arXiv subjects

Michael Lässig

Publications and source records attributed to Michael Lässig.

At least 19 recordsLinked to original sources

arXiv2025

Adaptive ratchets and the evolution of molecular complexity

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.

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arXiv2024

Concepts and methods for predicting viral evolution

The seasonal human influenza virus undergoes rapid evolution, leading to significant changes in circulating viral strains from year to year. These changes are typically driven by adaptive mutations, particularly in the antigenic epitopes, the regions of the viral surface protein haemagglutinin targeted by human antibodies. Here we describe a consistent set of methods for data-driven predictive analysis of viral evolution. Our pipeline integrates four types of data: (1) sequence data of viral isolates collected on a worldwide scale, (2) epidemiological data on incidences, (3) antigenic characterization of circulating viruses, and (4) intrinsic viral phenotypes. From the combined analysis of these data, we obtain estimates of relative fitness for circulating strains and predictions of clade frequencies for periods of up to one year. Furthermore, we obtain comparative estimates of protection against future viral populations for candidate vaccine strains, providing a basis for pre-emptive vaccine strain selection. Continuously updated predictions obtained from the prediction pipeline for influenza and SARS-CoV-2 are available on the website https://previr.app.

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arXiv2024

Nonequilibrium antigen recognition during infections and vaccinations

The immune response to an acute primary infection is a coupled process of antigen proliferation, molecular recognition by naive B cells, and their subsequent proliferation and antibody shedding. This process contains a fundamental problem: the recognition of an exponentially time-dependent antigen signal. Here we show that B cells can efficiently recognise new antigens by a tuned kinetic proofreading mechanism, where the molecular recognition machinery is adapted to the complexity of the immune repertoire. This process produces potent, specific and fast recognition of antigens, maintaining a spectrum of genetically distinct B cell lineages as input for affinity maturation. We show that the proliferation-recognition dynamics of a primary infection is a generalised Luria-Delbrück process, akin to the dynamics of the classic fluctuation experiment. This map establishes a link between signal recognition dynamics and evolution. We derive the resulting statistics of the activated immune repertoire: antigen binding affinity, expected size, and frequency of active B cell clones are related by power laws, which define the class of generalised Luria-Delbrück processes. Their exponents depend on the antigen and B cell proliferation rate, the number of proofreading steps, and the lineage density of the naive repertoire. We extend the model to include spatio-temporal processes, including the diffusion-recognition dynamics of a vaccination. Empirical data of activated mouse immune repertoires are found to be consistent with activation involving about three proofreading steps. The model predicts key clinical characteristics of acute infections and vaccinations, including the emergence of elite neutralisers and the effects of immune ageing. More broadly, our results establish infections and vaccinations as a new probe into the global architecture and functional principles of immune repertoires.

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arXiv2022

Stochasticity of infectious outbreaks and consequences for optimal interventions

Global strategies to contain a pandemic, such as social distancing and protective measures, are designed to reduce the overall transmission rate between individuals. Despite such measures, essential institutions, including hospitals, schools, and food producing plants, remain focal points of local outbreaks. Here we develop a model for the stochastic outbreak dynamics in such local communities. We derive analytical expressions for the probability of containment of the outbreak, which is complementary to the probability of seeding a deterministically growing epidemic. This probability depends on the statistics of the intra-community contact network and the initial conditions, in particular, on the contact degree of patient zero. Based on this model, we suggest surveillance protocols by which individuals are tested proportionally to their degree in the contact network. We characterize the efficacy of contact-based protocols as a function of the epidemiological and the contact network parameters, and show numerically that such protocols outperform random testing.

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arXiv2022

Vaccination shapes evolutionary trajectories of SARS-CoV-2

The large-scale evolution of the SARS-CoV-2 virus has been marked by rapid turnover of genetic clades. New variants show intrinsic changes, notably increased transmissibility, as well as antigenic changes that reduce the cross-immunity induced by previous infections or vaccinations. How this functional variation shapes the global evolutionary dynamics has remained unclear. Here we show that selection induced by vaccination impacts on the recent antigenic evolution of SARS-CoV-2; other relevant forces include intrinsic selection and antigenic selection induced by previous infections. We obtain these results from a fitness model with intrinsic and antigenic fitness components. To infer model parameters, we combine time-resolved sequence data, epidemiological records, and cross-neutralisation assays. This model accurately captures the large-scale evolutionary dynamics of SARS-CoV-2 in multiple geographical regions. In particular, it quantifies how recent vaccinations and infections affect the speed of frequency shifts between viral variants. Our results show that timely neutralisation data can be harvested to identify hotspots of antigenic selection and to predict the impact of vaccination on viral evolution.

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arXiv2021

Antigenic waves of virus-immune co-evolution

The evolution of many microbes and pathogens, including circulating viruses such as seasonal influenza, is driven by immune pressure from the host population. In turn, the immune systems of infected populations get updated, chasing viruses even further away. Quantitatively understanding how these dynamics result in observed patterns of rapid pathogen and immune adaptation is instrumental to epidemiological and evolutionary forecasting. Here we present a mathematical theory of co-evolution between immune systems and viruses in a finite-dimensional antigenic space, which describes the cross-reactivity of viral strains and immune systems primed by previous infections. We show the emergence of an antigenic wave that is pushed forward and canalized by cross-reactivity. We obtain analytical results for shape, speed, and angular diffusion of the wave. In particular, we show that viral-immune co-evolution generates a new emergent timescale, the persistence time of the wave's direction in antigenic space, which can be much longer than the coalescence time of the viral population. We compare these dynamics to the observed antigenic turnover of influenza strains, and we discuss how the dimensionality of antigenic space impacts on the predictability of the evolutionary dynamics. Our results provide a concrete and tractable framework to describe pathogen-host co-evolution.

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arXiv2020

Predicting trajectories and mechanisms of antibiotic resistance evolution

Bacteria evolve resistance to antibiotics by a multitude of mechanisms. A central, yet unsolved question is how resistance evolution affects cell growth at different drug levels. Here we develop a fitness model that predicts growth rates of common resistance mutants from their effects on cell metabolism. We map metabolic effects of resistance mutations in drug-free environments and under drug challenge; the resulting fitness trade-off defines a Pareto surface of resistance evolution. We predict evolutionary trajectories of dosage-dependent growth rates and resistance levels, as well as the prevalent resistance mechanism depending on drug and nutrient levels. These predictions are confirmed by empirical growth curves and genomic data of E. coli populations. Our results show that resistance evolution, by coupling major metabolic pathways, is strongly intertwined with systems biology and ecology of microbial populations.

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arXiv2020

Adaptive evolution of hybrid bacteria by horizontal gene transfer

Horizontal gene transfer is an important factor in bacterial evolution that can act across species boundaries. Yet, we know little about rate and genomic targets of cross-lineage gene transfer, and about its effects on the recipient organism's physiology and fitness. Here, we address these questions in a parallel evolution experiment with two Bacillus subtilis lineages of 7% sequence divergence. We observe rapid evolution of hybrid organisms: gene transfer swaps ~12% of the core genome in just 200 generations, and 60% of core genes are replaced in at least one population. By genomics, transcriptomics, fitness assays, and statistical modeling, we show that transfer generates adaptive evolution and functional alterations in hybrids. Specifically, our experiments reveal a strong, repeatable fitness increase of evolved populations in the stationary growth phase. By genomic analysis of the transfer statistics across replicate populations, we infer that selection on HGT has a broad genetic basis: 40% of the observed transfers are adaptive. At the level of functional gene networks, we find signatures of negative and positive selection, consistent with hybrid incompatibilities and adaptive evolution of network functions. Our results suggest that gene transfer navigates a complex cross-lineage fitness landscape, bridging epistatic barriers along multiple high-fitness paths.

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arXiv2019

Multi-lineage evolution in viral populations driven by host immune systems

Viruses evolve in the background of host immune systems that exert selective pressure and drive viral evolutionary trajectories. This interaction leads to different evolutionary patterns in antigenic space. Examples observed in nature include the effectively one-dimensional escape characteristic of influenza A and the prolonged coexistence of lineages in influenza B. Here we use an evolutionary model for viruses in the presence of immune host systems with finite memory to delineate parameter regimes of these patterns in a in two-dimensional antigenic space. We find that for small effective mutation rates and mutation jump ranges, a single lineage is the only stable solution. Large effective mutation rates combined with large mutational jumps in antigenic space lead to multiple stably co-existing lineages over prolonged evolutionary periods. These results combined with observations from data constrain the parameter regimes for the adaptation of viruses, including influenza.

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arXiv2018

Survival of the simplest: the cost of complexity in microbial evolution

The evolution of microbial and viral organisms often generates clonal interference, a mode of competition between genetic clades within a population. In this paper, we show that interference strongly constrains the genetic and phenotypic complexity of evolving systems. Our analysis uses biophysically grounded evolutionary models for an organism's quantitative molecular phenotypes, such as fold stability and enzymatic activity of genes. We find a generic mode of asexual evolution called phenotypic interference with strong implications for systems biology: it couples the stability and function of individual genes to the population's global speed of evolution. This mode occurs over a wide range of evolutionary parameters appropriate for microbial populations. It generates selection against genome complexity, because the fitness cost of mutations increases faster than linearly with the number of genes. Recombination can generate a distinct mode of sexual evolution that eliminates the superlinear cost. We show that positive selection can drive a transition from asexual to facultative sexual evolution, providing a specific, biophysically grounded scenario for the evolution of sex. In a broader context, our analysis suggests that the systems biology of microbial organisms is strongly intertwined with their mode of evolution.

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arXiv2017

The asexual genome of Drosophila

The rate of recombination affects the mode of molecular evolution. In high-recombining sequence, the targets of selection are individual genetic loci; under low recombination, selection collectively acts on large, genetically linked genomic segments. Selection under linkage can induce clonal interference, a specific mode of evolution by competition of genetic clades within a population. This mode is well known in asexually evolving microbes, but has not been traced systematically in an obligate sexual organism. Here we show that the Drosophila genome is partitioned into two modes of evolution: a local interference regime with limited effects of genetic linkage, and an interference condensate with clonal competition. We map these modes by differences in mutation frequency spectra, and we show that the transition between them occurs at a threshold recombination rate that is predictable from genomic summary statistics. We find the interference condensate in segments of low-recombining sequence that are located primarily in chromosomal regions flanking the centromeres and cover about 20% of the Drosophila genome. Condensate regions have characteristics of asexual evolution that impact gene function: the efficacy of selection and the speed of evolution are lower and the genetic load is higher than in regions of local interference. Our results suggest that multicellular eukaryotes can harbor heterogeneous modes and tempi of evolution within one genome. We argue that this variation generates selection on genome architecture.

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arXiv2015

Multiple-line inference of selection on quantitative traits

Trait differences between species may be attributable to natural selection. However, quantifying the strength of evidence for selection acting on a particular trait is a difficult task. Here we develop a population-genetic test for selection acting on a quantitative trait which is based on multiple-line crosses. We show that using multiple lines increases both the power and the scope of selection inference. First, a test based on three or more lines detects selection with strongly increased statistical significance, and we show explicitly how the sensitivity of the test depends on the number of lines. Second, a multiple-line test allows to distinguish different lineage-specific selection scenarios. Our analytical results are complemented by extensive numerical simulations. We then apply the multiple-line test to QTL data on floral character traits in plant species of the Mimulus genus and on photoperiodic traits in different maize strains, where we find a signatures of lineage-specific selection not seen in a two-line test.

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arXiv2014

Epidemiological and evolutionary analysis of the 2014 Ebola virus outbreak

The 2014 epidemic of the Ebola virus is governed by a genetically diverse viral population. In the early Sierra Leone outbreak, a recent study has identified new mutations that generate genetically distinct sequence clades. Here we find evidence that major Sierra Leone clades have systematic differences in growth rate and reproduction number. If this growth heterogeneity remains stable, it will generate major shifts in clade frequencies and influence the overall epidemic dynamics on time scales within the current outbreak. Our method is based on simple summary statistics of clade growth, which can be inferred from genealogical trees with an underlying clade-specific birth-death model of the infection dynamics. This method can be used to perform realtime tracking of an evolving epidemic and identify emerging clades of epidemiological or evolutionary significance.

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arXiv2014

Rate and cost of adaptation in the Drosophila Genome

Recent studies have consistently inferred high rates of adaptive molecular evolution between Drosophila species. At the same time, the Drosophila genome evolves under different rates of recombination, which results in partial genetic linkage between alleles at neighboring genomic loci. Here we analyze how linkage correlations affect adaptive evolution. We develop a new inference method for adaptation that takes into account the effect on an allele at a focal site caused by neighboring deleterious alleles (background selection) and by neighboring adaptive substitutions (hitchhiking). Using complete genome sequence data and fine-scale recombination maps, we infer a highly heterogeneous scenario of adaptation in Drosophila. In high-recombining regions, about 50% of all amino acid substitutions are adaptive, together with about 20% of all substitutions in proximal intergenic regions. In low-recombining regions, only a small fraction of the amino acid substitutions are adaptive, while hitchhiking accounts for the majority of these changes. Hitchhiking of deleterious alleles generates a substantial collateral cost of adaptation, leading to a fitness decline of about 30/2N per gene and per million years in the lowest-recombining regions. Our results show how recombination shapes rate and efficacy of the adaptive dynamics in eukaryotic genomes.

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arXiv2014

Adaptive evolution of molecular phenotypes

Molecular phenotypes link genomic information with organismic functions, fitness, and evolution. Quantitative traits are complex phenotypes that depend on multiple genomic loci. In this paper, we study the adaptive evolution of a quantitative trait under time-dependent selection, which arises from environmental changes or through fitness interactions with other co-evolving phenotypes. We analyze a model of trait evolution under mutations and genetic drift in a single-peak fitness seascape. The fitness peak performs a constrained random walk in the trait amplitude, which determines the time-dependent trait optimum in a given population. We derive analytical expressions for the distribution of the time-dependent trait divergence between populations and of the trait diversity within populations. Based on this solution, we develop a method to infer adaptive evolution of quantitative traits. Specifically, we show that the ratio of the average trait divergence and the diversity is a universal function of evolutionary time, which predicts the stabilizing strength and the driving rate of the fitness seascape. From an information-theoretic point of view, this function measures the macro-evolutionary entropy in a population ensemble, which determines the predictability of the evolutionary process. Our solution also quantifies two key characteristics of adapting populations: the cumulative fitness flux, which measures the total amount of adaptation, and the adaptive load, which is the fitness cost due to a population's lag behind the fitness peak.

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arXiv2013

Universality and predictability in molecular quantitative genetics

Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. We review recent developments in evolutionary theory and experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis, which is often at least partially unknown. We show that universal measurements can be used to infer selection on a quantitative trait, which determines its evolutionary mode of conservation or adaptation. Furthermore, universality is closely linked to predictability of trait evolution across lineages. We argue that universal trait statistics extends over a range of cellular scales and opens new avenues of quantitative evolutionary systems biology.

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arXiv2010

Significance analysis and statistical mechanics: an application to clustering

This paper addresses the statistical significance of structures in random data: Given a set of vectors and a measure of mutual similarity, how likely does a subset of these vectors form a cluster with enhanced similarity among its elements? The computation of this cluster p-value for randomly distributed vectors is mapped onto a well-defined problem of statistical mechanics. We solve this problem analytically, establishing a connection between the physics of quenched disorder and multiple testing statistics in clustering and related problems. In an application to gene expression data, we find a remarkable link between the statistical significance of a cluster and the functional relationships between its genes.

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arXiv2007

From Protein Interactions to Functional Annotation: Graph Alignment in Herpes

Sequence alignment forms the basis of many methods for functional annotation by phylogenetic comparison, but becomes unreliable in the `twilight' regions of high sequence divergence and short gene length. Here we perform a cross-species comparison of two herpesviruses, VZV and KSHV, with a hybrid method called graph alignment. The method is based jointly on the similarity of protein interaction networks and on sequence similarity. In our alignment, we find open reading frames for which interaction similarity concurs with a low level of sequence similarity, thus confirming the evolutionary relationship. In addition, we find high levels of interaction similarity between open reading frames without any detectable sequence similarity. The functional predictions derived from this alignment are consistent with genomic position and gene expression data.

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