TY - GEN AB - Based on the intuitive derivation of the dynamics of SIM allele frequency pM in the main text, we present a heuristic prediction for the long-term SIM allele frequencies with χ > 1 stresses and compare it to numerical simulations. AU - Lukacisinova, Marta AU - Novak, Sebastian AU - Paixao, Tiago ID - 9851 TI - Heuristic prediction for multiple stresses ER - TY - GEN AB - We show how different combination strategies affect the fraction of individuals that are multi-resistant. AU - Lukacisinova, Marta AU - Novak, Sebastian AU - Paixao, Tiago ID - 9852 TI - Resistance frequencies for different combination strategies ER - TY - GEN AU - Nikolic, Nela AU - Schreiber, Frank AU - Dal Co, Alma AU - Kiviet, Daniel AU - Bergmiller, Tobias AU - Littmann, Sten AU - Kuypers, Marcel AU - Ackermann, Martin ID - 9844 TI - Source data for figures and tables ER - TY - JOUR AB - Restriction–modification systems are widespread genetic elements that protect bacteria from bacteriophage infections by recognizing and cleaving heterologous DNA at short, well-defined sequences called restriction sites. Bioinformatic evidence shows that restriction sites are significantly underrepresented in bacteriophage genomes, presumably because bacteriophages with fewer restriction sites are more likely to escape cleavage by restriction–modification systems. However, how mutations in restriction sites affect the likelihood of bacteriophage escape is unknown. Using the bacteriophage l and the restriction–modification system EcoRI, we show that while mutation effects at different restriction sites are unequal, they are independent. As a result, the probability of bacteriophage escape increases with each mutated restriction site. Our results experimentally support the role of restriction site avoidance as a response to selection imposed by restriction–modification systems and offer an insight into the events underlying the process of bacteriophage escape. AU - Pleska, Maros AU - Guet, Calin C ID - 561 IS - 12 JF - Biology Letters SN - 1744-9561 TI - Effects of mutations in phage restriction sites during escape from restriction–modification VL - 13 ER - TY - THES AB - Restriction-modification (RM) represents the simplest and possibly the most widespread mechanism of self/non-self discrimination in nature. In order to provide bacteria with immunity against bacteriophages and other parasitic genetic elements, RM systems rely on a balance between two enzymes: the restriction enzyme, which cleaves non-self DNA at specific restriction sites, and the modification enzyme, which tags the host’s DNA as self and thus protects it from cleavage. In this thesis, I use population and single-cell level experiments in combination with mathematical modeling to study different aspects of the interplay between RM systems, bacteria and bacteriophages. First, I analyze how mutations in phage restriction sites affect the probability of phage escape – an inherently stochastic process, during which phages accidently get modified instead of restricted. Next, I use single-cell experiments to show that RM systems can, with a low probability, attack the genome of their bacterial host and that this primitive form of autoimmunity leads to a tradeoff between the evolutionary cost and benefit of RM systems. Finally, I investigate the nature of interactions between bacteria, RM systems and temperate bacteriophages to find that, as a consequence of phage escape and its impact on population dynamics, RM systems can promote acquisition of symbiotic bacteriophages, rather than limit it. The results presented here uncover new fundamental biological properties of RM systems and highlight their importance in the ecology and evolution of bacteria, bacteriophages and their interactions. AU - Pleska, Maros ID - 202 SN - 2663-337X TI - Biology of restriction-modification systems at the single-cell and population level ER - TY - JOUR AB - The behaviour of gene regulatory networks (GRNs) is typically analysed using simulation-based statistical testing-like methods. In this paper, we demonstrate that we can replace this approach by a formal verification-like method that gives higher assurance and scalability. We focus on Wagner’s weighted GRN model with varying weights, which is used in evolutionary biology. In the model, weight parameters represent the gene interaction strength that may change due to genetic mutations. For a property of interest, we synthesise the constraints over the parameter space that represent the set of GRNs satisfying the property. We experimentally show that our parameter synthesis procedure computes the mutational robustness of GRNs—an important problem of interest in evolutionary biology—more efficiently than the classical simulation method. We specify the property in linear temporal logic. We employ symbolic bounded model checking and SMT solving to compute the space of GRNs that satisfy the property, which amounts to synthesizing a set of linear constraints on the weights. AU - Giacobbe, Mirco AU - Guet, Calin C AU - Gupta, Ashutosh AU - Henzinger, Thomas A AU - Paixao, Tiago AU - Petrov, Tatjana ID - 1351 IS - 8 JF - Acta Informatica SN - 00015903 TI - Model checking the evolution of gene regulatory networks VL - 54 ER - TY - JOUR AB - Evolutionary algorithms (EAs) form a popular optimisation paradigm inspired by natural evolution. In recent years the field of evolutionary computation has developed a rigorous analytical theory to analyse the runtimes of EAs on many illustrative problems. Here we apply this theory to a simple model of natural evolution. In the Strong Selection Weak Mutation (SSWM) evolutionary regime the time between occurrences of new mutations is much longer than the time it takes for a mutated genotype to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a stochastic process evolving one genotype by means of mutation and selection between the resident and the mutated genotype. The probability of accepting the mutated genotype then depends on the change in fitness. We study this process, SSWM, from an algorithmic perspective, quantifying its expected optimisation time for various parameters and investigating differences to a similar evolutionary algorithm, the well-known (1+1) EA. We show that SSWM can have a moderate advantage over the (1+1) EA at crossing fitness valleys and study an example where SSWM outperforms the (1+1) EA by taking advantage of information on the fitness gradient. AU - Paixao, Tiago AU - Pérez Heredia, Jorge AU - Sudholt, Dirk AU - Trubenova, Barbora ID - 1336 IS - 2 JF - Algorithmica SN - 01784617 TI - Towards a runtime comparison of natural and artificial evolution VL - 78 ER - TY - JOUR AB - BceRS and PsdRS are paralogous two-component systems in Bacillus subtilis controlling the response to antimicrobial peptides. In the presence of extracellular bacitracin and nisin, respectively, the two response regulators (RRs) bind their target promoters, PbceA or PpsdA, resulting in a strong up-regulation of target gene expression and ultimately antibiotic resistance. Despite high sequence similarity between the RRs BceR and PsdR and their known binding sites, no cross-regulation has been observed between them. We therefore investigated the specificity determinants of PbceA and PpsdA that ensure the insulation of these two paralogous pathways at the RR–promoter interface. In vivo and in vitro analyses demonstrate that the regulatory regions within these two promoters contain three important elements: in addition to the known (main) binding site, we identified a linker region and a secondary binding site that are crucial for functionality. Initial binding to the high-affinity, low-specificity main binding site is a prerequisite for the subsequent highly specific binding of a second RR dimer to the low-affinity secondary binding site. In addition to this hierarchical cooperative binding, discrimination requires a competition of the two RRs for their respective binding site mediated by only slight differences in binding affinities. AU - Fang, Chong AU - Nagy-Staron, Anna A AU - Grafe, Martin AU - Heermann, Ralf AU - Jung, Kirsten AU - Gebhard, Susanne AU - Mascher, Thorsten ID - 1084 IS - 1 JF - Molecular Microbiology SN - 0950382X TI - Insulation and wiring specificity of BceR like response regulators and their target promoters in Bacillus subtilis VL - 104 ER - TY - JOUR AB - Understanding the relation between genotype and phenotype remains a major challenge. The difficulty of predicting individual mutation effects, and particularly the interactions between them, has prevented the development of a comprehensive theory that links genotypic changes to their phenotypic effects. We show that a general thermodynamic framework for gene regulation, based on a biophysical understanding of protein-DNA binding, accurately predicts the sign of epistasis in a canonical cis-regulatory element consisting of overlapping RNA polymerase and repressor binding sites. Sign and magnitude of individual mutation effects are sufficient to predict the sign of epistasis and its environmental dependence. Thus, the thermodynamic model offers the correct null prediction for epistasis between mutations across DNA-binding sites. Our results indicate that a predictive theory for the effects of cis-regulatory mutations is possible from first principles, as long as the essential molecular mechanisms and the constraints these impose on a biological system are accounted for. AU - Lagator, Mato AU - Paixao, Tiago AU - Barton, Nicholas H AU - Bollback, Jonathan P AU - Guet, Calin C ID - 954 JF - eLife SN - 2050084X TI - On the mechanistic nature of epistasis in a canonical cis-regulatory element VL - 6 ER - TY - JOUR AB - A nonlinear system possesses an invariance with respect to a set of transformations if its output dynamics remain invariant when transforming the input, and adjusting the initial condition accordingly. Most research has focused on invariances with respect to time-independent pointwise transformations like translational-invariance (u(t) -> u(t) + p, p in R) or scale-invariance (u(t) -> pu(t), p in R>0). In this article, we introduce the concept of s0-invariances with respect to continuous input transformations exponentially growing/decaying over time. We show that s0-invariant systems not only encompass linear time-invariant (LTI) systems with transfer functions having an irreducible zero at s0 in R, but also that the input/output relationship of nonlinear s0-invariant systems possesses properties well known from their linear counterparts. Furthermore, we extend the concept of s0-invariances to second- and higher-order s0-invariances, corresponding to invariances with respect to transformations of the time-derivatives of the input, and encompassing LTI systems with zeros of multiplicity two or higher. Finally, we show that nth-order 0-invariant systems realize – under mild conditions – nth-order nonlinear differential operators: when excited by an input of a characteristic functional form, the system’s output converges to a constant value only depending on the nth (nonlinear) derivative of the input. AU - Lang, Moritz AU - Sontag, Eduardo ID - 1007 JF - Automatica SN - 0005-1098 TI - Zeros of nonlinear systems with input invariances VL - 81C ER -