythmicity and hard excitation have been proved to exist in biochemical networks. Through bifurcation analysis on these two synthetic cellular networks, we analyze the function of network structure for the collapse and revival of birhythmicity and hard excitation with the variation of parameters. The results have illustrated that the bifurcation space can be divided into four subspaces for which the dynamical behaviors of the system are generically distinct. Our analysis corroborates the results obtained by numerical simulation of the dynamics. |
| format | Article |
| id | doaj-art-4dc8a0bb38464889a61ee809c4e78505 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-4dc8a0bb38464889a61ee809c4e785052025-02-03T00:59:10ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/694854694854Birhythmicity and Hard Excitation from Coupled Synthetic Feedback LoopsAimin Chen0Caixia Liu1Junwei Wang2Institute of Applied Mathematics, Henan University, Kaifeng 475004, ChinaSchool of Mathematics and Information Science, Henan University, Kaifeng 475004, ChinaSchool of Informatics, Guangdong University of Foreign Studies, Guangzhou 510006, ChinaSynthetic biology opens up the possibility of creating circuits that would not survive in the natural world and studying their behaviors in living cells, expanding our notion of biology. Based on this, we analyze on a synthetic biological system the effect of coupling between two instability-generating mechanisms. The systems considered are two topologically equivalent synthetic networks. In addition to simple periodic oscillations and stable steady state, the system can exhibit a variety of new modes of dynamic behavior: coexistence between two stable periodic regimes (birhythmicity) and coexistence of a stable periodic regime with a stable steady state (hard excitation). Birhythmicity and hard excitation have been proved to exist in biochemical networks. Through bifurcation analysis on these two synthetic cellular networks, we analyze the function of network structure for the collapse and revival of birhythmicity and hard excitation with the variation of parameters. The results have illustrated that the bifurcation space can be divided into four subspaces for which the dynamical behaviors of the system are generically distinct. Our analysis corroborates the results obtained by numerical simulation of the dynamics.http://dx.doi.org/10.1155/2014/694854 |
| spellingShingle | Aimin Chen Caixia Liu Junwei Wang Birhythmicity and Hard Excitation from Coupled Synthetic Feedback Loops Journal of Applied Mathematics |
| title | Birhythmicity and Hard Excitation from Coupled Synthetic Feedback Loops |
| title_full | Birhythmicity and Hard Excitation from Coupled Synthetic Feedback Loops |
| title_fullStr | Birhythmicity and Hard Excitation from Coupled Synthetic Feedback Loops |
| title_full_unstemmed | Birhythmicity and Hard Excitation from Coupled Synthetic Feedback Loops |
| title_short | Birhythmicity and Hard Excitation from Coupled Synthetic Feedback Loops |
| title_sort | birhythmicity and hard excitation from coupled synthetic feedback loops |
| url | http://dx.doi.org/10.1155/2014/694854 |
| work_keys_str_mv | AT aiminchen birhythmicityandhardexcitationfromcoupledsyntheticfeedbackloops AT caixialiu birhythmicityandhardexcitationfromcoupledsyntheticfeedbackloops AT junweiwang birhythmicityandhardexcitationfromcoupledsyntheticfeedbackloops |