Theory on the dynamics of oscillatory loops in the transcription factor networks.
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Though there is a period-buffering, the amplitudes of oscillators coupled through -OR- type logic are more sensitive to perturbations in the parameters associated with the promoter state dynamics than -AND- type.Further analysis shows that the period of -AND- type coupled dual-feedback oscillators can be tuned without conceding on the amplitudes.Using these results we derive the basic design principles governing the robust and tunable synthetic gene oscillators without compromising on their amplitudes.
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PubMed Central - PubMed
Affiliation: Department of Biotechnology, Bhupat and Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India.
ABSTRACT
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We develop a detailed theoretical framework for various types of transcription factor gene oscillators. We further demonstrate that one can build genetic-oscillators which are tunable and robust against perturbations in the critical control parameters by coupling two or more independent Goodwin-Griffith oscillators through either -OR- or -AND- type logic. Most of the coupled oscillators constructed in the literature so far seem to be of -OR- type. When there are transient perturbations in one of the -OR- type coupled-oscillators, then the overall period of the system remains constant (period-buffering) whereas in case of -AND- type coupling the overall period of the system moves towards the perturbed oscillator. Though there is a period-buffering, the amplitudes of oscillators coupled through -OR- type logic are more sensitive to perturbations in the parameters associated with the promoter state dynamics than -AND- type. Further analysis shows that the period of -AND- type coupled dual-feedback oscillators can be tuned without conceding on the amplitudes. Using these results we derive the basic design principles governing the robust and tunable synthetic gene oscillators without compromising on their amplitudes. Related in: MedlinePlus |
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Mentions: Contrasting from the configuration given in Figure 2B1, the limit-cycle orbits of the coupled oscillators depicted in Figures 2B2-3 are robust against transient imbalances in the control parameters. The minimum achievable value of the critical Hill coefficient seems to be Cnh = 4 for the oscillator with A-OR-B type logic (Figure 2B2) whereas Cnh = 2 for the coupled oscillators with A-AND-B type logic (Figure 2B3). Results suggest that the limit cycle orbit of coupled oscillators with A-AND-B and A-OR-B type logics are stable one. When there are temporal perturbations in Group I parameters associated with one of the Goodwin oscillators (TF gene A/B) then the other unperturbed oscillator responds to the changes in the behavior of the perturbed oscillator depending on the type of logical coupling between them. As shown in Figures 7A1-2, B1-2 and C1-2 in case of A-OR-B coupling an increase in the magnitude of Group I parameters associated with one of the oscillators A/B does not change the period of the entire system of oscillators (period-buffering) though there is a decrease in the amplitude of the oscillator that is perturbed in . The decrease in the amplitude might be partially owing to the period-buffering effect. In case of A-AND-B type logical coupling, increase in the magnitude of Group I parameters increases the period of oscillations and decreases the amplitude of the entire system of oscillators that includes both TF genes A/B. Figures 8A1-4 suggest that an increase in the parameter of one of the oscillators initially increases the amplitude of other oscillator to a maximum which then decreases later. Perturbations in Group I parameters associated with one of the oscillators A/B also results in a phase-shift in cases of both A-AND-B and A-OR-B type logical couplings as shown in Figures 7-8A1-2 and B1-2. Whereas perturbation in affects only the amplitude and does not affect the phases of the coupled oscillators A and B as shown in Figures 7-8C1-2. Here one should note that in case of A-OR-B type coupling the parameter will be split into where we have the indices as given in Eqs (21). Above results corresponding to A-OR-B type logical coupling with respect to changes in the parameter are valid only when the temporal perturbations are the same for a given promoter of TF gene A/B. This means that for TF gene A (here we have subscript ) the extent of perturbation should be the same for both and while the set of parameters associated with the TF gene B () remains unperturbed. Here one should note that controls the dynamics associated with the binding of end-product of TF gene ‘H’ at its own promoter whereas controls the dynamics associated with the binding of end-product of TF gene ‘K’ at the promoter of TF gene ‘H’ as we have shown in Eqs (21). When there are perturbations in only one of these two split parameters (as ) then the coupled system of oscillators seems to be dynamically unstable and also produces modulated beats as shown in Figures 7A3-4. The period of such beats increases as the imbalance in the set of split parameters increases as shown in Figures 7A5-6. These dynamical instabilities as well as beats abruptly disappear once the perturbations in are removed. Whereas the system of coupled oscillators relaxes back to the initial unperturbed limit-cycle orbit through asymptotic spirals upon removal of perturbations in case of Group I control parameters . Results from Figures 7 and 8 suggest that coupled oscillators with -AND- type logic are more robust against promoter state perturbations than the -OR- type coupling. Period of a network of oscillators can be easily fine-tuned by manipulating merely one of the oscillators when the mode of coupling is via -AND- type. |
View Article: PubMed Central - PubMed
Affiliation: Department of Biotechnology, Bhupat and Jyoti Mehta School of Biosciences, Indian Institute of Technology Madras, Chennai, Tamil Nadu, India.