Insertions and Deletions: Computational Methods, Evolutionary Dynamics, and Biological Applications

Insertions and deletions constitute the second most important source of natural genomic variation. Insertions and deletions make up to 25% of genomic variants in humans and are involved in complex evolutionary processes including genomic rearrangements, adaptation, and speciation. Recent advances in long-read sequencing technologies allow detailed inference of insertions and deletion variation in species and populations. Yet, despite their importance, evolutionary studies have traditionally ignored or mishandled insertions and deletions due to a lack of comprehensive methodologies and statistical models of insertions and deletion dynamics. Here, we discuss methods for describing insertions and deletion variation and modeling insertions and deletions over evolutionary time. We provide practical advice for tackling insertions and deletions in genomic sequences and illustrate our discussion with examples of insertions and deletion-induced effects in human and other natural populations and their contribution to evolutionary processes. We outline promising directions for future developments in statistical methodologies that would allow researchers to analyze insertions and deletion variation and their effects in large genomic data sets and to incorporate insertions and deletions in evolutionary inference.

Sensitive inference of alignment-safe intervals from biodiverse protein sequence clusters using EMERALD

Sequence alignments are the foundations of life science research, but most innovation so far focuses on optimal alignments, while information derived from suboptimal solutions is ignored. We argue that one optimal alignment per pairwise sequence comparison is a reasonable approximation when dealing with very similar sequences but is insufficient when exploring the biodiversity of the protein universe at tree-of-life scale. To overcome this limitation, we introduce pairwise alignment-safety to uncover the amino acid positions robustly shared across all suboptimal solutions. We implement EMERALD, a software library for alignment-safety inference, and apply it to 400k sequences from the SwissProt database.

A probabilistic model for indel evolution: differentiating insertions from deletions

Insertions and deletions (indels) are common molecular evolutionary events. However, probabilistic models for indel evolution are under-developed due to their computational complexity. Here, we introduce several improvements to indel modeling: 1) While previous models for indel evolution assumed that the rates and length distributions of insertions and deletions are equal, here we propose a richer model that explicitly distinguishes between the two; 2) we introduce numerous summary statistics that allow approximate Bayesian computation-based parameter estimation; 3) we develop a method to correct for biases introduced by alignment programs, when inferring indel parameters from empirical data sets; and 4) using a model-selection scheme, we test whether the richer model better fits biological data compared with the simpler model. Our analyses suggest that both our inference scheme and the model-selection procedure achieve high accuracy on simulated data. We further demonstrate that our proposed richer model better fits a large number of empirical data sets and that, for the majority of these data sets, the deletion rate is higher than the insertion rate.

The Cumulative Indel Model: Fast and Accurate Statistical Evolutionary Alignment

Sequence alignment is essential for phylogenetic and molecular evolution inference, as well as in many other areas of bioinformatics and evolutionary biology. Inaccurate alignments can lead to severe biases in most downstream statistical analyses. Statistical alignment based on probabilistic models of sequence evolution addresses these issues by replacing heuristic score functions with evolutionary model-based probabilities. However, score-based aligners and fixed-alignment phylogenetic approaches are still more prevalent than methods based on evolutionary indel models, mostly due to computational convenience. Here, I present new techniques for improving the accuracy and speed of statistical evolutionary alignment. The "cumulative indel model" approximates realistic evolutionary indel dynamics using differential equations. "Adaptive banding" reduces the computational demand of most alignment algorithms without requiring prior knowledge of divergence levels or pseudo-optimal alignments. Using simulations, I show that these methods lead to fast and accurate pairwise alignment inference. Also, I show that it is possible, with these methods, to align and infer evolutionary parameters from a single long synteny block ($\approx$530 kbp) between the human and chimp genomes. The cumulative indel model and adaptive banding can therefore improve the performance of alignment and phylogenetic methods. [Evolutionary alignment; pairHMM; sequence evolution; statistical alignment; statistical genetics.].

A Model of Indel Evolution by Finite-State, Continuous-Time Machines

We introduce a systematic method of approximating finite-time transition probabilities for continuous-time insertion-deletion models on sequences. The method uses automata theory to describe the action of an infinitesimal evolutionary generator on a probability distribution over alignments, where both the generator and the alignment distribution can be represented by pair hidden Markov models (HMMs). In general, combining HMMs in this way induces a multiplication of their state spaces; to control this, we introduce a coarse-graining operation to keep the state space at a constant size. This leads naturally to ordinary differential equations for the evolution of the transition probabilities of the approximating pair HMM. The TKF91 model emerges as an exact solution to these equations for the special case of single-residue indels. For the more general case of multiple-residue indels, the equations can be solved by numerical integration. Using simulated data, we show that the resulting distribution over alignments, when compared to previous approximations, is a better fit over a broader range of parameters. We also propose a related approach to develop differential equations for sufficient statistics to estimate the underlying instantaneous indel rates by expectation maximization. Our code and data are available at https://github.com/ihh/trajectory-likelihood.

Statistical compression of protein sequences and inference of marginal probability landscapes over competing alignments using finite state models and Dirichlet priors

The information criterion of minimum message length (MML) provides a powerful statistical framework for inductive reasoning from observed data. We apply MML to the problem of protein sequence comparison using finite state models with Dirichlet distributions. The resulting framework allows us to supersede the ad hoc cost functions commonly used in the field, by systematically addressing the problem of arbitrariness in alignment parameters, and the disconnect between substitution scores and gap costs. Furthermore, our framework enables the generation of marginal probability landscapes over all possible alignment hypotheses, with potential to facilitate the users to simultaneously rationalize and assess competing alignment relationships between protein sequences, beyond simply reporting a single (best) alignment. We demonstrate the performance of our program on benchmarks containing distantly related protein sequences.

AVAILABILITY AND IMPLEMENTATION

The open-source program supporting this work is available from: http://lcb.infotech.monash.edu.au/seqmmligner.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.