Viral invasion fitness across a continuum from lysis to latency

Abstract

The prevailing paradigm in ecological studies of viruses and their microbial hosts is that the reproductive success of viruses depends on the proliferation of the 'predator', that is, the virus particle. Yet, viruses are obligate intracellular parasites, and the virus genome-the actual unit of selection-can persist and proliferate from one cell generation to the next without lysis or the production of new virus particles. Here, we propose a theoretical framework to quantify the invasion fitness of viruses using an epidemiological cell-centric metric that focuses on the proliferation of viral genomes inside cells instead of virus particles outside cells. This cell-centric metric enables direct comparison of viral strategies characterized by obligate killing of hosts (e.g. via lysis), persistence of viral genomes inside hosts (e.g. via lysogeny), and strategies along a continuum between these extremes (e.g. via chronic infections). As a result, we can identify environmental drivers, life history traits, and key feedbacks that govern variation in viral propagation in nonlinear population models. For example, we identify threshold conditions given relatively low densities of susceptible cells and relatively high growth rates of infected cells in which lysogenic and other chronic strategies have higher potential viral reproduction than lytic strategies. Altogether, the theoretical framework helps unify the ongoing study of eco-evolutionary drivers of viral strategies in natural environments.

Keywords: ecology; epidemiology; evolution; mathematical modeling; microbiology.

Figure 1.

Schematic of obligately lytic, chronic, and latent strategies, give a population perspective (top) and individual perspective (bottom). Top, The nonlinear dynamics for each model are presented in Section 2. Bottom, The basic reproduction number accounts for complete cycles beginning with infected cells. In the obligately lytic case, only three virions of many infect cells, these are progeny, aka new mothers. In the chronic case, the mother cell divides once and two progeny virions infect new cells. In the latent case, the mother cell divides three times before it is removed. In all of these examples, the total reproduction number is the same, albeit with differing contributions from horizontal and vertical transmission routes.

Figure 2.

Virus reproduction as a function of burst size and susceptible cell density. The contours denote the log₁₀ of ${\mathcal{R}}_0$, as measured using Eq. (22), given variation in burst size, β, and susceptible cell density, S*. Viruses invade when ${\mathcal{R}}_{\text{hor}}>1$ or, equivalently when ${\hspace{0.17em}\text{log}\hspace{0.17em}}_{10}{\mathcal{R}}_{\text{hor}}>0$. Contours denote combinations of $(\beta ,S^{\ast })$ of equivalent ${\mathcal{R}}_{\mathit{hor}}$. Additional parameters that affect viral reproduction are $\varphi =6.7\times {10}^{-10}$ ml/h and m = 1/24 h⁻¹.

Figure 3.

Basic reproduction number of temperate viruses as a function of susceptible cell density. The increasing (red) line denotes the horizontal ${\mathcal{R}}_0$ if temperate phage infect then always lyse cells. The decreasing (blue) line denotes the vertical ${\mathcal{R}}_0$ if temperate viruses always integrate with their hosts. Relevant parameters are β = 50, $\varphi =6.7\times {10}^{-10}$ ml/h, $K=7.5\times {10}^7$ ml^{– 1}, and $b\prime =0.32$, 0.54 and 1 h⁻¹ as well as $d\prime =0.75$, 0.44, and 0.24 h⁻¹ for the three lysogeny curves from bottom to top respectively.

Figure 4.

Viral strategies with the highest ${\mathcal{R}}_0$ vary with susceptible host density, including exclusively vertical (bold blue, left), mixed (bold green, middle), and horizontal (bold red, right) modes of transmission. Relevant parameters are (i) for obligately lytic viruses (red): β  =  100, $\varphi =6.7\times {10}^{-10}$ ml/h, and m = 0.13 h⁻¹; (ii) for chronic viruses (green): $b\prime =0.68$ h⁻¹, $d\prime =0.63$ h⁻¹, α  =  20 h⁻¹, $\varphi =3.4\times {10}^{-10}$ ml/h, and m = 0.04 h⁻¹; (iii) for temperate viruses, given vertical transmission (blue) $b\prime =0.54$ h⁻¹, $d\prime =0.44$ h⁻¹, where $K=7.5\times {10}^7$ ml^{– 1} in all three scenarios given variation in $S^{\ast }$.