Team:William and Mary/Dynamic Control
Abstract
One of our major goals in developing the pdt speed-control system was to allow future teams to obtain control over the dynamical properties of their circuits through modifications that they make at the level of a single genetic part. As a proof-of-concept demonstration of this capability, we construct an Incoherent Feedforward Loop (IFFL) circuit whose dynamical properties are controlled by Lon activity. We demonstrate that we can predictably tune the sharpness of the circuit’s pulsatile response simply by swapping the choice of pdt.
Design
One of the simplest examples of a dynamical circuit is the incoherent feed forward loop (IFFL), which consists of three proteins X, Y, and Z which regulate each other such that X activates Y and Z, and Y represses Z. This circuit architecture can generate a pulsatile response upon activation of X (Figure 1).
Figure 1: Schematic of an Incoherent Feedforward Loop (IFFL) circuit. X, Y, and Z represent arbitrary transcription factors. At t=0, the production of X is activated. In region (1), the molecules of X activate the production of both Z and Y. However, the concentration of Y is insufficient to significantly repress the production of Z, so its concentration increases. In region (2), the concentration of Y has grown sufficiently large that it now exerts a significant repressive effect on the production of Z. This causes the concentration of Z to decrease. In region (3), the repressive effect from Y and the activating effect from X have balanced and the circuit has reached its steady state.
By tuning the properties of the different interactions within the circuit, one can control the overall dynamics of its response. For example, there are several ways to control the sharpness of the pulse in the circuit’s temporal response. One approach is to increase the strength of Y’s repression of Z (Figure 2, red arrow). This will cause the circuit’s relaxation to it steady state to occur more quickly, narrowing the width of the pulse. One could also increase the speed of X’s activation of Z (Figure 2, green arrow), which increases the slope of the circuit’s initial rise to its peak.
Figure 2: Tuning dynamical properties of the pulsatile response of the IFFL circuit. (Red Arrow) Increasing the strength of the repression of Z by Y causes the width of the pulse to decrease, as the speed of the transition from the pulse peak to the steady state is set by Y’s repression of Z. (Green Arrow) Increasing the speed of the activation of Z by X causes the circuit to rise faster to its peak. The result of these effects is a sharpening of the pulse.