Engineering bacteria to solve the Burnt Pancake Problem
- Karmella A Haynes1Email author,
- Marian L Broderick4,
- Adam D Brown3,
- Trevor L Butner3,
- James O Dickson2,
- W Lance Harden2,
- Lane H Heard3, 6,
- Eric L Jessen3,
- Kelly J Malloy3,
- Brad J Ogden2,
- Sabriya Rosemond1, 5,
- Samantha Simpson1,
- Erin Zwack1,
- A Malcolm Campbell1,
- Todd T Eckdahl3,
- Laurie J Heyer2 and
- Jeffrey L Poet4
© Haynes et al. 2008
Received: 09 December 2007
Accepted: 20 May 2008
Published: 20 May 2008
We investigated the possibility of executing DNA-based computation in living cells by engineering Escherichia coli to address a classic mathematical puzzle called the Burnt Pancake Problem (BPP). The BPP is solved by sorting a stack of distinct objects (pancakes) into proper order and orientation using the minimum number of manipulations. Each manipulation reverses the order and orientation of one or more adjacent objects in the stack. We have designed a system that uses site-specific DNA recombination to mediate inversions of genetic elements that represent pancakes within plasmid DNA.
Inversions (or "flips") of the DNA fragment pancakes are driven by the Salmonella typhimurium Hin/hix DNA recombinase system that we reconstituted as a collection of modular genetic elements for use in E. coli. Our system sorts DNA segments by inversions to produce different permutations of a promoter and a tetracycline resistance coding region; E. coli cells become antibiotic resistant when the segments are properly sorted. Hin recombinase can mediate all possible inversion operations on adjacent flippable DNA fragments. Mathematical modeling predicts that the system reaches equilibrium after very few flips, where equal numbers of permutations are randomly sorted and unsorted. Semiquantitative PCR analysis of in vivo flipping suggests that inversion products accumulate on a time scale of hours or days rather than minutes.
The Hin/hix system is a proof-of-concept demonstration of in vivo computation with the potential to be scaled up to accommodate larger and more challenging problems. Hin/hix may provide a flexible new tool for manipulating transgenic DNA in vivo.
The biological equivalent of a burnt pancake is a functional module of DNA such as a promoter or coding region (Fig. 1a). Similar to burnt pancakes in the BPP, DNA modules have directionality (5' to 3'), require a specific order of the units (e.g., promoter followed by coding region) and can be flipped (cut, inverted, and spliced in vivo by cellular machinery). We designed a modular system in which pancake stacks are assembled from flippable DNA segments. Flipping of the DNA segment "pancakes" is mediated by a Salmonella typhimurium-derived DNA recombination system. In Salmonella, Hin DNA recombinase catalyzes an inversion reaction that regulates the expression of alternative flagellin genes by switching the orientation of a promoter located on a 1 kb invertible DNA segment [9, 10]. Two palindromic 26 bp hix sequences flank the invertible DNA segment and serve as the recognition sites for cleavage and strand exchange. A ~70 bp cis-acting recombinational enhancer (RE) increases efficiency of protein-DNA complex formation . We have reconstituted the genetic elements required for DNA inversion as a collection of modular genetic elements for use in E. coli. Our system is a proof-of-concept genetic computing device that manipulates plasmid DNA processors within living cells.
Results and discussion
Design and construction of a Hin/hix-based DNA recombination system
DNA inversion occurs very rapidly in vitro. Protein-DNA complex assembly, strand cleavage, inversion, and ligation occur in less than 1 minute . 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  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 [13, 14].
HinLVA flips and sorts hixC-flanked DNA segments in vivo
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 [15, 16]. The loss of four negative supercoils after each inversion event  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.
Two-pancake permutations and their phenotypes
BPP Plasmid construct a
mRFP expression on amp, IPTG c
Growth on tet, amp, IPTG d
RR-hixC-tetA(C) rev -RBS rev -hixC-pLac rev -hixC
RR-hixC-pLac-hixC-tetA(C) rev -RBS rev -hixC
RR-hixC-RBS-tetA(C)-hixC-pLac rev -hixC
RR-hixC-pLac rev -hixC-RBS-tetA(C)-hixC
RR-hixC-tetA(C) rev -RBS rev -hixC-pLac-hixC
RR-hixC-pLac rev -hixC-tetA(C) rev -RBS rev -hixC
Modeling and detection of phenotypic output
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 (lacIQ), 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 lacIQ binding sites than available repressor protein . The addition of IPTG appears to slow the growth of (1, 2) transformants; this might be result of toxic TetA(C) over expression . 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) [20, 21] 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  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 . 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).
We have demonstrated that a modified Hin/hix DNA recombination system can be used in vivo to manipulate at least two adjacent hixC-flanked DNA segments; HinLVA and hixC are sufficient for DNA inversion activity. The RE is not required, although it may play some role in preventing aberrant flips that lead to plasmid knotting  and subsequent plasmid loss . Thus, the RE might be added to BPP plasmids to increase DNA recombination efficiency. Once phenotypic output is optimized for this system, the kinetics of flipping (i.e., number of flips per unit of time) could be determined by comparing Markov Chain model simulation output to in vivo pancake sorting. Comparing actual cell survival to the survival probabilities predicted by our model should also enable us to determine whether flipping is biased for different sized DNA fragments.
The Hin/hix DNA recombination system could be used for other biological engineering applications. We have developed a set of modular genetic elements (hixC, RE, and HinLVA) that expands the repertoire of molecular tools for enzyme-mediated DNA manipulation in vivo. As with Cre/loxP from P1 bacteriophage  and Flp/FRT from yeast , Hin/hix may open avenues for recombinase-mediated transgene engineering. For instance, hixC-flanked promoters and other regulatory elements could function as flippable genetic toggle switches to regulate gene expression just as Hin mediates the expression of flagellin genes in Salmonella. Manipulation of genetic elements within a transgene at a single insertion site eliminates the problem of genomic position effects associated with independently introducing variants of transgenes at different loci. Furthermore, adjacent genetic elements could be rearranged at a single locus (e.g., switching the positions of a promoter and transcriptional insulator to test how well the insulator blocks transcription). The ability of Hin recombinase to invert large and small DNA fragments and adjacent flippable elements demonstrates the potential flexibility of the Hin/hix system.
The capability of HinLVA to flip adjacent DNA segments indicates that this system could be scaled up to accommodate more complex pancake stacks. As an application in comparative genomics, flippable DNA segment arrays could serve as a model to improve our understanding of syntenic genome rearrangements that have occurred during evolution. Chromosomal regions exist as syntenic modules arranged in different orders and orientations in the genomes of related species. Each syntenic module can be considered a burnt pancake that has a particular order and orientation. Phylogenetic relationships between species can be inferred by using BPP mathematical modeling to compute the minimum number of rearrangements that link two syntenic genomes (see  for review). Hin-mediated rearrangements of an array containing different sized DNA fragments would help refine the mathematical model by accounting for the impact of differences in sequence composition and lengths of syntenic modules. Using Hin/hix to sort DNA fragment permutations in vivo expands the horizons for the emerging field of applied DNA-based computing.
Construction of parts and plasmids
All genetic elements reported here are standardized parts (prefixed "BBa_" and "pSB") that are flanked by universal "BioBrick" cloning sites  and are documented and distributed by the MIT Registry of Standard Biological Parts .E. coli strain JM109 was used for cloning and as the chassis for our system. The recombinational enhancer (RE, BBa_J3101) , hixC (BBa_J44000) , 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" . 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) ).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 . 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 .
Hin-mediated DNA recombination
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).
Detection of DNA inversions
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.
Availability and requirements
Vector BBa_J64100 was generously provided by J. Tabor. KAH, WLH, JOD and EZ were supported by HHMI grant 52005120. SR was supported by a grant from iGEM at the Massachusetts Institute of Technology. ADB, MLB, TLB, ELJ KJM, BJO, JLP, LHH, and TTE were supported by the Missouri Western State University Summer Research Institute. LJH and AMC worked pro bono. KAH, AMC, LJH, and TTE are members of the Genome Consortium for Active Teaching . We thank the reviewers for their help with improving the final manuscript.
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