Session U27: Population Dynamics in Antibiotics and Time-Varying Environments

Immune repertoire dynamics out of steady state

Over the last ten years high-throughput sequencing has enabled increasingly quantitative measurements of the diversity of lymphocyte receptor repertoires. A striking finding of these sequencing efforts has been that the clone sizes of cells sharing the same receptor are heavy-tail distributed. Here, we show how such long tails can emerge out of steady state from a simple neutral model for immune repertoire formation. In our theory homeostatic proliferation leads to a founder effect, which produces transient but long-lived power-law scaling of clone sizes. In a human cohort study we find evidence for the prediction that early founded clones are overrepresented among the largest clones. We show how the slow multidecadal decay of this overrepresentation suggests a dynamical model of immune aging in which peripheral selection only slowly reshapes the initially established repertoire. Overall, our work suggests a mechanism through which dynamical processes early in life can have a strong and long-lasting influence on the adaptive immune system with potential implications for pathogen defense and autoimmunity.   

The role of drug kinetics on the evolution of resistance.

Emergence of drug resistance due to treatment non-adherence is a problem especially in chronic prolonged viral infections like the Human Immunodeficiency virus (HIV) and Hepatitis B (HBV) and C (HCV) viruses. Long acting drugs are being developed as one way to address this problem. Though this promises to be useful in the context of treatment adherence, we do not yet know how this would affect resistance.

With this in mind, we analyze the effect of dosing intervals on the establishment of drug resistance due to mutants existing prior to treatment (pre-existing) and those that are produced during treatment (rescue) in the presence of time-dependent drug profiles.

We find that there exists an initial time-frame after treatment initiation that has the most influence on the establishment probability of the drug resistant strain. Depending upon the nature of the drug kinetics during this time as well as infection parameters, increasing the dosing interval might be better or worse for the establishment of resistance. Our results suggest that drug kinetics affect selection and competition in the system in a complicated manner and should be factored in while designing new treatment strategies.   

The Dynamics of Human Society Evolution: An Energetics Approach

Human society is an open system that evolves by coupling with various known and unknown (energy) fluxes. How do these dynamics precisely unfold? Energetics may provide further insights. We expand on Navier-Stokes’ approach to study non-equilibrium dynamics in a field that evolves with time. Based on the ‘social field theory’, an induction of the classical field theories, we define social force, social energy and Hamiltonian of an individual in a society. The equations for the evolution of an individual and society are sketched based on the time-dependent Hamiltonian that includes power dynamics. In this paper, we will demonstrate that Lotka-Volterra type equations can be derived from the Hamiltonian equation in the social field.   

Understanding the Dynamics of Antibiotic Resistance in Microbial Communities using Tensor Methods

Spatial heterogeneity plays an important role in the evolution of drug resistance, but relatively little is known about resistance in complex spatial profiles of selection pressure. We have developed a toy model of stochastic microbial dynamics to investigate how different spatial profiles of selection pressure impact the time to fixation of a resistant allele using mean first passage time calculations. While our previous results established that spatial profiles can dramatically speed or slow the emergence of resistance, they provide little information about the trajectory taken by the system to reach fixation. We now expand our analysis to consider the third-order tensor composed of the time to fixation from all possible intermediate states of the system. We develop several methods to deconstruct this tensor into quantities that allow us to gain insight into the evolutionary dynamics of the system as it reaches fixation. We use a 3-D convolution to relate fixation times of neighboring states and a modified CP decomposition to reduce the fixation time tensor into single-microhabitat fixation profiles lacking spatial structure. We demonstrate that these tools allow us to intuitively understand the emergence of fixation in spatially-structured systems.   

Evolving generalists in optimal cycling environments

To persist and thrive in ever changing conditions, living organisms must adapt to new challenges while maintaining performance to prior related tasks. How this ability to generalize evolves remains a puzzle. To evolve a proper defense against rapidly adapting pathogens, vertebrates’ adaptive immune system searches for broadly neutralizing antibodies through B cell affinity maturation. However, these generalist antibodies are hard to evolve and often outcompeted by specialists fitter in any particular environment. Using a generative approach, we find that switching between environments neither too similar nor too different can efficiently evolve fit generalists, via dynamically enlarging their attractor basins in sequence space. We further demonstrate that changing environments before populations reach a steady state can mobilize specialists but leave generalists undisturbed, thereby allowing specialists to evolve into generalists and not specialize again. Our framework predicts optimal correlations between vaccine antigens to be cycled at intermediate timescales for reliably evolving generalists. These design principles exploit nonequilibrium fitness ‘seascapes’ to drive populations into genotypes unevolvable in static environments.   

Search strategies that find generalists in time varying environments

Many evolutionary and ecological processes can be seen as a search process for fitter genotypes or spatial regions with more resources. Time varying environments are often thought to naturally bias such search processes towards generalists, i.e., regions with relatively smaller changes in fitness or resources over time. But it is not clear what underlying characteristics of a search process lead to this effect.

Here we consider several search processes in biology such as foraging in real space, growth of microtubules towards chromosomes, and evolution towards fitter genotypes in sequence space. We find that a class of biased random walks that we call `directed’ are naturally driven towards generalists by time varying environments at intermediate timescales; this class includes classic E. coli chemotaxis with run times modulated by food availability and constant tumble times. However, closely related `undirected’ biased walks are not driven towards generalists, such as chemotaxis with constant run times but modulated tumble times. The distinction between directed and undirected walks corresponds to the Ito and Stratonovich ambiguity in stochastic calculus. Our work provides examples where the microscopic details of biological search have macroscopic consequences.   

Time-Dependent Effective Sampling Bias in Populations with Broad Offspring Numbers

It has been increasingly recognized that natural populations exhibit broad family size distributions, either because offspring numbers are strongly variable or because range expansion processes generate jackpot events. Despite recent progress in the neutral dynamics induced by broad offspring numbers, our knowledge of their interactions with selection remains limited, except for certain special cases. Here, we establish a number of new scaling relations about the fixation probability, the extinction time and the site frequency spectrum that arise when offspring
numbers are distributed according to a power law with divergent variance. Finally, we validate the new findings within semi-pushed traveling waves, which are microscopic models that give rise to the power law of offspring numbers.   

Using environmental noise to hedge one's evolutionary bets

Bet-hedging is an adaptation strategy commonly used by organisms living in unpredictable environments: Each individual randomly expresses one of many possible phenotypes so that a subset of the population may survive. The random choice of phenotypes is usually attributed to stochastic biochemical processes internal to the organism, such as multi-stable dynamics of the gene regulatory network. Alternatively, the organism may rely on randomness that is present (and probably abundant) in the external environment. We illustrate the latter possibility using a model of "environment-to-phenotype mapping". That is, we let the organism's phenotype depend on an environmental signal, and numerically evolve such dependence to maximize the population growth rate. We show that, even when the signal is extremely noisy and uninformative of the true environment, the organism can still benefit from the signal by using it as a source of randomness for bet-hedging.   

Clocks, Anticipation, and Growth in Bacteria

Circadian rhythms are widespread across all kingdoms of life, and they are frequently assumed to provide an adaptive benefit by allowing organisms to anticipate diel cycles in their environment. Yet it has proven extremely difficult to determine precisely how such anticipation confers a fitness advantage. Here, we use mathematical modeling to address this question for nitrogen-fixing cyanobacteria.¹ By extending recent work on growth laws in E. coli,² we show that it is difficult to change the composition of the proteome when the growth rate is small, and thus that the average growth rate can be increased by using a clock to anticipate the onset of darkness by switching to a dark-adapted proteome late in the day, when growth rates are still large.

¹ M. Monti, D.K. Lubensky, and P.R. ten Wolde, arXiv:1805.04538.
² D.W. Erickson et al., Nature 551, 119-23 (2017).   

Minimal model reveals key features of vaccination protocols that optimally elicit broadly neutralizing antibodies

During affinity maturation, B cell populations evolve in response to time-varying environments within germinal centers (GC). Recent simulations and experiments have shown that controlling the temporal application and degree of “frustration” (i.e. conflicting selection forces) within the GC crucially determines the successful production of broadly neutralizing antibodies (bnAbs). A one-dimensional fitness landscape enables us to quantify frustration as the change in entropy of the imposed fitness distribution as the selection forces change with time. Using a simple birth-death model, we then find that an optimal temporal profile of frustration maximizes bnAb production and determines the mechanisms underlying this result. The vaccination protocol requires a relatively low optimal level of frustration during GC priming to maintain the correct level of B cell diversity so that the surviving B cells have a high chance of evolving into bnAbs upon subsequently increasing the frustration by choosing appropriately designed vaccine immunogens. Our results also illustrate the importance of clonal interference in bnAb evolution due to time-varying environments.   

Predicting antibiotic resistance evolution

Bacteria can rapidly evolve resistance to antibiotics. Resistance mutations confer a fitness advantage in the presence of the drug, which is frequently coupled to a fitness cost in drug-free environments. But how do these effects set the strength of resistance elicited by a given drug dosage and the resulting cell growth? Here we develop a fitness model that predicts dosage-dependent growth rates of common resistance mutations. Selection experiments in E. coli populations at moderate drug levels reveal multiple resistance mutations of different strength, most of which affect membrane genes. By reducing both drug and nutrient uptake, these mutations cause antagonistic effects on cell metabolism and growth. Our fitness model maps this tradeoff and defines a Pareto surface of resistance evolution. We show that optimal mutants elicited at a given drug level occur at a specific point on this surface, leading to predictable dosage-dependent growth. Our analysis delineates the dosage regime where broad, membrane-mediated resistance evolution is prevalent compared to mere physiological response and drug-specific target mutations. These results show that drug resistance evolution, by coupling major metabolic pathways, is strongly intertwined with the systems biology of the cell.