Sagi Snir

In bacterial and archaeal genomes, functionally linked genes often cluster in operons that enable coregulation of expression of these genes and production of their protein products in stoichiometric amounts. Many operons are shared by genomes of distantly related bacteria and archaea due in part to evolutionary conservation and in part to horizontal gene transfer (HGT). In contrast, similarity between species in their gene order along the chromosome can be merely a result of evolutionary closeness such that synteny has not yet been disrupted by genome dynamic events occurring during evolution. In general, however, accurate differentiation of operons from spurious gene clusters is a non-trivial task that depends on an underlying model of neutral genome evolution. Here, we employ a recently developed stochastic model of genome rearrangement (“jump model”) that accounts for HGT across prokaryote species evolving along a phylogenetic tree to infer the size distribution of shared gene strings (synteny blocks) under neutral evolution. Analytic expressions are derived for the expected number of synteny blocks of a given size (or of maximal size) depending on the evolutionary distance between the genomes and the rates of different types of evolutionary events. This analysis is related to the well-studied family of stick-breaking problems, but the discrete structure and stochastic nature of the evolutionary process provide for the development of a simple, independent model. We demonstrate the predictive power of this model by computer simulations of synthetic data as well as by simulating genomes on real trees obtained from the Alignable Tight Genome Clusters database.

The epigenetic pacemaker (EPM) model uses DNA methylation data to predict human epigenetic age. The methylation values are collected from different individuals and are considered to be of medical importance. Sharing these data publicly among labs and other third parties for model calculation purposes may violate the privacy of personal medical records. The use of standard encryption approaches can prevent the exposure of these personal records to third parties when at rest, but running computations on the data requires decrypting it first, and thus exposing the entire data to the computing party. This work proposes computing EPM while limiting data exposure by employing cryptographic secure computing techniques including homomorphic encryption. Our protocol has rigorous privacy guarantees against passive computationally bounded adversaries in the two-server model. Our results show good correlation with low accuracy error between the model with and without encryption. These results can serve as a pilot for data security measures integrated in vast medical applications where personal privacy is imperative. ¹

Evolution of bacterial and archaeal genomes is highly dynamic including extensive gene gain via horizontal gene transfer and gene loss as well as different types of genome rearrangements, such as inversions and translocations, so that gene order is not highly conserved even among closely related organisms. We sought to quantify the contributions of different genome dynamics processes to the evolution of the gene order relying on the recently developed “jump” model of gene translocation. The jump model has been completely solved analytically and provides the exact distribution of syntenic gene block lengths (SBL) in compared genomes based on gene translocations alone. Comparing the SBL distribution predicted by the jump model with the distributions empirically observed for multiple groups of closely related bacterial and archaeal genomes, we obtained robust estimates of the genome rearrangement to gene flux (gain and loss) ratio. In most groups of bacteria and archaea, this ratio was found to be on the order of 0.1 indicating that the loss of synteny in the evolution of bacteria and archaea is driven primarily by gene gain and loss rather than by gene translocation. Significance Evolution of bacterial and archaeal genomes is a highly dynamic process that includes extensive gene gain via horizontal gene transfer and gene loss as well as different types of genome rearrangements, so that gene order is not highly conserved even among closely related organisms. We developed a theoretical framework to quantify the contributions of different genome dynamics processes to the evolution of the gene order and found that in most groups of bacteria and archaea, the genome rearrangement to gene flux (combined gain and loss) is on the order of 0.1. Thus, the loss of genomic synteny in the evolution of bacteria and archaea appears to be driven primarily by gene gain and loss rather than by gene translocation.

The advent of the genomic era has produced an incredible wealth and resolution of molecular data, posing an unprecedented challenge for molecular systematics, necessitating novel techniques and paradigms. Consequently, whole genome approaches were developed to extract the evolutionary signal by taking advantage of a larger amount of data. In parallel and in light of the understanding that in prokaryotes, genome dynamics (GD) events, primarily gene gain and loss, provide a significantly richer signal than point mutations in ubiquitous housekeeping genes, GD-based approaches were suggested. However, proper modeling of these data and the processes generating them has lagged in their pace of accumulation, both because of a lack of deep understanding and because of technical difficulties. Among the central hurdles of accurate modeling of real data is the relaxation of rate constancy, particularly the untying of gain and loss rates. This relaxation violates key assumptions such as constant genome sizes, gene set, and model reversibility and has vast implications for implementation. This work presents a generic stochastic model, the two-ratio process (TRP), which encompasses and deals with these complications. As a special case, it contains the Poissonian process with different gene gain and loss rates as a form of the Birth-Death process with varying population sizes. The lack of reversibility invalidates traditional phylogenetic approaches, yielding a novel two-stage phylogenetic approach in which accurate, bidirectional parameters are first inferred for triplets and later combined by a special cherry-picking method to a complete tree. We show by algebraic techniques that this method is theoretically statistically consistent. The method implemented by the software TDDR (Triplets Directed Distances Reconstruction) was applied to synthetic data, showing an advantage over other approaches handling similar data but without the same model assumption. We also applied it to the Alignable Tight Genomic Clusters (ATGC) Database, which showed a high adequacy to the observed data. The TDDR code is available on GitHub: https://github.com/YoavDvir/TDDR .

The genomic era has opened up vast opportunities in molecular systematics, one of which is deciphering the evolutionary history in fine detail. Under this mass of data, analyzing the point mutations of standard markers is often too crude and slow for fine-scale phylogenetics. Nevertheless, genome dynamics (GD) events provide alternative, often richer information. The synteny index (SI) between a pair of genomes combines gene order and gene content information, allowing the comparison of genomes of unequal gene content, together with order considerations of their common genes. Recently, genome dynamics has been modeled as a continuous-time Markov process, and gene distance in the genome as a birth–death–immigration process. Nevertheless, due to complexities arising in this setting, no precise and provably consistent estimators could be derived, resulting in heuristic solutions. Here, we extend this modeling approach by using techniques from birth–death theory to derive explicit expressions of the system’s probabilistic dynamics in the form of rational functions of the model parameters. This, in turn, allows us to infer analytically accurate distances between organisms based on their SI. Subsequently, we establish additivity of this estimated evolutionary distance (a desirable property yielding phylogenetic consistency). Applying the new measure in simulation studies shows that it provides accurate results in realistic settings and even under model extensions such as gene gain/loss or over a tree structure. In the real-data realm, we applied the new formulation to unique data structure that we constructed—the ordered orthology DB—based on a new version of the EggNOG database, to construct a tree with more than 4.5K taxa. To the best of our knowledge, this is the largest gene-order-based tree constructed and it overcomes shortcomings found in previous approaches. Constructing a GD-based tree allows to confirm and contrast findings based on other phylogenetic approaches, as we show.