Color Coding for the Fragment-Based Docking, Design and Equilibrium Statistics of Protein-Binding ssRNAs.

We revisit the fragment-based docking and design of single-stranded RNA aptamers (ssRNAs), consisting of k nucleotides, onto a rigid protein. Fragments, representing short sequences of (modified) nucleotides, are individually docked as poses onto the protein surface using a force field. Compatible poses are then assembled while optimizing for an additive notion of energy, to obtain stable conformations that can either be constrained to represent an input ssRNA sequence (docking) or left unconstrained (design). However, a brute-force enumeration of clash-free conformations quickly becomes prohibitive due to their superexponential ( Θ ( n k ) worst-case) combinatorial explosion, hindering the potential of fragment-based methods towards docking and design. In this work, we adapt the color-coding technique, introduced by Alon, Yuster and Zwick, to optimize over self-avoiding fragment assemblies in time/space linear on n the number of poses, and in time only exponential on k the number of fragments. The dynamic programming algorithm at the core of our method is surprisingly simple, and can be extended to produce suboptimal candidates, or modified to perform Boltzmann sampling of candidates assemblies. Using a rejection principle, and further optimized by a clique decomposition of clashing poses, these algorithms can be leveraged into efficient algorithms optimizing over clash-free complexes. The resulting sampling procedure can further be adapted into statistically-consistent estimators for any computable feature of interest. We showcase some of the capabilities of this new framework by reanalyzing a set of 7 documented ssRNA-protein complexes, demonstrating its practical relevance and versatility.