Alexander E. Lobkovsky

Viral Diversity Threshold for Adaptive Immunity in Prokaryotes

ABSTRACT Bacteria and archaea face continual onslaughts of rapidly diversifying viruses and plasmids. Many prokaryotes maintain adaptive immune systems known as clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated genes (Cas). CRISPR-Cas systems are genomic sensors that serially acquire viral and plasmid DNA fragments (spacers) that are utilized to target and cleave matching viral and plasmid DNA in subsequent genomic invasions, offering critical immunological memory. Only 50% of sequenced bacteria possess CRISPR-Cas immunity, in contrast to over 90% of sequenced archaea. To probe why half of bacteria lack CRISPR-Cas immunity, we combined comparative genomics and mathematical modeling. Analysis of hundreds of diverse prokaryotic genomes shows that CRISPR-Cas systems are substantially more prevalent in thermophiles than in mesophiles. With sequenced bacteria disproportionately mesophilic and sequenced archaea mostly thermophilic, the presence of CRISPR-Cas appears to depend more on environmental temperature than on bacterial-archaeal taxonomy. Mutation rates are typically severalfold higher in mesophilic prokaryotes than in thermophilic prokaryotes. To quantitatively test whether accelerated viral mutation leads microbes to lose CRISPR-Cas systems, we developed a stochastic model of virus-CRISPR coevolution. The model competes CRISPR-Cas-positive (CRISPR-Cas+) prokaryotes against CRISPR-Cas-negative (CRISPR-Cas−) prokaryotes, continually weighing the antiviral benefits conferred by CRISPR-Cas immunity against its fitness costs. Tracking this cost-benefit analysis across parameter space reveals viral mutation rate thresholds beyond which CRISPR-Cas cannot provide sufficient immunity and is purged from host populations. These results offer a simple, testable viral diversity hypothesis to explain why mesophilic bacteria disproportionately lack CRISPR-Cas immunity. More generally, fundamental limits on the adaptability of biological sensors (Lamarckian evolution) are predicted. IMPORTANCE A remarkable recent discovery in microbiology is that bacteria and archaea possess systems conferring immunological memory and adaptive immunity. Clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated genes (CRISPR-Cas) are genomic sensors that allow prokaryotes to acquire DNA fragments from invading viruses and plasmids. Providing immunological memory, these stored fragments destroy matching DNA in future viral and plasmid invasions. CRISPR-Cas systems also provide adaptive immunity, keeping up with mutating viruses and plasmids by continually acquiring new DNA fragments. Surprisingly, less than 50% of mesophilic bacteria, in contrast to almost 90% of thermophilic bacteria and Archaea, maintain CRISPR-Cas immunity. Using mathematical modeling, we probe this dichotomy, showing how increased viral mutation rates can explain the reduced prevalence of CRISPR-Cas systems in mesophiles. Rapidly mutating viruses outrun CRISPR-Cas immune systems, likely decreasing their prevalence in bacterial populations. Thus, viral adaptability may select against, rather than for, immune adaptability in prokaryotes. A remarkable recent discovery in microbiology is that bacteria and archaea possess systems conferring immunological memory and adaptive immunity. Clustered regularly interspaced short palindromic repeats (CRISPR) and CRISPR-associated genes (CRISPR-Cas) are genomic sensors that allow prokaryotes to acquire DNA fragments from invading viruses and plasmids. Providing immunological memory, these stored fragments destroy matching DNA in future viral and plasmid invasions. CRISPR-Cas systems also provide adaptive immunity, keeping up with mutating viruses and plasmids by continually acquiring new DNA fragments. Surprisingly, less than 50% of mesophilic bacteria, in contrast to almost 90% of thermophilic bacteria and Archaea, maintain CRISPR-Cas immunity. Using mathematical modeling, we probe this dichotomy, showing how increased viral mutation rates can explain the reduced prevalence of CRISPR-Cas systems in mesophiles. Rapidly mutating viruses outrun CRISPR-Cas immune systems, likely decreasing their prevalence in bacterial populations. Thus, viral adaptability may select against, rather than for, immune adaptability in prokaryotes.

Universal distribution of protein evolution rates as a consequence of protein folding physics

The hypothesis that folding robustness is the primary determinant of the evolution rate of proteins is explored using a coarse-grained off-lattice model. The simplicity of the model allows rapid computation of the folding probability of a sequence to any folded conformation. For each robust folder, the network of sequences that share its native structure is identified. The fitness of a sequence is postulated to be a simple function of the number of misfolded molecules that have to be produced to reach a characteristic protein abundance. After fixation probabilities of mutants are computed under a simple population dynamics model, a Markov chain on the fold network is constructed, and the fold-averaged evolution rate is computed. The distribution of the logarithm of the evolution rates across distinct networks exhibits a peak with a long tail on the low rate side and resembles the universal empirical distribution of the evolutionary rates more closely than either distribution resembles the log-normal distribution. The results suggest that the universal distribution of the evolutionary rates of protein-coding genes is a direct consequence of the basic physics of protein folding.

Predictability of evolutionary trajectories in fitness landscapes.

Experimental studies on enzyme evolution show that only a small fraction of all possible mutation trajectories are accessible to evolution. However, these experiments deal with individual enzymes and explore a tiny part of the fitness landscape. We report an exhaustive analysis of fitness landscapes constructed with an off-lattice model of protein folding where fitness is equated with robustness to misfolding. This model mimics the essential features of the interactions between amino acids, is consistent with the key paradigms of protein folding and reproduces the universal distribution of evolutionary rates among orthologous proteins. We introduce mean path divergence as a quantitative measure of the degree to which the starting and ending points determine the path of evolution in fitness landscapes. Global measures of landscape roughness are good predictors of path divergence in all studied landscapes: the mean path divergence is greater in smooth landscapes than in rough ones. The model-derived and experimental landscapes are significantly smoother than random landscapes and resemble additive landscapes perturbed with moderate amounts of noise; thus, these landscapes are substantially robust to mutation. The model landscapes show a deficit of suboptimal peaks even compared with noisy additive landscapes with similar overall roughness. We suggest that smoothness and the substantial deficit of peaks in the fitness landscapes of protein evolution are fundamental consequences of the physics of protein folding.

Evolutionary Dynamics of the Prokaryotic Adaptive Immunity System CRISPR-Cas in an Explicit Ecological Context

A stochastic, agent-based mathematical model of the coevolution of the archaeal and bacterial adaptive immunity system, CRISPR-Cas, and lytic viruses shows that CRISPR-Cas immunity can stabilize the virus-host coexistence rather than leading to the extinction of the virus. In the model, CRISPR-Cas immunity does not specifically promote viral diversity, presumably because the selection pressure on each single proto-spacer is too weak. However, the overall virus diversity in the presence of CRISPR-Cas grows due to the increase of the host and, accordingly, the virus population size. Above a threshold value of total viral diversity, which is proportional to the viral mutation rate and population size, the CRISPR-Cas system becomes ineffective and is lost due to the associated fitness cost. Our previous modeling study has suggested that the ubiquity of CRISPR-Cas in hyperthermophiles, which contrasts its comparative low prevalence in mesophiles, is due to lower rates of mutation fixation in thermal habitats. The present findings offer a complementary, simpler perspective on this contrast through the larger population sizes of mesophiles compared to hyperthermophiles, because of which CRISPR-Cas can become ineffective in mesophiles. The efficacy of CRISPR-Cas sharply increases with the number of proto-spacers per viral genome, potentially explaining the low information content of the proto-spacer-associated motif (PAM) that is required for spacer acquisition by CRISPR-Cas because a higher specificity would restrict the number of spacers available to CRISPR-Cas, thus hampering immunity. The very existence of the PAM might reflect the tradeoff between the requirement of diverse spacers for efficient immunity and avoidance of autoimmunity.

Replaying the Tape of Life: Quantification of the Predictability of Evolution

The question whether adaptation follows a deterministic route largely prescribed by the environment or can proceed along a large number of alternative trajectories has engaged extensive research over the recent years. Experimental evolution studies enabled by advances in high throughput techniques for genome sequencing and manipulation, along with increasingly detailed mathematical modeling of fitness landscapes, are beginning to allow quantitative exploration of the repeatability of evolutionary trajectories. It is becoming clear that evolutionary trajectories in static correlated fitness landscapes are substantially non-random but the relative contributions of determinism and stochasticity in the evolution of specific phenotypes strongly depend on the specific conditions, particularly the magnitude of the selective pressure and the number of available beneficial mutations.

The Vast, Conserved Mammalian lincRNome

We compare the sets of experimentally validated long intergenic non-coding (linc)RNAs from human and mouse and apply a maximum likelihood approach to estimate the total number of lincRNA genes as well as the size of the conserved part of the lincRNome. Under the assumption that the sets of experimentally validated lincRNAs are random samples of the lincRNomes of the corresponding species, we estimate the total lincRNome size at approximately 40,000 to 50,000 species, at least twice the number of protein-coding genes. We further estimate that the fraction of the human and mouse euchromatic genomes encoding lincRNAs is more than twofold greater than the fraction of protein-coding sequences. Although the sequences of most lincRNAs are much less strongly conserved than protein sequences, the extent of orthology between the lincRNomes is unexpectedly high, with 60 to 70% of the lincRNA genes shared between human and mouse. The orthologous mammalian lincRNAs can be predicted to perform equivalent functions; accordingly, it appears likely that thousands of evolutionarily conserved functional roles of lincRNAs remain to be characterized.

Gene frequency distributions reject a neutral model of genome evolution.

Evolution of prokaryotes involves extensive loss and gain of genes, which lead to substantial differences in the gene repertoires even among closely related organisms. Through a wide range of phylogenetic depths, gene frequency distributions in prokaryotic pangenomes bear a characteristic, asymmetrical U-shape, with a core of (nearly) universal genes, a “shell” of moderately common genes, and a “cloud” of rare genes. We employ mathematical modeling to investigate evolutionary processes that might underlie this universal pattern. Gene frequency distributions for almost 400 groups of 10 bacterial or archaeal species each over a broad range of evolutionary distances were fit to steady-state, infinite allele models based on the distribution of gene replacement rates and the phylogenetic tree relating the species in each group. The fits of the theoretical frequency distributions to the empirical ones yield model parameters and estimates of the goodness of fit. Using the Akaike Information Criterion, we show that the neutral model of genome evolution, with the same replacement rate for all genes, can be confidently rejected. Of the three tested models with purifying selection, the one in which the distribution of replacement rates is derived from a stochastic population model with additive per-gene fitness yields the best fits to the data. The selection strength estimated from the fits declines with evolutionary divergence while staying well outside the neutral regime. These findings indicate that, unlike some other universal distributions of genomic variables, for example, the distribution of paralogous gene family membership, the gene frequency distribution is substantially affected by selection.

Inevitability of Genetic Parasites

Abstract Almost all cellular life forms are hosts to diverse genetic parasites with various levels of autonomy including plasmids, transposons and viruses. Theoretical modeling of the evolution of primordial replicators indicates that parasites (cheaters) necessarily evolve in such systems and can be kept at bay primarily via compartmentalization. Given the (near) ubiquity, abundance and diversity of genetic parasites, the question becomes pertinent: are such parasites intrinsic to life? At least in prokaryotes, the persistence of parasites is linked to the rate of horizontal gene transfer (HGT). We mathematically derive the threshold value of the minimal transfer rate required for selfish element persistence, depending on the element duplication and loss rates as well as the cost to the host. Estimation of the characteristic gene duplication, loss and transfer rates for transposons, plasmids and virus-related elements in multiple groups of diverse bacteria and archaea indicates that most of these rates are compatible with the long term persistence of parasites. Notably, a small but non-zero rate of HGT is also required for the persistence of non-parasitic genes. We hypothesize that cells cannot tune their horizontal transfer rates to be below the threshold required for parasite persistence without experiencing highly detrimental side-effects. As a lower boundary to the minimum DNA transfer rate that a cell can withstand, we consider the process of genome degradation and mutational meltdown of populations through Muller’s ratchet. A numerical assessment of this hypothesis suggests that microbial populations cannot purge parasites while escaping Muller’s ratchet. Thus, genetic parasites appear to be virtually inevitable in cellular organisms.

Immunity, suicide or both? Ecological determinants for the combined evolution of anti-pathogen defense systems

BackgroundParasite-host arms race is one of the key factors in the evolution of life. Most cellular life forms, in particular prokaryotes, possess diverse forms of defense against pathogens including innate immunity, adaptive immunity and programmed cell death (altruistic suicide). Coevolution of these different but interacting defense strategies yields complex evolutionary regimes.ResultsWe develop and extensively analyze a computational model of coevolution of different defense strategies to show that suicide as a defense mechanism can evolve only in structured populations and when the attainable degree of immunity against pathogens is limited. The general principle of defense evolution seems to be that hosts do not evolve two costly defense mechanisms when one is sufficient. Thus, the evolutionary interplay of innate immunity, adaptive immunity and suicide, leads to an equilibrium state where the combination of all three defense strategies is limited to a distinct, small region of the parameter space. The three strategies can stably coexist only if none of them are highly effective. Coupled adaptive immunity-suicide systems, the existence of which is implied by the colocalization of genes for the two types of defense in prokaryotic genomes, can evolve either when immunity-associated suicide is more efficacious than other suicide systems or when adaptive immunity functionally depends on the associated suicide system.ConclusionsComputational modeling reveals a broad range of outcomes of coevolution of anti-pathogen defense strategies depending on the relative efficacy of different mechanisms and population structure. Some of the predictions of the model appear compatible with recent experimental evolution results and call for additional experiments.

Virus-host arms race at the joint origin of multicellularity and programmed cell death.

Unicellular eukaryotes and most prokaryotes possess distinct mechanisms of programmed cell death (PCD). How an “altruistic” trait, such as PCD, could evolve in unicellular organisms? To address this question, we developed a mathematical model of the virus-host co-evolution that involves interaction between immunity, PCD and cellular aggregation. Analysis of the parameter space of this model shows that under high virus load and imperfect immunity, joint evolution of cell aggregation and PCD is the optimal evolutionary strategy. Given the abundance of viruses in diverse habitats and the wide spread of PCD in most organisms, these findings imply that multiple instances of the emergence of multicellularity and its essential attribute, PCD, could have been driven, at least in part, by the virus-host arms race.