Kristina Crona

Designing antibiotic cycling strategies by determining and understanding local adaptive landscapes.

The evolution of antibiotic resistance among bacteria threatens our continued ability to treat infectious diseases. The need for sustainable strategies to cure bacterial infections has never been greater. So far, all attempts to restore susceptibility after resistance has arisen have been unsuccessful, including restrictions on prescribing [1] and antibiotic cycling [2], [3]. Part of the problem may be that those efforts have implemented different classes of unrelated antibiotics, and relied on removal of resistance by random loss of resistance genes from bacterial populations (drift). Here, we show that alternating structurally similar antibiotics can restore susceptibility to antibiotics after resistance has evolved. We found that the resistance phenotypes conferred by variant alleles of the resistance gene encoding the TEM β-lactamase (bla TEM) varied greatly among 15 different β-lactam antibiotics. We captured those differences by characterizing complete adaptive landscapes for the resistance alleles bla TEM-50 and bla TEM-85, each of which differs from its ancestor bla TEM-1 by four mutations. We identified pathways through those landscapes where selection for increased resistance moved in a repeating cycle among a limited set of alleles as antibiotics were alternated. Our results showed that susceptibility to antibiotics can be sustainably renewed by cycling structurally similar antibiotics. We anticipate that these results may provide a conceptual framework for managing antibiotic resistance. This approach may also guide sustainable cycling of the drugs used to treat malaria and HIV.

The changing geometry of a fitness landscape along an adaptive walk.

It has recently been noted that the relative prevalence of the various kinds of epistasis varies along an adaptive walk. This has been explained as a result of mean regression in NK model fitness landscapes. Here we show that this phenomenon occurs quite generally in fitness landscapes. We propose a simple and general explanation for this phenomenon, confirming the role of mean regression. We provide support for this explanation with simulations, and discuss the empirical relevance of our findings.

Rational design of antibiotic treatment plans: a treatment strategy for managing evolution and reversing resistance.

The development of reliable methods for restoring susceptibility after antibiotic resistance arises has proven elusive. A greater understanding of the relationship between antibiotic administration and the evolution of resistance is key to overcoming this challenge. Here we present a data-driven mathematical approach for developing antibiotic treatment plans that can reverse the evolution of antibiotic resistance determinants. We have generated adaptive landscapes for 16 genotypes of the TEM β-lactamase that vary from the wild type genotype “TEM-1” through all combinations of four amino acid substitutions. We determined the growth rate of each genotype when treated with each of 15 β-lactam antibiotics. By using growth rates as a measure of fitness, we computed the probability of each amino acid substitution in each β-lactam treatment using two different models named the Correlated Probability Model (CPM) and the Equal Probability Model (EPM). We then performed an exhaustive search through the 15 treatments for substitution paths leading from each of the 16 genotypes back to the wild type TEM-1. We identified optimized treatment paths that returned the highest probabilities of selecting for reversions of amino acid substitutions and returning TEM to the wild type state. For the CPM model, the optimized probabilities ranged between 0.6 and 1.0. For the EPM model, the optimized probabilities ranged between 0.38 and 1.0. For cyclical CPM treatment plans in which the starting and ending genotype was the wild type, the probabilities were between 0.62 and 0.7. Overall this study shows that there is promise for reversing the evolution of resistance through antibiotic treatment plans.

Inferring genetic interactions from comparative fitness data

Darwinian fitness is a central concept in evolutionary biology. In practice, however, it is hardly possible to measure fitness for all genotypes in a natural population. Here, we present quantitative tools to make inferences about epistatic gene interactions when the fitness landscape is only incompletely determined due to imprecise measurements or missing observations. We demonstrate that genetic interactions can often be inferred from fitness rank orders, where all genotypes are ordered according to fitness, and even from partial fitness orders. We provide a complete characterization of rank orders that imply higher order epistasis. Our theory applies to all common types of gene interactions and facilitates comprehensive investigations of diverse genetic interactions. We analyzed various genetic systems comprising HIV-1, the malaria-causing parasite Plasmodium vivax, the fungus Aspergillus niger, and the TEM-family of β-lactamase associated with antibiotic resistance. For all systems, our approach revealed higher order interactions among mutations.

Epistasis and Entropy

Epistasis is a key concept in the theory of adaptation. Indicators of epistasis are of interest for large systems where systematic fitness measurements may not be possible. Some recent approaches depend on information theory. We show that considering shared entropy for pairs of loci can be misleading. The reason is that shared entropy does not imply epistasis for the pair. This observation holds true also in the absence of higher order epistasis. We discuss a method for reducing the number of false positives. However, our main conclusion is that entropy-based approaches have serious limitations in this context.

Polytopes, Graphs and Fitness Landscapes

Darwinian evolution can be illustrated as an uphill walk in a landscape, where the surface consists of genotypes, the height coordinates represent fitness, and each step corresponds to a point mutation. Epistasis, roughly defined as the dependence between the fitness effects of mutations, is a key concept in the theory of adaptation. Important recent approaches depend on graphs and polytopes. Fitness graphs are useful for describing coarse properties of a landscape, such as mutational trajectories and the number of peaks. The graphs have been used for relating global and local properties of fitness landscapes. The geometric theory of gene interaction, or the shape theory, is the most fine-scaled approach to epistasis. Shapes, defined as triangulations of polytopes for any number of loci, replace the well established concepts of positive and negative epistasis for two mutations. From the shape one can identify the fittest populations, i.e., populations where allele shuffling (recombination) will not increase the mean fitness. Shapes and graphs provide complementary information. The approaches make no structural assumptions about the underlying fitness landscapes, which make them well suited for empirical work.

RECOMBINATION AND PEAK JUMPING

We show that genetic recombination can be a powerful mechanism for escaping suboptimal peaks. Recent studies of empirical fitness landscapes reveal complex gene interactions and multiple peaks. However, classical work on recombination largely ignores the effect of complex gene interactions. Briefly, we restrict to fitness landscapes where the global peak is difficult to access. If the optimal genotype can be generated by shuffling genes present in the population, then recombination will produce the genotype. If, in addition, recombination is sufficiently rare, then the proportion of the genotype is expected to increase. Specifically, we consider landscapes where shuffling of suboptimal peak genotypes can produce the global peak genotype. The advantage of recombination we identify has no correspondence for 2-locus systems or for smooth landscapes. The effect of recombination indicated is sometimes extreme, also for rare recombination, in the sense that shutting off recombination could result in the organism failing to adapt. A standard question about recombination is whether the mechanism tends to accelerate or decelerate adaptation. However, we argue that extreme effects may be more important than how the majority falls. In a limited sense, our result can be considered a support for Sewall Wright’s view that adaptation sometimes works better in subdivided populations.

Chapter 3 – Adaptation and Fitness Graphs

Understanding evolutionary processes is important in the study of medicine and agriculture. In many instances, the underlying cause for novel pathogens, pests, and antimicrobial drug resistance are complex evolutionary processes. Such processes may initially go unnoticed if the first mutations have moderate effects. However, the end result may be a radically altered organism. DNA sequencing and other laboratory techniques provide detailed information on systems involving several mutations and complex gene interactions. Making sense of such data is an important challenge in modern biology. Recent discrete approaches, including graphs and polytopes, have proved useful. The main focus of this chapter is fitness graphs, an elementary and yet effective approach to complex biological systems.