doi: 10.1371/journal.pone.0041019.
Epub 2012 Jul 31.
Tuning genetic clocks employing DNA binding sites
Affiliations
- PMID: 22859962
- PMCID: PMC3409220
- DOI: 10.1371/journal.pone.0041019
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Tuning genetic clocks employing DNA binding sites
PLoS One.
2012.
Abstract
Periodic oscillations play a key role in cell physiology from the cell cycle to circadian clocks. The interplay of positive and negative feedback loops among genes and proteins is ubiquitous in these networks. Often, delays in a negative feedback loop and/or degradation rates are a crucial mechanism to obtain sustained oscillations. How does nature control delays and kinetic rates in feedback networks? Known mechanisms include proper selection of the number of steps composing a feedback loop and alteration of protease activity, respectively. Here, we show that a remarkably simple means to control both delays and effective kinetic rates is the employment of DNA binding sites. We illustrate this design principle on a widely studied activator-repressor clock motif, which is ubiquitous in natural systems. By suitably employing DNA target sites for the activator and/or the repressor, one can switch the clock "on" and "off" and precisely tune its period to a desired value. Our study reveals a design principle to engineer dynamic behavior in biomolecular networks, which may be largely exploited by natural systems and employed for the rational design of synthetic circuits.
Conflict of interest statement
Figures
Diagram (a) illustrates the activator-repressor motif. Diagram (b) and (c) illustrate the systems after the addition of DNA binding sites with affinity to the activator and the repressor, respectively. Diagram (d) illustrates the case in which both types of DNA binding sites are present.
The above plots illustrate the trajectories of system (1) for both Functional and Non-Functional Clocks. The parameters in the simulation were 
, 
, 
and 
. In the Functional Clock, 
whereas in the Non-Functional Clock, 
. Parameters 
and 
were chosen to give about 500–2000 copies of protein per cell for activated promoters. Parameters 
and 
were chosen to give about 1–10 copies per cell for non-activated promoters.
, , and . In the Functional Clock, whereas in the Non-Functional Clock, . Parameters and were chosen to give about 500–2000 copies of protein per cell for activated promoters. Parameters and were chosen to give about 1–10 copies per cell for non-activated promoters.
The plots illustrate the trajectories of system (5) 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 activator load is 
. (b) Bifurcation diagram with load as parameter. A continuation of the equilibrium as a function of the load parameter 
shows that, for this set of parameters, the amount of load to the activator required to stop the clock is on the order of the affinity coefficient 
, with the bifurcation occurring at 
. The analysis was made on the full system (5) with the same parameters as before. The solid lines indicate a stable trajectory (the limit cycle to the left side of the Hopf bifurcation point and the equilibrium point to the right side of the Hopf bifurcation point). The dotted line indicates an unstable equilibrium point.
, , , , , , and . The amount of DNA binding sites in the system with no load is whereas in the system with activator load is . (b) Bifurcation diagram with load as parameter. A continuation of the equilibrium as a function of the load parameter shows that, for this set of parameters, the amount of load to the activator required to stop the clock is on the order of the affinity coefficient , with the bifurcation occurring at . The analysis was made on the full system (5) with the same parameters as before. The solid lines indicate a stable trajectory (the limit cycle to the left side of the Hopf bifurcation point and the equilibrium point to the right side of the Hopf bifurcation point). The dotted line indicates an unstable equilibrium point.
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 
.
, , , , , , and . The amount of DNA binding sites in the system with no load is whereas in the system with repressor load is . (b) 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) .
The plots above are stochastic realizations of an activator-repressor clock with 
and containing 5 copies of activator and repressor genes. (a) Functional clock stops with load to the activator. We show that, with the chosen parameters, it is possible to stop the clock with an amount of load that is roughly 100 times higher than the copy number of the circuit. (b) Load to the repressor leads to robust oscillation. We show that, the it is possible to generate robust oscillation with roughly 400 times the number of circuit genes with the choice of parameters above.
and containing 5 copies of activator and repressor genes. (a) Functional clock stops with load to the activator. We show that, with the chosen parameters, it is possible to stop the clock with an amount of load that is roughly 100 times higher than the copy number of the circuit. (b) Load to the repressor leads to robust oscillation. We show that, the it is possible to generate robust oscillation with roughly 400 times the number of circuit genes with the choice of parameters above.
(a) When compared to the isolated system, the amplitude of oscillations in system (20) increases when we add exclusively DNA binding sites with affinity to the repressor (
, 
). However, if we simultaneously add DNA binding sites with affinity to the activator, the amplitude is not affected as much (
). (b) The period of system (20) can be changed with no effect on the amplitude when DNA binding sites with affinity to both the repressor and the activator are added simultaneously. The upper plot shows that a similar increase of period observed via the addition of repressor load can be obtained via the simultaneous addition of activator and repressor load. This second method has the advantage of not generating an increase in the amplitude, as shown in the lower plot. In this simulation we assumed the ratio 
. Parameters of the activator repressor system used in the simulation were 
, 
, 
, 
, 
, 
and 
, 
. In the traces showing only repressor load 
, while the traces showing simultaneous repressor and activator load, 
.
, ). However, if we simultaneously add DNA binding sites with affinity to the activator, the amplitude is not affected as much (). (b) The period of system (20) can be changed with no effect on the amplitude when DNA binding sites with affinity to both the repressor and the activator are added simultaneously. The upper plot shows that a similar increase of period observed via the addition of repressor load can be obtained via the simultaneous addition of activator and repressor load. This second method has the advantage of not generating an increase in the amplitude, as shown in the lower plot. In this simulation we assumed the ratio . Parameters of the activator repressor system used in the simulation were , , , , , and , . In the traces showing only repressor load , while the traces showing simultaneous repressor and activator load, .Similar articles
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This work was in part funded by AFOSR Grant Number FA9550-09-1-0211 and NSF-CIF Grant Number 1058127. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript.
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