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FoldRNA - RNA secondary structure prediction through energy minimization
Program for RNA secondary structure prediction based on dynamic programming (Nussinov and Jackonson, 1978, Zuker, 2005). For energy calculation nearest neighbor energy rules are used. Pseudoknots are not allowed.
FoldRNA uses energy parameters similar to mfold.
FoldRNA uses energy parameters mainly from:
Turner D.H. and Sugimoto N. (1988) RNA structure prediction
Ann.Rev.Biophys.Biophys.Chem. 17, pp. 167-92; Table 1
METHOD DESCRIPTION:
FoldRNA predicts optimal and suboptimal secondary structures of RNA using
dynamic algorithm for energy minimization .
Solution of a long sequence is decomposed into solutions of smaller problems:
Let's define E(i,j) = minimum energy for subchain starting at i and ending at j, and a(i,j) = energy of pair i,j.
If values E(i,j) are calculated for line which is maximally close to main diagonal of matrix LxL, where L = sequence length.
(min. hairpin loop should have size not less than 3 nt), then we can find step by step this values for lines
next after this, using the following recursion scheme (4 possible cases):
Recursion (iteration over length):
E(i,j)=min{
E(i+1,j),
E(i,j-1),
E(i+1,j-1)+a(i,j),
min ( E(i,k) + E(k+1,j) )
i<k<j
}
When all matrix is filled, the programs searches for lowest value of E(i,j), and then restores by the matrix corresponding secondary structure and sends it to output.
Output example
Program RNAfold (Softberry Inc.) | Version 1.0
FoldRNA Vienna format:
Length: 183 Energy: -80.0 78% in Helices
10 20 30 40 50 60
GUGAAUGAAAGAGUUGGGACAAGAGAAACGCAAAGAAACUGACAGAAGAGAGUGAGCACA
((((..((.(((((((((((((((((.(((..((((..(((((((((((((((((((((.
70 80 90 100 110 120
CAAAGGCAAUUUGCAUAUCAUUGCACUUGCUUCUCUUGCGUGCUCACUGCUCUUUCUGUC
(((((((((..((((......)))).))))))...))).))))))))).))))).)))))
130 140 150 160 170 180
AGAUUCCGGUGCUGAUCUCUUUGGCCUGUCUUCGUUCUCUAUGUCUCAAUCUCUCUCUAU
))....(((.(((((.....)))))))))))))))))))).))))))))).))).))..)
190
CAC
)))
FoldRNA GCG format:
Length: 183 Energy: -80.0
1 G 0 2 183 1
2 U 1 3 182 2
3 G 2 4 181 3
4 A 3 5 180 4
5 A 4 6 0 5
6 U 5 7 0 6
7 G 6 8 177 7
8 A 7 9 176 8
9 A 8 10 0 9
10 A 9 11 174 10
11 G 10 12 173 11
12 A 11 13 172 12
13 G 12 14 170 13
14 U 13 15 169 14
15 U 14 16 168 15
16 G 15 17 167 16
17 G 16 18 166 17
18 G 17 19 165 18
19 A 18 20 164 19
20 C 19 21 163 20
21 A 20 22 162 21
22 A 21 23 160 22
23 G 22 24 159 23
24 A 23 25 158 24
25 G 24 26 157 25
26 A 25 27 156 26
27 A 26 28 0 27
28 A 27 29 155 28
29 C 28 30 154 29
30 G 29 31 153 30
31 C 30 32 0 31
32 A 31 33 0 32
33 A 32 34 152 33
34 A 33 35 151 34
35 G 34 36 150 35
36 A 35 37 149 36
37 A 36 38 0 37
38 A 37 39 0 38
39 C 38 40 122 39
40 U 39 41 121 40
41 G 40 42 120 41
42 A 41 43 119 42
43 C 42 44 118 43
44 A 43 45 117 44
45 G 44 46 116 45
46 A 45 47 114 46
47 A 46 48 113 47
48 G 47 49 112 48
49 A 48 50 111 49
50 G 49 51 110 50
51 A 50 52 108 51
52 G 51 53 107 52
53 U 52 54 106 53
54 G 53 55 105 54
55 A 54 56 104 55
56 G 55 57 103 56
57 C 56 58 102 57
58 A 57 59 101 58
59 C 58 60 100 59
60 A 59 61 0 60
61 C 60 62 98 61
62 A 61 63 97 62
63 A 62 64 96 63
64 A 63 65 92 64
65 G 64 66 91 65
66 G 65 67 90 66
67 C 66 68 89 67
68 A 67 69 88 68
69 A 68 70 87 69
70 U 69 71 0 70
71 U 70 72 0 71
72 U 71 73 85 72
73 G 72 74 84 73
74 C 73 75 83 74
75 A 74 76 82 75
76 U 75 77 0 76
77 A 76 78 0 77
78 U 77 79 0 78
79 C 78 80 0 79
80 A 79 81 0 80
81 U 80 82 0 81
82 U 81 83 75 82
83 G 82 84 74 83
84 C 83 85 73 84
85 A 84 86 72 85
86 C 85 87 0 86
87 U 86 88 69 87
88 U 87 89 68 88
89 G 88 90 67 89
90 C 89 91 66 90
91 U 90 92 65 91
92 U 91 93 64 92
93 C 92 94 0 93
94 U 93 95 0 94
95 C 94 96 0 95
96 U 95 97 63 96
97 U 96 98 62 97
98 G 97 99 61 98
99 C 98 100 0 99
100 G 99 101 59 100
101 U 100 102 58 101
102 G 101 103 57 102
103 C 102 104 56 103
104 U 103 105 55 104
105 C 104 106 54 105
106 A 105 107 53 106
107 C 106 108 52 107
108 U 107 109 51 108
109 G 108 110 0 109
110 C 109 111 50 110
111 U 110 112 49 111
112 C 111 113 48 112
113 U 112 114 47 113
114 U 113 115 46 114
115 U 114 116 0 115
116 C 115 117 45 116
117 U 116 118 44 117
118 G 117 119 43 118
119 U 118 120 42 119
120 C 119 121 41 120
121 A 120 122 40 121
122 G 121 123 39 122
123 A 122 124 0 123
124 U 123 125 0 124
125 U 124 126 0 125
126 C 125 127 0 126
127 C 126 128 148 127
128 G 127 129 147 128
129 G 128 130 146 129
130 U 129 131 0 130
131 G 130 132 145 131
132 C 131 133 144 132
133 U 132 134 143 133
134 G 133 135 142 134
135 A 134 136 141 135
136 U 135 137 0 136
137 C 136 138 0 137
138 U 137 139 0 138
139 C 138 140 0 139
140 U 139 141 0 140
141 U 140 142 135 141
142 U 141 143 134 142
143 G 142 144 133 143
144 G 143 145 132 144
145 C 144 146 131 145
146 C 145 147 129 146
147 U 146 148 128 147
148 G 147 149 127 148
149 U 148 150 36 149
150 C 149 151 35 150
151 U 150 152 34 151
152 U 151 153 33 152
153 C 152 154 30 153
154 G 153 155 29 154
155 U 154 156 28 155
156 U 155 157 26 156
157 C 156 158 25 157
158 U 157 159 24 158
159 C 158 160 23 159
160 U 159 161 22 160
161 A 160 162 0 161
162 U 161 163 21 162
163 G 162 164 20 163
164 U 163 165 19 164
165 C 164 166 18 165
166 U 165 167 17 166
167 C 166 168 16 167
168 A 167 169 15 168
169 A 168 170 14 169
170 U 169 171 13 170
171 C 170 172 0 171
172 U 171 173 12 172
173 C 172 174 11 173
174 U 173 175 10 174
175 C 174 176 0 175
176 U 175 177 8 176
177 C 176 178 7 177
178 U 177 179 0 178
179 A 178 180 0 179
180 U 179 181 4 180
181 C 180 182 3 181
182 A 181 183 2 182
183 C 182 184 0 183