Suffix conjugates for a class of morphic subshifts

Let A be a finite alphabet and f: A^* --> A^* be a morphism with an iterative fixed point f^\omega(\alpha), where \alpha{} is in A. Consider the subshift (X, T), where X is the shift orbit closure of f^\omega(\alpha) and T: X --> X is the shift map. Let S be a finite alphabet that is in bijective correspondence via a mapping c with the set of nonempty suffixes of the images f(a) for a in A. Let calS be a subset S^N be the set of infinite words s = (s_n)_{n\geq 0} such that \pi(s):= c(s_0)f(c(s_1)) f^2(c(s_2))... is in X. We show that if f is primitive and f(A) is a suffix code, then there exists a mapping H: calS --> calS such that (calS, H) is a topological dynamical system and \pi: (calS, H) --> (X, T) is a conjugacy; we call (calS, H) the suffix conjugate of (X, T). In the special case when f is the Fibonacci or the Thue-Morse morphism, we show that the subshift (calS, T) is sofic, that is, the language of calS is regular

Molecular principles underlying dual RNA specificity in the Drosophila SNF protein

The first RNA recognition motif of the Drosophila SNF protein is an example of an RNA binding protein with multi-specificity. It binds different RNA hairpin loops in spliceosomal U1 or U2 small nuclear RNAs, and only in the latter case requires the auxiliary U2A′ protein. Here we investigate its functions by crystal structures of SNF alone and bound to U1 stem-loop II, U2A′ or U2 stem-loop IV and U2A′, SNF dynamics from NMR spectroscopy, and structure-guided mutagenesis in binding studies. We find that different loop-closing base pairs and a nucleotide exchange at the tips of the loops contribute to differential SNF affinity for the RNAs. U2A′ immobilizes SNF and RNA residues to restore U2 stem-loop IV binding affinity, while U1 stem-loop II binding does not require such adjustments. Our findings show how U2A′ can modulate RNA specificity of SNF without changing SNF conformation or relying on direct RNA contacts