Collaborative Research: Branching in RNA Secondary Structures

该项目将开发数学工具，以更好地了解具有重要细胞功能的生物分子的结构。RNA是一种源于DNA的单链分子，在各种生物学作用中都是必不可少的。除了将储存在DNA中的信息转化为蛋白质外，一些RNA还控制着重要的细胞过程。RNA链必须折叠成特定的形状才能发挥这些作用。然而，尽管对常用的预测RNA结构的能量模型进行了一系列改进，但对较长RNA序列的折叠预测的准确性并不令人满意。这个项目将使用几何组合学来洞察当前能源模型预测的稳定性和准确性。解决这些与生物相关的问题导致了重要的数学问题，这些问题与多面体几何和离散优化领域的活跃研究领域相交。该项目的结果将用于改进预测RNA折叠的软件，并帮助分子生物学家研究RNA功能。此外，作为该项目的一部分，研究人员将培训研究生和本科生在数学和生物学的交界处进行研究。这项研究将在几何组合学和分子生物学的结合点上，在离散数学生物学的发展领域内促进生物学理解和数学知识。控制分支的熵代价的仿射能量函数是当前最近邻热力学模型的一个已知缺陷。然而，这种对生化现实的粗略近似受到计算效率的高度限制，非常适合于数学建模和分析。利用几何组合学的方法(多面体及其正规扇)首次对生物RNA序列的分支进行了参数分析。与生物学相关的问题，包括用于RNA二级结构预测的热力学优化方法中当前分支参数的准确性和稳定性，将使用几何组合学的方法来解决。然后将通过解决表征、比较和近似的挑战来描述这些RNA分支多面体的相似和不同之处。这将为当前预测方法无法区分本地分支特征和大量次优结构提供新的见解。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

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.