Modeling RNA sequence-structure-function relationships with multiscale higher-order graph neural networks

Abstract: RNAs play central roles in regulating, maintaining, and defending the genomes of all organisms, with regulatory RNA sequences controlling almost all aspects of gene expression. Many of these RNA functions are linked to RNA structures that mediate interactions amongst cellular gene expression machinery, bind ligands, and perform catalysis. A central goal in biology then has been to solve the ‘RNA folding problem’ – to understand how RNA sequence determines RNA folding which governs RNA function. Once deciphered, the solution to the RNA folding problem would improve our understanding of living systems and our ability to program RNAs for biotechnologies. Graph neural networks (GNNs) are a promising new mathematical approach to modeling biomolecules, but currently do not have the mathematical properties needed to capture the features of large RNA molecules that can exist in multiple states. Here we propose to develop a new theory of graph modeling that encodes multiscale interactions within the graph architecture, preserving necessary properties of equivariance. To do so, we will derive new mathematical relationships of multiscale equivariant message passing and prove that the resulting model is the most general possible permutation equivariant multiscale neural architecture. By advancing the theory of higher order multiscale GNNs we will create a new, broadly applicable general class of neural architectures, which will apply to create a new approach to modeling RNA sequence-structure-function relationships.