Adaptive evolution of molecular phenotypes

Otwinowski

Plotkin

2015

Preprint

Self Cite

The vertebrate adaptive immune system provides a flexible and diverse set of molecules to neutralize pathogens. Yet, viruses such as HIV can cause chronic infections by evolving as quickly as the adaptive immune system, forming an evolutionary arms race. Here we introduce a mathematical framework to study the coevolutionary dynamics of antibodies with antigens within a host. We focus on changes in the binding interactions between the antibody and antigen populations, which result from the underlying stochastic evolution of genotype frequencies driven by mutation, selection, and drift. We identify the critical viral and immune parameters that determine the distribution of antibody-antigen binding affinities. We also identify definitive signatures of coevolution that measure the reciprocal response between antibodies and viruses, and we introduce experimentally measurable quantities that quantify the extent of adaptation during continual coevolution of the two opposing populations. Using this analytical framework, we infer rates of viral and immune adaptation based on time-shifted neutralization assays in two HIV-infected patients. Finally, we analyze competition between clonal lineages of antibodies and characterize the fate of a given lineage in terms of the state of the antibody and viral populations. In particular, we derive the conditions that favor the emergence of broadly neutralizing antibodies, which may be useful in designing a vaccine against HIV. IntroductionIt takes decades for humans to reproduce, but our pathogens can reproduce in less than a day. How can we coexist with pathogens whose potential to evolve is 10 4 -times faster than our own? In vertebrates, the answer lies in their adaptive immune system, which uses recombination, mutation, and selection to evolve a response on the same time-scale at which pathogens themselves evolve.One of the central actors in the adaptive immune system are B-cells, which recognize pathogens using highly diverse membrane-bound receptors. Naive B-cells are created by processes which generate extensive genetic diversity in their receptors via recombination, insertions and deletions, and hypermutations [1] which can potentially produce ∼ 10 18 variants in a human repertoire [2]. This estimate of potential lymphocyte diversity outnumbers the total population size of B-cells in humans, i.e., ∼ 10 10 [3,4]. During an infection, B-cells aggregate to form germinal centers, where they hypermutate at a rate of about ∼ 10 −3 per base pair per cell division over a region of 1-2 kilo base pairs [5]. The B-cell hypermutation rate is approximately 4 − 5 orders of magnitude larger than an average germline mutation rate per cell division in humans [6]. Mutated B-cells compete for survival and proliferation signals from helper T-cells, based on the B-cell receptor's binding to antigens. This form of natural selection is known as affinity maturation, and * Correspondence should be addressed to: Armita Nourmohammad (armitan@princeton.edu).† Authors with equal contribution it can incr...

Section: Modelmentioning

confidence: 99%

“…The fitness flux φ(t) characterizes the adaptive response of a population by genotypic or phenotypic changes in a population [37,42,43,69,70]. The cumulative fitness flux, Φ(τ ) = t+τ t φ(t )dt , measures the total amount of adaptation over an evolutionary period τ [43,69].…”

Section: Fitness Flux and The Co-evolutionary Transfer Fluxmentioning

confidence: 99%

Host-pathogen coevolution and the emergence of broadly neutralizing antibodies in chronic infections

Otwinowski

Plotkin

2015

Preprint

Self Cite

“…However, fluctuations of covariance are much faster compared to the mean phenotype, and therefore, covariance can be approximated by its stationary ensemble-averaged estimate [20,21]. Moreover, even in the presence of moderately strong selection pressure, the phenotypic covariance depends only weakly on the strength of selection and is primarily determined by the supply of mutations in a population [21,22]. Therefore, we also assume that the phenotypic covariance matrix remains approximately constant over time, throughout evolution.…”

Section: A Model Of Multi-variate Phenotypic Evolutionmentioning

confidence: 99%

Optimal evolutionary control for artificial selection on molecular phenotypes

Eksin

2019

Preprint

Self Cite

Controlling an evolving population is an important task in modern molecular genetics, including in directed evolution to improve the activity of molecules and enzymes, breeding experiments in animals and in plants, and in devising public health strategies to suppress evolving pathogens. An optimal intervention to direct evolution should be designed by considering its impact over an entire stochastic evolutionary trajectory that follows. As a result, a seemingly suboptimal intervention at a given time can be globally optimal as it can open opportunities for desirable actions in the future. Here, we propose a feedback control formalism to devise globally optimal artificial selection protocol to direct the evolution of molecular phenotypes. We show that artificial selection should be designed to counter evolutionary tradeoffs among multi-variate phenotypes to avoid undesirable outcomes in one phenotype by imposing selection on another. Control by artificial selection is challenged by our ability to predict molecular evolution. We develop an information theoretical framework and show that molecular time-scales for evolution under natural selection can inform how to monitor a population to acquire sufficient predictive information for an effective intervention with artificial selection. Our formalism opens a new avenue for devising optimal artificial selection for directed evolution of molecular functions.

“…Generic evolutionary processes of quantitative traits have two additional load components, which may become dominant over drift load: the diversity load for polymorphic traits, which is proportional to μ , and the adaptive load in a fitness seascape, which arises from the lag of the population behind the moving fitness peak and is proportional to υ / μ (where υ is the driving rate defined in the text) [42]. The different scaling of these load components with the mutation rate μ expresses a generic feature of adaptive processes: higher mutation rates increase the equilibrium load, but facilitate adaptive changes.…”

Section: Universality In Molecular Evolutionmentioning

confidence: 99%

“…If we are not interested in details of individual peak shifts, we can promote the model (1) to a stochastic fitness seascape, which is characterized a single additional parameter υ . This parameter is defined as the mean squared peak displacement, measured in units of and per unit of evolutionary time, and is called the driving rate of selection [42]. Our population ensemble now includes the stochasticity of selection; that is, individual populations of this ensemble differ in the realizations of the peak displacement process.…”

Section: Evolutionary Modes Of Quantitative Traitsmentioning

confidence: 99%

Universality and predictability in molecular quantitative genetics

Held

Lässig

2013

Preprint

Self Cite

Molecular traits, such as gene expression levels or protein binding affinities, are increasingly accessible to quantitative measurement by modern high-throughput techniques. Such traits measure molecular functions and, from an evolutionary point of view, are important as targets of natural selection. We review recent developments in evolutionary theory and experiments that are expected to become building blocks of a quantitative genetics of molecular traits. We focus on universal evolutionary characteristics: these are largely independent of a trait's genetic basis, which is often at least partially unknown. We show that universal measurements can be used to infer selection on a quantitative trait, which determines its evolutionary mode of conservation or adaptation. Furthermore, universality is closely linked to predictability of trait evolution across lineages. We argue that universal trait statistics extends over a range of cellular scales and opens new avenues of quantitative evolutionary systems biology. * * Authors with equal contributions.