TABLE I.
Measuring Ruggedness of Stability and Folding Rate Maps
| Stability map (Scheme A) |
Stability map (Scheme B) |
Folding rate map (Scheme A) |
Folding rate map (Scheme B) |
|||||
|---|---|---|---|---|---|---|---|---|
| da | Ne (re%)b | Nn (rn%)c | Ne (re%)b | Nn (rn%)c | Ne (re%)b | Nn (rn%)c | Ne (re%)b | Nn (rn%)c |
| 1 | 94 (99%) | 13 (–) | 214 (93%) | 17 (–) | 26 (88%) | 10 (–) | 58 (91%) | 10 (–) |
| 2 | 180 (97%) | 48 (96%) | 996 (88%) | 111 (95%) | 106 (84%) | 16 (87%) | 193 (87%) | 34 (88%) |
| 3 | 165 (87%) | 67 (85%) | 2400 (85%) | 373 (97%) | 176 (80%) | 53 (96%) | 547 (83%) | 90 (81%) |
| 4 | 143 (82%) | 53 (77%) | 3428 (81%) | 731 (98%) | 174 (84%) | 64 (95%) | 1171 (85%) | 214 (82%) |
| 5 | 88 (89%) | 51 (98%) | 3050 (77%) | 908 (99%) | 143 (81%) | 56 (98%) | 1852 (76%) | 393 (82%) |
| 6 | 15 (80%) | 25 (100%) | 1735 (76%) | 751 (99%) | 51 (71%) | 43 (100%) | 2325 (75%) | 538 (82%) |
| 7 | 3 (100%) | 568 (76%) | 422 (99%) | 12 (50%) | 15 (100%) | 2349 (73%) | 631 (86%) | |
| 8 | 74 (81%) | 148 (99%) | 3 (100%) | 1943 (71%) | 616 (85%) | |||
| 9 | 1 (0%) | 23 (96%) | 1231 (72%) | 485 (86%) | ||||
| 10 | 1 (0%) | 563 (63%) | 289 (91%) | |||||
| 11 | 197 (63%) | 124 (85%) | ||||||
| 12 | 41 (63%) | 50 (94%) | ||||||
| 13 | 3 (100%) | 10 (90%) | ||||||
| 14 | 1 (100%) | |||||||
d, the distance from the optimal sequence can be defined for a node, which is a sequence with the target structure as the unique global energy minimum, or for an edge, which is a single mutation that connects two nodes. For a node, d is defined as the Hamming distance between the node and the optimal sequence. For an edge, d is defined to be the smaller d of the two nodes it connects. Note that the optimal sequences are different in all four maps studied (see circled sequences in Fig. 1 and Fig. 2).
Edge-based analysis. All edges are classified as either pointing toward the optimal sequence or otherwise. An edge points toward the optimal sequence if and only if between the two nodes that the edge connects, the node closer to the optimal sequence also has a higher stability or folding rate. Ne is the total number of edges for a given distance d from the optimal sequence. re is the percentage of these edges that point toward the optimal sequence.
Node-based analysis. All nodes are classified as either pointing toward the optimal sequence or otherwise. A node points toward the optimal sequence if among the neighboring nodes (including itself), the node with the highest stability or folding rate is also closer to the optimal sequence than the current node. Nn is the total number of nodes for a given distance d from the optimal sequence. rn is the percentage of these nodes that point toward the optimal sequence.