Team:MIT/Modeling

Introduction

Expected pathway

Figure 1: Simplified representation of miRNA translational repression. Out of the many repression pathways known to be used, the figure displays increased degradation of mRNA directed by miRNA.

Ordinary Differential Equations

Figure 2: Collection of ODEs used to model miRNA translational repression. M₀ represents new mRNA created by transcription. F₀, M, and F represent mRNA ribosomal complexes in various stages of initiation, with R being the finished mRNA-ribosomal complex ready for translation. M’₀, F’₀, M’, F’, and R’ represent their respective RNA constructs with miRNA bound. P is the protein output. B is mRNA sequestered in P bodies and is ignored for purpose of simplicity.

Analysis

Figure 3: ODEs with miRNA binding improving degradation rate ten times above unbound. All other repression mechanisms were turned off. Note that time axis is in increments of the inverse of the degradation rate. The quantification for mRNA and protein output have no units and are relative amounts.

Observable Differences

Figure 4: Simplified representation of the miRNA repression system. k_t is the rate of transcription at which mRNA is being constructed, k_d represents the rate at which unbound mRNA is lost, including degradation and post-translational cleavage, k_b is the rate of binding of mRNA by miRNA, and k’_d represents the rate at which bound mRNA is lost.

We can simplify the system by removing protein and using the ratio of mRNA levels with and without miRNA to determine how much protein expression decreases. The ordinary differential equations for the system can be used to solve for equilibrium conditions.

Without miRNA

At equilibrium


With miRNA


At equilibrium

Protein drop-off can be estimated by the ratio of mRNA available for translation

Given that miRNA binding doesn’t directly block translation

If miRNA binding does directly block translation

In an in vitro experiment where we would transfect mammalian cells to observe the effect of miRNA repression, kt and kb will be functions of the transfection efficiency, and can be modeled as such. Thus, using the equilibrium ratios procured and randomly generating numbers for transfection efficiency and scatter, we can simulate expected behavior from flow-cytometry readouts.

Figure 5: Results from a simulated flow cytometry readout. Variable T was attached to the constants related to transfected parts and randomly distributed on a log scale with random variation. miRNA that increases degradation without preventing ribosomal attachment shows a step-down but does not cause a noticeable slope change. miRNA that interrupts ribosomal attachment would change slope.

The lack of a clear difference between no miRNA and miRNA that don’t inhibit ribosomal recruitment readouts can be explained by looking at its net mRNA ratio (1). The ratio has a net order of zero for transfection dependent terms, meaning the drop-off in protein expression is only a constant multiple. This will be shown as a vertical shift away down but will not cause a change in slope, making detection of miRNA activity in in vitro systems difficult.

On the other hand, miRNA blocking ribosomal attachment has a distinct pattern from unrepressed systems. This is because the drop-off rate increases with transfection efficiency, making the output visibly different on a loglog graph.

Conclusion

Given that output units are not precisely defined, it was originally planned to quantify L7Ae output from experimental results before modeling the high sensors. However, due to L7Ae’s overwhelming ability as a repressor, it was difficult to quantify and explain L7Ae dynamics.

The difficulty for miRNA repression systems that don’t block ribosomal binding may explain the ambiguousness of our low sensor data. Within in vivo systems where expression of circuit components are generally lower and more controlled, the threshold of the low sensor system may be sufficient to respond appropriately for diagnostic functions. However, that makes quantification and in vitro testing difficult at the moment without a way to clearly distinguish control groups from experimental groups. In the future, we plan to test the circuits in cell lines with native miRNA expression to gauge in vivo response.