TY - CONF AB - When designing genetic circuits, the typical primitives used in major existing modelling formalisms are gene interaction graphs, where edges between genes denote either an activation or inhibition relation. However, when designing experiments, it is important to be precise about the low-level mechanistic details as to how each such relation is implemented. The rule-based modelling language Kappa allows to unambiguously specify mechanistic details such as DNA binding sites, dimerisation of transcription factors, or co-operative interactions. Such a detailed description comes with complexity and computationally costly executions. We propose a general method for automatically transforming a rule-based program, by eliminating intermediate species and adjusting the rate constants accordingly. To the best of our knowledge, we show the first automated reduction of rule-based models based on equilibrium approximations. Our algorithm is an adaptation of an existing algorithm, which was designed for reducing reaction-based programs; our version of the algorithm scans the rule-based Kappa model in search for those interaction patterns known to be amenable to equilibrium approximations (e.g. Michaelis-Menten scheme). Additional checks are then performed in order to verify if the reduction is meaningful in the context of the full model. The reduced model is efficiently obtained by static inspection over the rule-set. The tool is tested on a detailed rule-based model of a λ-phage switch, which lists 92 rules and 13 agents. The reduced model has 11 rules and 5 agents, and provides a dramatic reduction in simulation time of several orders of magnitude. AU - Beica, Andreea AU - Guet, Calin C AU - Petrov, Tatjana ID - 1524 TI - Efficient reduction of kappa models by static inspection of the rule-set VL - 9271 ER - TY - JOUR AB - In bacteria, replicative aging manifests as a difference in growth or survival between the two cells emerging from division. One cell can be regarded as an aging mother with a decreased potential for future survival and division, the other as a rejuvenated daughter. Here, we aimed at investigating some of the processes involved in aging in the bacterium Escherichia coli, where the two types of cells can be distinguished by the age of their cell poles. We found that certain changes in the regulation of the carbohydrate metabolism can affect aging. A mutation in the carbon storage regulator gene, csrA, leads to a dramatically shorter replicative lifespan; csrA mutants stop dividing once their pole exceeds an age of about five divisions. These old-pole cells accumulate glycogen at their old cell poles; after their last division, they do not contain a chromosome, presumably because of spatial exclusion by the glycogen aggregates. The new-pole daughters produced by these aging mothers are born young; they only express the deleterious phenotype once their pole is old. These results demonstrate how manipulations of nutrient allocation can lead to the exclusion of the chromosome and limit replicative lifespan in E. coli, and illustrate how mutations can have phenotypic effects that are specific for cells with old poles. This raises the question how bacteria can avoid the accumulation of such mutations in their genomes over evolutionary times, and how they can achieve the long replicative lifespans that have recently been reported. AU - Boehm, Alex AU - Arnoldini, Markus AU - Bergmiller, Tobias AU - Röösli, Thomas AU - Bigosch, Colette AU - Ackermann, Martin ID - 1250 IS - 4 JF - PLoS Genetics TI - Genetic manipulation of glycogen allocation affects replicative lifespan in E coli VL - 12 ER - TY - GEN AU - Boehm, Alex AU - Arnoldini, Markus AU - Bergmiller, Tobias AU - Röösli, Thomas AU - Bigosch, Colette AU - Ackermann, Martin ID - 9873 TI - Quantification of the growth rate reduction as a consequence of age-specific mortality ER - TY - JOUR AB - Parasitism creates selection for resistance mechanisms in host populations and is hypothesized to promote increased host evolvability. However, the influence of these traits on host evolution when parasites are no longer present is unclear. We used experimental evolution and whole-genome sequencing of Escherichia coli to determine the effects of past and present exposure to parasitic viruses (phages) on the spread of mutator alleles, resistance, and bacterial competitive fitness. We found that mutator alleles spread rapidly during adaptation to any of four different phage species, and this pattern was even more pronounced with multiple phages present simultaneously. However, hypermutability did not detectably accelerate adaptation in the absence of phages and recovery of fitness costs associated with resistance. Several lineages evolved phage resistance through elevated mucoidy, and during subsequent evolution in phage-free conditions they rapidly reverted to nonmucoid, phage-susceptible phenotypes. Genome sequencing revealed that this phenotypic reversion was achieved by additional genetic changes rather than by genotypic reversion of the initial resistance mutations. Insertion sequence (IS) elements played a key role in both the acquisition of resistance and adaptation in the absence of parasites; unlike single nucleotide polymorphisms, IS insertions were not more frequent in mutator lineages. Our results provide a genetic explanation for rapid reversion of mucoidy, a phenotype observed in other bacterial species including human pathogens. Moreover, this demonstrates that the types of genetic change underlying adaptation to fitness costs, and consequently the impact of evolvability mechanisms such as increased point-mutation rates, depend critically on the mechanism of resistance. AU - Wielgoss, Sébastien AU - Bergmiller, Tobias AU - Bischofberger, Anna M. AU - Hall, Alex R. ID - 5749 IS - 3 JF - Molecular Biology and Evolution SN - 0737-4038 TI - Adaptation to parasites and costs of parasite resistance in mutator and nonmutator bacteria VL - 33 ER - TY - CONF AB - We introduce a general class of distances (metrics) between Markov chains, which are based on linear behaviour. This class encompasses distances given topologically (such as the total variation distance or trace distance) as well as by temporal logics or automata. We investigate which of the distances can be approximated by observing the systems, i.e. by black-box testing or simulation, and we provide both negative and positive results. AU - Daca, Przemyslaw AU - Henzinger, Thomas A AU - Kretinsky, Jan AU - Petrov, Tatjana ID - 1093 TI - Linear distances between Markov chains VL - 59 ER - TY - CONF AB - We present a new algorithm for the statistical model checking of Markov chains with respect to unbounded temporal properties, including full linear temporal logic. The main idea is that we monitor each simulation run on the fly, in order to detect quickly if a bottom strongly connected component is entered with high probability, in which case the simulation run can be terminated early. As a result, our simulation runs are often much shorter than required by termination bounds that are computed a priori for a desired level of confidence on a large state space. In comparison to previous algorithms for statistical model checking our method is not only faster in many cases but also requires less information about the system, namely, only the minimum transition probability that occurs in the Markov chain. In addition, our method can be generalised to unbounded quantitative properties such as mean-payoff bounds. AU - Daca, Przemyslaw AU - Henzinger, Thomas A AU - Kretinsky, Jan AU - Petrov, Tatjana ID - 1234 TI - Faster statistical model checking for unbounded temporal properties VL - 9636 ER - TY - JOUR AB - Restriction-modification (RM) systems represent a minimal and ubiquitous biological system of self/non-self discrimination in prokaryotes [1], which protects hosts from exogenous DNA [2]. The mechanism is based on the balance between methyltransferase (M) and cognate restriction endonuclease (R). M tags endogenous DNA as self by methylating short specific DNA sequences called restriction sites, whereas R recognizes unmethylated restriction sites as non-self and introduces a double-stranded DNA break [3]. Restriction sites are significantly underrepresented in prokaryotic genomes [4-7], suggesting that the discrimination mechanism is imperfect and occasionally leads to autoimmunity due to self-DNA cleavage (self-restriction) [8]. Furthermore, RM systems can promote DNA recombination [9] and contribute to genetic variation in microbial populations, thus facilitating adaptive evolution [10]. However, cleavage of self-DNA by RM systems as elements shaping prokaryotic genomes has not been directly detected, and its cause, frequency, and outcome are unknown. We quantify self-restriction caused by two RM systems of Escherichia coli and find that, in agreement with levels of restriction site avoidance, EcoRI, but not EcoRV, cleaves self-DNA at a measurable rate. Self-restriction is a stochastic process, which temporarily induces the SOS response, and is followed by DNA repair, maintaining cell viability. We find that RM systems with higher restriction efficiency against bacteriophage infections exhibit a higher rate of self-restriction, and that this rate can be further increased by stochastic imbalance between R and M. Our results identify molecular noise in RM systems as a factor shaping prokaryotic genomes. AU - Pleska, Maros AU - Qian, Long AU - Okura, Reiko AU - Bergmiller, Tobias AU - Wakamoto, Yuichi AU - Kussell, Edo AU - Guet, Calin C ID - 1243 IS - 3 JF - Current Biology TI - Bacterial autoimmunity due to a restriction-modification system VL - 26 ER - TY - JOUR AB - Gene regulation relies on the specificity of transcription factor (TF)–DNA interactions. Limited specificity may lead to crosstalk: a regulatory state in which a gene is either incorrectly activated due to noncognate TF–DNA interactions or remains erroneously inactive. As each TF can have numerous interactions with noncognate cis-regulatory elements, crosstalk is inherently a global problem, yet has previously not been studied as such. We construct a theoretical framework to analyse the effects of global crosstalk on gene regulation. We find that crosstalk presents a significant challenge for organisms with low-specificity TFs, such as metazoans. Crosstalk is not easily mitigated by known regulatory schemes acting at equilibrium, including variants of cooperativity and combinatorial regulation. Our results suggest that crosstalk imposes a previously unexplored global constraint on the functioning and evolution of regulatory networks, which is qualitatively distinct from the known constraints that act at the level of individual gene regulatory elements. AU - Friedlander, Tamar AU - Prizak, Roshan AU - Guet, Calin C AU - Barton, Nicholas H AU - Tkacik, Gasper ID - 1358 JF - Nature Communications TI - Intrinsic limits to gene regulation by global crosstalk VL - 7 ER - TY - CONF 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 their runtime 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 occurrence of new mutations is much longer than the time it takes for a new beneficial mutation to take over the population. In this situation, the population only contains copies of one genotype and evolution can be modelled as a (1+1)-type process where the probability of accepting a new genotype (improvements or worsenings) depends on the change in fitness. We present an initial runtime analysis of SSWM, quantifying its performance for various parameters and investigating differences to the (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 - Sudholt, Dirk AU - Heredia, Jorge AU - Trubenova, Barbora ID - 1430 T2 - Proceedings of the 2015 Annual Conference on Genetic and Evolutionary Computation TI - First steps towards a runtime comparison of natural and artificial evolution ER - TY - JOUR AB - The theory of population genetics and evolutionary computation have been evolving separately for nearly 30 years. Many results have been independently obtained in both fields and many others are unique to its respective field. We aim to bridge this gap by developing a unifying framework for evolutionary processes that allows both evolutionary algorithms and population genetics models to be cast in the same formal framework. The framework we present here decomposes the evolutionary process into its several components in order to facilitate the identification of similarities between different models. In particular, we propose a classification of evolutionary operators based on the defining properties of the different components. We cast several commonly used operators from both fields into this common framework. Using this, we map different evolutionary and genetic algorithms to different evolutionary regimes and identify candidates with the most potential for the translation of results between the fields. This provides a unified description of evolutionary processes and represents a stepping stone towards new tools and results to both fields. AU - Paixao, Tiago AU - Badkobeh, Golnaz AU - Barton, Nicholas H AU - Çörüş, Doğan AU - Dang, Duccuong AU - Friedrich, Tobias AU - Lehre, Per AU - Sudholt, Dirk AU - Sutton, Andrew AU - Trubenova, Barbora ID - 1542 JF - Journal of Theoretical Biology TI - Toward a unifying framework for evolutionary processes VL - 383 ER - TY - JOUR AB - In this paper, we present a method for reducing a regular, discrete-time Markov chain (DTMC) to another DTMC with a given, typically much smaller number of states. The cost of reduction is defined as the Kullback-Leibler divergence rate between a projection of the original process through a partition function and a DTMC on the correspondingly partitioned state space. Finding the reduced model with minimal cost is computationally expensive, as it requires an exhaustive search among all state space partitions, and an exact evaluation of the reduction cost for each candidate partition. Our approach deals with the latter problem by minimizing an upper bound on the reduction cost instead of minimizing the exact cost. The proposed upper bound is easy to compute and it is tight if the original chain is lumpable with respect to the partition. Then, we express the problem in the form of information bottleneck optimization, and propose using the agglomerative information bottleneck algorithm for searching a suboptimal partition greedily, rather than exhaustively. The theory is illustrated with examples and one application scenario in the context of modeling bio-molecular interactions. AU - Geiger, Bernhard AU - Petrov, Tatjana AU - Kubin, Gernot AU - Koeppl, Heinz ID - 1840 IS - 4 JF - IEEE Transactions on Automatic Control SN - 0018-9286 TI - Optimal Kullback-Leibler aggregation via information bottleneck VL - 60 ER - TY - GEN AU - Tugrul, Murat AU - Paixao, Tiago AU - Barton, Nicholas H AU - Tkačik, Gašper ID - 9712 TI - Other fitness models for comparison & for interacting TFBSs ER - TY - GEN AB - Parasitism creates selection for resistance mechanisms in host populations and is hypothesized to promote increased host evolvability. However, the influence of these traits on host evolution when parasites are no longer present is unclear. We used experimental evolution and whole-genome sequencing of Escherichia coli to determine the effects of past and present exposure to parasitic viruses (phages) on the spread of mutator alleles, resistance, and bacterial competitive fitness. We found that mutator alleles spread rapidly during adaptation to any of four different phage species, and this pattern was even more pronounced with multiple phages present simultaneously. However, hypermutability did not detectably accelerate adaptation in the absence of phages and recovery of fitness costs associated with resistance. Several lineages evolved phage resistance through elevated mucoidy, and during subsequent evolution in phage-free conditions they rapidly reverted to nonmucoid, phage-susceptible phenotypes. Genome sequencing revealed that this phenotypic reversion was achieved by additional genetic changes rather than by genotypic reversion of the initial resistance mutations. Insertion sequence (IS) elements played a key role in both the acquisition of resistance and adaptation in the absence of parasites; unlike single nucleotide polymorphisms, IS insertions were not more frequent in mutator lineages. Our results provide a genetic explanation for rapid reversion of mucoidy, a phenotype observed in other bacterial species including human pathogens. Moreover, this demonstrates that the types of genetic change underlying adaptation to fitness costs, and consequently the impact of evolvability mechanisms such as increased point-mutation rates, depend critically on the mechanism of resistance. AU - Wielgoss, Sébastien AU - Bergmiller, Tobias AU - Bischofberger, Anna M. AU - Hall, Alex R. ID - 9719 TI - Data from: Adaptation to parasites and costs of parasite resistance in mutator and non-mutator bacteria ER - TY - JOUR AB - Evolution of gene regulation is crucial for our understanding of the phenotypic differences between species, populations and individuals. Sequence-specific binding of transcription factors to the regulatory regions on the DNA is a key regulatory mechanism that determines gene expression and hence heritable phenotypic variation. We use a biophysical model for directional selection on gene expression to estimate the rates of gain and loss of transcription factor binding sites (TFBS) in finite populations under both point and insertion/deletion mutations. Our results show that these rates are typically slow for a single TFBS in an isolated DNA region, unless the selection is extremely strong. These rates decrease drastically with increasing TFBS length or increasingly specific protein-DNA interactions, making the evolution of sites longer than ∼ 10 bp unlikely on typical eukaryotic speciation timescales. Similarly, evolution converges to the stationary distribution of binding sequences very slowly, making the equilibrium assumption questionable. The availability of longer regulatory sequences in which multiple binding sites can evolve simultaneously, the presence of “pre-sites” or partially decayed old sites in the initial sequence, and biophysical cooperativity between transcription factors, can all facilitate gain of TFBS and reconcile theoretical calculations with timescales inferred from comparative genomics. AU - Tugrul, Murat AU - Paixao, Tiago AU - Barton, Nicholas H AU - Tkacik, Gasper ID - 1666 IS - 11 JF - PLoS Genetics TI - Dynamics of transcription factor binding site evolution VL - 11 ER - TY - CONF 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 logics. 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 - 1835 TI - Model checking gene regulatory networks VL - 9035 ER - TY - JOUR AB - Background: Bacterial Dsb enzymes are involved in the oxidative folding of many proteins, through the formation of disulfide bonds between their cysteine residues. The Dsb protein network has been well characterized in cells of the model microorganism Escherichia coli. To gain insight into the functioning of the Dsb system in epsilon-Proteobacteria, where it plays an important role in the colonization process, we studied two homologs of the main Escherichia coli Dsb oxidase (EcDsbA) that are present in the cells of the enteric pathogen Campylobacter jejuni, the most frequently reported bacterial cause of human enteritis in the world. Methods and Results: Phylogenetic analysis suggests the horizontal transfer of the epsilon-Proteobacterial DsbAs from a common ancestor to gamma-Proteobacteria, which then gave rise to the DsbL lineage. Phenotype and enzymatic assays suggest that the two C. jejuni DsbAs play different roles in bacterial cells and have divergent substrate spectra. CjDsbA1 is essential for the motility and autoagglutination phenotypes, while CjDsbA2 has no impact on those processes. CjDsbA1 plays a critical role in the oxidative folding that ensures the activity of alkaline phosphatase CjPhoX, whereas CjDsbA2 is crucial for the activity of arylsulfotransferase CjAstA, encoded within the dsbA2-dsbB-astA operon. Conclusions: Our results show that CjDsbA1 is the primary thiol-oxidoreductase affecting life processes associated with bacterial spread and host colonization, as well as ensuring the oxidative folding of particular protein substrates. In contrast, CjDsbA2 activity does not affect the same processes and so far its oxidative folding activity has been demonstrated for one substrate, arylsulfotransferase CjAstA. The results suggest the cooperation between CjDsbA2 and CjDsbB. In the case of the CjDsbA1, this cooperation is not exclusive and there is probably another protein to be identified in C. jejuni cells that acts to re-oxidize CjDsbA1. Altogether the data presented here constitute the considerable insight to the Epsilonproteobacterial Dsb systems, which have been poorly understood so far. AU - Grabowska, Anna AU - Wywiał, Ewa AU - Dunin Horkawicz, Stanislaw AU - Łasica, Anna AU - Wösten, Marc AU - Nagy-Staron, Anna A AU - Godlewska, Renata AU - Bocian Ostrzycka, Katarzyna AU - Pieńkowska, Katarzyna AU - Łaniewski, Paweł AU - Bujnicki, Janusz AU - Van Putten, Jos AU - Jagusztyn Krynicka, Elzbieta ID - 1894 IS - 9 JF - PLoS One TI - Functional and bioinformatics analysis of two Campylobacter jejuni homologs of the thiol-disulfide oxidoreductase, DsbA VL - 9 ER - TY - JOUR AB - We consider a continuous-time Markov chain (CTMC) whose state space is partitioned into aggregates, and each aggregate is assigned a probability measure. A sufficient condition for defining a CTMC over the aggregates is presented as a variant of weak lumpability, which also characterizes that the measure over the original process can be recovered from that of the aggregated one. We show how the applicability of de-aggregation depends on the initial distribution. The application section is devoted to illustrate how the developed theory aids in reducing CTMC models of biochemical systems particularly in connection to protein-protein interactions. We assume that the model is written by a biologist in form of site-graph-rewrite rules. Site-graph-rewrite rules compactly express that, often, only a local context of a protein (instead of a full molecular species) needs to be in a certain configuration in order to trigger a reaction event. This observation leads to suitable aggregate Markov chains with smaller state spaces, thereby providing sufficient reduction in computational complexity. This is further exemplified in two case studies: simple unbounded polymerization and early EGFR/insulin crosstalk. AU - Ganguly, Arnab AU - Petrov, Tatjana AU - Koeppl, Heinz ID - 2056 IS - 3 JF - Journal of Mathematical Biology TI - Markov chain aggregation and its applications to combinatorial reaction networks VL - 69 ER - TY - JOUR AB - Understanding the effects of sex and migration on adaptation to novel environments remains a key problem in evolutionary biology. Using a single-cell alga Chlamydomonas reinhardtii, we investigated how sex and migration affected rates of evolutionary rescue in a sink environment, and subsequent changes in fitness following evolutionary rescue. We show that sex and migration affect both the rate of evolutionary rescue and subsequent adaptation. However, their combined effects change as the populations adapt to a sink habitat. Both sex and migration independently increased rates of evolutionary rescue, but the effect of sex on subsequent fitness improvements, following initial rescue, changed with migration, as sex was beneficial in the absence of migration but constraining adaptation when combined with migration. These results suggest that sex and migration are beneficial during the initial stages of adaptation, but can become detrimental as the population adapts to its environment. AU - Lagator, Mato AU - Morgan, Andrew AU - Neve, Paul AU - Colegrave, Nick ID - 2083 IS - 8 JF - Evolution TI - Role of sex and migration in adaptation to sink environments VL - 68 ER - TY - GEN AB - Understanding the effects of sex and migration on adaptation to novel environments remains a key problem in evolutionary biology. Using a single-cell alga Chlamydomonas reinhardtii, we investigated how sex and migration affected rates of evolutionary rescue in a sink environment, and subsequent changes in fitness following evolutionary rescue. We show that sex and migration affect both the rate of evolutionary rescue and subsequent adaptation. However, their combined effects change as the populations adapt to a sink habitat. Both sex and migration independently increased rates of evolutionary rescue, but the effect of sex on subsequent fitness improvements, following initial rescue, changed with migration, as sex was beneficial in the absence of migration but constraining adaptation when combined with migration. These results suggest that sex and migration are beneficial during the initial stages of adaptation, but can become detrimental as the population adapts to its environment. AU - Lagator, Mato AU - Morgan, Andrew AU - Neve, Paul AU - Colegrave, Nick ID - 9747 TI - Data from: Role of sex and migration in adaptation to sink environments ER - TY - JOUR AB - In rapidly changing environments, selection history may impact the dynamics of adaptation. Mutations selected in one environment may result in pleiotropic fitness trade-offs in subsequent novel environments, slowing the rates of adaptation. Epistatic interactions between mutations selected in sequential stressful environments may slow or accelerate subsequent rates of adaptation, depending on the nature of that interaction. We explored the dynamics of adaptation during sequential exposure to herbicides with different modes of action in Chlamydomonas reinhardtii. Evolution of resistance to two of the herbicides was largely independent of selection history. For carbetamide, previous adaptation to other herbicide modes of action positively impacted the likelihood of adaptation to this herbicide. Furthermore, while adaptation to all individual herbicides was associated with pleiotropic fitness costs in stress-free environments, we observed that accumulation of resistance mechanisms was accompanied by a reduction in overall fitness costs. We suggest that antagonistic epistasis may be a driving mechanism that enables populations to more readily adapt in novel environments. These findings highlight the potential for sequences of xenobiotics to facilitate the rapid evolution of multiple-drug and -pesticide resistance, as well as the potential for epistatic interactions between adaptive mutations to facilitate evolutionary rescue in rapidly changing environments. AU - Lagator, Mato AU - Colegrave, Nick AU - Neve, Paul ID - 2036 IS - 1794 JF - Proceedings of the Royal Society of London Series B Biological Sciences TI - Selection history and epistatic interactions impact dynamics of adaptation to novel environmental stresses VL - 281 ER -