Synthetic feedback control using an RNAi-based gene-regulatory device

Background Homeostasis within mammalian cells is achieved through complex molecular networks that can respond to changes within the cell or the environment and regulate the expression of the appropriate genes in response. The development of biological components that can respond to changes in the cellular environment and interface with endogenous molecules would enable more sophisticated genetic circuits and greatly advance our cellular engineering capabilities. Results Here we describe a platform that combines a ligand-responsive ribozyme switch and synthetic miRNA regulators to create an OFF genetic control device based on RNA interference (RNAi). We developed a mathematical model to highlight important design parameters in programming the quantitative performance of RNAi-based OFF control devices. By modifying the ribozyme switch integrated into the system, we demonstrated RNAi-based OFF control devices that respond to small molecule and protein ligands, including the oncogenic protein E2F1. We utilized the OFF control device platform to build a negative feedback control system that acts as a proportional controller and maintains target intracellular protein levels in response to increases in transcription rate. Conclusions Our work describes a novel genetic device that increases the level of silencing from a miRNA in the presence of a ligand of interest, effectively creating an RNAi-based OFF control device. The OFF switch platform has the flexibility to be used to respond to both small molecule and protein ligands. Finally, the RNAi-based OFF switch can be used to implement a negative feedback control system, which maintains target protein levels around a set point level. The described RNAi-based OFF control device presents a powerful tool that will enable researchers to engineer homeostasis in mammalian cells. Electronic supplementary material The online version of this article (doi:10.1186/s13036-015-0002-3) contains supplementary material, which is available to authorized users.


Supplementary Text 1. Description of mathematical model
Variable definitions: G I = nascent OFF control device transcript (without miRNA) G M = full-length OFF control device transcript G I-Bound = nascent OFF control device transcript (without miRNA) bound to input ligand G M-Bound = full-length OFF control device transcript bound to input ligand miR = RISC-associated mature miRNA P = ligand that binds the ribozyme switch TG = target gene mRNA TP = target gene protein k trs-OFF = transcription rate of the OFF control device transcript k deg-OFF = degradation rate of the full-length OFF control device transcript k cleave = cleavage rate of the unbound ribozyme switch k cleave-bound = cleavage rate of the ligand-bound ribozyme switch k a = association rate constant of ligand and ribozyme switch k d = dissociation rate constant of ligand and ribozyme switch k mature = rate of transition from G I to G M k miR = rate constant describing formation of mature miRNA from primary miRNA k deg-miR = degradation rate constant of mature miRNA K m = Concentration of G at which miR degradation of the transcript is half of the maximum k deg = degradation rate constant of target gene mRNA k cat = catalytic constant for miR degradation of target gene transcript We developed a simple mathematical model describing the rate of microRNA formation resulting from our OFF control device. To accomplish this, we track the transcription of the OFF control device and divide it into two distinct steps. The first step is the transcription of the upstream ribozyme. The transcript in which the upstream ribozyme is transcribed and the downstream microRNA is not yet transcribed we call a nascent transcript, (G I ). A full-length transcript, (G M ), encodes the entire OFF control device, including the downstream microRNA(s), and is formed from a nascent transcript with a rate constant, k mature .
Both full-length and nascent transcripts include a ribozyme switch that is able to bind a ligand of interest, (P), with an association rate constant, k a, and a dissociation rate constant, k d. We define the transcripts bound to the ligand as new species, G I-Bound and G M-Bound . The ribozyme switch cleaves at a rate k cleave when unbound and at the rate k cleave-B when bound to the ligand. The model assumes that after ribozyme cleavage the transcript is rapidly degraded and no further transcription or microRNA formation can occur.
Mature miRNAs are formed from the pri-miRNA in the full-length transcripts at a rate k miR . We assume that once a pre-miRNA is formed from the pri-miRNA through microprocessor cleavage, the transcript that harbored the pri-miRNA is rapidly degraded.
These processes are described by the coupled ordinary differential equations provided below.
The level of target gene expression that results from different levels of miRNA within the cell is calculated from a previously described model 1 . Briefly, we describe miRNA-mediated transcript degradation using a Michaelis-Menten like term in which the RISC-associated mature miRNA complex (miR) acts as an enzyme and the target gene mRNA (TG) acts as the substrate.
From this, the equation for target protein formation is: Both k cat and K m are fitted parameters and are unique to each miRNA-target gene pair. The parameters for both GFP-and DsRed-targeting miRNAs were determined previously 1 using least-squares non-linear regression curve fit for the implicit equation using Graphpad prism software and bounding the K m with a maximum value of 10,000 nM, in accordance with values reported in the literature 2 .
The series of differential equations used in the model (equations 1-7) was solved using an ordinary differential equation solver in MATLAB (Mathworks, Ipswich, MA).
Parameters that were not obtained experimentally were estimated using a non-linear least squares optimization method using the MATLAB Optimization toolbox. A summary of the model parameters and how they were derived is provided in Supplementary Table 1.
Using these parameters, we modified the model slightly to describe the case of the OFF control device used to exert negative feedback control. Rather than having two variables to represent both the ligand of interest, P, and the target protein, TP, in this case the target gene protein is the input ligand of interest, and thus these variables are represented by a single variable, TP. The feedback system can be represented using the block diagram above, where the maximum protein level is the input, target protein level is the output, and the miRNA level is the control action. The series of differential equations was solved in the same way as described for the OFF control device case.
Supplemental Figure 1. Overview of ribozyme switch design. Ribozyme switches were designed by combining 3 distinct components: the sTRSV hammerhead ribozyme (grey), an aptamer (blue), and a transmitter (red) that joins the aptamer to loop II of the hammerhead ribozyme. With no ligand present, the ribozyme switch primarily adopts a conformation in which the ribozyme component is catalytically active and will cleave. The ligand will bind to a conformation in which the aptamer is formed, which shifts the conformational distribution to this ribozyme-inactive conformation such that cleavage is reduced. The sequences used in each ribozyme switch are listed in Supplementary Table  3 using the same color scheme to indicate the individual components.

Supplemental Figure 2. Non-cleaving ribozyme controls for different spacer lengths.
GFP expression for OFF control devices with a non-cleaving ribozyme placed at various distances upstream of a GFP-targeting miRNA.