Virus-Host Interactions Shape Viral Dispersal Giving Rise to Distinct Classes of Traveling Waves in Spatial Expansions

Wolfram Möbius,Nikhil Krishnan,Diana Fusco,Tongfei Liu,Michael Hunter

doi:10.1103/physrevx.11.021066

Wolfram Möbius, Nikhil Krishnan + Show 3 more

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https://doi.org/10.1103/physrevx.11.021066

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Abstract

Reaction-diffusion waves have long been used to describe the growth and spread of populations undergoing a spatial range expansion. Such waves are generally classed as either pulled, where the dynamics are driven by the very tip of the front and stochastic fluctuations are high, or pushed, where cooperation in growth or dispersal results in a bulk-driven wave in which fluctuations are suppressed. These concepts have been well studied experimentally in populations where the cooperation leads to a density-dependent growth rate. By contrast, relatively little is known about experimental populations that exhibit density-dependent dispersal. Using bacteriophage T7 as a test organism, we present novel experimental measurements that demonstrate that the diffusion of phage T7, in a lawn of host E. coli, is hindered by steric interactions with host bacteria cells. The coupling between host density, phage dispersal and cell lysis caused by viral infection results in an effective density-dependent diffusion coefficient akin to cooperative behavior. Using a system of reaction-diffusion equations, we show that this effect can result in a transition from a pulled to pushed expansion. Moreover, we find that a second, independent density-dependent effect on phage dispersal spontaneously emerges as a result of the viral incubation period, during which phage is trapped inside the host unable to disperse. Additional stochastic agent-based simulations reveal that lysis time dramatically affects the rate of diversity loss in viral expansions. Taken together, our results indicate both that bacteriophage can be used as a controllable laboratory population to investigate the impact of density-dependent dispersal on evolution, and that the genetic diversity and adaptability of expanding viral populations could be much greater than is currently assumed.

Highlights

Spatial range expansions are ubiquitous in nature, from the expansion of invasive plant species, through the migration of ancient human populations, to the range shifts of many organisms to higher altitudes and latitudes due to climate change [1,2,3,4,5,6,7,8]
We find that the presence and location of these transitions are controlled by two independent effects that alter the density-dependent diffusion of the virus: the first is associated with the excluded-volume interactions with the surrounding bacteria, while the second spontaneously emerges from the viral infection dynamic, which prevents a viral particle from diffusing during infection of the host
We first experimentally quantify how the diffusion of phage in a bacterial lawn is hindered by steric interactions with the host bacterial cells, resulting in a density-dependent diffusion coefficient

Summary

Introduction

Spatial range expansions are ubiquitous in nature, from the expansion of invasive plant species, through the migration of ancient human populations, to the range shifts of many organisms to higher altitudes and latitudes due to climate change [1,2,3,4,5,6,7,8]. One of the hallmarks of spatial expansions is the rapid loss of genetic diversity due to the enhanced fluctuations at the front [9,10]. This effect can, be significantly mitigated in the presence of density-dependent growth [11,12], such as an Allee effect [13], or density-dependent dispersal, where individuals in highly dense patches tend to disperse more quickly [14]. It has recently been shown theoretically that the ratio between the deterministic velocity of the front and that of its linearized approximation is sufficient to classify the expansions in three distinct types of traveling waves, nominally pulled, semipushed, and fully pushed, which, respectively, exhibit qualitatively distinct behaviors in the decay of heterozygosity, the stochastic wandering of the front position, and the probability distribution of the most recent common ancestor [14,15]

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