Statistical framework to determine indel-length distribution.

MOTIVATION: Insertions and deletions (indels) of short DNA segments, along with substitutions, are the most frequent molecular evolutionary events. Indels were shown to affect numerous macro-evolutionary processes. Because indels may span multiple positions, their impact is a product of both their rate and their length distribution. An accurate inference of indel-length distribution is important for multiple evolutionary and bioinformatics applications, most notably for alignment software. Previous studies counted the number of continuous gap characters in alignments to determine the best-fitting length distribution. However, gap-counting methods are not statistically rigorous, as gap blocks are not synonymous with indels. Furthermore, such methods rely on alignments that regularly contain errors and are biased due to the assumption of alignment methods that indels lengths follow a geometric distribution. RESULTS: We aimed to determine which indel-length distribution best characterizes alignments using statistical rigorous methodologies. To this end, we reduced the alignment bias using a machine-learning algorithm and applied an Approximate Bayesian Computation methodology for model selection. Moreover, we developed a novel method to test if current indel models provide an adequate representation of the evolutionary process. We found that the best-fitting model varies among alignments, with a Zipf length distribution fitting the vast majority of them. AVAILABILITY AND IMPLEMENTATION: The data underlying this article are available in Github, at https://github.com/elyawy/SpartaSim and https://github.com/elyawy/SpartaPipeline.

An Approximate Bayesian Computation Approach for Modeling Genome Rearrangements.

The inference of genome rearrangement events has been extensively studied, as they play a major role in molecular evolution. However, probabilistic evolutionary models that explicitly imitate the evolutionary dynamics of such events, as well as methods to infer model parameters, are yet to be fully utilized. Here, we developed a probabilistic approach to infer genome rearrangement rate parameters using an Approximate Bayesian Computation (ABC) framework. We developed two genome rearrangement models, a basic model, which accounts for genomic changes in gene order, and a more sophisticated one which also accounts for changes in chromosome number. We characterized the ABC inference accuracy using simulations and applied our methodology to both prokaryotic and eukaryotic empirical datasets. Knowledge of genome-rearrangement rates can help elucidate their role in evolution as well as help simulate genomes with evolutionary dynamics that reflect empirical genomes.

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.

Ancestral sequence reconstruction: accounting for structural information by averaging over replacement matrices.

MOTIVATION: Ancestral sequence reconstruction (ASR) is widely used to understand protein evolution, structure and function. Current ASR methodologies do not fully consider differences in evolutionary constraints among positions imposed by the three-dimensional (3D) structure of the protein. Here, we developed an ASR algorithm that allows different protein sites to evolve according to different mixtures of replacement matrices. We show that assigning replacement matrices to protein positions based on their solvent accessibility leads to ASR with higher log-likelihoods compared to naïve models that assume a single replacement matrix for all sites. Improved ASR log-likelihoods are also demonstrated when solvent accessibility is predicted from protein sequences rather than inferred from a known 3D structure. Finally, we show that using such structure-aware mixture models results in substantial differences in the inferred ancestral sequences. AVAILABILITY AND IMPLEMENTATION: http://fastml.tau.ac.il. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Extreme amyloid polymorphism in Staphylococcus aureus virulent PSMα peptides.

Members of the Staphylococcus aureus phenol-soluble modulin (PSM) peptide family are secreted as functional amyloids that serve diverse roles in pathogenicity and may be present as full-length peptides or as naturally occurring truncations. We recently showed that the activity of PSMα3, the most toxic member, stems from the formation of cross-α fibrils, which are at variance with the cross-ß fibrils linked with eukaryotic amyloid pathologies. Here, we show that PSMα1 and PSMα4, involved in biofilm structuring, form canonical cross-ß amyloid fibrils wherein ß-sheets tightly mate through steric zipper interfaces, conferring high stability. Contrastingly, a truncated PSMα3 has antibacterial activity, forms reversible fibrils, and reveals two polymorphic and atypical ß-rich fibril architectures. These architectures are radically different from both the cross-α fibrils formed by full-length PSMα3, and from the canonical cross-ß fibrils. Our results point to structural plasticity being at the basis of the functional diversity exhibited by S. aureus PSMαs.

The cytotoxic Staphylococcus aureus PSMα3 reveals a cross-α amyloid-like fibril.

Amyloids are ordered protein aggregates, found in all kingdoms of life, and are involved in aggregation diseases as well as in physiological activities. In microbes, functional amyloids are often key virulence determinants, yet the structural basis for their activity remains elusive. We determined the fibril structure and function of the highly toxic, 22-residue phenol-soluble modulin α3 (PSMα3) peptide secreted by Staphylococcus aureus PSMα3 formed elongated fibrils that shared the morphological and tinctorial characteristics of canonical cross-ß eukaryotic amyloids. However, the crystal structure of full-length PSMα3, solved de novo at 1.45 angstrom resolution, revealed a distinctive "cross-α" amyloid-like architecture, in which amphipathic α helices stacked perpendicular to the fibril axis into tight self-associating sheets. The cross-α fibrillation of PSMα3 facilitated cytotoxicity, suggesting that this assembly mode underlies function in S. aureus.

Preparation of Crystalline Samples of Amyloid Fibrils and Oligomers.

The molecular structures of amyloid fibers and oligomers are required in order to understand and control their formation. Yet, their partially disordered and polymorphic nature hinders structural analyses. Fortunately, short segments from amyloid proteins, which exhibit similar biophysical properties to the full-length proteins, also form fibrils and oligomers and their atomic structures can be determined. Here we describe experimental procedures used to assess fiber-forming capabilities of amyloid peptide segments and their crystallization.