Ljubljana/model

Model

We built a theoretical model to show how the positive feedback loop made of T7 RNA polymerase (T7 RNAP) gene under the control of its T7 promoter affects the behaviour of the system, particularly amplification. Initially, active T7 RNAP molecules are generated by any of the three sources: split-ubiquitin reconstitution and endogenour ubiquitin protease, TEV protease reconstitution or cleavage by the HIV protease. In all cases, T7 polymerase translocates into the nucleus, where it transcribes an effector gene, as well as T7 RNAP gene (self-amplification). The idea behind introducing such a positive feedback loop was that the initial signal might be too low and could fade if not amplied to a sufficient level.

Model built in Cell Designer

Figure 1: Comprehensive view of the engineered pathway. Split ubiquitin pathway is shown at the lower half and HIV protease at the upper half. HIV protease synthesis pathway after the infection is simplified in this model.

Signal Amplification

Plots of the amount of the active T7 RNAP (red line) and effector (blue line) versus time. The infection begins at time 0. Parameters are selected arbitrarily and the simulation should be used to evaluate the behavior of the system under different gene ratios:

Figure 2a) Simulation with 2 copies of the effector gene and no T7 RNAP genes present in the nucleus.	Figure 2b) Simulation with 50 copies of the effector gene and no T7 RNAP genes present in the nucleus.
Figure 2c) simulation with 2 copies of the effector gene and 2 copies of T7 RNAP genes present in the nucleus (the red line is hidden under the green line because of the same transcription and translation kinetics parameters).	Figure 2d) simulation with 50 copies of the effector and 2 copies of T7 RNAP genes present in nucleus.
Figure 2e) simulation with 2 copies of the effector and 50 copies of T7 RNAP genes present in nucleus.

As expected, in case (a), where no additional amplification was designed, the amount of the effector increases linearily with time. With more copies of the effector gene present, the slope increases (b). In case (c) with amplification through T7 RNAP, we were expecting the effector amount to grow exponentially. However, contrary to simple reasoning, this is not the case unless the number of effector gene copies is much larger than the number of T7 RNAP gene copies. This can be explained by a limiting rate of transcription; the maximal transcription rate is determined by how many polymerase molecules can bind to the promoter in a certain span of time. Therefore, if the number of polymerase molecules is already high, the system becomes saturated very soon and any further increase of polymerase concentration does not increase expression rate, so no exponential growth of effector concentration occurs. However, if we increase the number of effector gene copies (d), the system does not readily become saturated and we observe an exponential growth of effector concentration. After a certain time, the number of polymerase molecules increases, and effector genes become saturated. This again results in a linear growth of effector concentration.

The model clearly showed that in order to successfully amplify the initiatial signal, it is optimal to use a much larger number of effector genes than of T7 RNAP genes.

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