Entropy predicts sensitivity of pseudorandom seeds

Abstract

Seed design is important for sequence similarity search applications such as read mapping and average nucleotide identity (ANI) estimation. Whilek-mers and spacedk-mers are likely the most well-known and used seeds, sensitivity suffers at high error rates, particularly when indels are present. Recently, we developed a pseudo-random seeding construct, strobemers, which were empirically demonstrated to have high sensitivity also at high indel rates. However, the study lacked a deeper understanding of why. In this study, we propose a model to estimate the entropy of a seed and find that seeds with high entropy, according to our model, in most cases have high match sensitivity. Our discovered seed randomness-sensitivity relationship explains why some seeds perform better than others, and the relationship provides a framework for designing even more sensitive seeds. We also present three new strobemer seed constructs, mixedstrobes, altstrobes, and multistrobes. We use both simulated and biological data to demonstrate that our new seed constructs improve sequence-matching sensitivity to other strobemers. We show that the three new seed constructs are useful for read mapping and ANI estimation. For read mapping, we implement strobemers into minimap2 and observe 30% faster alignment time and 0.2% higher accuracy than usingk-mers when mapping reads at high error rates. As for ANI-estimation, we find that higher entropy seeds have a higher rank correlation between estimated and true ANI.

Designing efficient randstrobes for sequence similarity analyses

“…For the runtime, we evaluated randstrobes parametrized as ( n = 2, l = 20, w min = 21, w max = 100) and ( n = 2, l = 20, w min = 21, w max = 1000) since the window size affects runtime. Strobemers with n > 3 show no substantial gain in the context of sequence matching at the cost of additional runtime [12](although they have been modified and used for specific scenarios [8]). Also, the relative performance can be extrapolated from the n = 2 and n = 3 cases, since the construction is recursive, therefore, we omit them in this study.…”

“…The methods to select strobes differ [18], and using alternating strobe lengths has also been explored [12]. However, randstrobes were shown to be more sensitive for sequence matching than other methods using fixed strobe lengths (minstrobes and hybridstrobes) [18], and simpler to construct than alternating strobe lengths (altstrobes and multistrobes) [12], and is so far most commonly implemented in practice, e.g., [20,15,23]. Therefore, we will consider only the randstrobes method in this study.…”

“…In [12], we also found that the sensitivity of strobemers, measured as producing at least one seed match in a mutated region of fixed length, is strongly correlated with the pseudo-randomness of the seed construct (measured through entropy), where higher entropy yields higher sensitivity. In [12], we also introduced new strobemer variations, further improving sequence matching performance. Despite the introduction of these new variations, randstrobes remain the simplest and most used construct.…”

“…While there are applications that use other strobemer types [8], randstrobes have been most frequently used, e.g., for short-read mapping [20], transcriptomic long-read normalization [15], and read classification [23] in bioinformatic applications. Our recent proof-of-concept study also shows that randstrobes can provide accurate sequence similarity ranking through estimating the Jaccard distance [12].…”

“…As randomness is important for sensitivity [12], we propose several new methods to perform the core operations in randstrobes (hashing, linking, and comparison) beyond previously published methods [18,20,23]. We also observe several types of bias (Fig.…”