Flippin’ Pancakes:
An Undergraduate Synthetic Biology Research Project
Jeff Poet
Missouri Western State University
Missouri MAA, March 30, 2007
Based on joint work with colleagues and students from Missouri Western in St. Joseph,
Missouri and Davidson College in Davidson, North Carolina
Abstract: Description of an interdisciplinary, inter-institutional synthetic biology
research project involving undergraduates at Missouri Western and Davidson College in
2006. We made progress in engineering E. coli to solve a graph theory problem.
Note: This is a reproduction of a talk given based on a PowerPoint presentation which is
available at www.missouriwestern.edu/~poet/.
Submitted to The Electronic Proceedings of the Missouri MAA, April 2007
Synthetic biology is a relatively new branch of science defined to be the application of
engineering principles and mathematical modeling to the design and construction of
biological parts, devices, and systems with applications in energy, medicine, and
technology.
The field of synthetic biology is on the cutting edge of science. Discover magazine
created a brand new award for the scientist of the year and the first ever recipient of the
award was a leader in this new field, Jay Keasling of University of California-Berkeley.
One principle of engineering that synthetic biologists seek to apply to this new field is the
categorization of parts by function. The synthetic biology community agrees on the
properties of the various types of parts and monitors the quality control of the parts. A
second principle used in synthetic biology is the standardization of the assembly of parts,
leading to efficiency and the natural byproduct of specialization.
DNA has directionality. Figure 1, below, illustrates the standard assembly procedure to
insert the Blue Part into a circular plasmid upstream of the Green Part. E, X, S, and P are
strings of DNA which can be cut with enzymes and repieced together in the biology
laboratory using molecular biology protocols.
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Figure 1: Standard assembly procedure
-----------------------------------------------------------------------------------------------------------A standard biological part is a string of DNA with the appropriate prefix E-X attached
upstream and the appropriate suffix S-P downstream. MIT maintains the Registry of
Standard Biological Parts and makes this collection of parts available at no charge to
participants of the International Genetically Engineered Machines (iGEM) community, of
which we were a part in 2006.
Figure 2 illustrates the engineering notion of abstraction as it applies to synthetic biology.
Abstraction allows different synthetic biologists to specialize at one level while
interacting with those who specialize on the level above and below. The field of
synthetic biology is largely functioning on the levels of DNA and parts at this time but as
knowledge in the field grows, individuals in the field will spend more time at the upper
levels of abstraction.
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Figure 2: Levels of abstraction in synthetic biology
-----------------------------------------------------------------------------------------------------------Synthetic biologists even use blueprints. The photo in Figure 3 is of the systems and
parts diagram from our laboratory chalkboard in August 2006. It describes the plan for
the assembly of our project.
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Figure 3: System and parts diagram from MWSU laboratory chalkboard
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The iGEM project is modeled after the collegiate robot competition. Teams of
undergraduates from institutions around the world “compete” to further the frontiers of
the field of synthetic biology. While it is referred to as a competition, a main objective of
iGEM is to provide a collaborative and supportive environment for new scientific
discovery. The iGEM collaborative community establishes a new model for research:
one that reaches across disciplines, reaches across institution types, coordinates efforts of
individuals in multiple geographic regions, and utilizes undergraduate creativity. The
iGEM year concludes with an annual “Jamboree” – a celebration of student achievement.
iGEM began with four teams from the East Coast in 2004, expanded to 13 teams in 2005
from around the country with a few international teams, and included 39 teams from the
US and around the world in 2006. It is of note that Missouri Western is one of only three
primarily undergraduate institutions, another being our collaborating institution,
Davidson College, in North Carolina.
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Figure 4: iGEM2006 teams from around the world
-----------------------------------------------------------------------------------------------------------The Missouri Western and Davidson College teams combined our efforts to engineer E.
coli to solve a variation of a classic problem from computer science known as the
Pancake Problem. The Classic Pancake Problem is as follows: Suppose one is given a
plate on which there is a stack of pancakes of varying sizes. While holding the plate in
one hand, imagine using a spatula to manipulate the pancakes so that they are sorted by
size with the smallest pancake on top and the largest pancake on bottom. Such a
manipulation would include flipping some number of pancakes from the top of the stack
and turning over the stack. In computer science this is known as “sorting by prefix
reversals.” There are two goals of the pancake problem: The first is to determine the
minimum number of flips required to put a particular starting stack of pancakes into
order. The second is to determine which, of all the possible stacks of n different sized
pancakes requires the most flips. Note that the last problem is currently an open question
for n>13. We hope to provide a proof of concept for using the computation power of
massive parallel processing of in vivo computing by engineering E. coli to solve a
relatively small version of a related problem.
Figure 5 shows one way of flipping the pancakes to sort the original stack, which we can
abstractly think of as corresponding to the permutation (2,4,3,1) into the sorted stack
(1,2,3,4). This is one solution to the problem requiring five flips. Figure 6 shows a more
efficient way of sorting that uses only three flips (which, with work not shown here, turns
out to be minimal).
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Figure 5: Sorting (2,4,3,1) in 5 steps
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Figure 6: Sorting (2,4,3,1) in the minimal 3 steps
-----------------------------------------------------------------------------------------------------------It turns out that because of the directionality of DNA, we had to consider a modification
of the Classic Pancake Problem referred to in the literature as the Burnt Pancake
Problem. This modification adds the condition that each of the pancakes (still of various
sizes) is also burnt on one side only and a proper ordering the pancake not only has the
pancakes arranged from smallest on top to largest on bottom, but also has each pancake
oriented with the burnt side down (so the customer won’t see the burnt side!) The two
goals of the problem remain the same: To identify the least number of flips to sort a
particular stack and to identify the starting stack that requires the greatest number of flips.
A burnt pancake stack can be represented as a signed permutation. An illustration of a
solution for a burnt pancake stack is given in Figure 7.
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Figure 7: Illustration of burnt pancake flipping of (4,1,2,3) to (1,2,3,4)
-----------------------------------------------------------------------------------------------------------Recall that we are trying to get E. coli to work this problem. To do so, we reconstituted
the hin-hix recombination mechanism that exists naturally in Salmonella typhimurium
and built the components of this mechanism as standard biological parts for use in E. coli.
This was definitely a non-trivial pursuit and required careful planning, intense
experimental design, and a large amount of troubleshooting when seemingly wellconstructed plans did not produce the expected or desired results in the biology lab.
Some of these parts were synthesized from scratch; others were obtained by modifying
existing parts with inventive techniques.
The version of the Burnt Pancake Problem was a variation of the one stated above.
Because of the recombination mechanism, we were not able (as of yet anyway) to control
the flipping to involve only one end of the DNA strand (i.e. the top portion of the stack of
pancakes). The mechanism functions by cutting the DNA in predesignated locations and
then recombining the DNA with the segment reversed. This segment of DNA could be at
the beginning of the strand, the middle, or the end. Thus, we conceive of our version of
the problem as a Two Spatula Burnt Pancake Problem in which a single “flip” is consists
of removing a top portion of the stack (or no pancake), flipping the top portion of the
remaining stack (or possible the entire remaining stack), and then replace the top portion
in its original orientation. This is illustrated in Figure 8 below.
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Figure 8: Illustration of a single two-spatula flip
-----------------------------------------------------------------------------------------------------------The following graph was created by MWSU student Marian Broderick using Geometer’s
SketchPad and illustrates the relationships between the signed permutations of three burnt
pancakes under these two-spatula flips. Note that there are 48 such signed permutations
corresponding to the possible arrangements and alignments of 3 burnt pancakes. The
graph below represents the Northern Hemisphere of a graph placed on a sphere with one
vertex at the North Pole, five on the Arctic Circle, eleven on the Tropic of Capricorn, and
fourteen on the Equator. The Southern Hemisphere is identical to the Northern
Hemisphere. To make the full graph, the two halves should be joined at the equator with
the lone point one the equator in the Northern Hemisphere with the two green edges (at
bottom) coinciding with the lone point on the equator on the Southern Hemisphere graph
X
with three magenta edges (at top). This will result in each vertex of the graph
(corresponding to a signed permutation of three burnt pancakes) to be joined with an edge
to five vertices corresponding to five of the signed permutations that can be reached with
a single two-spatula flip. In addition, each vertex should be considered as adjacent to its
antipodal vertex on the sphere. This edge corresponds to the flipping of the entire stack.
The edges are color-coded to denote the number of pancakes turned over in each twospatula flip.
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Figure 9: Northern Hemisphere of Permutation Graph for 3 Burnt Pancakes
-----------------------------------------------------------------------------------------------------------Plans for the 2007 iGEM year, which begins May of 2007 and ends with the Jamboree at
MIT in Boston in November, include continuing the collaboration with Drs. Eckdahl,
Campbell, and Heyer and teams of students from Missouri Western and Davidson
College. We believe that the flipping mechanism used for the Pancake Problem can be reemployed for use in other math problems. We plan to pursue the Hamiltonian Path
Problem in 2007 with possible extensions to the Traveling Salesman Problem after that.
I wish to acknowledge the following for their contributions to this project:
Colleagues Todd Eckdahl (MWSU Biology), Malcolm Campbell (Davidson Biology),
Laurie Heyer (Davidson Mathematics), and Karmella Haynes (Davidson Biology
postdoc)
Students from Missouri Western Marian Broderick, Adam Brown, Trevor Butner, Eric
Jessen, Kelly Malloy, Brad Ogden, Lane Heard (2007 graduate of Central HS, St. Jo)
Students from Davidson College Lance Harden, Samantha Simpson, Erin Zwack, and
Sabriya Rosemond (of Hampton University)
Randy Rettburg, Andrew Hessel, and the rest of the IGEM community
Administration of Missouri Western for financial support of project and travel