Retroactivity Attenuation in Bio-Molecular Systems Based on Timescale Separation

As with several engineering systems, bio-molecular systems display impedance-like effects at interconnections, called retroactivity. In this paper, we propose a mechanism that exploits the natural timescale separation present in bio-molecular systems to attenuate retroactivity. Retroactivity enters the dynamics of a bio-molecular system as a state dependent disturbance multiplied by gains that can be very large. By virtue of the system structure, retroactivity can be arbitrarily attenuated by internal system gains even when these are much smaller than the gains multiplying retroactivity terms. This result is obtained by employing a suitable change of coordinates and a nested application of the singular perturbation theorem on the finite time interval. As an application example, we show that two modules extracted from natural signal transduction pathways have a remarkable capability of attenuating retroactivity, which is certainly desirable in any (engineered or natural) signal transmission system.United States. Air Force Office of Scientific Research (AFOSR Award FA9550-09-1-0211

Retroactivity to the Output of Transcription Devices: Quantification and Insulation.

Traditional engineering often relies on hierarchical design techniques to build com- plex systems from simpler subsystems. This technique requires modularity, a prop- erty that states that the input/output characteristics of a system are not affected by interconnections. In this work we investigate retroactivity, an impedance-like effect in biomolecular systems that makes the behavior of a system change upon intercon- nection. We show, through analysis and experiments, that retroactivity in synthetic biology circuits is responsible for substantial changes in a system dynamic response. In order to construct circuits modularly, we propose the design of insulation de- vices, which, similar to insulating amplifiers in electronics, attenuate retroactivity effects and recover modular behavior. Our technique is based on a novel disturbance attenuation approach based on singular perturbation theory.PHDElectrical Engineering: SystemsUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/95939/1/jayanthi_1.pd

Tuning Genetic Clocks Employing DNA Binding Sites

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.United States. Air Force Office of Scientific Research (Grant FA9550-09-1-0211)National Science Foundation (U.S.). (Communication and Information Foundations) (Grant 1058127

Tuning an activator-repressor clock employing retroactivity

Activator-repressor systems have been shown to be capable of oscillations and are therefore an important clock motif in the field of Synthetic and Systems Biology. In this paper, we propose a method to regulate oscillatory behavior in such systems by the addition of DNA binding sites for the proteins involved in the clock network. We show that the retroactivity effect caused by this addition can effectively change the relative timescales among the protein dynamics and impact the behavior of the clock. We also employ root locus analysis to obtain a graphical interpretation of the results

Retroactivity Controls the Temporal Dynamics of Gene Transcription

Just like in many engineering systems, impedance-like effects, called retroactivity, arise at the interconnection of biomolecular circuits, leading to unexpected changes in a circuit's behavior. In this paper, we provide a combined experimental and theoretical study to characterize the effects of retroactivity on the temporal dynamics of a gene transcription module in vivo. The response of the module to an inducer was measured both in isolation and when the module was connected to downstream clients. The connected module, when compared to the isolated module, responded selectively to the introduction of the inducer versus its withdrawal. Specifically, a "sign-sensitive delay" appeared, in which the connected module displayed a time delay in the response to induction and anticipation in the response to de-induction. The extent of these effects can be made larger by increasing the amounts of downstream clients and/or their binding affinity to the output protein of the module. Our experimental results and mathematical formulas make it possible to predict the extent of the change in the dynamic behavior of a module after interconnection. They can be employed to both recover the predictive power of a modular approach to understand systems or as an additional design tool to shape the temporal behavior of gene transcription. Keywords: control systems; dynamic response; modularity; retroactivity; synthetic biologyUnited States. Air Force Office of Scientific Research (Grant FA9550-10-1-02

Effect of the trace of the Jacobian on the stability of the equilibrium.

<p>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.</p

Tuning the period without affecting the amplitude.

<p>(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, .</p