Biological systems have evolved to amazingly complex states, yet we do not understand in general how evolution operates to generate increasing genetic and functional complexity. Molecular recognition sites are short genome segments or peptides binding a cognate recognition target of sufficient sequence similarity. Such sites are simple, ubiquitous modules of sequence information, cellular function, and evolution. Here we show that recognition sites, if coupled to a time-dependent target, can rapidly evolve to complex states with larger code length and smaller coding density than sites recognising a static target. The underlying fitness model contains selection for recognition, which depends on the sequence similarity between site and target, and a uniform cost per unit of code length. Site sequences are shown to evolve in a specific adaptive ratchet, which produces selection of different strength for code extensions and compressions. Ratchet evolution increases the adaptive width of evolved sites, accelerating the adaptation to moving targets and facilitating refinement and innovation of recognition functions. We apply these results to the recognition of fast-evolving antigens by the human immune system. Our analysis shows how molecular complexity can evolve as a collateral to selection for function in a dynamic environment.

Targeted cancer therapies often induce a reversible drug-tolerant state in subpopulations of cells, akin to bacterial persistence. Precise characterization of these “cancer persisters” may inform the design of more effective treatment strategies. A previous investigation into the transition to persistence of colorectal cancer cell lines has revealed a distinct dependence on drug presence and concentration, not typical of bacterial systems. Leveraging these findings, this study uses mathematical modeling to explore intermittent treatment protocols aimed at diminishing the long-term fitness of the treated population, thereby enhancing therapeutic efficacy. We adapt a mathematical model originally designed for bacteria to describe colorectal cancer population dynamics in response to a series of treatment and release cycles. The model predicts the long-term increase or reduction of a treated population, as well as its asymptotic composition, leading us to identify success and failure regions within a clinically accessible parameter space, also in combination with hypothetical drugs that act on persisters. Strikingly, our analysis suggests, perhaps counter-intuitively, that optimal treatment outcomes may be achieved in correspondence of non-zero recovery periods and lower than currently administered in the clinics drug concentrations. Furthermore, by incorporating patient drug pharmacokinetics in the model, we demonstrate that intermittent dosing strategies currently explored in clinical trials can be optimized to potentially rival the efficacy of continuous dosing regimens. These findings underscore the potential of mathematical models in guiding the design of optimal treatment protocols by fine-tuning non-trivial decisional trade-offs.

Microtubules are polymers required for chromosome segregation. Their drug-induced hyperstabilization impairs chromosome segregation and is an established anti-cancer therapy. How cells respond to microtubule hyperstabilization, however, is incompletely understood. To study this, we evolved budding yeast cells expressing a microtubule-hyperstabilizing tubulin mutant and isolated adapted strains. Aneuploidy of specific chromosomes carrying the microtubule regulators STU2 and VIK1/KAR3 was the first observable adaptation. In the longer run, aneuploidies were outcompeted by mutations in α- or β-tubulin, partially overlapping with mutations in cancer patients. Thus, compensation of microtubule hyperstabilization follows a restrained and reproducible path where new mutations combine with the original offending mutation on the same carrier. While partly compensatory, several mutations failed to re-establish fully normal microtubule dynamics. Sustained growth relied on the mitotic checkpoint, indicating that extended mitotic timing limits the genomic instability caused by reduced microtubule dynamics. Our results predict a potential vulnerability of cells resistant to microtubule-hyperstabilizing agents.

DNA sequence mutability in tumors with chromosomal instability is conventionally believed to remain uniform, constant, and low, based on the assumption that further mutational accrual in a context of marked aneuploidy is evolutionarily disadvantageous. However, this concept lacks robust experimental verification. We adapted the principles of mutation accumulation experiments, traditionally performed in lower organisms, to clonal populations of patient-derived tumoroids and empirically measured the spontaneous rates of accumulation of new DNA sequence variations in seven chromosomally unstable, microsatellite stable colorectal cancers (CRCs) and one microsatellite unstable CRC. Our findings revealed heterogeneous mutation rates (MRs) across different tumors, with variations in magnitude within microsatellite stable tumors as prominent as those distinguishing them from microsatellite unstable tumors. Moreover, comparative assessment of microsatellite stable primary tumors and matched synchronous metastases consistently documented a pattern of MR intensification during tumor progression. Therefore, wide-range diversity and progression-associated evolvability of DNA sequence mutational instability emerge as unforeseen hallmarks of microsatellite stable CRC, complementing karyotype alterations as selectable traits to increase genetic variation.One sentence summary Tumors with chromosomal instability accrue DNA sequence mutations at highly variable rates, which increase during metastatic progression.### Competing Interest StatementL.T. has received research grants from Menarini, Merck KGaA, Merus, Pfizer, Servier and Symphogen. The other authors declare no conflicts.

Cancers feature substantial intratumoral heterogeneity of genetic and phenotypically distinct lineages. Although interactions between coexisting lineages are emerging as a potential contributor to tumor evolution, the extent and nature of these interactions remain largely unknown. We postulated that tumors develop ecological interactions that sustain diversity and facilitate metastasis. Using a combination of fluorescent barcoding, mathematical modeling, metabolic analysis, and in vivo models, we show that the Allee effect, i.e., growth dependency on population size, is a feature of tumor lineages and that cooperative ecological interactions between lineages alleviate the Allee barriers to growth in a model of triple-negative breast cancer. Soluble metabolite exchange formed the basis for these cooperative interactions and catalyzed the establishment of a polyclonal community that displayed enhanced metastatic dissemination and outgrowth in xenograft models. Our results highlight interclonal metabolite exchange as a key modulator of tumor ecology and a contributing factor to overcoming Allee effect-associated growth barriers to metastasis.

The horizontal transfer of genes is fundamental for the eco-evolutionary dynamics of microbial communities, such as oceanic plankton, soil, and the human microbiome. In the case of an acquired beneficial gene, classic population genetics would predict a genome-wide selective sweep, whereby the genome spreads clonally within the community and together with the beneficial gene, removing genome diversity. Instead, several sources of metagenomic data show the existence of “gene-specific sweeps”, whereby a beneficial gene spreads across a bacterial community, maintaining genome diversity. Several hypotheses have been proposed to explain this process, including the decreasing gene flow between ecologically distant populations, frequency-dependent selection from linked deleterious allelles, and very high rates of horizontal gene transfer. Here, we propose an additional possible scenario grounded in eco-evolutionary principles. Specifically, we show by a mathematical model and simulations that a metacommunity where species can occupy multiple patches, acting together with a realistic (moderate) HGT rate, helps maintain genome diversity. Assuming a scenario of patches dominated by single species, our model predicts that diversity only decreases moderately upon the arrival of a new beneficial gene, and that losses in diversity can be quickly restored. We explore the generic behaviour of diversity as a function of three key parameters, frequency of insertion of new beneficial genes, migration rates and horizontal transfer rates.Our results provides a testable explanation for how diversity can be maintained by gene-specific sweeps even in the absence of high horizontal gene transfer rates.

The early development of aneuploidy from an accidental chromosome missegregation shows contrasting effects. On the one hand, it is associated with significant cellular stress and decreased fitness. On the other hand, it often carries a beneficial effect and provides a quick (but typically transient) solution to external stress. These apparently controversial trends emerge in several experimental contexts, particularly in the presence of duplicated chromosomes. However, we lack a mathematical evolutionary modeling framework that comprehensively captures these trends from the mutational dynamics and the trade-offs involved in the early stages of aneuploidy. Here, focusing on chromosome gains, we address this point by introducing a fitness model where a fitness cost of chromosome duplications is contrasted by a fitness advantage from the dosage of specific genes. The model successfully captures the experimentally measured probability of emergence of extra chromosomes in a laboratory evolution setup. Additionally, using phenotypic data collected in rich media, we explored the fitness landscape, finding evidence supporting the existence of a per-gene cost of extra chromosomes. Finally, we show that the substitution dynamics of our model, evaluated in the empirical fitness landscape, explains the relative abundance of duplicated chromosomes observed in yeast population genomics data. These findings lay a firm framework for the understanding of the establishment of newly duplicated chromosomes, providing testable quantitative predictions for future observations.

Compelling evidence shows that cancer persister cells represent a major limit to the long-term efficacy of targeted therapies. However, the phenotype and population dynamics of cancer persister cells remain unclear. We developed a quantitative framework to study persisters by combining experimental characterization and mathematical modeling. We found that, in colorectal cancer, a fraction of persisters slowly replicates. Clinically approved targeted therapies induce a switch to drug-tolerant persisters and a temporary 7- to 50-fold increase of their mutation rate, thus increasing the number of persister-derived resistant cells. These findings reveal that treatment may influence persistence and mutability in cancer cells and pinpoint inhibition of error-prone DNA polymerases as a strategy to restrict tumor recurrence.

When cancer cells are exposed to lethal doses of targeted therapies, the emergence of a subpopulation of drug-tolerant persister cells (DTPs) is often observed. We previously reported that colorectal cancer (CRC) cells exposed to targeted therapies activate an adaptive mutability stress response, involving DNA damage induction and a switch to low-fidelity DNA replication. Therefore, targeted treatment might lead to increased mutation rate in DTPs, but mutation rates of cancer cells during treatment have not been quantitatively assessed. Here, we combined biological experiments and mathematical modelling to characterize emergence and dynamics of DTPs. From this, we extrapolated parameters governing dynamics of cancer cells populations and designed a modified Luria-Delbrück assay on mammalian cells (MC-LD) to quantify mutations rates of CRC cells under standard growth conditions and during exposure to targeted therapy. We selected mismatch repair proficient CRC cell lines sensitive to different clinically used therapeutic agents, and derived clones to be used for experiments. By monitoring cell dynamics in drug-response growth assays, we found that CRC cells exposed to targeted therapy display a biphasic killing curve reaching a stable plateau, a pattern indicative of emergence of DTPs. By fitting model estimation to population growth assays, we predicted that, even if a subgroup of DTPs predated treatment, the majority of them emerged only upon exposure to targeted therapies. We also observed that DTPs slowly replicate under treatment, as shown by Carboxy fluorescein succinimidyl ester (CFSE) analysis and staining with 5-ethynyl-2’-deoxyuridine (EdU). We used these population dynamics parameters to design the MC-LD assay. CRC clones were plated in several 96-multiwell plates each, and after an expansion phase in standard culture conditions, treatment was added. After 3-4 weeks, a minority of wells showed growth of resistant colonies: based on the measured growth rates, we could predict that the resistant cells arose before treatment by spontaneous mutation. The remaining wells contained a homogenous population of DTPs. After several weeks of treatment, when pre-treatment resistant clones would have already emerged, late-emerging resistant colonies appeared in a subset of wells in which DTPs had previously been detected. Using the number of residual DTPs and resistant colonies to infer mutation rates, we found a 7- to 50-fold increase (depending on the cell line) in DTPs’ mutation rate compared to sensitive cells.In conclusion, we developed a new assay which allows quantitative comparisons of spontaneous and drug-induced mutation rates in cancer cells and showed that adaptive mutability in DTPs leads to increased mutation rates. This approach could be used to measure whether and how a wide range of environmental conditions affect DTP phenotype and mutation rates in mammalian cells. Citation Format: Alberto Sogari, Mariangela Russo, Simone Pompei, Mattia Corigliano, Giovanni Crisafulli, Andrea Bertotti, Marco Gherardi, Federica Di Nicolantonio, Marco Cosentino Lagomarsino, Alberto Bardelli. A modified Luria-Delbrück assay allows quantification of colorectal cancer persister cells’ mutation rate [abstract]. In: Proceedings of the American Association for Cancer Research Annual Meeting 2022; 2022 Apr 8-13. Philadelphia (PA): AACR; Cancer Res 2022;82(12_Suppl):Abstract nr 2613.

ABSTRACTMicrotubules, polymers of alpha- and beta-tubulin, are essential cellular components. When microtubule polymerization is hindered, cells are delayed in mitosis, but eventually they manage to proliferate with massive chromosome missegregation. Several studies have analyzed the first cell division upon microtubules impairing conditions. Here, we asked how cells cope on the long term. Taking advantage of mutations in beta-tubulin, we evolved in the lab for ∼150 generations 24 populations of yeast cells unable to properly polymerize microtubules. At the end of the evolution experiment, cells re-gained the ability to form microtubules, and were less sensitive to microtubule depolymerizing drugs. Whole genome sequencing allowed us to identify genes recurrently mutated (tubulins and kinesins) as well as the pervasive duplication of chromosome VIII. We confirmed that mutations found in these genes and disomy of chromosome VIII allow cells to compensate for the original mutation in beta-tubulin. The mutations we identified were mostly gain-of-function, likely re-allowing the proper use of the mutated form of beta-tubulin. When we analyzed the temporal order of mutations leading to resistance in independent populations, we observed multiple times the same series of events: disomy of chromosome VIII followed by one additional adaptive mutation in either tubulins or kinesins. Analyzing the epistatic interactions among different mutations, we observed that some mutations benefited from the disomy of chromosome VIII and others did not. Given that tubulins are highly conserved among eukaryotes, our results are potentially relevant for understanding the emergence of resistance to drugs targeting microtubules, widely used for cancer treatment.

Compelling evidence shows that cancer persister cells limit the efficacy of targeted therapies. However, it is unclear whether persister cells are induced by anticancer drugs, and if their mutation rate quantitatively increases during treatment. Here, combining experimental characterization and mathematical modeling, we show that, in colorectal cancer, persisters are induced by drug treatment and show a 7- to 50-fold increase of mutation rate when exposed to clinically approved targeted therapies. These findings reveal that treatment may influence persistence and mutability in cancer cells and pinpoints new strategies to restrict tumor recurrence.

The reconstruction of phylogenies of cultural artefacts represents an open problem that mixes theoretical and computational challenges. Existing benchmarks rely on simulated phylogenies, where hypotheses on the underlying evolutionary mechanisms are unavoidable, or on real data phylogenies, for which no true evolutionary history is known. Here we introduce a web-based game, Copystree , where users create phylogenies of manuscripts through successive copying actions in a fully monitored setup. While players enjoy the experience, Copystree allows to build artificial phylogenies whose evolutionary processes do not obey any predefined theoretical mechanisms, being generated instead with the unpredictability of human creativity. We present the analysis of the data gathered during the first set of experiments and use the artificial phylogenies gathered for a first test of existing phylogenetic algorithms.

The reconstruction of phylogenies of cultural artefacts represents an open problem thatmixes theoretical and computational challenges. Existing benchmarks rely on simulated phylogenies, where hypotheses on the underlying evolutionary mechanisms are unavoidable, or on real data phylogenies, for which no true evolutionary history is known. Here we introduce a web-based game, Copystree, where users create phylogenies of manuscripts through successive copying actions in a fully monitored setup. While players enjoy the experience, Copystree allows to build artificial phylogenies whose evolutionary processes do not obey any predefined theoretical mechanisms, being generated instead with the unpredictability of human creativity. We present the analysis of the data gathered during the first set of experiments and use the artificial phylogenies gathered for a first test of existing phylogenetic algorithms.

Seasonal influenza is controlled through vaccination campaigns. Evolution of influenza virus antigens means that vaccines must be updated to match novel strains, and vaccine effectiveness depends on the ability of scientists to predict nearly a year in advance which influenza variants will dominate in upcoming seasons. In this review, we highlight a promising new surveillance tool: predictive models. Based on data-sharing and close collaboration between the World Health Organization and academic scientists, these models use surveillance data to make quantitative predictions regarding influenza evolution. Predictive models demonstrate the potential of applied evolutionary biology to improve public health and disease control. We review the state of influenza predictive modeling and discuss next steps and recommendations to ensure that these models deliver upon their considerable biomedical promise.

We present a numerical model for the evolution of pathogens organised in discrete antigenic clusters, where individuals in the same clusters have the same fitness. The fitness of each cluster is a decreasing function of the total number of cluster members appeared in the population. Cluster transition is modelled with inclusion and exclusion of dynamical epistatic effects. In both cases we observe a continuous transition, driven by the mutation rate, from a dynamics with single clusters alternating in time to the coexistence of many clusters in the population. The transition between the two regimes is investigated in terms of the key parameters of the model. We find that the location and the scaling of this transition can be explained in terms of the time of first appearance of a new cluster in the population. The presence of dynamical epistatic effects results in a shift of the value of the mutation rate where the transition occurs.

Human Influenza A virus undergoes recurrent changes in the hemagglutinin (HA) surface protein, primarily involved in the human antibody recognition. Relevant antigenic changes, enabling the virus to evade host immune response, have been recognized to occur in parallel to multiple mutations at antigenic sites in HA. Yet, the role of correlated mutations (epistasis) in driving the molecular evolution of the virus still represents a challenging puzzle. Further, though circulation at a global geographic level is key for the survival of Influenza A, its role in shaping the viral phylodynamics remains largely unexplored. Here we show, through a sequence based epidemiological model, that epistatic effects between amino acids substitutions, coupled with a reservoir that mimics worldwide circulating viruses, are key determinants that drive human Influenza A evolution. Our approach explains all the up-to-date observations characterizing the evolution of H3N2 subtype, including phylogenetic properties, nucleotide fixation patterns and composition of antigenic clusters.

A new word, phylodynamics, was coined to emphasize the interconnection between phylogenetic properties, as observed for instance in a phylogenetic tree, and the epidemic dynamics of viruses, where selection, mediated by the host immune response, and transmission play a crucial role. The challenges faced when investigating the evolution of RNA viruses call for a virtuous loop of data collection, data analysis and modeling. This already resulted both in the collection of massive sequences databases and in the formulation of hypotheses on the main mechanisms driving qualitative differences observed in the (reconstructed) evolutionary patterns of different RNA viruses. Qualitatively, it has been observed that selection driven by the host immune response induces an uneven survival ability among co-existing strains. As a consequence, the imbalance level of the phylogenetic tree is manifestly more pronounced if compared to the case when the interaction with the host immune system does not play a central role in the evolutive dynamics. While many imbalance metrics have been introduced, reliable methods to discriminate in a quantitative way different level of imbalance are still lacking. In our work, we reconstruct and analyze the phylogenetic trees of six RNA viruses, with a special emphasis on the human Influenza A virus, due to its relevance for vaccine preparation as well as for the theoretical challenges it poses due to its peculiar evolutionary dynamics. We focus in particular on topological properties. We point out the limitation featured by standard imbalance metrics, and we introduce a new methodology with which we assign the correct imbalance level of the phylogenetic trees, in agreement with the phylodynamics of the viruses. Our thorough quantitative analysis allows for a deeper understanding of the evolutionary dynamics of the considered RNA viruses, which is crucial in order to provide a valuable framework for a quantitative assessment of theoretical predictions.

Historical linguistics aims at inferring the most likely language phylogenetic tree starting from information concerning the evolutionary relatedness of languages. The available information are typically lists of homologous (lexical, phonological, syntactic) features or characters for many different languages: a set of parallel corpora whose compilation represents a paramount achievement in linguistics.From this perspective the reconstruction of language trees is an example of inverse problems: starting from present, incomplete and often noisy, information, one aims at inferring the most likely past evolutionary history. A fundamental issue in inverse problems is the evaluation of the inference made. A standard way of dealing with this question is to generate data with artificial models in order to have full access to the evolutionary process one is going to infer. This procedure presents an intrinsic limitation: when dealing with real data sets, one typically does not know which model of evolution is the most suitable for them. A possible way out is to compare algorithmic inference with expert classifications. This is the point of view we take here by conducting a thorough survey of the accuracy of reconstruction methods as compared with the Ethnologue expert classifications. We focus in particular on state-of-the-art distance-based methods for phylogeny reconstruction using worldwide linguistic databases.In order to assess the accuracy of the inferred trees we introduce and characterize two generalizations of standard definitions of distances between trees. Based on these scores we quantify the relative performances of the distance-based algorithms considered. Further we quantify how the completeness and the coverage of the available databases affect the accuracy of the reconstruction. Finally we draw some conclusions about where the accuracy of the reconstructions in historical linguistics stands and about the leading directions to improve it.

Phylogenetic methods have recently been rediscovered in several interesting areas among which immunodynamics, epidemiology and many branches of evolutionary dynamics. In many interesting cases the reconstruction of a correct phylogeny is blurred by high mutation rates and/or horizontal transfer events. As a consequence, a divergence arises between the true evolutionary distances and the distances between pairs of taxa as inferred from the available data, making the phylogenetic reconstruction a challenging problem. Mathematically this divergence translates in the non-additivity of the actual distances between taxa and the quest for new algorithms able to efficiently cope with these effects is wide open. In distance-based reconstruction methods, two properties of additive distances were extensively exploited as antagonist criteria to drive phylogeny reconstruction: on the one hand a local property of quartets, i.e. sets of four taxa in a tree, the four-point condition; on the other hand, a recently proposed formula that allows to write the tree length as a function of the distances between taxa, the Pauplin's formula. A deeper comprehension of the effects of the non-additivity on the inspiring principles of the existing reconstruction algorithms is thus of paramount importance. In this paper we present a comparative analysis of the performances of the most important distance-based phylogenetic algorithms. We focus in particular on the dependence of their performances on two main sources of non-additivity: back-mutation processes and horizontal transfer processes. The comparison is carried out in the framework of a set of generative algorithms for phylogenies that incorporate non-additivity in a tunable way.