Estimating mutation rates under heterogeneous stress responses.

Exposure to environmental stressors, including certain antibiotics, induces stress responses in bacteria. Some of these responses increase mutagenesis and thus potentially accelerate resistance evolution. Many studies report increased mutation rates under stress, often using the standard experimental approach of fluctuation assays. However, single-cell studies have revealed that many stress responses are heterogeneously expressed in bacterial populations, which existing estimation methods have not yet addressed. We develop a population dynamic model that considers heterogeneous stress responses (subpopulations of cells with the response off or on) that impact both mutation rate and cell division rate, inspired by the DNA-damage response in Escherichia coli (SOS response). We derive the mutant count distribution arising in fluctuation assays under this model and then implement maximum likelihood estimation of the mutation-rate increase specifically associated with the expression of the stress response. Using simulated mutant count data, we show that our inference method allows for accurate and precise estimation of the mutation-rate increase, provided that this increase is sufficiently large and the induction of the response also reduces the division rate. Moreover, we find that in many cases, either heterogeneity in stress responses or mutant fitness costs could explain similar patterns in fluctuation assay data, suggesting that separate experiments would be required to identify the true underlying process. In cases where stress responses and mutation rates are heterogeneous, current methods still correctly infer the effective increase in population mean mutation rate, but we provide a novel method to infer distinct stress-induced mutation rates, which could be important for parameterising evolutionary models.

Quantifying stochastic establishment of mutants in microbial adaptation.

Studies of microbial evolution, especially in applied contexts, have focused on the role of selection in shaping predictable, adaptive responses to the environment. However, chance events - the appearance of novel genetic variants and their establishment, i.e. outgrowth from a single cell to a sizeable population - also play critical initiating roles in adaptation. Stochasticity in establishment has received little attention in microbiology, potentially due to lack of awareness as well as practical challenges in quantification. However, methods for high-replicate culturing, mutant labelling and detection, and statistical inference now make it feasible to experimentally quantify the establishment probability of specific adaptive genotypes. I review methods that have emerged over the past decade, including experimental design and mathematical formulas to estimate establishment probability from data. Quantifying establishment in further biological settings and comparing empirical estimates to theoretical predictions represent exciting future directions. More broadly, recognition that adaptive genotypes may be stochastically lost while rare is significant both for interpreting common lab assays and for designing interventions to promote or inhibit microbial evolution.

Stochastic bacterial population dynamics restrict the establishment of antibiotic resistance from single cells.

A better understanding of how antibiotic exposure impacts the evolution of resistance in bacterial populations is crucial for designing more sustainable treatment strategies. The conventional approach to this question is to measure the range of concentrations over which resistant strain(s) are selectively favored over a sensitive strain. Here, we instead investigate how antibiotic concentration impacts the initial establishment of resistance from single cells, mimicking the clonal expansion of a resistant lineage following mutation or horizontal gene transfer. Using two Pseudomonas aeruginosa strains carrying resistance plasmids, we show that single resistant cells have <5% probability of detectable outgrowth at antibiotic concentrations as low as one-eighth of the resistant strain's minimum inhibitory concentration (MIC). This low probability of establishment is due to detrimental effects of antibiotics on resistant cells, coupled with the inherently stochastic nature of cell division and death on the single-cell level, which leads to loss of many nascent resistant lineages. Our findings suggest that moderate doses of antibiotics, well below the MIC of resistant strains, may effectively restrict de novo emergence of resistance even though they cannot clear already-large resistant populations.

Evolutionary consequences of feedbacks between within-host competition and disease control.

Lay Summary: Competition often occurs among diverse parasites within a single host, but control efforts could change its strength. We examined how the interplay between competition and control could shape the evolution of parasite traits like drug resistance and disease severity.

Effective polyploidy causes phenotypic delay and influences bacterial evolvability.

Whether mutations in bacteria exhibit a noticeable delay before expressing their corresponding mutant phenotype was discussed intensively in the 1940s to 1950s, but the discussion eventually waned for lack of supportive evidence and perceived incompatibility with observed mutant distributions in fluctuation tests. Phenotypic delay in bacteria is widely assumed to be negligible, despite the lack of direct evidence. Here, we revisited the question using recombineering to introduce antibiotic resistance mutations into E. coli at defined time points and then tracking expression of the corresponding mutant phenotype over time. Contrary to previous assumptions, we found a substantial median phenotypic delay of three to four generations. We provided evidence that the primary source of this delay is multifork replication causing cells to be effectively polyploid, whereby wild-type gene copies transiently mask the phenotype of recessive mutant gene copies in the same cell. Using modeling and simulation methods, we explored the consequences of effective polyploidy for mutation rate estimation by fluctuation tests and sequencing-based methods. For recessive mutations, despite the substantial phenotypic delay, the per-copy or per-genome mutation rate is accurately estimated. However, the per-cell rate cannot be estimated by existing methods. Finally, with a mathematical model, we showed that effective polyploidy increases the frequency of costly recessive mutations in the standing genetic variation (SGV), and thus their potential contribution to evolutionary adaptation, while drastically reducing the chance that de novo recessive mutations can rescue populations facing a harsh environmental change such as antibiotic treatment. Overall, we have identified phenotypic delay and effective polyploidy as previously overlooked but essential components in bacterial evolvability, including antibiotic resistance evolution.

Population Heterogeneity in Mutation Rate Increases the Frequency of Higher-Order Mutants and Reduces Long-Term Mutational Load.

Mutation rate is a crucial evolutionary parameter that has typically been treated as a constant in population genetic analyses. However, the propensity to mutate is likely to vary among co-existing individuals within a population, due to genetic polymorphisms, heterogeneous environmental influences, and random physiological fluctuations. We review the evidence for mutation rate heterogeneity and explore its consequences by extending classic population genetic models to allow an arbitrary distribution of mutation rate among individuals, either with or without inheritance. With this general new framework, we rigorously establish the effects of heterogeneity at various evolutionary timescales. In a single generation, variation of mutation rate about the mean increases the probability of producing zero or many simultaneous mutations on a genome. Over multiple generations of mutation and selection, heterogeneity accelerates the appearance of both deleterious and beneficial multi-point mutants. At mutation-selection balance, higher-order mutant frequencies are likewise boosted, while lower-order mutants exhibit subtler effects; nonetheless, population mean fitness is always enhanced. We quantify the dependencies on moments of the mutation rate distribution and selection coefficients, and clarify the role of mutation rate inheritance. While typical methods of estimating mutation rate will recover only the population mean, analyses assuming mutation rate is fixed to this mean could underestimate the potential for multi-locus adaptation, including medically relevant evolution in pathogenic and cancerous populations. We discuss the potential to empirically parameterize mutation rate distributions, which have to date hardly been quantified.

Influence of recombination on acquisition and reversion of immune escape and compensatory mutations in HIV-1.

Following transmission, HIV-1 adapts in the new host by acquiring mutations that allow it to escape from the host immune response at multiple epitopes. It also reverts mutations associated with epitopes targeted in the transmitting host but not in the new host. Moreover, escape mutations are often associated with additional compensatory mutations that partially recover fitness costs. It is unclear whether recombination expedites this process of multi-locus adaptation. To elucidate the role of recombination, we constructed a detailed population dynamics model that integrates viral dynamics, host immune response at multiple epitopes through cytotoxic T lymphocytes, and viral evolution driven by mutation, recombination, and selection. Using this model, we compute the expected waiting time until the emergence of the strain that has gained escape and compensatory mutations against the new host's immune response, and reverted these mutations at epitopes no longer targeted. We find that depending on the underlying fitness landscape, shaped by both costs and benefits of mutations, adaptation proceeds via distinct dominant pathways with different effects of recombination, in particular distinguishing escape and reversion. When adaptation at a single epitope is involved, recombination can substantially accelerate immune escape but minimally affects reversion. When multiple epitopes are involved, recombination can accelerate or inhibit adaptation depending on the fitness landscape. Specifically, recombination tends to delay adaptation when a purely uphill fitness landscape is accessible at each epitope, and accelerate it when a fitness valley is associated with each epitope. Our study points to the importance of recombination in shaping the adaptation of HIV-1 following its transmission to new hosts, a process central to T cell-based vaccine strategies.

Quantifying Age-dependent Extinction from Species Phylogenies.

Several ecological factors that could play into species extinction are expected to correlate with species age, i.e., time elapsed since the species arose by speciation. To date, however, statistical tools to incorporate species age into likelihood-based phylogenetic inference have been lacking. We present here a computational framework to quantify age-dependent extinction through maximum likelihood parameter estimation based on phylogenetic trees, assuming species lifetimes are gamma distributed. Testing on simulated trees shows that neglecting age dependence can lead to biased estimates of key macroevolutionary parameters. We then apply this method to two real data sets, namely a complete phylogeny of birds (class Aves) and a clade of self-compatible and -incompatible nightshades (Solanaceae), gaining initial insights into the extent to which age-dependent extinction may help explain macroevolutionary patterns. Our methods have been added to the R package TreePar.

Phylogenetic analysis accounting for age-dependent death and sampling with applications to epidemics.

The reconstruction of phylogenetic trees based on viral genetic sequence data sequentially sampled from an epidemic provides estimates of the past transmission dynamics, by fitting epidemiological models to these trees. To our knowledge, none of the epidemiological models currently used in phylogenetics can account for recovery rates and sampling rates dependent on the time elapsed since transmission, i.e. age of infection. Here we introduce an epidemiological model where infectives leave the epidemic, by either recovery or sampling, after some random time which may follow an arbitrary distribution. We derive an expression for the likelihood of the phylogenetic tree of sampled infectives under our general epidemiological model. The analytic concept developed in this paper will facilitate inference of past epidemiological dynamics and provide an analytical framework for performing very efficient simulations of phylogenetic trees under our model. The main idea of our analytic study is that the non-Markovian epidemiological model giving rise to phylogenetic trees growing vertically as time goes by can be represented by a Markovian "coalescent point process" growing horizontally by the sequential addition of pairs of coalescence and sampling times. As examples, we discuss two special cases of our general model, described in terms of influenza and HIV epidemics. Though phrased in epidemiological terms, our framework can also be used for instance to fit macroevolutionary models to phylogenies of extant and extinct species, accounting for general species lifetime distributions.

Evolutionary rescue: linking theory for conservation and medicine.

Evolutionary responses that rescue populations from extinction when drastic environmental changes occur can be friend or foe. The field of conservation biology is concerned with the survival of species in deteriorating global habitats. In medicine, in contrast, infected patients are treated with chemotherapeutic interventions, but drug resistance can compromise eradication of pathogens. These contrasting biological systems and goals have created two quite separate research communities, despite addressing the same central question of whether populations will decline to extinction or be rescued through evolution. We argue that closer integration of the two fields, especially of theoretical understanding, would yield new insights and accelerate progress on these applied problems. Here, we overview and link mathematical modelling approaches in these fields, suggest specific areas with potential for fruitful exchange, and discuss common ideas and issues for empirical testing and prediction.

Pre-existence and emergence of drug resistance in a generalized model of intra-host viral dynamics.

Understanding the source of drug resistance emerging within a treated patient is an important problem, from both clinical and basic evolutionary perspectives. Resistant mutants may arise de novo either before or after treatment is initiated, with different implications for prevention. Here we investigate this problem in the context of chronic viral diseases, such as human immunodeficiency virus (HIV) and hepatitis B and C viruses (HBV and HCV). We present a unified model of viral population dynamics within a host, which can capture a variety of viral life cycles. This allows us to identify which results generalize across various viral diseases, and which are sensitive to the particular virus's life cycle. Accurate analytical approximations are derived that allow for a solid understanding of the parameter dependencies in the system. We find that the mutation-selection balance attained prior to treatment depends on the step at which mutations occur and the viral trait that incurs the cost of resistance. Life cycle effects and key parameters, including mutation rate, infected cell death rate, cost of resistance, and drug efficacy, play a role in determining when mutations arising during treatment are important relative to those pre-existing.

Dietary flaxseed inhibits atherosclerosis in the LDL receptor-deficient mouse in part through antiproliferative and anti-inflammatory actions.

Dietary flaxseed has been shown to have potent antiatherogenic effects in rabbits. The purpose of the present study was to investigate the antiatherogenic capacity of flaxseed in an animal model that more closely represents the human atherosclerotic condition, the LDL receptor-deficient mouse (LDLrKO), and to identify the cellular mechanisms for these effects. LDLrKO mice were administered a regular diet (RG), a 10% flaxseed-supplemented diet (FX), or an atherogenic diet containing 2% cholesterol alone (CH) or supplemented with 10% flaxseed (CF), 5% flaxseed (CF5), 1% flaxseed (CF1), or 5% coconut oil (CS) for 24 wk. LDLrKO mice fed a cholesterol-supplemented diet exhibited a rise in plasma cholesterol without a change in triglycerides and an increase in atherosclerotic plaque formation. The CS mice exhibited elevated levels of plasma cholesterol, triglycerides, and saturated fatty acids and an increase in plaque development. Supplementation of the cholesterol-enriched diet with 10% (wt/wt) ground flaxseed lowered plasma cholesterol and saturated fatty acids, increased plasma ALA, and inhibited plaque formation in the aorta and aortic sinus compared with mice fed a diet supplemented with only dietary cholesterol. The expression of proliferating cell nuclear antigen (PCNA) and the inflammatory markers IL-6, mac-3, and VCAM-1 was increased in aortic tissue from CH and CS mice. This expression was significantly reduced or normalized when flaxseed was included in the diet. Our results demonstrate that dietary flaxseed can inhibit atherosclerosis in the LDLrKO mouse through a reduction of circulating cholesterol levels and, at a cellular level, via antiproliferative and anti-inflammatory actions.

Selected technologies to control genes and their products for experimental and clinical purposes.

"On-demand" regulation of gene expression is a powerful tool to elucidate the functions of proteins and biologically-active RNAs. We describe here three different approaches to the regulation of expression or activity of genes or proteins. Promoter-based regulation of gene expression was among the most rapidly developing techniques in the 1980s and 1990 s. Here we provide basic information and also some characteristics of the metallothionein-promoter-based system, the tet-off system, Muristerone-A-regulated expression through the ecdysone response element, RheoSwitch, coumermycin/novobiocin-regulated gene expression, chemical dimerizer-based promoter activation systems, the "Dual Drug Control" system, "constitutive androstane receptor"-based regulation of gene expression, and RU486/mifepristone-driven regulation of promoter activity. A large part of the review concentrates on the principles and usage of various RNA interference techniques (RNAi: siRNA, shRNA, and miRNA-based methods). Finally, the last part of the review deals with historically the oldest, but still widely used, methods of temperature-dependent regulation of enzymatic activity or protein stability (temperature-sensitive mutants). Due to space limitations we do not describe in detail but just mention the tet-regulated systems and also fusion-protein-based regulation of protein activity, such as estrogen-receptor fusion proteins. The information provided below is aimed to assist researchers in choosing the most appropriate method for the planned development of experimental systems with regulated expression or activity of studied proteins.