Team:TU Munich/Modeling
From 2010.igem.org
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OverviewWe simulated the termination and anti-termination properties of our signal-terminator constructs with the Kinefold web server and used some standard estimations for diffusive terms. Our main goal was to prove that our constructs work and that termination is stopped efficiently, that is, that the signal molecule binds and anti-terminations occurs before the RNA polymerase falls off. DiffusionThe question whether anti-termination occurs is not only guided by the folding process of the signal-terminator pair, but also by how long the signal takes to diffuse to the terminator sequence.
To account for the diffusion time, we estimated the hit rate τ (following 6.), which is the time until the signal meets the terminator sequence for the first time:
where D is the diffusion constant, a the radius of gyration of the signal molecule and r the radius of the cell.
where n is the length of the signal which is 0,3 nm/monomer, l is the persistency length which is following (5.) 2nm for single-stranded RNA. Thus, for a signal of length 32 nt, a = 6,4 nm. The diffusion constant D was obtained by
where kB is the Boltzmann constant and T is the absolute temperature. Thus, for a cell containing 100 signal molecules, the signal needs 0,1518 s until it first hits the terminator sequence. CloseAs the folding time is significantly larger than the diffusion and thus much less relevant for modeling our signal-terminator constructs, we didn't employ more elaborate techniques to model diffusion. SwitchHis-terminatorTerminator sequence: Both terminator and signal sequence comprise two parts:
We modeled the signal-terminator interaction for 2, 4-32 nt signal length and proved that the signal sequence binds to the terminator sequence and impedes the terminator folding, thus the polymerase doesn't fall off and the output signal is produced. The minimal free-energy structure of the folded terminator including the random signaling part is shown in the figure "His-terminator" below: Our full signal sequence of length 32 nt completly binds to the terminator and anti-termination is successful: On the other hand the picture for a signal length of only 2 nt shows that such a small signal length is not sufficient for anti-termination. But already a signal of length 16 nt binds to the terminator so that it cannot fold completely anymore.
However, for the folding time linker length dependence is significant as one can see in the figure below. But, as, for us, the fact whether the terminator is folding or not is crucial and the videos below show that for appropriate signal length the terminator is not folding. Concerning this fact, for all linker lengths we tested there was only a dependence on the signal length but the results were independent from the linker length. Hence, the linker length dependence can be neglected.
RNA folding path videosFor this video the signal is only 2 nt long. One can see that the terminator is folding and that the signal cannot bind to the terminator sequence due to its short length. Media:TU_Munich_iGEM2010_sstraub_2.mov The video for 16 nt signal length shows that the terminator is already hindered from folding completely. Media:TU_Munich_iGEM2010_sstraub_16.mov This video is done for full signal length of 32 nt. One can see that the terminator does not fold at all as the signal immediately binds to the terminator sequence as it is synthesized. Media:TU_Munich_iGEM2010_sstraub_32.mov Optimization of the signal sequenceWe also tried to optimize our signal sequence to find the minimal sequence length which still enables anti-termination. For this optimization kept the random signaling part constant and varied the part which partially binds to the His-terminator and vice versa to see which length is sufficient for anti-termination for each case. Then we combined the results to find a optimal signal.
When varying the part which partially binds to the His-terminator we found that having only the 2 nt of this part together with the random signaling part suffices for anti-termination as the picture and the corresponding video below show. Trp-terminatorResultsNetworkModelingResultsOutlook |