Sequences Associated with Transitions

The example

CGGAUGUGCGUAGACCGAUCGGGCUGUAGCCAGGGAGCUAACGAAACCGUGUGAACCAUCCGCACUGCAUCUGACA
27 (((((((.(((((.((.....)))).((((......))))))).....(((((.......))))).)))))))...
GGGAUGCACGUGGACCGGGAAGGCUGUAGCGAACGAGCUAACGAAAACGUGCAAGUGAAGUGCACUGCAUCCCCGG
GGGAUGCACGUGGACCGGGAAGGCUGUAGCUAACGAGCUAACGAAAACGUGCAAGUGAAGUGCACUGCAUCCCCGG
28 (((((((.(((((.((.....)))).(((((....)))))))).....(((((.......))))).)))))))...
GGGAUGCACGUAGACCGGGAAGGCUGUAGCGAAGGCGCUAGCGAAGAUGUGCGAAUUUAAUGCACCGUGUCCCAAU
shows the sequences underlying the transition from shape 27 on the evolutionary path of Figure 1A to shape 28. The shapes are represented by a "balanced parentheses" notation.

The first sequence S1 (preceding the representation of shape 27) is derived from the preceding sequence folding into shape 26 (not shown) by a point mutation at the position indicated in red. S1 folds into shape 27, and, according to our definition of an evolutionary path, it innovates the reactor with that shape. The next sequence, S2, (shown after shape 27) is another sequence folding into shape 27. S2 mutated at the red position and gave rise to the next sequence in the table which at that time innovated the reactor with shape 28. S1 and S2 are neutral sequences folding both into 27. They are separated by about 116 time units (see the Evolutionary Path Table). S1 and S2 differ at the positions indicated in blue which show the accumulation of neutral mutations while the trajectory drifted for 116 time units on the neutral sequence network associated with shape 27 (which, by the way, has no fitness advantage over shape 28). With regard to Figure 1A S1 is the sequence associated with the green step on shape 27, and S2 is the sequence associated with leaving the plateau of 27, stepping on shape 28.

See the discussion for some more observations.