DNA inversion occurs very rapidly in vitro. Protein-DNA complex assembly, strand cleavage, inversion, and ligation occur in less than 1 minute 11. Therefore, we engineered Hin/hix inversion to be more tractable to regulation and kinetic studies by decreasing inversion efficiency. Hin was cloned from S. typhimurium by PCR. An ssrA LVA protein degradation tag 12 was added to the C-terminal DNA binding domain to prevent over accumulation of Hin and to achieve tighter control of DNA inversion. In Salmonella, the asymmetrical palindromic sequences hixL and hixR flank the invertible DNA segment and serve as the recognition sites for cleavage and strand exchange. Our system uses hixC, a composite symmetrical hix site that shows higher binding affinity for Hin and a 16-fold slower inversion rate than wild type sites hixL and hixR 1314.

To build a proof-of-concept model, we designed a two-pancake BPP containing the Lac promoter (pLac) and a tetracycline resistance coding region with a ribosomal binding site upstream (RBS-tetA(C)), each flanked by hixC sites (Fig. 2). Each configuration of this two-pancake stack is represented by a mathematical signed permutation. For instance, hixC-RBS-tetA(C)-hixC-pLac_rev-hixC is represented as the signed permutation "(2, -1)" where RBS-tetA(C) is 2 and pLac is 1. The positive value (2) represents the forward orientation of RBS-tetA(C) and the negative value (-1) represents the reverse orientation of pLac, denoted pLac_rev (pLac reversed). The eight possible signed permutations can be plotted as vertices of a graph (Fig. 1b). Two signed permutations are connected by an edge if it is possible to convert one permutation to the other with a flip of one or two pancakes. When flipping occurs at random, the starting permutation can be converted into any of its three neighboring permutations. In cells, after a given amount of time (i.e., number of flips), flipping is stopped by manual cell lysis, BPP plasmids are purified and transformed into new cells lacking HinLVA, and solved BPP plasmids are detected by resistance to tetracycline (pLac driven RBS-tetA(C) expression) in each colony. The time point at which the BPP is first solved at random reflects the minimal number of flips required to solve the BPP.

In order to solve the BPP, HinLVA must be able to flip single pancakes of varying sizes, flip adjacent segments independently, and sort segments by flipping multiple pancakes simultaneously. First, we tested HinLVA-mediated inversion on single hixC-flanked DNA segments of different lengths. HinLVA successfully flips the 1212 bp RBS-tetA(C) segment (Fig. 3a). The length of RBS-tetA(C) is comparable to the segment that is inverted by Hin recombinase in Salmonella 910. HinLVA can also flip the much shorter 200 bp hixC-flanked promoter (Fig. 3b). Restriction digest fragments indicate approximately equal molar amounts of both conformations (forward and reverse), suggesting that flipping of one DNA pancake has reached equilibrium ~24 hours after transformation. These data indicate that HinLVA-mediated inversion reconstituted in E. coli is not limited by fragment size, at least not within the range of 200 – 1212 bp.

Next, we cotransformed cells with a BPP plasmid containing a hixC-flanked RBS-tetA(C)_rev coding region and a hixC-flanked pLac promoter (permutation (-2, 1)) and a HinLVA expression plasmid (Fig. 2). The RE was omitted from the BPP plasmid to slow the rate of inversion. We used multiplex semiquantitative PCR (sqPCR) to monitor flipping of the two adjacent hixC-flanked DNA segments. Each of the four internal rearrangements can be detected by a sqPCR amplicon of a distinct size (Fig. 4a). Eleven hours after transformation, single colonies were picked for whole cell sqPCR. Bands from all four configurations were visible in samples where (-2, 1) was cotransformed with HinLVA (Fig. 4b). Flipping occurred in the absence of the RE, demonstrating that HinLVA and a pair of hixC sites are sufficient for a functional Hin/hix DNA inversion system in E. coli. The starting pancake arrangement (-2, 1) is the predominant plasmid in all colonies tested. Plasmids generated from a single flip of either RBS-tetA(C) (pancake 2) or pLac (pancake 1) are the next most frequent, while plasmids generated from two sequential flips of both pancakes 2 and 1 are the least common. We could not detect significant bias for flipping of the larger RBS-tetA(C) segment or the smaller pLac promoter (Fig. 4c), suggesting that flipping is not influenced by the size of the DNA segment.

The sqPCR results suggest that flipping has not yet reached equilibrium after 11 hours of HinLVA activity in the absence of RE. Plasmid supercoiling might be a limiting factor. Hin-mediated inversion requires a negatively supercoiled plasmid DNA substrate 1516. The loss of four negative supercoils after each inversion event 17 might require cells to undergo cell division to reset optimal supercoiling before a second inversion event can occur. Based on the 4 hour lag time and 36 minute maximum doubling rate of the cotransformed cells, we estimate that no more than 12 doublings occurred before sqPCR analysis. Twelve cell divisions appear to be insufficient to allow the distribution of rearrangements to reach equilibrium.

Finally, we assessed simultaneous inversion of both DNA pancakes. In order to accomplish this operation, Hin must recognize the outer-most hixC sites and ignore the central hixC site between the segments. Inversion of the entire permutation (-2, 1) generates permutation (-1, 2) in which the pLac promoter is repositioned to drive mRFP reporter expression (Fig. 5a). Inversion of the promoter alone, producing (-2, -1), is insufficient to induce detectable levels of mRFP (Table 1). Colonies containing HinLVA and the (-2, 1) BPP plasmid were grown as a liquid culture then the Hin-exposed BPP plasmids were isolated and transformed into bacteria. About one third of the cell colonies appeared red (Fig. 5b) indicating that simultaneous inversion of both DNA segments occurred at a high frequency. Thus, HinLVA is capable of mediating the inversion of at least two adjacent flippable DNA segments.

We sought to use the power and sensitivity of antibiotic resistance phenotype screening to detect solved BPP plasmids. sqPCR analyzes one colony at a time and requires several plasmids to generate a detectable PCR amplicon, whereas screening can rapidly distinguish a single solved BPP plasmid from millions of unsolved plasmids in a cell culture. Permutations (1, 2) and (-2, -1) both encode a functional tetracycline resistance gene that should allow cells to live in the presence of tetracycline. The other six permutations encode a disrupted tetracycline resistance gene and should lead to cell death in the presence of tetracycline. Based on these predicted phenotypic outputs, we designed a mathematical model of random flipping over time (successive flips) to predict how cell survival (the percentage of solved pancake stacks) might change over time. We modeled flipping as a Markov Chain in which each of the possible eight signed permutations is a state. Our model is synonymous with a random walk on the graph in Figure 1b. We assumed that any segment of DNA flanked by two hixC sites (pancake 1, pancake 2, or both) is equally likely to be flipped by HinLVA and that all flips in the population of cells happen synchronously. According to this model, the probability of a plasmid being properly sorted after k flips is determined by the number of paths of length k from the initial state to the solution state, divided by the total number of paths of length k from the initial state to any state. For instance, there are six paths of length 3 from initial state (2, 1) to solution state (1, 2) (Fig. 1b); because there are 27 possible paths of length 3 that start at (2, 1), the probability of being in a solution state after three flips is 6/27 (22%). We observed two interesting features of the output from a simulation of random flipping (Fig. 6). First, the conversion of unsolved BPP plasmids towards and away from the solution state reaches equilibrium at 25% survival after five flips. Second, several starting arrangements show equivalent behavior as they approach equilibrium (i.e., (1, -2) and (-1, 2)). The simulation output has implications for further design of our system. If our model is correct, only one representative from each class of equivalent starting configurations needs to be tested. Furthermore, if equilibrium (25% survival) is reached after only five flips, slowing Hin-mediated inversion by omitting the RE may be required to detect significant changes in cell survival over time.

As an initial step towards carrying out flipping in vivo, we manually constructed all eight pancake permutations (excluding the RE) and transformed them into cells to confirm their phenotypes. We observed several unexpected outcomes. In cells that contain a strong pLac repressor (lacI^Q), BPP plasmids (1, 2) and (-2, -1) showed significant tetracycline resistance without activation of pLac by IPTG. We also observed that HinLVA-mediated inversion does not require induction of the pLac promoter on the HinLVA plasmid, indicating general leakiness of pLac promoter activity probably due to more lacI^Q binding sites than available repressor protein 18. The addition of IPTG appears to slow the growth of (1, 2) transformants; this might be result of toxic TetA(C) over expression 19. We expected to detect mRFP expression from all four plasmids that contain reversed pLac. However, reversed pLac fails to induce mRFP expression when it is positioned after tetA(C) (i.e., RBS-mRFP-hixC-RBS-tetA(C)-hixC-pLac_rev-hixC). Increased distance from mRFP or the DNA structure of tetA(C) 2021 might block transcription of mRFP.

We found it surprising that four constructs in which pLac is not in the proper position and/or orientation to drive expression of tetA(C) were able to confer tetracycline resistance; in the presence of IPTG, three of these showed more robust growth than cells carrying (1, 2). When the pLac promoter was removed from the construct, cells were still tetracycline resistant (data not shown), thus pLac is not required for expression in the pBR322-derived cloning vector we had been using (pSB4A3). Read-through transcription by RNA polymerase binding to the antibiotic resistance marker promoter or degenerate promoter sequences within the vector backbone 22 could result in tetA(C) expression in the tetracycline resistant scrambled permutations (1, -2), (-1, 2), (-2, 1), and (2, 1). We constructed an "insulated" vector (pSB1A7) containing forward and reverse double transcription terminator sequences to shield RBS-tetA(C) from read-through transcription. In pSB1A7, there was no expression of RBS-tetA(C) (forward or reverse) when pLac was removed from the construct. Arrangements (1, 2) and (-2, -1) produced tetracycline resistance, as expected. Surprisingly, we also observed tetracycline resistance in the insulated vector when pLac was reversed relative to tetA(C) in arrangements (-1, 2) and (-2, 1), suggesting reverse promoter activity from pLac. Unlike forward transcription initiated from pLac, backwards transcription did not respond to IPTG as determined by cell growth; IPTG induction of forward transcription from pLac led to overexpression of tetA(C) and subsequent cell death 19. Due to the backwards promoter activity of pLac, our manually built set of permutations are not distinguishable by phenotype, thus phenotype alone is insufficient to perform computation using pLac and RBS-tetA(C). The observations described above demonstrate that the construction of synthetic biological devices can reveal unexpected characteristics of well-studied DNA elements (e.g., pLac).

All genetic elements reported here are standardized parts (prefixed "BBa_" and "pSB") that are flanked by universal "BioBrick" cloning sites 28 and are documented and distributed by the MIT Registry of Standard Biological Parts 29.E. coli strain JM109 was used for cloning and as the chassis for our system. The recombinational enhancer (RE, BBa_J3101) 30, hixC (BBa_J44000) 13, RBS_rev (BBa_J44001) and pBAD_rev (BBa_J44002) were assembled from 20 – 60 bp DNA oligomers that were designed using the "Oligo Cuts Optimization Program" 31. EcoRI (5') and PstI (3') single stranded extensions were manually added to the terminal oligomers. An equimolar mix of single-stranded oligomers in 1× annealing buffer [100 mM NaCl; 10 mM Tris-HCl, pH 7.4] was incubated at 100°C for 5 minutes, then slowly cooled to ambient temperature in a water bath to produce double stranded DNA with EcoRI (5') and PstI (3') single stranded overhangs. The annealed DNA was ligated into linearized (EcoRI and PstI digested) cloning vector pSB1A2 using T4 ligase (Promega). Hin (BBa_J31000), HinLVA (BBa_J31001), and tetA(C) (BBa_J31007), and were cloned by polymerase chain reaction (PCR). Standard BioBrick prefix cloning sites (EcoRI, NotI and XbaI) or suffix cloning sites (SpeI, NotI and PstI) were included in the forward or reverse PCR primer, respectively. PCR amplicons were digested with EcoRI and PstI, electrophoresed in an agarose gel, purified, and ligated into a linearized cloning vector. Hin [GenBank: see Availability and requirements section for URL] was cloned from Salmonella typhimurium Ames strain TA100 genomic DNA using forward primer 5'-GCATGAATTCGCGGCCGCTCTAGATGGCTACTATTGGGTATATTC and reverse primer 5'-ATGCCTGCAGGCGGCCGCAACTAGTTAATTCATTCGTTTTTTTATAC. HinLVA was generated by PCR amplification of Hin (BBa_J31000) using forward primer 5'-TCTGGAATTCGCGGCCGCATCTAGAGATG and reverse primer 5'-CTGCAGGCGGCCGCTACTAGTATTAAGCTACTAAAGCGTAGTTTTCGTCGTTTGCAGCATTCATTCGTTTTTTTATAC containing a ssrA LVA degradation tag (based on gfp(down, LVA) 12).tetA(C) was cloned from vector pSB1AT3 using forward primer 5'-GCATTCTAGATGAAATCTAACAATGCGCTCATC and reverse primer 5'-ATGCACTAGTTAGGTCGAGGTGGCCCGGC; the amplicon was cloned using a XbaI/SpeI digest. Reversed parts were generated by PCR amplification of MIT Registry parts using a forward primer containing SpeI and a reverse primer containing XbaI: tetA(C)_rev (BBa_J31006) – forward 5'-ATGCACTAGTATGAAATCTAACAATGCGCTCATC and reverse 5'-GCATTCTAGATTAGGTCGAGGTGGCCCGGC; pLac_rev (BBa_J31013) – forward 5'-ATGCACTAGTACAATACGCAAACCGCCTCTC and reverse 5'-GCATTCTAGAGTGTGTGAAATTGTTATCCGC; mRFP_rev (BBa_J31008) – forward 5'-ATGCACTAGTATGGCTTCCTCCGAAGACGT and reverse 5'-GCATTCTAGATTAAGCACCGGTGGAGTGAC. Correct sizes and sequences of the genetic elements described above were confirmed by XbaI/SpeI double digestion and DNA sequencing. The constructs shown in Figure 2, the eight two-pancake BPP plasmids (Table 1), and the HinLVA expression vector were assembled using the standard BioBrick assembly method 27. Proper assembly of construction intermediates was confirmed by EcoRI/PstI double digestion. Fully assembled two-pancake BPP constructs (1, 2) (BBa_S03684), (-2, -1) (BBa_S03681), (1, -2) (BBa_S03685), (-2, 1) (BBa_S03679), (-1, 2) (BBa_S03687), (-2, 1) (BBa_S03680), (2, 1) (BBa_S03677), and (-1, -2) (BBa_S03688) were confirmed by sequencing. BPP constructs were inserted into low copy pSC101 vector pSB4A3 (Fig. 2) and subsequently tested in insulated high copy pMB1 vector pSB1A7. pLac-RBS-HinLVA-TT (BBa_S03536) was inserted into low copy ColE1 vector BBa_J64100 (from Jeffrey J. Tabor) to create the HinLVA plasmid (Fig. 2). The cloning vectors are described in 29.

Growth of transformed colonies on LB agar and in shaking liquid cultures took place overnight at 37°C. For single DNA segment flipping assays (Fig. 3), constructs containing the HinLVA gene on the same vector as the invertible segment (BBa_J44006 – pLac-RBS-HinLVA-TT-hixC-pBAD-hixC-RBS-tetA(C)-TT-RE or pLac-RBS-HinLVA-TT-pBAD-hixC-RBS-tetA(C)-hixC-TT-RE in vector pSB1A2) were transformed into JM109 chemically competent cells. After growth on selective media (LB agar plus 100 μg/mL ampicillin), single colonies were grown in liquid selective media (LB plus 100 μg/mL ampicillin) overnight. For the two-pancake stack flipping assay, 10 ng each of a plasmid containing a two-pancake stack (Table 1) and the HinLVA expression plasmid were combined in 5 μL sterile distilled H₂O and co-transformed into Z-competent JM109 chemically competent cells according to the manufacturer's protocol (Zymo Research). Cells were grown at 37°C on LB agar selective media (20 μg/mL ampicillin, 50 μg/mL chlroamphenicol).

Inversions of single hixC-flanked DNA segments were detected by restriction digests (Fig. 3). Plasmid DNA was purified from each culture (Promega Wizard and Zymo Zyppy miniprep systems), digested with NheI, and resolved by agarose (Fig. 3a) or polyacrylamide (Fig. 3b) gel electrophoresis. Inversions of adjacent hixC-flanked segments were detected by multiplex semiquantitative PCR (sqPCR) (Fig. 4). 11 hours following transformation, 46 visible co-transformant colonies were picked from LB agar selective media and subjected to whole cell multiplex sqPCR (95°C, 10 min.; 95°C, 30 sec., 60°C, 30 sec., and 72°C, 15 sec. for 26 cycles). Each colony was suspended in 60 μL 1× PCR mix (Promega Green master mix plus 0.7 μM primers pLacR 5'-GAATCGGCCAACGCGCGGGG, pLacF 5'-GTTTCCCGACTGGAAAGCGG, TetR 5'-GTAGAGGATCCACAGGACGG and TetF 5'-TCGTAGGACAGGTGCCGGCA). 0.1 pmol of an equimolar mix of all 8 two-pancake BPP plasmids or 0.1 pmol of the (-2, 1) BPP plasmid alone was used as the template in a control PCR reaction. During PCR, an 11 μL aliquot was collected from each reaction after cycles 18, 20, 22, 24 and 26. Samples were electrophoresed on a 1.5% agarose gel and photographed under ultraviolet light using a BioRad imager. Band intensities were quantified using BioRad Quantity One imaging software. The detectable band threshold was set at 10,000 (after background subtraction).

To detect simultaneous flipping of two DNA segments (described in Fig. 5) single co-transformed colonies were picked from agar plates and grown in selective liquid media (20 μg/mL ampicillin, 50 μg/mL chlroamphenicol). To eliminate the Hin plasmid after flipping, plasmid DNA was purified from the liquid cultures and transformed into new competent cells. Cells were grown on LB agar containing 20 μg/mL ampicillin to select for transformants that contained a recombined BPP plasmid, and 40 μg/mL IPTG to induce pLac-driven expression of mRFP. mRFP expression was detected under ultraviolet light and photographed using a BioRad imager.