Figure 1

The Burnt Pancake Problem can be modeled using genetic elements. (A) Sorting of a scrambled two-pancake stack (rectangles) where the smaller burnt pancake (1, blue) and the larger burnt pancake (2, purple) are in the wrong order (2, 1). First, the whole stack is flipped and both pancakes are turned burnt side up (hatched shading). The next two flips turn the small then the large pancake golden side up (solid shading) resulting in a properly sorted stack (1, 2). Analogous DNA segment arrangements are shown below. Sorting of the promoter (1, blue arrow) and coding region (2, purple arrow) into (1, 2) is required for gene expression. (B) The process of sorting scrambled pancake stack (2, 1) into the solution (1, 2) is plotted on a graph. The eight possible arrangements of the pancake stack are shown as signed permutations at the vertices. (2, 1) is converted into the three neighboring permutations by a flip of a single pancake (arrow) or both pancakes simultaneously (double headed arrow). Six distinct paths of length 3 can convert (2, 1) into (1, 2). The flipping pathway highlighted in red corresponds to the flips shown in part A