Monotonicity of Fitness Landscapes and Mutation Rate Control

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher’s work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms

Monotonicity of Fitness Landscapes and Mutation Rate Control

A common view in evolutionary biology is that mutation rates are minimised. However, studies in combinatorial optimisation and search have shown a clear advantage of using variable mutation rates as a control parameter to optimise the performance of evolutionary algorithms. Much biological theory in this area is based on Ronald Fisher's work, who used Euclidean geometry to study the relation between mutation size and expected fitness of the offspring in infinite phenotypic spaces. Here we reconsider this theory based on the alternative geometry of discrete and finite spaces of DNA sequences. First, we consider the geometric case of fitness being isomorphic to distance from an optimum, and show how problems of optimal mutation rate control can be solved exactly or approximately depending on additional constraints of the problem. Then we consider the general case of fitness communicating only partial information about the distance. We define weak monotonicity of fitness landscapes and prove that this property holds in all landscapes that are continuous and open at the optimum. This theoretical result motivates our hypothesis that optimal mutation rate functions in such landscapes will increase when fitness decreases in some neighbourhood of an optimum, resembling the control functions derived in the geometric case. We test this hypothesis experimentally by analysing approximately optimal mutation rate control functions in 115 complete landscapes of binding scores between DNA sequences and transcription factors. Our findings support the hypothesis and find that the increase of mutation rate is more rapid in landscapes that are less monotonic (more rugged). We discuss the relevance of these findings to living organisms

Opposing effects of final population density and stress on Escherichia coli mutation rate

Evolution depends on mutations. For an individual genotype, the rate at which mutations arise is known to increase with various stressors (stress-induced mutagenesis-SIM) and decrease at high final population density (density-associated mutation-rate plasticity-DAMP). We hypothesised that these two forms of mutation-rate plasticity would have opposing effects across a nutrient gradient. Here we test this hypothesis, culturing Escherichia coli in increasingly rich media. We distinguish an increase in mutation rate with added nutrients through SIM (dependent on error-prone polymerases Pol IV and Pol V) and an opposing effect of DAMP (dependent on MutT, which removes oxidised G nucleotides). The combination of DAMP and SIM results in a mutation rate minimum at intermediate nutrient levels (which can support 7 × 10  cells ml ). These findings demonstrate a strikingly close and nuanced relationship of ecological factors-stress and population density-with mutation, the fuel of all evolution

Environmental pleiotropy and demographic history direct adaptation under antibiotic selection

Evolutionary rescue following environmental change requires mutations permitting population growth in the new environment. If change is severe enough to prevent most of the population reproducing, rescue becomes reliant on mutations already present. If change is sustained, the fitness effects in both environments, and how they are associated-termed 'environmental pleiotropy'-may determine which alleles are ultimately favoured. A population's demographic history-its size over time-influences the variation present. Although demographic history is known to affect the probability of evolutionary rescue, how it interacts with environmental pleiotropy during severe and sustained environmental change remains unexplored. Here, we demonstrate how these factors interact during antibiotic resistance evolution, a key example of evolutionary rescue fuelled by pre-existing mutations with pleiotropic fitness effects. We combine published data with novel simulations to characterise environmental pleiotropy and its effects on resistance evolution under different demographic histories. Comparisons among resistance alleles typically revealed no correlation for fitness-i.e., neutral pleiotropy-above and below the sensitive strain's minimum inhibitory concentration. Resistance allele frequency following experimental evolution showed opposing correlations with their fitness effects in the presence and absence of antibiotic. Simulations demonstrated that effects of environmental pleiotropy on allele frequencies depended on demographic history. At the population level, the major influence of environmental pleiotropy was on mean fitness, rather than the probability of evolutionary rescue or diversity. Our work suggests that determining both environmental pleiotropy and demographic history is critical for predicting resistance evolution, and we discuss the practicalities of this during in vivo evolution

Spontaneous mutation rate is a plastic trait associated with population density across domains of life.

Rates of random, spontaneous mutation can vary plastically, dependent upon the environment. Such plasticity affects evolutionary trajectories and may be adaptive. We recently identified an inverse plastic association between mutation rate and population density at 1 locus in 1 species of bacterium. It is unknown how widespread this association is, whether it varies among organisms, and what molecular mechanisms of mutagenesis or repair are required for this mutation-rate plasticity. Here, we address all 3 questions. We identify a strong negative association between mutation rate and population density across 70 years of published literature, comprising hundreds of mutation rates estimated using phenotypic markers of mutation (fluctuation tests) from all domains of life and viruses. We test this relationship experimentally, determining that there is indeed density-associated mutation-rate plasticity (DAMP) at multiple loci in both eukaryotes and bacteria, with up to 23-fold lower mutation rates at higher population densities. We find that the degree of plasticity varies, even among closely related organisms. Nonetheless, in each domain tested, DAMP requires proteins scavenging the mutagenic oxidised nucleotide 8-oxo-dGTP. This implies that phenotypic markers give a more precise view of mutation rate than previously believed: having accounted for other known factors affecting mutation rate, controlling for population density can reduce variation in mutation-rate estimates by 93%. Widespread DAMP, which we manipulate genetically in disparate organisms, also provides a novel trait to use in the fight against the evolution of antimicrobial resistance. Such a prevalent environmental association and conserved mechanism suggest that mutation has varied plastically with population density since the early origins of life

Adaptivna mutacija: bomo preziveli genetske vescine bakterij?

The origin and dynamics of genetic variations is one of the key questions in the modem science that has still not come out with a final answer. Emerging concepts regarding genetic variation have always produced a great controversy because they hold a key to unlock a great mystery of evolution. With such a powerful motivation scientist working in the molecular biology, genetics and biochemistry gathered a vast amount of experimental data showing us that a genome is a dynamic, hierarchically organized and complex integrated system for storing and processing information. Dynamic balance between stability and mutability of DNA nucleotide sequences is essential for a proper functioning of the organism. Beside many DNA repairing proteins and DNA protective mechanisms organisms possess also biochemical systems capable of changing DNA information. One of the most controversial and at the same time the most informative one is a phenomenon called adaptive mutation. We shall review findings concerning the phenomenon of adaptive mutation in prokaryotes and point out an urgent need for the upgrade of the awkward neo-darvinistic view on the origin .of the genetic variation.Izvor in dinamika genetskih variacij je eden od kljucnih vprasanj modeme znanosti, ki se vedno caka na dokoncen odgovor. Koncepti v zvezi z genetskimi variacijami povzrocajo veliko polemik, saj nosijo kljuc do skrivnosti evolucije. Molekularni biologi, genetiki in biokemiki, so zavoljo tako mocnega motiva zbrali ogromno kolicino eksperimentalnih podatkov, ki kazejo, da je genom dinamicen, hiearhicno organiziran in kompleksno integriran sistem za shranjevanje inobdelovanje informacij. Dinamicno ravnotezje med stabilnostjo in spremenljivostjo DNK zapisaje nujno za pravilno funkcioniranje organizma. Poleg stevilnih DNK popravljalnih proteinov in DNK varovalnih mehanizmov, imajo organizmi tudi biokemicne sisteme, sposobne spreminjanja DNK informacije. Eden najbolj polemicnih in hkrati najbolj poucnihje fenomen imenovan adaptivna mutacija. Najin namenje pregledati dognanja o adaptivni mutaciji pri prokariontih in pokazati, da je nadgradnja togega neodarvinisticnega pogleda na izvor genetskih variacij, nujno potrebna

Adaptive mutation: shall we survive bacterial genetic skills?

The origin and dynamics of genetic variations is one of the key questions in the modem science that has still not come out with a final answer. Emerging concepts regarding genetic variation have always produced a great controversy because they hold a key to unlock a great mystery of evolution. With such a powerful motivation scientist working in the molecular biology, genetics and biochemistry gathered a vast amount of experimental data showing us that a genome is a dynamic, hierarchically organized and complex integrated system for storing and processing information. Dynamic balance between stability and mutability of DNA nucleotide sequences is essential for a proper functioning of the organism. Beside many DNA repairing proteins and DNA protective mechanisms organisms possess also biochemical systems capable of changing DNA information. One of the most controversial and at the same time the most informative one is a phenomenon called adaptive mutation. We shall review findings concerning the phenomenon of adaptive mutation in prokaryotes and point out an urgent need for the upgrade of the awkward neo-darvinistic view on the origin .of the genetic variation

Stopnja rastno odvisnih in adaptivnih mutacij v ebgR in transpozicija IS30 v bakteriji Escherichia coli K-12 pri različnih zunajceličnih koncentracijah Mg2+

During starvation on carbon and energy Escherichia coli K-12 cells, modified to possess EbgA51 as the only く-galactosidase enzyme, experience adaptive mutations in the ebgR repressor gene. In this way, cells acquire the capacity to utilize the lactulose as the only source of carbon and energy and begin to grow. Adaptive mutations at ebgR are mediated largely by insertion sequences, 40% of adaptive mutants contain IS30 insertions. Also, besides sensing extracellular Mg2+, a PhoP-PhoQ system decreases the adaptive mutation rate to ebgR in a to-date unknown way. By performing fluctuation tests and genetic analyses, we tested the hypothesis that Mg2+ plays an important role in the adaptive mutation at ebgR. Results gathered with phoP and phoQ mutant strains demonstrated that the adaptive, but not the growth-dependent, mutation rate is increased by a high extracellular Mg2+ concentration. In an Mg2+-rich environment, the phoQ cells experience a nearly identical adaptive mutation rate as the wild-type strain. Results with the wild-type strain show that the relation between the levels of PhoP-PhoQ expression and the adaptive mutation rate is not as straightforward as expected and that different Mg2+ concentrations do not affect IS30 transposition. We discuss the possible role of magnesium in the adaptive mutation process.Med stradanjem ogljika in energije pride v celicah Escherichia coli K-12, modificiranih tako, da kodirajo EbgA51 kot edino beta-galaktozidazo, do adaptivnih mutacij v represorskem genu ebgR. Na ta način celice pridobijo sposobnost uporabe laktuloze kot edinega vira ogljika in energije ter začnejo zrastjo. Adaptivne mutacije v ebgR so uravnane v veliki meri z insercijskimi sekvencami, 40% adaptivnih mutant vsebuje IS30. Prav tako dvokomponentniregulatorni sistem PhoP-PhoQ – poleg zaznavanja zunajceličnega Mg2+ – znižuje stopnjo adap- tivnih mutacij ebgR na še vedno neznan način. S pomočjo luktuacijskih testov in genetskimi analizami smo preverili hipotezo, da ima Mg2+ pomembno vlogo v procesu adaptivne mutacije. Dobljeni rezultati s phoPin phoQ mutantami kažejo, da se ob povečani zunajcelični koncentraciji Mg2+ zviša stopnja adaptivnih mutacij, stopnja rastno odvisnih mutacij pa ostanene spremenjena. V okolju z veliko Mg2+ imajo phoQ mutante skoraj enako stopnjo adaptivnih mutacij kot celice divjega tipa. Rezultati poskusov z divjim sevom pa kažejo, da odnos med izražanjem PhoP-PhoQ in adaptivno mutacijo ni preprost, različni koncentraciji Mg2+ pa ne vplivata na transpozicijo IS30. V članku razpravljamo o možni vlogi magnezija v procesu adaptivne mutacije