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. 2012 Jul 31;7(7):e41019. doi: 10.1371/journal.pone.0041019

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© 2012 Jayanthi, Del Vecchio

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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The plots illustrate the trajectories of system (14) with two different amounts of load. The parameters in the simulation were , , , , , , and . The amount of DNA binding sites in the system with no load is whereas in the system with repressor load is . (b) Hopf Bifurcation with as a parameter. A continuation of the equilibrium as a function of the load parameter shows that, for this set of parameters, the amount of load required to activate the clock is in the same order of magnitude as that of the the affinity coefficient , with bifurcation occurring at . This plot was obtained via continuation of system (14) with the same parameters as before. Solid lines indicate a stable trajectory (limit cycle to the right of the Hopf bifurcation and the equilibrium to its right). The dotted line indicates an unstable equilibrium point. (c) Period increases as a function of the repressor load .

Inline graphic — The plots illustrate the trajectories of system (14) with two different amounts of load. The parameters in the simulation were , , , , , , and . The amount of DNA binding sites in the system with no load is whereas in the system with repressor load is . (b) Hopf Bifurcation with as a parameter. A continuation of the equilibrium as a function of the load parameter shows that, for this set of parameters, the amount of load required to activate the clock is in the same order of magnitude as that of the the affinity coefficient , with bifurcation occurring at . This plot was obtained via continuation of system (14) with the same parameters as before. Solid lines indicate a stable trajectory (limit cycle to the right of the Hopf bifurcation and the equilibrium to its right). The dotted line indicates an unstable equilibrium point. (c) Period increases as a function of the repressor load .