The Bacterial Full Adder

Abstract The Full Adder project seeks to create bacteria that can add two one-bit numbers. Such an organism would be the biological equivalent of a digital full adder, which is a fundamental building block of complex electronic circuits. Since many teams have difficulty creating even simple circuits like XOR gates, this project would seem nearly impossible. However, we have found that the problem can be greatly simplified if we use a simple “encoding” on the outputs of the full adder. Subsequently designing a second circuit to “decode” the output is theoretically significantly easier than creating a complete full adder outright. Our insights may prove useful to any genetic engineer or synthetic biologist working on highly complex systems.

General Overview
Engineering Problems Construction of a bacterial full adder faces two immediate obstacles. First, an electrical full adder requires at least 5 logic gates. However, a single AND gate in bacteria may require as many as 11 BioBricks (as shown by the Peking team in 2009). Chaining together tens of BioBricks would be very difficult and may result in plasmids that are difficult to transform. Second, many of the current “logic gate” circuits are not easily connected to each other. For example, the ETH 2006 XOR gate can not be connected to the Davidson-Missouri Western (DMW) 2008 XOR gate since the inputs and outputs are not the same; ETH has PoPS (Polymerase Per Second) inputs and output, but DMW uses various chemicals. Simply using PoPS-only parts may be an attractive solution, but that may exacerbate the first problem as parts with PoPS inputs and outputs tend to be more complex. Furthermore, there is a significant possibility of some PoPS parts interfering with the operation of other PoPS parts as these are huge, complex circuits, many of which share some parts. Insights We had two major insights into the obstacles to create the Full Adder. First, we developed a method to create biological AND gates. Second, we found that, if we change the output of the full adder from two outputs to three outputs (our so-called encoding), we can create the circuit with four AND gates. Of course, this is no longer a faithful rendition of a full adder. However, the methods we used to create the AND gates should be helpful in the creation of a whole new generation of fusion proteins, and it should be easier to create another circuit that converts our three output adder to a standard two output adder than creating a single monolithic full adder circuit.

Peking 2009 AND Gate
Light Response One AND gate that we decided to use was created previously by the Peking 2009 iGEM team. It relies on T7ptag, T7 polymerase with two early amber mutations (stop codons) such that normal translation will result in a truncated non-functional protein, and SupD, a tRNA which allows for translation through amber stop codons (an amber suppressor). So, if just T7ptag or just SupD is expressed, there will not be any functional T7 polymerase, but if both T7ptag and SupD are expressed, then functional T7 polymerase will be created. To complete the gate, we place T7ptag on one inducible promoter (our first input), SupD on a different inducible promoter (our second input), and our output on a T7 promoter. This system relies on the fact that basal transcription from the T7 promoter is extremely low, but once functional T7 polymerase is present, transcription is very high.

Split Fluorescent Proteins

Overview We sought genetically encoded AND gates because they are easier to link together. These often consist of two components that are individually non-functional but are functional when co-expressed. Ghosh et al. created exactly that with their split green fluorescent protein (GFP). They cut GFP, which usually displays green fluorescence, into two parts, each of which did not fluoresce. Then they fused dimer-forming leucine zipper domains to each part. They dubbed the two parts nzGFP and czGFP. The dimerization of the leucine zipper domains allows nzGFP and czGFP to reconstitute a functional GFP when expressed together. Zhang et al. created similar split GFP, CFP, and YFP (green, cyan, and yellow fluorescent proteins) for use in C. elegans microscopy. (image) Split fluorescent proteins function essentially as AND gates. The inputs are activators of whatever promoter we place the split fluorescent proteins under and the output is fluorescence. The primary advantage of this system is its simplicity. It requires just two proteins and two coding sequences. The primary disadvantage of this system is that the output is limited to fluorescence, though engineering of other split proteins can relieve this constraint.   Construction As mentioned previously, a significant amount of the research on these split fluorescent proteins has been done in C. elegans. Unfortunately, many of these C. elegans constructs contain introns, making them unsuitable for expression in E. coli. We therefore decided to recreate split GFP, CFP, and YFP constructs using GFP, CFP, and YFP from the Parts Registry. In order to construct the split proteins, we created BioBricks of the leucine zipper domains with the easily fusable RFC25 prefix and suffix. These standardized parts will facilitate future split protein construction. As demonstrated by our circuit, split proteins have the potential to greatly simplify genetic circuits. To construct split GFP, we first cloned the zipper domains from nzGFP and czGFP with the RFC25 prefix and suffix. Then we mutagenized GFP (BBa_E0040) so that it contained the necessary restriction sites in the correct positions in order to create nzGFP and czGFP. Finally, we digested and ligated the parts. This method is very general and should be easy to apply in searches for other split proteins.

Bacterial Full Adder Circuit
Introduction As described before, we did not create a completely faithful representation of a full adder. When we were first planning the circuit, one major simplifying (and simple) insight we had was that the full adder is just a counting machine. The output only depends on how many inputs are activated; it does not matter which ones are on. With this observation, we could look at the adder as a four state switch, whose state depends on how many inputs are on. This was much easier to work with as demonstrated by the difference in complexity of the two tables below. Inputs State (Output our circuit gives) 0 A (No output) 1 B (RFP) 2 C (RFP and GFP) 3 D (RFP, GFP, and CFP) Our circuit relies on three inducible/repressible promoters to sense inputs: pBad, pLacL, and ptrpL. It is important to note, however, that since the type of signal is not important, these promoters can be interchanged with other promoters, allowing for a wide variety of adders specific to different kinds of signals. The 0 input for each promoter is the input that renders no transcription from the corresponding promoter. Since ptrpL is an inducible repressor, the 0 input is, counter-intuitively, tryptophan-supplemented media. The 0 input for the other two promoters occurs in media that is not supplemented with the corresponding inducer. The 1 input for each promoter is just the opposite. Legend: RFP - full length red fluorescent protein. GFP1 - N-terminal half of split green fluorescent protein (nzGFP). GFP2 - C-terminal half of split green fluorescent protein (czGFP). GFP - full length green fluorescent protein. CFP1 - N-terminal half of split cyan fluorescent protein (nzCFP). CFP2 - C-terminal half of split cyan fluorescent protein (czCFP). T7 ptag - T7 polymerase with amber mutation. supD - Amber mutation suppressor. The easiest way to understand the circuit is to go on a case-by-case basis. For simplicity, we have labeled the promoters A, B, and C. Note that our target outputs are given in Figure Y above. We will indicate whether a promoter is activated or inactivated and ignore the details of how the promoter is activated or inactivated. Zero inputs - Desired output: no fluorescence Without activation at the promoters and assuming low basal transcription, we should see no fluorescence. One input - Desired output: Red fluorescence If only A is activated, then functional RFP, nzGFP, and T7ptag are produced. Since czGFP and supD are not produced, nzGFP and T7ptag are non-functional. Therefore, we should only observe RFP output. If only B is activated, then functional RFP, nzGFP, and supD are produced. Again, we should only observe RFP output. If only C is activated, then functional RFP, czGFP, and nzCFP are produced. Once again, we should only observe RFP output. Two inputs - Desired output: Red and green fluorescence If A and B are activated, we should observe RFP output, as before. Transcription from both A and B result in nzGFP. Since there is no czGFP, nzGFP should remain non-functional. However, supD and T7 ptag are created, allowing transcription from the T7 promoter, expressing non-split, functional GFP and czCFP. Since nzCFP is not created, czCFP remains non-functional. Therefore, we expect only RFP and GFP output. If A and C are activated, we should observe see RFP output as before. Transcription from promoter A gives nzGFP and promoter C gives czGFP, allowing formation of functional GFP. T7 ptag is also created but supD is not, so T7 ptag should remain non-functional. Finally, nzCFP is created without its partner. So we should observe RFP and GFP output. If B and C are activated, we have a similar situation, but instead of non-functional T7 ptag, we have non-functional supD. So we should observe RFP and GFP output. Three inputs - Desired output: Red, green, and cyan fluorescence If everything is activated, everything is created, so we should observe RFP, GFP, and CFP output. Back to an electrical circuit After designing the circuit, we wondered how different our adder is from an electrical full adder. To answer this question, we needed to know what kind of electrical circuit our genetic circuit corresponds to. Figure W: Full Adder Electrical Circuit Figure Z: Full Adder Genetic Circuit We see that our circuit has one additional output and consists of only 4 AND gates. Although there are many different ways to construct a digital full adder, there are none that use only 4 gates (one of the simplest ones is shown, which uses 5 gates) and none that use only AND gates. Because of the additional output, we say our output is “encoded.”

Results
Overview Unfortunately, we were unable to finish constructing our circuit in time for the wiki freeze. The following parts have been submitted to the Registry of Standard Biological Parts.