Davidson 2006

Figure 2 3-D structure of a Hin protein complex bound to DNA. View the [http://www.rcsb.org/pdb/explore/explore.do?structureId=1ZR4 interactive 3-D Jmol image].

Every segment of DNA flanked by a pair of HixC sites is a "pancake" capable of being inverted. Hin invertase recognizes pairs of HixC sites and inverts the DNA fragment in between the two HixC sites with the help of the Fis protein bound to the RE. In our system, selectable phenotypes (including antibiotic resistance and RFP expression), depend upon the proper arrangement of a series of HixC-flanked DNA segments in a plasmid. This allows us to select for cells that have successfully solved the puzzle. An example of a sorted stack of two pancakes is shown in Figure 3. There are 7 other configurations of 2 pancakes. If we increase the number of pancakes to 4, there are 384 configurations. In general, there are 2ⁿ n! configurations of n pancakes, a combinatorial explosion of possibilities. How many should we build and test? Which ones are most informative? We need a mathematical model to help answer this question.

Figure 3 A sorted stack of two biological "pancakes"

Mathematical Model: Our mathematical representation of a stack of pancakes is a signed permutation, in which each numerical value represents the pancake size and the sign of the number represents the orientation. For example, (1, 2, 3, 4) is a sorted stack of four pancakes, all in the proper order and orientation, and (-2, 4, -1, 3) is the scrambled stack of four pancakes shown on the far left of Figure 1. Note that pancakes 1 and 2 are negative, indicating that these two pancakes are in the wrong orientation (burnt side up).

Figure 4 Simulation results for two pancakes

From these simulations, and similar results for stacks of 3 and 4 pancakes, we discovered that the probability of a plasmid being sorted after k flips was determined by how many ways the solution could be obtained. Several initial configurations had essentially the same graph in our simulations because they had the same number of ways of being sorted. Only one representative from each of these "families" of initial configurations needs to be built and tested.

Parts used in this project were designed by two iGEM Teams

• [http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2006partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2006&group=Davidson Davidson]
• [http://partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2006partsregistry.org/cgi/partsdb/pgroup.cgi?pgroup=iGEM2006&group=Missouri Missouri Western]
  
  

Modeling

• Modeling pancake flipping: deducing kinetics and size biases
• Using modeling to choose which families of unsolved pancake stacks to start with
• Modeling the effect of plasmid copy number

• Defining a DNA pancake - what parts are flippable?
• Read-through from the carrier vector backbone leads to uncontrolled Tet expression and uncontrolled flipping
• New vector insulates parts from read-through, but is not compatible with parts carrying double terminator B0015
• Solution: design pancake constructs without double terminator B0015
• Two-pancake stacks - we increased the size of the pancake stack
• Dealing with biological equivalence - distinguishing 1,2 from -2,-1 using an RFP reporter

• Consequences of devices
  • Practical: proof-of-concept for bacterial computers, data storage
  • Basic research: transgene rearrangement in vivo, insights into evolution that has occurred via DNA rearrangements
• Next steps: can solve problem but need control over kinetics
• Lessons learned:
  • Troubleshooting, communication, teamwork, publicity
  • Math and Biology meshed really well and even uncovered a new proof
  • Multiple campuses can increase capacity through communication and cooperation
  • Size of school is not a limiting factor
  • We had a blast and learned heaps!!!