LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

Digital Information Encoding on DNA 161
Fig. 3. Code size in error-preventing DNA Codes. Also shown are the percentages
of pairwise Gibbs energies in three regions for each code (crosshybridizing:
third bar from top, and noncrosshybrizing: top two.)
the mildest hybridization condition represented by such large τ. LetN = |B| be
the cardinality of B. Without loss of generality, it will be assumed that strings
to be encoded are written in a four letter alphabet {a, c, g, t}.
Given a string x (ordinarily much larger than n), x is said to be h-dependent
of B is there some concatenation c of elements of B such that x will hybridize to
c under stringency τ, i.e., |c, x| ≤τ. Shredding x to the corresponding fragments
according to the components of c in B leads to the following slightly weaker but
more manageable definition. The signature of x with respect to B is a vector V
of size N obtained as follows. Shredding x to |X|/n fragments of size n or less,
Vi is the number of fragments f of x that are within threshold τ of strand i in
B, i.e., such that |f,i|