Collaborative Research: Branching in RNA Secondary Structures

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This project will develop mathematical tools to better understand the structure of biomolecules with important cellular functions. RNA, a single-strand molecule derived from DNA, is essential in various biological roles. Besides converting the information stored in DNA into proteins, some RNAs control vital cell processes. RNA chains must fold into specific shapes to serve these roles. However, despite the series of refinements to the commonly-used energy model for predicting RNA structure, the accuracy of folding predictions for longer RNA sequences is not satisfying. This project will use geometric combinatorics to gain insights into the stability and accuracy of predictions from the current energy model. Addressing these biologically relevant questions leads to important mathematical problems which intersect with active research areas in polyhedral geometry and discrete optimization. Results from this project will be used to improve software predicting RNA folding and assist molecular biologists studying RNA function. Additionally, as part of the project, the investigators will train graduate and undergraduate students in research at the interface of mathematics and biology.This research will advance biological understanding and mathematical knowledge within the developing field of discrete mathematical biology at the juncture between geometric combinatorics and molecular biology. The affine energy function which governs the entropic cost of branching is a known shortcoming of the current nearest neighbor thermodynamic model. However, this coarse approximation to biochemical reality, which is highly constrained by computational efficiency, is well-suited to mathematical modeling and analysis. Methods from geometric combinatorics (polytopes and their normal fans) will be used to give the first parametric analysis of the branching of biological RNA sequences. Biologically relevant questions, including the accuracy and stability of the current branching parameters in thermodynamic optimization methods for RNA secondary structure prediction, will be addressed using methods from geometric combinatorics. The similarities and differences of these RNA branching polytopes will then be delineated by addressing the challenges of characterization, comparison, and approximation. This will provide new insight into the inability of current prediction methods to distinguish native branching characteristics from the large number of suboptimal structures.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.