LNCS 2950 - Aspects of Molecular Computing (Frontmatter Pages)

An Algorithm for Testing Structure Freeness of Biomolecular Sequences 269
The loop length of a hairpin c with a base pair (i, j) is defined as the number
of unpaired bases j − i − 1. The loop length of a bulge loop or an internal loop
with base pairs (i, j) and(p, q) ((p, q) < (i, j)) is also defined as the number of
unpaired bases p − i + j − q − 2. The loop length mismatch of an internal loop
with base pairs (i, j) and(p, q) ((p, q) < (i, j)) is defined as |(p − i) − (j − q)|.
Let (i, j) be the element in T such that for any (p, q) ∈ T with (p, q) �= (i, j),
(p, q) < (i, j) holds.SinceTis linear, such an element is determined uniquely.
Then, the substructure of α(T ) consisting of the pair (i, j) and unpaired bases
which are not surrounded by (i, j) is called a free end structure of α(T ).
By |α) we denote a hairpin consisting of a sequence α with a base pair
between α[1] and α[|α|]. By |−→ α|
|β|
we denote a 2-cycle consisting of two sequences
←−
α and β with base pairs between α[1] and β[|β|] and between α[|α|] andβ[1].
−→
α|
By β|
we denote a free end structure consisting of two sequences α and β with
←−
a base pair between α[|α|] andβ[1].
2.2 Free Energy Calculation
Free energy value is assigned to each cycle or free end structure. Experimental
evidence is used to determine such free energy values. The method for assigning
free energy values is given as follows 5 : (See Figure 1.)
1.ThefreeenergyE(c) of a hairpin c with a base pair (i, j) is dependent on
the base pair (i, j), the bases i+1,j−1 adjacent to (i, j), and its loop length
l:
E(c) =h1(α[i],α[j],α[i +1],α[j − 1]) + h2(l),
where h1,h2 are experimentally obtained functions. The function h2 is positive
and there exists a constant L such that for the range l>L, h2 is weakly
monotonically increasing.
2. The free energy E(c) of a stacked pair c with base pairs (i, j)and(i+1,j−1)
is dependent on the base pairs (i, j), (i +1,j− 1):
E(c) =s1(α[i],α[j],α[i +1],α[j − 1]),
where s1 is an experimentally obtained function.
3. ThefreeenergyE(c) of a bulge loop c with base pairs (i, j)and(p, q)((p, q) <
(i, j)) is dependent on the base pairs (i, j), (p, q), and its loop length l:
E(c) =b1(α[i],α[j],α[p],α[q]) + b2(l),
where b1,b2 are experimentally obtained functions. The function b2 is positive
and weakly monotonically increasing.
5 The calculation method presented here is in a general form so that it can be specialized
to be equivalent to the one used in standard RNA packages such as ViennaRNA
([13]), mfold ([18]), etc.