Overview

We simulated the termination and antitermination properties of our signal-terminator constructs with the Kinefold web server^[1] 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 antiterminations occurs before the RNA polymerase falls off.
The Kinefold web server provides a web interface for stochastic folding simulations of nucleic acids and offers the choice of renaturation or co-transcriptional folding. The folding paths are simulated at the level of helix formation and dissociation as these stochastic formation and the removal of individual helices are known to be the limiting steps of RNA folding kinetics.
For our purposes, co-transcriptional folding was the appropriate choice: Folding proceeds while the sequence is being synthesized from its 5' to 3' ends at a speed of 3 ms per newly added base (for RNA polymerase T7 phage). Thus, the transcript starts to fold before the whole sequence is fully available.
Kinefold offers the possibility to include additional bases (X) which do not pair to model hybridization dynamics between two sequences. In order to simulate how the binding of the signal molecule prevents termination we linked the signal via a linker sequence consisting of 'X' bases to the sequence of the terminator.
For each signal-terminator pair we did batch simulations with various random seeds in order to guarantee accuracy.
We also varied signal length form two base pairs to full signal length which provides insight in how long the signal needs to be in order to bind to the terminator and how long this process takes at least.

Results

Diffusion

The question whether antitermination 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.

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As the folding time (at least 1,7 sec for full signal length) is significantly larger than the estimated diffusion time (0,1518 sec), diffusion does not play an important role and thus can be neglected in the modeling our signal-terminator constructs.

Switch

We performed Kinefold simulations for the His-terminator, the Trp-terminator and for the T7-terminator, each with the corresponding signal. For each terminator-signal construct there are folding path videos available below and we also optimized the signal sequences. We find that all our toogle switch works well with all three terminators.

I. His-terminator

Terminator sequence:
5' UCGGCUUCAACGUGCUCCACGAAAGCCCCCGGAAGAUGCAUCUUCCGGGGGCUUUUUUUUU 3'
Signal sequence:
5' CCGGGGGCUUUCGUGGAGCACGUUGAAGCCGA 3'

Both terminator and signal sequence comprise two parts:

• His-terminator and a part which partially binds to the His-terminator respectively (marked green),
• random signaling part and antisense to the random signaling part respectively (marked red).

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.

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Results

We showed that in theoretical simulations the His-terminator works perfectly as the terminator itself is relatively stable (minimal free-energy structure is at -31,3 kcal/mol) whereas for appropriate signal length the terminator is not folding at all, that is antitermination occurs before the RNA polymerase can fall off. We also demonstrated that a quite short signal length of 8 nt is sufficient for antitermination to happen (shorter signal length means shorter folding time).

II. Trp-terminator

Terminator sequence:
5' ACGCGACAUAUCAGCUUAGAAUACCCAGCCCGCCUAAUGAGCGGGCUUUUUUUU 3'
Signal sequence:
5' GGCGGGCUGGGUAUUCUAAGCUGAUAUGUCGCGU 3'

Both terminator and signal sequence comprise three parts:

• Trp-terminator and a part which partially binds to the Trp-terminator respectively (marked green),
• a natural sequence part upstream of the Trp-terminator binding to the terminator in antitermination state and a part which binds to the upstream sequence of the terminator respectively (marked yellow),
• random signaling part and antisense to the random signaling part respectively (marked red).

The Trp-terminator turned out to be less stable than the His-terminator. The folded terminator is not the minimal free-energy structure for the given the RNA sequence, it's only the third minimal one at -12.9 kcal/mol compared with the His-terminator which has a minimal free-energy structure at -31.3 kcal/mol. The folded terminator including the natural sequence part upstream of the Trp-terminator binding to the terminator in antitermination state and the random signaling part is shown in the figure "Trp-terminator" below:

Our full signal sequence of length 34 nt completly binds to the terminator and antitermination is successful:

Trp-terminator plus signal

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Results

We showed that in theory the Trp-terminator should function properly. Although the terminator itself is less stable (minimal free-energy structure is at -12,9 kcal/mol) than the His-terminator for appropriate signal length the terminator is not folding, thus antitermination occurs. We also demonstrated that a quite short signal length of 10 nt is sufficient for successful antitermination.

T7-terminator

Terminator sequence:
5' CUCUGCCGCACGUAU AGCAUAACCCCUUGGGGCCUCUAAACGGGUCUUGAGGGGUUUUUUG 3'
Signal sequence:
5' AAGGGGUUAUGCUAUACGUGCGGCAGAG 3'

Both terminator and signal sequence comprise two parts:

• T7-terminator and a part which partially binds to the T7-terminator respectively (marked green),
• random signaling part and antisense to the random signaling part respectively (marked red).

We also modeled the T7-terminator which is also less stable than the His-terminator. Its minimal free-energy structure is at -23.1 kcal/mol. The folded terminator including the random signaling part is shown in the figure "T7-terminator" below:

Our full signal sequence of length 28 nt completly binds to the terminator and anti-termination is successful:

T7-terminator plus signal

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Results

We demonstrated that in theoretical simulations the T7-terminator work well. It's less stable (minimal free-energy structure is at -23,1 kcal/mol) than the His-terminator (and rather a lot of bases are unpaired), but its more stable than the Trp-terminator. For appropriate signl length the terminator is not folding at all, that is antitermination occurs. We also demonstrated that a quite short signal length of 8 nt is sufficient for antitermination to happen.

Logic gate

Here we tried to model a AND gate. We used the His-terminator and two corresponding signals with different random signaling parts. Having different signaling parts is necessary, as if one uses the same one in both signals, the AND gate will always have the output 'true'. This is because the signal sequence would first destroy the first terminator and when the second one is synthesized it might bind to the second one. We linked all the sequences with a 34 X linker. As above both terminator and signal sequences comprise two parts:

• His-terminator and a part which partially binds to the His-terminator respectively (marked green),
• random signaling part and antisense to the random signaling part respectively (marked red).
  

His-terminator sequence 1:
UCGGCUUCAACGUGCUCCACGAAAGCCCCCGGAAGAUGCAUCUUCCGGGGGCUUUUUUUUU 3'
Signal sequence 1:
5' CCGGGGGCUUUCGUGGAGCACGUUGAAGCCGA 3'
His-terminator sequence 2:
UCGUUCAACGUACACCUCGG GAAAGCCCCCGGAAGAUGCAUCUUCCGGGGGCUUUUUUUUU 3'
Signal sequence 2:
5' CCGGGGGCUUUCCCGAGGUGUACGUUGAACGA 3'

As the picture below displays both of the signals successfully bound to the terminators, thus as both input signals are present (that it both input are '1') the AND gate also returns the value '1' as both terminator are destroyed.

We also tried to model an AND gate with the optimized signals which also worked as the picture below shows.

RNA folding path videos

We created folding path videos for the AND gate. One can see how both signal sequences bind to the terminator sequences as those are synthesized and none of the terminators can fold.

For the optimized signal which was sufficient to destroy a single terminator above, the video shows that there are some periods of times when the signal is hindered from binding to the terminator sequence by the other structures, e.g. the linker sequence.

Outlook

So far there is no RNA folding program that is specialized on modeling the interaction of two sequences not to speak of a whole network consisting of RNA based switches and signaling sequences. Combining the concepts of Kinefold^[4] and Vienna^[5] and using sets of secondary structures that are adjusted to having two sequences instead of only one sequence one could get rid of the bulky linkers. The linkers we used did not play a significant role for our simulation as we were just handling one terminator and one signal sequence, but for larger networks they are likely to be sterically hindering. This obstacle has to be overcome to allow reliable in silcio modeling of RNA devices.

With appropriate software RNA devices like our switches could in future be used to interconnect BioBricks, as demonstrated on our Software page, and to simulate those interconnections at elementary step resolution.

References

[1] A. Xayaphoummine, T. Bucher and H. Isambert, Kinefold web server for RNA/DNA folding path and structure prediction including pseudoknots and knots, 2005, Nucleic Acids Research, Vol. 33, Web Server issue W605–W610. [2] Berg, v. Hippel, 1985. [3] Rippe, Making contacts on a nucleic acid polymer, 2001, TRENDS in Biochemical Sciences. [4] A. Xayaphoummine, T. Bucher, F. Thalmann, and H. Isambert, Prediction and statistics of pseudoknots in RNA structures using exactly clustered stochastic simulations, December 23, 2003, 15310–15315 PNAS vol. 100 no. 26. [5] Christoph Flamm, Walter Fontana, Ivo L. Hofacker, and Peter Schuster, RNA folding at elementary step resolution, RNA (2000), 6:325–338 Cambridge University Press. [6] David H. Mathews, Jeffrey Sabina, Michael Zuker and Douglas H. Turner, Expanded Sequence Dependence of Thermodynamic Parameters Improves Prediction of RNA Secondary Structure, 1999, J. Mol. Biol. (1999) 288, 911-940.