  Generative probabilistic models emerge as a new paradigm in data-driven,
evolution-informed design of biomolecular sequences. This paper introduces a
novel approach, called Edge Activation Direct Coupling Analysis (eaDCA),
tailored to the characteristics of RNA sequences, with a strong emphasis on
simplicity, efficiency, and interpretability. eaDCA explicitly constructs
sparse coevolutionary models for RNA families, achieving performance levels
comparable to more complex methods while utilizing a significantly lower number
of parameters. Our approach demonstrates efficiency in generating artificial
RNA sequences that closely resemble their natural counterparts in both
statistical analyses and SHAPE-MaP experiments, and in predicting the effect of
mutations. Notably, eaDCA provides a unique feature: estimating the number of
potential functional sequences within a given RNA family. For example, in the
case of cyclic di-AMP riboswitches (RF00379), our analysis suggests the
existence of approximately $\mathbf{10^{39}}$ functional nucleotide sequences.
While huge compared to the known $< \mathbf{4,000}$ natural sequences, this
number represents only a tiny fraction of the vast pool of nearly
$\mathbf{10^{82}}$ possible nucleotide sequences of the same length (136
nucleotides). These results underscore the promise of sparse and interpretable
generative models, such as eaDCA, in enhancing our understanding of the
expansive RNA sequence space.
