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. 2009 Aug 28;5(8):e1000483. doi: 10.1371/journal.pcbi.1000483

Table 2. Singlet transducer (single-sequence SCFG) of the TKF Structure Tree model.

Source→Destinatioon probability Source→Destinatioon probability
Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic Inline graphic
Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic Inline graphic Inline graphic Inline graphic
Inline graphic Inline graphic
Inline graphic 1
Inline graphic 1

The state types for this model are shown in Table 1. The singlet transducer generates ancestral RNA sequences and structures. We use the notation of formal grammars to represent state transformation rules; for example, the rule Inline graphic corresponds to (in a Pair HMM) an Inline graphic state Inline graphic emitting a nucleotide Inline graphic and then making a self-transition. Both loop (Inline graphic and Inline graphic) and stem (Inline graphic and Inline graphic) sequence evolve as TKF sequences with length parameters Inline graphic and Inline graphic (defined in “A simple model of RNA structural evolution”). Inline graphic and Inline graphic are the equilibrium distributions of unpaired nucleotides Inline graphic and paired nucleotides Inline graphic and are normalized such that Inline graphic and Inline graphic. The bifurcation state Inline graphic is used to end stem sequences (only loop sequences are allowed to transition to the empty string).