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Theory on the dynamics of oscillatory loops in the transcription factor networks.

Murugan R - PLoS ONE (2014)

Bottom Line: 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.

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.

ABSTRACT
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.

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Various types of transcription factor based genetic oscillators.In case of positive regulation the combinatorial transcription factors bound at cis-regulatory modules enhance the initiation of transcription by strengthening the RNAPII-promoter interactions through their distal action (positive arrows) whereas in case of negative regulation, the RNAPII-promoter complex will be destabilized by the combinatorial TFs present at CRMs (negative arrows). A. Goodwin-Griffith oscillator. B1. One-to-one dual feedback oscillator. Here the end-product of TF gene A binds at the promoter of TF gene B and down-regulates it whereas the end-product of TF gene B binds with the promoter of TF gene A and down-regulates it. B2. Two independent Goodwin-Griffith oscillators are coupled through -OR- type logic with NN-NN configuration. Here the promoter of TF gene A will have binding sites for the end-products of both TF gene A and B and so on for TF gene B. B3. GG oscillators are coupled through -AND- type logic with N-N configuration. B4. GG oscillators are coupled through -OR- type logic with NN-PP configuration. B5. GG oscillators are coupled through -OR- type logic with NP-NP configuration. B6. Possible robust synthetic gene oscillator. Here K is the booster TF gene that is coupled to N-N type dual feedback oscillator via –OR- gate. C1. Repressilator that is built with three TF genes by cyclic coupling. C2. Three independent Goodwin-Griffith modules are coupled through -OR-type logic. Here dashed lines show the fully interconnected network. C3. Three independent Goodwin-Griffith modules with -AND-type logic. Here dashed lines show the fully interconnected network.
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pone-0104328-g002: Various types of transcription factor based genetic oscillators.In case of positive regulation the combinatorial transcription factors bound at cis-regulatory modules enhance the initiation of transcription by strengthening the RNAPII-promoter interactions through their distal action (positive arrows) whereas in case of negative regulation, the RNAPII-promoter complex will be destabilized by the combinatorial TFs present at CRMs (negative arrows). A. Goodwin-Griffith oscillator. B1. One-to-one dual feedback oscillator. Here the end-product of TF gene A binds at the promoter of TF gene B and down-regulates it whereas the end-product of TF gene B binds with the promoter of TF gene A and down-regulates it. B2. Two independent Goodwin-Griffith oscillators are coupled through -OR- type logic with NN-NN configuration. Here the promoter of TF gene A will have binding sites for the end-products of both TF gene A and B and so on for TF gene B. B3. GG oscillators are coupled through -AND- type logic with N-N configuration. B4. GG oscillators are coupled through -OR- type logic with NN-PP configuration. B5. GG oscillators are coupled through -OR- type logic with NP-NP configuration. B6. Possible robust synthetic gene oscillator. Here K is the booster TF gene that is coupled to N-N type dual feedback oscillator via –OR- gate. C1. Repressilator that is built with three TF genes by cyclic coupling. C2. Three independent Goodwin-Griffith modules are coupled through -OR-type logic. Here dashed lines show the fully interconnected network. C3. Three independent Goodwin-Griffith modules with -AND-type logic. Here dashed lines show the fully interconnected network.

Mentions: The Goodwin-Griffith oscillator consists of a negatively self-regulated gene (we denote it as TF gene A) which codes for a transcription factor protein (Figure 2A). We denote the cellular concentrations (mol/lit, M) of its mRNA as ma, protein as pa, the transformed end-product as za and the complex of promoter with the end-product as xa. Here the total cellular concentration of promoter is dza and the overall promoter state occupancy by the end-product will be Xa = xa/dza where Xa(0, 1). Though there is only one copy of the promoter by definition, we use a continuous type probability variable Xa to describe promoter state occupancy mainly to account for its partially occupied status [8], [9]. The transcription and translation rates are denoted as kma (Ms−1) and kpa (s−1) respectively. The first order decay rate constants corresponding to mRNA and TF protein are γma (s−1) and γpa (s−1) respectively. The first order on- and off-rates associated with the transformation of protein into the matured end-product are denoted as λaf (s−1) and λar (s−1) and the corresponding dimensionless dissociation constant is . The overall forward and reverse rate constants associated with the binding and unbinding of na numbers of end-product molecules with the respective cis-regulatory modules (CRMs) of the promoter of TF gene A are kaf () and kar (s−1) and the corresponding dissociation constant is defined as (). To simplify the analysis further we introduce the following scaling transformations to project the time and concentration variables into the dimensionless space.


Theory on the dynamics of oscillatory loops in the transcription factor networks.

Murugan R - PLoS ONE (2014)

Various types of transcription factor based genetic oscillators.In case of positive regulation the combinatorial transcription factors bound at cis-regulatory modules enhance the initiation of transcription by strengthening the RNAPII-promoter interactions through their distal action (positive arrows) whereas in case of negative regulation, the RNAPII-promoter complex will be destabilized by the combinatorial TFs present at CRMs (negative arrows). A. Goodwin-Griffith oscillator. B1. One-to-one dual feedback oscillator. Here the end-product of TF gene A binds at the promoter of TF gene B and down-regulates it whereas the end-product of TF gene B binds with the promoter of TF gene A and down-regulates it. B2. Two independent Goodwin-Griffith oscillators are coupled through -OR- type logic with NN-NN configuration. Here the promoter of TF gene A will have binding sites for the end-products of both TF gene A and B and so on for TF gene B. B3. GG oscillators are coupled through -AND- type logic with N-N configuration. B4. GG oscillators are coupled through -OR- type logic with NN-PP configuration. B5. GG oscillators are coupled through -OR- type logic with NP-NP configuration. B6. Possible robust synthetic gene oscillator. Here K is the booster TF gene that is coupled to N-N type dual feedback oscillator via –OR- gate. C1. Repressilator that is built with three TF genes by cyclic coupling. C2. Three independent Goodwin-Griffith modules are coupled through -OR-type logic. Here dashed lines show the fully interconnected network. C3. Three independent Goodwin-Griffith modules with -AND-type logic. Here dashed lines show the fully interconnected network.
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pone-0104328-g002: Various types of transcription factor based genetic oscillators.In case of positive regulation the combinatorial transcription factors bound at cis-regulatory modules enhance the initiation of transcription by strengthening the RNAPII-promoter interactions through their distal action (positive arrows) whereas in case of negative regulation, the RNAPII-promoter complex will be destabilized by the combinatorial TFs present at CRMs (negative arrows). A. Goodwin-Griffith oscillator. B1. One-to-one dual feedback oscillator. Here the end-product of TF gene A binds at the promoter of TF gene B and down-regulates it whereas the end-product of TF gene B binds with the promoter of TF gene A and down-regulates it. B2. Two independent Goodwin-Griffith oscillators are coupled through -OR- type logic with NN-NN configuration. Here the promoter of TF gene A will have binding sites for the end-products of both TF gene A and B and so on for TF gene B. B3. GG oscillators are coupled through -AND- type logic with N-N configuration. B4. GG oscillators are coupled through -OR- type logic with NN-PP configuration. B5. GG oscillators are coupled through -OR- type logic with NP-NP configuration. B6. Possible robust synthetic gene oscillator. Here K is the booster TF gene that is coupled to N-N type dual feedback oscillator via –OR- gate. C1. Repressilator that is built with three TF genes by cyclic coupling. C2. Three independent Goodwin-Griffith modules are coupled through -OR-type logic. Here dashed lines show the fully interconnected network. C3. Three independent Goodwin-Griffith modules with -AND-type logic. Here dashed lines show the fully interconnected network.
Mentions: The Goodwin-Griffith oscillator consists of a negatively self-regulated gene (we denote it as TF gene A) which codes for a transcription factor protein (Figure 2A). We denote the cellular concentrations (mol/lit, M) of its mRNA as ma, protein as pa, the transformed end-product as za and the complex of promoter with the end-product as xa. Here the total cellular concentration of promoter is dza and the overall promoter state occupancy by the end-product will be Xa = xa/dza where Xa(0, 1). Though there is only one copy of the promoter by definition, we use a continuous type probability variable Xa to describe promoter state occupancy mainly to account for its partially occupied status [8], [9]. The transcription and translation rates are denoted as kma (Ms−1) and kpa (s−1) respectively. The first order decay rate constants corresponding to mRNA and TF protein are γma (s−1) and γpa (s−1) respectively. The first order on- and off-rates associated with the transformation of protein into the matured end-product are denoted as λaf (s−1) and λar (s−1) and the corresponding dimensionless dissociation constant is . The overall forward and reverse rate constants associated with the binding and unbinding of na numbers of end-product molecules with the respective cis-regulatory modules (CRMs) of the promoter of TF gene A are kaf () and kar (s−1) and the corresponding dissociation constant is defined as (). To simplify the analysis further we introduce the following scaling transformations to project the time and concentration variables into the dimensionless space.

Bottom Line: 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.

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.

ABSTRACT
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.

Show MeSH