An Efficient Algorithm for Upper Bound on the Partition Function of Nucleic Acids

It has been shown that minimum free energy structure for RNAs and RNA-RNA interaction is often incorrect due to inaccuracies in the energy parameters and inherent limitations of the energy model. In contrast, ensemble based quantities such as melting temperature and equilibrium concentrations can be more reliably predicted. Even structure prediction by sampling from the ensemble and clustering those structures by Sfold [7] has proven to be more reliable than minimum free energy structure prediction. The main obstacle for ensemble based approaches is the computational complexity of the partition function and base pairing probabilities. For instance, the space complexity of the partition function for RNA-RNA interaction is $O(n^4)$ and the time complexity is $O(n^6)$ which are prohibitively large [4,12]. Our goal in this paper is to give a fast algorithm, based on sparse folding, to calculate an upper bound on the partition function. Our work is based on the recent algorithm of Hazan and Jaakkola [10]. The space complexity of our algorithm is the same as that of sparse folding algorithms, and the time complexity of our algorithm is $O(MFE(n)\ell)$ for single RNA and $O(MFE(m, n)\ell)$ for RNA-RNA interaction in practice, in which $MFE$ is the running time of sparse folding and $\ell \leq n$ ($\ell \leq n + m$) is a sequence dependent parameter

The Rna Newton Polytope And Learnability Of Energy Parameters

Computational RNA secondary structure prediction has been a topic of much research interest for several decades now. Despite all the progress made in the field, even the state-of-the-art algorithms do not provide satisfying results, and the accuracy of output is limited for all the existent tools. Very complex energy models, different parameter estimation methods, and recent machine learning approaches had not been the answer for this problem. We believe that the first step to achieve results with high quality is to use the energy model with the potential for predicting accurate output. Hence, it is necessary to have a systematic way to analyze the suitability of an energy model. We introduced the notion of learnability to measure this suitability. A learnable energy model has at least one subset of parameters that can render every known RNA to date the minimum free energy structure, which means 100% accuracy. We also found the necessary condition for a model to be learnable and implemented the dynamic programming based algorithm to asses this condition for a set of RNAs. This algorithm computes the convex hull of all possible feature vectors for a sequence. With the partition function as a polynomial, this convex hull is also the Newton polytope of the partition function. To the best of our knowledge, this is the first systematic approach for evaluating the inherent capability of an energy model