LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

206 Tero Harju, Ion Petre, and Grzegorz Rozenberg
Example 6. Consider the micronuclear MDS arrangement of the actin I gene of
Sterkiella nova: α = M3M4M6M5M7M9M 2M1M8. Wehave
ϱ9(α) = 34 45 67 56 78 9 3 2289.
Since α is a realistic MDS arrangement, ϱ9(α) is a realistic legal string. ✷
The following example shows that there exist legal strings that are not realistic.
Example 7. The string u =234324islegal,butitisnotrealistic,sinceithasno
‘realistic parsing’. Indeed, suppose that there exists a realistic MDS arrangement
α such that u = ϱ4(α). Clearly, α must end with the MDS M4, sinceϱ4(M) �= 24
for all MDSs M. Similarly, since ϱ4(M) �= 32 for all MDSs M, α must end with
M2M4. Now,however,u = 2343ϱ4(M2M4) gives a contradiction, since 3 and
43 are not images of any MDSs M. ✷
4 Overlap Graphs of Legal Strings
Let u = a1a2 ...an ∈ Σ � be a legal string over Σ, whereai ∈ Σ ∪ Σ for each i.
Let for each letter a ∈ dom(u), i and j with 1 ≤ i