PMC:1459172 / 6116-10736
Annnotations
{"target":"https://pubannotation.org/docs/sourcedb/PMC/sourceid/1459172","sourcedb":"PMC","sourceid":"1459172","source_url":"https://www.ncbi.nlm.nih.gov/pmc/1459172","text":"RNA secondary structures\nA secondary structure S on a sequence x of length n is a set of base pairs (i, j), i \u003cj, such that\n0 (i, j) ∈ S implies that (xi, xj) is either a Watson-Crick (GC or AU) or a wobble (GU) base pair.\n1 Every sequence position i takes part in at most one base pair, i.e., S is a matching in the graph of \"legal\" base pairs that can be formed within sequence x.\n2 (i, j) ∈ S implies |i - j| ≥ 4, i.e., hairpin loops have at least three unpaired positions inside their closing pair.\n3 If (i, j) ∈ S and (k, l) ∈ S with i \u003ck, then either i \u003cj \u003ck \u003cl or i \u003ck \u003cl \u003cj. This condition rules out knots and pseudoknots. Together with condition 1 it implies that S is a circular matching [32,33].\nThe \"loops\" of S are planar faces of the unique planar embedding of the secondary structure graph (whose edges are the base pairs in S together with the backbone edges (i, i + 1), i = 1 ..., n - 1). Equivalently, the loops are the elements of the unique minimum cycle basis of the secondary structure graph [34]. The external loop consists of all those nucleotides that are not enclosed by a base pair in S. The standard energy model for RNA secondary structures associates an energy contribution to each loop L that depends on the loop type type(L) (hairpin loop, interior loop, bulge, stacked pair, or multi-branch loop) and the sequence of some or all of the nucleotides in the loop, x|L:\nε(L) = ε(type(L), x|L). (1)\nThe external loop does not contribute to the folding energy. The total energy of folding sequence x into a secondary structure S is then the sum over all loops of S. Energy parameters are available for both RNA [35] and single stranded DNA [36].\nHairpin loops are uniquely determined by their closing pair (i, j). The energy of a hairpin loop is tabulated in the form\n(i, j) = (xi, xi+1, ℓ, xj-1, xj) (2)\nwhere ℓ is the length of the loop (expressed as the number of its unpaired nucleotides). Each interior loop is determined by the two base pairs enclosing it. Its energy is tabulated as\n(i, j; k, l) = (xi, xi+1; ℓ1; xk-1, xk; xl, xl+1; ℓ2; xj-1, xj) (3)\nwhere ℓ1 is the length of the unpaired strand between i and k and ℓ2 is the length of the unpaired strand between l and j. Symmetry of the energy model dictates (i, j; k, l) = (l, k; j, i). If ℓ1 = ℓ2 = 0 we have a (stabilizing) stacked pair, if only one of ℓ1 and ℓ2 vanish we have a bulge. For multiloops, finally we have an additive energy model of the form = a + b × β + c × ℓ where ℓ is the length of multiloop (again expressed as the number of unpaired nucleotides) and β is the number of branches, not counting the branch in which the closing pair of the loop resides.\nSo-called dangling end contributions arise from the stacking of unpaired bases to an adjacent base pair. We have to distinguish two types of dangling ends: (1) interior dangles, where the unpaired base i + 1 stacks onto i of the adjacent basepair (i, j) and correspondingly j - 1 stacks onto j and (2) exterior dangles, where i - 1 stack onto i and j + 1 stacks on j. The corresponding energy contributions are denoted by and , respectively. Within the additive energy model, dangling end terms are interpreted as the contribution of 3' and 5' dangling nucleotides:\nHere | separates the dangling nucleotide position from the adjacent base pair, d5' (k - 1|k, l) thus is the energy of the nucleotide at position k - 1 when interacting with following base pair (k, l), while d3' (k, l|l + 1) scores the interaction of position l + 1 with the preceding pair (k, l).\nThe Vienna RNA Package currently implements three different models for handling the dangling-end contributions: They can be (a) ignored, (b) taken into account for every combination of adjacent bases and base pairs, or (c) a more complex model can be used in which the unpaired base can stack with at most one base pair. In cases (a) and (b) one can absorb the dangling end contributions in the loop energies (with the exception of contributions in the external loop). Model (c) strictly speaking violates the secondary structure model in that an unpaired base xi between two base pairs (xp, xi-1) and (xi+1, xq) has three distinct states with different energies: xi does not stack to its neighbors, xi stacks to xi-1, or xi+1. The algorithm then minimizes over these possibilities. While model (c) is the default for computing minimum free energy structures in most implementations such as RNAfold and mfold, it is not tractable in a partition function approach in a consistent way unless different positions of the dangling ends are explicitly treated as different configurations.","divisions":[{"label":"title","span":{"begin":0,"end":24}},{"label":"p","span":{"begin":25,"end":123}},{"label":"p","span":{"begin":124,"end":222}},{"label":"p","span":{"begin":223,"end":382}},{"label":"p","span":{"begin":383,"end":502}},{"label":"p","span":{"begin":503,"end":706}},{"label":"p","span":{"begin":707,"end":1398}},{"label":"p","span":{"begin":1399,"end":1430}},{"label":"p","span":{"begin":1431,"end":1676}},{"label":"p","span":{"begin":1677,"end":1798}},{"label":"p","span":{"begin":1799,"end":1839}},{"label":"p","span":{"begin":1840,"end":2024}},{"label":"p","span":{"begin":2025,"end":2096}},{"label":"p","span":{"begin":2097,"end":2673}},{"label":"p","span":{"begin":2674,"end":3240}},{"label":"p","span":{"begin":3241,"end":3537}}],"tracks":[{"project":"2_test","denotations":[{"id":"16722605-10329189-1692552","span":{"begin":1643,"end":1645},"obj":"10329189"},{"id":"16722605-9465037-1692553","span":{"begin":1672,"end":1674},"obj":"9465037"}],"attributes":[{"subj":"16722605-10329189-1692552","pred":"source","obj":"2_test"},{"subj":"16722605-9465037-1692553","pred":"source","obj":"2_test"}]}],"config":{"attribute types":[{"pred":"source","value type":"selection","values":[{"id":"2_test","color":"#99ec93","default":true}]}]}}