The Algebra of Gene Assembly in Ciliates

Abstract

The formal theory of intramolecular gene assembly in ciliates is fitted into the well-established theories of Euler circuits in 4-regular graphs, principal pivot transformations, and delta-matroids.

Sorting by reversals and the theory of 4-regular graphs

“…Due the similarity of the "signed permutations" of Figures 1 and 14, we see that the circle graph corresponding to Figure 16 is obtained from the circle graph of Figure 10 by removing vertices v 0 and v 7 . See [17] for more details on how the 4-regular multigraphs, circle graphs and delta-matroids can be used to study gene assembly in ciliates.…”

“…It has been shown that various other research topics can also be fit into the theory of circuit partitions of 4-regular multigraphs: examples include the theory of ribbon graphs (or embedded graphs) [8,20] and the theory of gene assembly in ciliates [17]. As such all these research topics arising from different contexts turn out to be strongly linked, and results from one research topic can often be carried over to another.…”

Graph Polynomials Motivated by Gene Rearrangements in Ciliates

“…This string-based formal model can be very naturally fitted within the well-developed theory of transformations of Eulerian circuits in 4-regular graphs [4]. An example using the Actin I gene of Sterkiella nova, taken from Prescott [18], is recalled below.…”

“…It turns out that the interplay of the successive operations can be much better understood in these more general settings compared to the string or graph settings. These generalizations for gene assembly are outlined in [4]. I 7 Here we recall the 4-regular graph representation that represents both the MIC and MAC form of a gene.…”