A stitch in time: Efficient computation of genomic DNA melting bubbles

TL;DR

This paper introduces an efficient O(NlogN) algorithm for genome-wide prediction of DNA melting bubbles, enabling rapid and exact computation of stitch profiles without approximations, useful for various genomic analyses.

Contribution

The paper presents a novel algorithm that significantly reduces the computational complexity of predicting DNA melting bubbles from quadratic to O(NlogN), without relying on approximations.

Findings

Algorithm achieves O(NlogN) complexity for genome-wide predictions.

Able to compute sequences of several megabases within memory limits.

Produces probabilistic stitch profiles for detailed genomic analysis.

Abstract

Background: It is of biological interest to make genome-wide predictions of the locations of DNA melting bubbles using statistical mechanics models. Computationally, this poses the challenge that a generic search through all combinations of bubble starts and ends is quadratic. Results: An efficient algorithm is described, which shows that the time complexity of the task is O(NlogN) rather than quadratic. The algorithm exploits that bubble lengths may be limited, but without a prior assumption of a maximal bubble length. No approximations, such as windowing, have been introduced to reduce the time complexity. More than just finding the bubbles, the algorithm produces a stitch profile, which is a probabilistic graphical model of bubbles and helical regions. The algorithm applies a probability peak finding method based on a hierarchical analysis of the energy barriers in the Poland-Scheraga model. Conclusions: Exact and fast computation of genomic stitch profiles is thus feasible. Sequences of several megabases have been computed, only limited by computer memory. Possible applications are the genome-wide comparisons of bubbles with promotors, TSS, viral integration sites, and other melting-related regions.