Replication of viruses in a growing plaque: a reaction-diffusion model

Abstract

An understanding of the viral replication process commonly referred to as "plaque growth" is developed in the context of a reaction-diffusion model. The interactions among three components: the virus, the healthy host, and the infected host are represented using rates of viral adsorption and desorption to the cell surface, replication and release by host lysis, and diffusion. The solution to the full model reveals a maximum in the dependence of the velocity of viral propagation on its equilibrium adsorption constant, suggesting that conditions can be chosen where viruses which adsorb poorly to their hosts will replicate faster in plaques than those which adsorb well. Analytic expressions for the propagation velocity as a function of the kinetic and diffusion parameters are presented for the limiting cases of equilibrated adsorption, slow adsorption, fast adsorption, and large virus yields. Hindered diffusion at high host concentrations must be included for quantitative agreement with experimental data.

Evolution of bacteriophage T7 in a growing plaque

“…Second, the plaque is an accessible historical record. As they multiply, phage populations are fixed in ever-expanding concentric rings, each (31); a conceptually similar system was originally developed to study the in vitro replication and evolution of RNA molecules (3). Finally, from a practical perspective, the system is inexpensive and easily implemented.…”

“…Differences in the adsorption rate or affinity of the phage to its host may play a role. For example, fast or high-affinity adsorption, which is advantageous in liquid culture, may be advantageous or disadvantageous for propagation in a plaque, depending on the concentration of the host (31).…”

Spatial invasion by a mutant pathogen

“…Such traveling waves of pathogens have been observed in the spread of epidemics (Murray, 1989) and in spatially structured experimental systems (Yin, 1993;Yin and McCaskill, 1992). The fact that such waves are common is not surprising mathematically; they are predicted by traveling wave solutions to RDE and by the shape theorem for IPS models.…”

“…This is all characterized mathematically by the "shape theorem" in the IPS literature (Durrett, 1988). This behavior is reflected in partial differential equation models of SIR dynamics via traveling waves and is readily observed experimentally in bacteriophage plaques (Koch, 1964;Yin, 1993;Yin and McCaskill, 1992) and other spatially extended host-pathogen systems.…”

“…Phagebacteria systems are ideal for experimental evolution studies in which short generation times and high mutation rates allow one to see evolution in "real time." These microbial host-pathogen systems can be studied in spatially structured environments to gain important insight into the role of space in their evolution (Koch, 1964;Yin, 1993;Yin and McCaskill, 1992). When inoculated in isolated spots on a lawn of bacteria growing on an agar plate, the phage form circular clearings (or plaques) that are visible with the unaided eye.…”