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Nowak, Martin

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Nowak

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Nowak, Martin

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Now showing 1 - 7 of 7
  • Publication

    The Time Scale of Evolutionary Innovation

    (Public Library of Science, 2014) Chatterjee, Krishnendu; Pavlogiannis, Andreas; Adlam, Ben; Nowak, Martin

    A fundamental question in biology is the following: what is the time scale that is needed for evolutionary innovations? There are many results that characterize single steps in terms of the fixation time of new mutants arising in populations of certain size and structure. But here we ask a different question, which is concerned with the much longer time scale of evolutionary trajectories: how long does it take for a population exploring a fitness landscape to find target sequences that encode new biological functions? Our key variable is the length, of the genetic sequence that undergoes adaptation. In computer science there is a crucial distinction between problems that require algorithms which take polynomial or exponential time. The latter are considered to be intractable. Here we develop a theoretical approach that allows us to estimate the time of evolution as function of We show that adaptation on many fitness landscapes takes time that is exponential in even if there are broad selection gradients and many targets uniformly distributed in sequence space. These negative results lead us to search for specific mechanisms that allow evolution to work on polynomial time scales. We study a regeneration process and show that it enables evolution to work in polynomial time.

  • Publication

    The Evolution of Cell-to-Cell Communication in a Sporulating Bacterium

    (Public Library of Science, 2012) van Gestel, Jordi; Nowak, Martin; Tarnita, Corina

    Traditionally microorganisms were considered to be autonomous organisms that could be studied in isolation. However, over the last decades cell-to-cell communication has been found to be ubiquitous. By secreting molecular signals in the extracellular environment microorganisms can indirectly assess the cell density and respond in accordance. In one of the best-studied microorganisms, Bacillus subtilis, the differentiation processes into a number of distinct cell types have been shown to depend on cell-to-cell communication. One of these cell types is the spore. Spores are metabolically inactive cells that are highly resistant against environmental stress. The onset of sporulation is dependent on cell-to-cell communication, as well as on a number of other environmental cues. By using individual-based simulations we examine when cell-to-cell communication that is involved in the onset of sporulation can evolve. We show that it evolves when three basic premises are satisfied. First, the population of cells has to affect the nutrient conditions. Second, there should be a time-lag between the moment that a cell decides to sporulate and the moment that it turns into a mature spore. Third, there has to be environmental variation. Cell-to-cell communication is a strategy to cope with environmental variation, by allowing cells to predict future environmental conditions. As a consequence, cells can anticipate environmental stress by initiating sporulation. Furthermore, signal production could be considered a cooperative trait and therefore evolves when it is not too costly to produce signal and when there are recurrent colony bottlenecks, which facilitate assortment. Finally, we also show that cell-to-cell communication can drive ecological diversification. Different ecotypes can evolve and be maintained due to frequency-dependent selection.

  • Publication

    Cooperation and the Fate of Microbial Societies

    (Public Library of Science, 2013) Allen, Benjamin; Nowak, Martin

    Microorganisms have been cooperating with each other for billions of years: by sharing resources, communicating with each other, and joining together to form biofilms and other large structures. These cooperative behaviors benefit the colony as a whole; however, they may be costly to the individuals performing them. This raises the question of how such cooperation can arise from natural selection. Mathematical modeling is one important avenue for exploring this question. Evolutionary experiments are another, providing us with an opportunity to see evolutionary dynamics in action and allowing us to test predictions arising from mathematical models. A new study in this issue of PLOS Biology investigates the evolution of a cooperative resource-sharing behavior in yeast. Examining the competition between cooperating and “cheating” strains of yeast, the authors find that, depending on the initial mix of strains, this yeast society either evolves toward a stable coexistence or collapses for lack of cooperation. Using a simple mathematical model, they show how these dynamics arise from eco-evolutionary feedback, where changes in the frequencies of strains are coupled with changes in population size. This study and others illustrate the combined power of modeling and experiment to elucidate the origins of cooperation and other fundamental questions in evolutionary biology.

  • Publication

    The timetable of evolution

    (American Association for the Advancement of Science, 2017) Knoll, Andrew; Nowak, Martin

    The integration of fossils, phylogeny, and geochronology has resulted in an increasingly well-resolved timetable of evolution. Life appears to have taken root before the earliest known minimally metamorphosed sedimentary rocks were deposited, but for a billion years or more, evolution played out beneath an essentially anoxic atmosphere. Oxygen concentrations in the atmosphere and surface oceans first rose in the Great Oxygenation Event (GOE) 2.4 billion years ago, and a second increase beginning in the later Neoproterozoic Era [Neoproterozoic Oxygenation Event (NOE)] established the redox profile of modern oceans. The GOE facilitated the emergence of eukaryotes, whereas the NOE is associated with large and complex multicellular organisms. Thus, the GOE and NOE are fundamental pacemakers for evolution. On the time scale of Earth’s entire 4 billion–year history, the evolutionary dynamics of the planet’s biosphere appears to be fast, and the pace of evolution is largely determined by physical changes of the planet. However, in Phanerozoic ecosystems, interactions between new functions enabled by the accumulation of characters in a complex regulatory environment and changing biological components of effective environments appear to have an important influence on the timing of evolutionary innovations. On the much shorter time scale of transient environmental perturbations, such as those associated with mass extinctions, rates of genetic accommodation may have been limiting for life.

  • Publication

    Phenotypic Heterogeneity and the Evolution of Bacterial Life Cycles

    (Public Library of Science, 2016) van Gestel, Jordi; Nowak, Martin

    Most bacteria live in colonies, where they often express different cell types. The ecological significance of these cell types and their evolutionary origin are often unknown. Here, we study the evolution of cell differentiation in the context of surface colonization. We particularly focus on the evolution of a ‘sticky’ cell type that is required for surface attachment, but is costly to express. The sticky cells not only facilitate their own attachment, but also that of non-sticky cells. Using individual-based simulations, we show that surface colonization rapidly evolves and in most cases leads to phenotypic heterogeneity, in which sticky and non-sticky cells occur side by side on the surface. In the presence of regulation, cell differentiation leads to a remarkable set of bacterial life cycles, in which cells alternate between living in the liquid and living on the surface. The dominant life stage is formed by the surface-attached colony that shows many complex features: colonies reproduce via fission and by producing migratory propagules; cells inside the colony divide labour; and colonies can produce filaments to facilitate expansion. Overall, our model illustrates how the evolution of an adhesive cell type goes hand in hand with the evolution of complex bacterial life cycles.

  • Publication

    Quantifying Clonal and Subclonal Passenger Mutations in Cancer Evolution

    (Public Library of Science, 2016) Bozic, Ivana; Gerold, Jeff; Nowak, Martin

    The vast majority of mutations in the exome of cancer cells are passengers, which do not affect the reproductive rate of the cell. Passengers can provide important information about the evolutionary history of an individual cancer, and serve as a molecular clock. Passengers can also become targets for immunotherapy or confer resistance to treatment. We study the stochastic expansion of a population of cancer cells describing the growth of primary tumors or metastatic lesions. We first analyze the process by looking forward in time and calculate the fixation probabilities and frequencies of successive passenger mutations ordered by their time of appearance. We compute the likelihood of specific evolutionary trees, thereby informing the phylogenetic reconstruction of cancer evolution in individual patients. Next, we derive results looking backward in time: for a given subclonal mutation we estimate the number of cancer cells that were present at the time when that mutation arose. We derive exact formulas for the expected numbers of subclonal mutations of any frequency. Fitting this formula to cancer sequencing data leads to an estimate for the ratio of birth and death rates of cancer cells during the early stages of clonal expansion.

  • Publication

    Prebiotic selection for motifs in a model of template-free elongation of polymers within compartments

    (Public Library of Science, 2017) Kinsler, Grant; Sinai, Sam; Lee, Nicholas Keone; Nowak, Martin

    The transition from prelife where self-replication does not occur, to life which exhibits self-replication and evolution, has been a subject of interest for many decades. Membranes, forming compartments, seem to be a critical component of this transition as they provide several concurrent benefits. They maintain localized interactions, generate electro-chemical gradients, and help in selecting cooperative functions as they arise. These functions pave the way for the emergence and maintenance of simple metabolic cycles and polymers. In the context of origin of life, evolution of information-carrying molecules and RNA based enzymes within compartments has been subject to intensive theoretical and experimental research. Hence, many experimental efforts aim to produce compartments that contain elongating polynucleotides (also referred to as protocells), which store information and perform catalysis. Despite impressive experimental progress, we are still relatively ignorant about the dynamics by which elongating polynucleotides can produce more sophisticated behaviors. Here we perform computer simulations to couple information production through template-free elongation of polymers with dividing compartments. We find that polymers with a simple ability—biasing the concentration of monomers within their own compartment—can acquire a selective advantage in prelife. We further investigate whether such a mechanism allows for cooperative dynamics to dominate over purely competitive ones. We show that under this system of biased monomer addition, even without template-directed self-replication, genetic motifs can emerge, compete, cooperate, and ultimately survive within the population.