Figure 1.
Diagram of recursive RNAi circuit.
RNAi takes place in two steps. Following input to the system of a double stranded RNA precursor (dsRNA), Dicer chops the dsRNA into small interfering RNA molecules (siRNA) which are then used by the RISC complex to direct cleavage of target messages. At the same time, genes encoding RNAi machinery as well as the reporter construct (in this case GFP) are transcribed into mRNA and then translated into protein (indicated by ovals in the diagram). RNAi repressed gene expression by providing an extra decay pathway for the targeted message, so that rather than being translated into protein the message was destroyed. In recursive RNAi, two dsRNA molecules are provided as input, one directed against the reporter gene and the other directed against a gene encoding part of the RNAi machinery itself. The measurable output of the system is the level of reporter protein (GFP).
Table 1.
Parameters of RNAi model.
Figure 2.
Phase plane diagram of recursive RNAi of Dicer.
Phase plane diagram of Dicer RNAi showing the nullclines for which the rate of change of either the siRNA (in blue) or Dicer protein (in red) equals zero. The two curves only intersect for one set of values, indicating a unique steady-state solution. The transient solution starting from an initial condition of normal dicer level and zero Dicer-directed siRNA is plotted in green, obtained by numerical integration. This simulation was conducted with an RNAi efficacy parameter gamma equal to 1.
Figure 3.
Restoration of reporter expression during recursive RNAi.
Predicted reporter expression in the presence (red curve) and absence (green curve) of Dicer-specific RNAi. As the two curves approach each other, the restoration becomes more difficult to detect.
Figure 4.
Figures of merit describing restoration efficiency plotted as a function of RNAi efficacy parameter gamma. Pink curve plots the relative restoration ratio R which measures the ratio of restoration relative to the initial level of knockdown. Larger R indicates that gene expression is restored to a level closer to its normal expression level in the absence of any RNAi, as required for switch-off/switch-on experiments [15]. Maximum value of R is 0.25 which occurs for γ = 2, corresponding to a system in which RNAi knocks down gene expression only three-fold. Blue curve plots the normalized absolute restoration Δ which is the reporter level during recursive RNAi minus the reporter level without recursive RNAi, expressed in units normalized by the pre-RNAi expression level of the reporter. Larger values indicate more easily detected restoration. Both curves show a peak, indicating optimal performance, at comparatively low values of gamma.
Figure 5.
Transient behavior of recursive RNAi.
Restoration of reporter levels during recursive RNAi of Dicer determined by numerical simulation. (A) Time-course of restoration of reporter gene level plotted as a function of time following recursive RNAi of Dicer, for different values of the RNAi efficacy parameter gamma. Curves show that even at transient time-points before reaching steady state, restoration is always higher for lower values of gamma. (B) Time required to reach 50% (blue) or 90% (red) of final steady-state restoration value, plotted versus RNAi efficacy parameter. (C) Restoration in reporter seen during recursive RNAi of Dicer at a specific time-point t1/2 defined as the time required for the same reporter gene to be knocked down to half its final level of knockdown in the absence of recursive RNAi. This curve provides a measure of the degree of restoration achieved at a standardized transient time-point, confirming that increasing values of gamma give decreasing restoration, even in the transient case.
Figure 6.
Improving performance of switch-off/switch-on experiments by unequal efficiency of targeting Dicer and Reporter.
In each graph the red curve shows reporter level when Dicer is targeted (switch-on state), and the blue curve shows reporter level when Dicer is not targeted (switch-off state). Results are plotted as a function of the efficacy with which the reporter is targeted by the siRNA (defined by parameter epsilon) relative to the efficacy with which Dicer is targeted. The first two graphs show results predicted for different values of overall RNAi efficacy parameter gamma. (A) gamma = 20. (B) gamma = 200. (C) shows results for gamma = 20 over an extended range of targeting efficacy epsilon, with values greater than 1 indicating that the reporter is targeted with higher efficiency than Dicer.
Figure 7.
Effect of RdRP-mediated amplification.
Each graph shows restoration versus time for numerical simulations of recursive RNAi experiments targeting Dicer. (A) gamma = 1. (B) gamma = 200. Within each graph, results for different values of the amplification efficacy parameter theta are given. Theta is proportional to the number of secondary siRNA molecules produced by RdRP for each targeted mRNA molecule. Modification of model equations to incorporate RdRP activity is described in Materials and Methods.
Figure 8.
Targeting non-essential components.
Graph shows level of reporter expression during recursive RNAi targeting components as a function of the degree to which the component is required for RNAi, indicated by requirement parameter rho. The equation describing this situation is derived in Materials and Methods. Graph plotted for γ = 200.
Figure 9.
Modeling transient transfection experiments.
(A) reporter gene expression levels with and without recursive RNAi of Dicer in which the source of dsRNA decays with first order kinetics to represent dilution of plasmids by cell division, with decay constant δ. All simulations run with γ = 10. (Blue, green, light blue) targeting of reporter only without targeting of RNAi components. (Red, orange, yellow) targeting of Dicer along with the reporter. Decay of dsRNA source leads to transient reduction in reporter that restores at a rate dependent on decay rate of source. Rapid decay of dsRNA source leads to less difference between recursive and non-recursive RNAi (compare δ = 1, where almost no difference is seen when Dicer is also targeted, with a tenfold slower decay rate δ = 0.1, where Dicer targeting clearly increases expression level during transient knockdown). (B) Dependence of restoration on RNAi efficacy parameter γ for different rates of dsRNA source (plasmid) decay.