In silico design and in vivo implementation of yeast gene Boolean gates

In our previous computational work, we showed that gene digital circuits can be automatically designed in an electronic fashion. This demands, first, a conversion of the truth table into Boolean formulas with the Karnaugh map method and, then, the translation of the Boolean formulas into circuit schemes organized into layers of Boolean gates and Pools of signal carriers. In our framework, gene digital circuits that take up to three different input signals (chemicals) arise from the composition of three kinds of basic Boolean gates, namely YES, NOT, and AND. Here we present a library of YES, NOT, and AND gates realized via plasmidic DNA integration into the yeast genome. Boolean behavior is reproduced via the transcriptional control of a synthetic bipartite promoter that contains sequences of the yeast VPH1 and minimal CYC1 promoters together with operator binding sites for bacterial (i.e. orthogonal) repressor proteins. Moreover, model-driven considerations permitted us to pinpoint a strategy for re-designing gates when a better digital performance is required. Our library of well-characterized Boolean gates is the basis for the assembly of more complex gene digital circuits. As a proof of concepts, we engineered two 2-input OR gates, designed by our software, by combining YES and NOT gates present in our library.


Promoter
Coding region Terminator

Materials and Methods
Plasmid name   Figure S3: 8 peaks alignment beads fluorescence. For every experiment (labelled with one or two yeast strain corresponding to closed gates) the initial and final values of the mean fluorescence of the 4 th (A) and the 6 th (B) peak are reported. Within a single experiment, the biggest variation we observed was of 2.1% (4 th peak) and 2.0% (6 th peak) of the initial mean fluorescence value.

Experimental results
Three different YES tetOp gate implementation     Table S5: Comparison of experimental and computational (*) relative fluorescence of AND lacOp-tetOp, and AND lacOp-tetOp-TI. The first input digit refers to tetracycline, the second one to IPTG.

VOLUME Value
Reference Protein decay rates k dp is the same for free and DNA-bound proteins. Their values are listed below (nuclear protein Pools). Notice that k el = gene length/v pol and k r el = gene length/v rib . The mRNA decay rate k d is defined by the terminator.    Figure S5: YES lacOp2 scheme. Schematic of the Boolean gate YES lacOp2. RNA Polymerase Pool is connected to both transcription units. In particular, this Pool exchanges a P oP S b flux with each promoter and receives a P oP S in flux from every terminator (for the sake of simplicity, we traced a single straight line between the Pool and each transcription unit and indicated as P oP S the information exchanged). The two promoters are also constantly informed (during a simulation) about the amount of RNA Polymerase available in the Pool (pol f ree ). An analogous description holds for the ribosome Pool (double connection to each mRNA Pool) whereas the spliceosome Pool has a single link to every Coding region. The IPTG Pool is connected to both the LacI Pool and the pLacOp2 promoter since IPTG can bind and inactivate LacI molecules both on the DNA and far from it. Therefore, the LacI Pool-which receives a flux of proteins (F aP S in from the cytoplasm-exchange with the pLacOp2 promoter a flux of active (F aP S b a ) and inactive (F aP S b i ) LacI and informs the promoter with the amount of currently available active repressors (R a ). Finally, the YFP Pool permits to read the circuit output during a computer simulation.

Constitutive pAct1 promoter
Species and fluxes p0 f free promoter (RNA polymerase binding site) p0 t promoter taken by RNA polymerases P ol f ree RNA polymerases available in the Polymerase Pool P ol cl RNA polymerase in the promoter cleaning phase. Sent as P oP S out to the lacI coding region P oP S b exchanged with the Polymerase Pool P oP S out sent to LacI coding region Notice that P ol cl is a fictitious species [8] since it does not appear explicitly into the circuit SBML file but it is replaced by the P oP S out flux. Reactions

LacI and YFP coding region
Species and fluxes P oP S in from the adjacent promoter Y f ree available spliceosome molecules into their Pool [P olA] RNA polymerase bound to the DNA before starting the elongation phase P ol el RNA polymerase in the promoter elongation phase. It is a fictitious species replaced by P oP S out spliceosome molecules bound to u mRN A n mRN A nuclear mRNA m mRN A mature mRNA. It is a fictitious species replaced by RN AP S out RN AP S out flux of mature mRNA sent to the corresponding mRNA Pool in the cytoplasm P oP S out sent to the adjacent terminator

Cyc1 terminator
Species and fluxes P oP S in from the adjacent coding region [P olT ] RNA polymerase bound to the terminator P ol f ree RNA polymerase leaving the DNA. Sent to the Polymerase Pool as P oP S out P oP S out sent to the Polymerase Pool

Fluxes calculation
IPTG is supposed to bind only LacI dimers.

Fluxes calculation
SiP S b = λS f ree R a − (µ + k dp )R i

Regulated pLacOp2 promoter
Species and fluxes P ol f ree RNA polymerases available in their Pool R a free active LacI molecules available in their Pool R i free inactive LacI molecules S f ree IPTG molecules available in their Pool RNA polymerase bound to the promoter (p0 is the polymerase binding site) LacI bound to the strong operator O 1 (close to the TATA box) LacI bound to the weak operator O 2 (close to the TSS) LacI bound to both operators P ol cl RNA polymerase in the promoter cleaning phase P ol cl lk RNA polymerase in the cleaning phase due to promoter leakage. This is a fictitious species P oP S b exchanged with the polymerase Pool P oP S out sent to the YFP coding region P oP S out lk sent to the YFP mRNA Pool in the cytoplasm Reactions

The YFP Pool
Species and fluxes F aP S in flux of YFP from the corresponding mRNA Pool Y F P YFP monomers Polymerase, ribosome, spliceosome, and IPTG Pools These Pools do not contain any reaction. They store molecules not bound to the DNA or the mRNA. The RNA Polymerase Pool exchanges a balance flux with each promoter in the nucleus and gets an input flux from every terminator; the ribosome Pool exchanges a balance flux and gets an input flux from each mRNA Pool in the cytoplasm; the spliceosome Pool exchanges a balance flux with each coding region, the IPTG Pool exchanges a balance flux with the LacI Pool and sends an output flux to the pLacOp2 promoter. Since a balance flux is the sum of an input and an output flux, the dynamics of the free molecules stored in these Pool is given by the following ordinary differential equation:

AND lacOp-tetOp
The AND lacOp-tetOp gate differs from the YES lacOp2 gate for the presence in the nucleus of a third transcription unit producing TetR and the promoter leading the synthesis of Citrine (pLacOpTetOp). Here, we give the modelling of the only pLacOpTetOp promoter since the models of the other Parts and Pools in the circuit are identical to the ones presented above. Reactions

Fluxes calculation
Notice that the model for the pLacOp promoter used in our computational analysis is the same as the one for pLacOpTetOp after removing the O 2 operator.