Phage infection fronts trigger early sporulation and viral entrapment in bacterial populations

TL;DR

Bacteria form spores in response to phage infections, creating barriers that slow down phage spread and may allow viruses to re-emerge later.

Contribution

The study reveals that phage infection fronts trigger sporulation rings, which limit phage productivity and alter population-scale dynamics.

Findings

Plaques on spore-forming B. subtilis were three times smaller than on non-spore-forming bacteria.

Phage plaque growth was halted early due to sporulation rings, not reduced growth speed.

Sporulation rings contained viable virospores, suggesting long-term viral re-emergence potential.

Abstract

Bacteriophages (phages) infect, lyse, and propagate within bacterial populations. However, physiological changes in bacterial cell state can protect against infection even within genetically susceptible populations. One such example is the generation of endospores by Bacillus and its relatives, characterized by a reversible state of reduced metabolic activity that protects cells against stressors including desiccation, energy limitation, antibiotics, and infection by phage. Here we tested how sporulation at the cellular scale impacts phage dynamics at population scales when propagating amongst B. subtilis in spatially structured environments. Plaques resulting from infection and lysis were approximately three-fold smaller on lawns of spore-forming bacteria vs. non-spore-forming bacteria. Analysis of plaque growth revealed that final plaque size was reduced due to an early termination of expanding phage plaques rather than the reduction of plaque growth speed. Microscopic imaging of the plaques revealed “sporulation rings,” i.e. spores enriched around plaque edges relative to phage-free regions. We developed a series of mathematical models of phage, bacteria, spores, and small molecules that recapitulate plaque dynamics. We show evidence that phage infections trigger the formation of sporulation rings that reduce the productivity of phage infections and halt plaque spread even when resources are available for infection and lysis further away from plaque centers. Moreover, sporulation rings are also enriched in viable virospores, suggesting that although dormancy limits phage infections at population scales in the near term, viruses may co-opt phage-avoidance strategies to re-emerge over the long term, opening new avenues to explore the entangled fates of phages and their bacterial hosts.

Figures

Plaque sizes of phage SPO1 with non-spore-forming mutant and spore-forming wild-type host. (A) Square cropped sections of size 2 cm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\times $\end{document} 2 cm from non-spore-forming mutant (left) and spore-forming wild type (right) plaque assays are shown. Both plaque assays were carried out as described in Section (Phage strains and plaque assay) and prepared in parallel with the same initial and growth conditions. (B) Final plaque size of the two plaque assays shown in panel A. The images were analyzed using binarization and watershed algorithm (see SI Section IV D 1). The plaque sizes (98 plaques for non-spore-forming mutant and 137 for spore-forming wild-type) were plotted using a violin plot and individual points are shown as a scatter plot. The median non-spore-forming mutant and spore-forming wild-type plaque sizes are shown through the horizontal bold lines. Mutant plaques have a radius of 1.43 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\pm $\end{document} 0.33 mm, and wild-type plaques have a radius of 0.64 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\pm $\end{document} 0.2 mm. A two sample t-test rejected the hypothesis that the two distributions have equal means (P < 10−3).

Time lapse of plaque growth for non-spore-forming mutant and spore-forming wild-type host. A traditional plaque assay was performed at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $37^\circ $\end{document} C and images were captured every 5 min over a period of 15 h. The plaque sizes were estimated for each time point (46 plaques for the non-spore-forming mutant and 100 plaques for the spore-forming wild type) using image analysis techniques summarized in Section (Image analysis) and described in detail in SI Section IV D 2. Cropped sections from the time-lapse are shown at 5 and 13 h for parts of the non-spore-forming mutant and spore-forming wild type plates. The mean of all plaques is shown in the solid line, and the standard deviation is shown in the shaded area. Intermediate images of the independent plaque trajectories are shown in Fig. S5.

Sporulation is enhanced around plaque edges. A Bright-field image of microplaque assay is shown in panel A and fluorescent images are shown in panels B, D, E, and F. Images A, B, D, and E were taken at 40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\times $\end{document} magnification and image F at 20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\times $\end{document} magnification. The microplaque assay was carried out with phage SPO1. The GFP image was adjusted to remove background fluorescence and enhance contrast (see Section IV D 4). (C) GFP analysis of image in panel B. An averaging filter is applied on the image in panel B to obtain an adjusted GFP image. The green component in every pixel is then computed based on the distance to the center of the plaque (see SI Section IV D 4). Distance to the center of the plaque is shown on the x-axis in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mu } \textrm{m}$\end{document} and GFP intensity in the adjusted image is shown on the y-axis. The solid line represents the mean and the shaded area is the standard deviation. Panels D, E, and F show microplaque assays at different time points, from earliest in panel D to latest in panel F. The image in panel D was taken within the first 8 h when only cells in the vicinity of the plaque were sporulating. The image in panel F was taken after 12 h when most of the cells have transitioned to spores.

Schematic comparison of Models R, V, and M. Each shape represents a specific element in the system. Squares correspond to explicit limited resources (R), susceptible bacteria (S), infected bacteria (I), dormant bacteria (D), bacteria transitioning to dormancy while exposed to viruses (E), free viruses (V), and signaling molecules (M). In the E and I boxes, the smaller boxes signify the potential number of E and I states, denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $n_{E}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $n_{I}$\end{document} respectively. The number of states defines the duration that cells spend in that state (see Methods-Mathematical modeling). For the E states, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $n_{E}$\end{document} can be set equal to zero, which corresponds to a direct transition from the susceptible state to the dormant state. The arrows indicate interactions, with their direction showing causal effects. The central elements of Model R, Model V, and Model M are highlighted. The three letters denote Resource for Model R, where we assume resource-only dependent dormancy; the Virus for Model V, where dormancy can be triggered by viral contact aside from starvation; and the Molecule for Model M, where we assume an infection-associated molecule is an additional, potential initiator for dormancy. Elements with solid lines are shared across all models, whereas elements with dashed lines are unique to specific models.

Impact of sporulation on plaque dynamics for Model R. (A) Overlay of experimental data and computational simulations shows the time evolution of the mean plaque radius for the S− and S+ strains in Models R. In the simulations, a plaque is defined as the area where cell density is less than 10% of the maximum density at that time point. The results exhibit robustness to variations in that threshold, attributed to the abrupt density changes at plaque boundaries. The inset panels show a snapshot from the spatial simulation of bacterial densities in Model R, taken at 15 h, corresponding to the terminal point of the time series, using parameters from Table SII. (B and C) The distribution of dormant cells for the S+ host. The arrangement of the simulation results aligns with that presented in Fig. 3B and C. Panel B shows the two-dimensional spatial distribution of dormant cells at t = 5 h after phage addition, while panel C displays the distance profile of dormant cells distribution starting from the center of the plaque. The solid line (primary y-axis) corresponds to results at time = 5 h and is effectively a 1D slice of the left panel at the same row, showing the radial distribution of dormant cells starting from the center of the plaque and moving outwards. The dashed line, plotted on the secondary y-axis, represents the progression of the solid line at 15 h.

Simulated plaque growth dynamics and distribution of dormant cells for Models V and M. The layout follows the same structure per model as in Fig. 5 (Model R) and Fig. 3B and C (experimental results), allowing for straightforward comparisons between the models. Rows are organized by model type, presenting results for Models V and M. The first two rows correspond to two indicative parameter sets for Model V, each representing one of the two qualitatively distinct behaviors that can reproduce the plaque growth dynamics (see Fig. S9). In this model, sp denotes the resource threshold at which direct viral interaction can trigger dormancy, while \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $p$\end{document} represents the probability that such an interaction leads to dormancy initiation rather than lytic infection. The third row presents the results for Model M. Similarly to the organization in Fig. 5, the left column (panels A, D, and G) depicts an overlay of experimental data and computational simulations showing the time evolution of the mean plaque radius for the S− and S+ strains. The middle column (panels B, E, and H) and the right column (panels C, F, and I) display the 2D spatial distribution and the 1D radial profile, respectively, of the dormant cell density for the S+ strain. The results shown in the middle column panels and the solid line in the right column panels correspond to t = h after phage addition, which lies within the time window of approximatelyt ≈ 3–7 h during which a transient peak in sporulation around the plaque emerges in our simulations. The simulations for both Model V and Model M are performed with nE = 10 as in [45] to introduce the experimentally observed delayed transition to dormancy (see Methods, Model V).

Virospore distribution profile. Comparison between experimental observations and model predictions for the spatial distribution of virospores. (A) Experimental measurements of virospore density as a function of distance from the center of the plaque, taken at time t = 18 h. (B–G) Simulation results from Model V. Panels in the middle row correspond to t = 5 h, and those in the bottom row to t = 15 h. Each column represents a different output: the left column (panels B and E) shows the 2D distribution of all dormant cells, the center column (panels C and F) shows cells that entered dormancy due to direct viral interaction (excluding starvation) which serve as a proxy for virospores, and the right column (panels D and G) compares radial profiles of total dormant cells and virus-induced dormant cells. A clear outward shift in the peak virospore density is observed, from the inner region (0–0.05 cm) at t = 5 h to a broader peripheral band (0.05–0.1 cm) at t = 15 h approximating the peak position of our experimental results. In both experimental and modeled profiles, virospores accumulate at the edge of the plaque, suggesting a consistent spatial pattern of dormancy induction.

Equations

$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial \tilde{R}}{\partial t} &= -\underbrace{g(\tilde{R}) S}_{\textrm{cell growth}}+ \underbrace{D_{R} \nabla^{2} \tilde{R}}_{\textrm{resource diffusion}} \nonumber\\ \frac{\partial S}{\partial t} &= \underbrace{ g(\tilde{R}) S} _{\textrm{cell growth}} - \underbrace{\phi SV}_{\textrm{viral infection}} - \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}}\nonumber\\ \frac{\partial I_{1}}{\partial t} &= \underbrace{\phi SV}_{\textrm{viral infection}} - \underbrace{\eta(\tilde{R}) n_{I} I_{1}}_{\textrm{to next infected state}}\nonumber\\ \frac{\partial I_{i}}{\partial t} &= \underbrace{\eta(\tilde{R}) n_{I} I_{i-1}}_{\textrm{from previous infected state}} - \underbrace{\eta(\tilde{R}) n_{I} I_{i}}_{\textrm{to next infected state or viral lysis}}\nonumber\\ \frac{\partial V}{\partial t} &= \underbrace{\beta \eta(\tilde{R}) I_{n_{I}}}_{\textrm{viral lysis}} - \underbrace{\omega V}_{\textrm{viral decay}} - \underbrace{\phi (S+I_{total})V}_{\textrm{viral infection}} + \underbrace{D_{V} \nabla^{2} V}_{\textrm{viral diffusion}}\nonumber\\ \frac{\partial D}{\partial t} &= \underbrace{f(\tilde{R})S.}_{\textrm{dormancy initiation}}\end{align*}\end{document}$$

$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} g(\tilde{R}) &= r_{max} \frac{\tilde{R}}{\tilde{K_{g}} + \tilde{R}} \end{align*}\end{document}$$

$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} f(\tilde{R}) &= \frac{d_{max}}{1+e^{s(\tilde{R}-\sigma)}} \end{align*}\end{document}$$

$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \eta(\tilde{R}) &= \eta_{max} \frac{g(\tilde{R})}{g(\tilde{R_{0}})}. \end{align*}\end{document}$$

$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial \tilde{R}}{\partial t} &= -\underbrace{g(\tilde{R}) (S+{\color{red}{E_{total}}})}_{\textrm{cell growth}} + \underbrace{D_{R} \nabla^{2} \tilde{R}}_{\textrm{resource diffusion}}\end{align*}\end{document}$$

$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial S}{\partial t} &= \underbrace{ g(\tilde{R}) S}_{\textrm{cell growth}} - \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} - \underbrace{{\color{red}{(1-f_{V}(\tilde{R}))}}\phi SV}_{\textrm{viral infection}} - \underbrace{{\color{red}{f_{V}(\tilde{R})}}\phi SV}_{\textrm{dormancy initiation}}\nonumber \\ \frac{\partial I_{1}}{\partial t} &= \underbrace{{\color{red}{(1-f_{V}(\tilde{R}))}}\phi (S+{\color{red}{E_{total}}})V}_{\textrm{viral infection}} - \underbrace{\eta(\tilde{R}) n_{I} I_{1}}_{\textrm{to next infected state}}\nonumber \\ \frac{\partial I_{i}}{\partial t} &= \underbrace{\eta(\tilde{R}) n_{I} I_{i-1}}_{\textrm{from previous infected state}} - \underbrace{\eta(\tilde{R}) n_{I} I_{i}}_{\textrm{to next infected state or viral lysis}}\nonumber \\ \frac{\partial V}{\partial t} &= \underbrace{\beta \eta(\tilde{R}) n_{I}I_{n_{I}}}_{\textrm{viral lysis}} - \underbrace{\phi (S+I_{total}+{\color{red}{E_{total}}})V}_{\textrm{viral infection}} - \underbrace{\omega V}_{\textrm{viral decay}} + \underbrace{D_{V} \nabla^{2} V}_{\textrm{viral diffusion}} \nonumber \\{\color{red}{\frac{\partial E_{1}}{\partial t}}} &= \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} + \underbrace{{\color{red}{f_{V}(\tilde{R})}}\phi SV}_{\textrm{dormancy initiation}} - \underbrace{{\color{red}{\lambda n_{E} E_{1}}}}_{\textrm{dormancy process}}\nonumber \\&\quad - \underbrace{{\color{red}{(1-f_{V}(\tilde{R}))\phi E_{1}V}}}_{\textrm{infection of exposed transitioning cells}}\nonumber \\{\color{red}{\frac{\partial E_{i}}{\partial t}}} &= \underbrace{{\color{red}{\lambda n_{E} E_{i-1}}}}_{\textrm{from previous transitioning state}} - \underbrace{{\color{red}{\lambda n_{E} E_{i}}}}_{\textrm{to next transitioning state or to dormancy}}\nonumber \\&\quad - \underbrace{{\color{red}{(1-f_{V}(\tilde{R}))\phi E_{i}V}}}_{\textrm{infection of exposed transitioning cells}}\nonumber \\ \frac{\partial D}{\partial t} &= \left\{ \begin{array}{@{}ll} \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} + \underbrace{{\color{red}{f_{V}(\tilde{R})}}\phi SV}_{\textrm{dormancy initiation}} & {\qquad, n_{E} = 0} \\ \underbrace{{\color{red}{\lambda n_{E} E_{n_{E}}}}}_{\textrm{transition to dormancy}} & {\qquad, n_{E}> 0}. \end{array}\right.\end{align*}\end{document}$$

$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial \tilde{R}}{\partial t} &= -\underbrace{g(\tilde{R}) (S+{\color{red}{E_{total}}})}_{\textrm{cell growth}} + \underbrace{D_{R} \nabla^{2} \tilde{R}}_{\textrm{resource diffusion}} \nonumber\\ \frac{\partial S}{\partial t} &= \underbrace{ g(\tilde{R}) S}_{\textrm{cell growth}} - \underbrace{\phi SV}_{\textrm{viral infection}} - \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} - \underbrace{{\color{blue}{{\mu} MS}}}_{\textrm{dormancy initiation}}\nonumber\\{\color{blue}{\frac{\partial M}{\partial t}}} &= \underbrace{{\color{blue}{m\eta(\tilde{R}) n_{I} I_{n_{I}}}}}_{\textrm{molecule from lysate}} - \underbrace{{\color{blue}{{\mu} MS}}}_{\textrm{dormancy initiation}} + \underbrace{{\color{blue}{D_{M} \nabla^{2} M}}}_{\textrm{molecule diffusion}} \nonumber\\ \frac{\partial I_{1}}{\partial t} &= \underbrace{\phi (S+{\color{red}{E_{total}}})V}_{\textrm{viral infection}} - \underbrace{\eta(\tilde{R}) n_{I} I_{1}}_{\textrm{to next infected state}}\end{align*}\end{document}$$

$$\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial I_{i}}{\partial t} &= \underbrace{\eta(\tilde{R}) n_{I} I_{i-1}}_{\textrm{from previous infected state}} - \underbrace{\eta(\tilde{R}) n_{I} I_{i}}_{\textrm{to next infected state or viral lysis}}\nonumber\\ \frac{\partial V}{\partial t} &= \underbrace{\beta \eta(\tilde{R}) n_{I} I_{n_{I}}}_{\textrm{viral lysis}} - \underbrace{\phi (S+I_{total}+{\color{red}{E_{total}}})V}_{\textrm{viral infection}} - \underbrace{\omega V}_{\textrm{viral decay}} + \underbrace{D_{V} \nabla^{2} V}_{\textrm{viral diffusion}}\nonumber\\{\color{red}{\frac{\partial E_{1}}{\partial t}}} &= \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} + \underbrace{{\color{blue}{{\mu} MS}}}_{\textrm{dormancy initiation}} - \underbrace{{\color{red}{\lambda n_{E} E_{1}}}}_{\textrm{dormancy initiation}} \nonumber \\&\quad- \underbrace{{\color{red}{\phi E_{1}V}}}_{\textrm{infection of exposed transitioning cells}}\nonumber\\{\color{red}{\frac{\partial E_{i}}{\partial t}}} &= \underbrace{{\color{red}{\lambda n_{E} E_{i-1}}}}_{\textrm{from previous transitioning state}} - \underbrace{{\color{red}{\lambda n_{E} E_{i}}}}_{\textrm{to next transitioning state or to dormancy}}\nonumber \\&\quad - \underbrace{{\color{red}{\phi E_{i}V}}}_{\textrm{infection of exposed transitioning cells}}\nonumber\\ \frac{\partial D}{\partial t} &= \underbrace{{\color{red}{\lambda n_{E} E_{n_{E}}}}.}_{\textrm{transition to dormancy}}\end{align*}\end{document}$$

Full text

Introduction

Dormancy is a survival strategy found across different types of organisms, including microorganisms. Through dormancy, bacteria enter a long-term, albeit reversible, state of reduced metabolic activity without cell division, enhancing survival in the face of environmental stress [1–3]. One ancient and prevalent type of dormancy in bacteria is endosporulation, which is found among Bacillus and Clostridia. Endosporulation is a complex developmental process that requires genome duplication prior to asymmetric septum production, followed by forespore formation and engulfment by the mother cell, which ultimately leads to the production of an endospore (or “spore”). Such spores are tolerant to a wide range of environmental stressors, including extreme temperatures, UV radiation, desiccation, and energy limitation [4]. Spores are abundant and have a cosmopolitan distribution (e.g. there is an excess of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 10^{28}\end{document} endospores in marine sediments alone [5]), can survive for extended periods of time (e.g. thousands or millions of years [6–9]), and can harbor genetic diversity given accumulation of genes in a dormant “seed bank” [3, 10, 11].

Dormancy also has the potential to protect microorganisms against viral infection. Phage can account for a significant fraction of bacterial mortality [12, 13]. In turn, bacteria have evolved a wide range of intracellular and extracellular mechanisms to prevent phage infection and/or inhibit the viral replication cycle [14–17]. Well-characterized anti-viral defense systems span surface-based resistance (e.g. modifications or deletion of receptors that prevent viral infection) to intracellular defense/immunity (e.g. CRISPR/Cas or resistance-modification systems [14, 18, 19]. However, phenotypic variants of genetically identical microbes can also provide a refuge from phage infection. Examples include the decrease of phage infection of stationary phase or slow-growing bacteria [20], persister cells [21], and endospores [22]. These phenotypic obstacles are not a guarantee of protection. For example, phage T4 is capable of infecting and lysing stationary phase Escherichia coli [23] and phage \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \lambda \end{document} can infect and lyse persister E. coli cells even if prophage induction is inhibited [24]. In the case of Bacillus endospores, the protective outer layer is distinct from that of the actively growing cell and can be depleted or devoid of phage receptor binding domains. As a result, phage adsorption to spores can be reduced significantly and in some cases effectively stopped altogether [22].

The ability of dormancy to reduce adsorption of virions to cell surfaces may have consequences for population-level feedback between viruses and microbial hosts. In well-mixed experimental systems, spores stabilized oscillatory host dynamics induced by phage, which reduced the extent of local population crashes [22]. The initiation and exit from dormancy may also be directly linked to interactions with viruses. Similarly, phage infections can trigger cell-specific dormancy initiation in Listeria ivanovii such that intracellular viral genomes can be eliminated during resuscitation out of dormancy [25, 26]—further mitigating the impacts of infection. Phage genomes may also encode for transcription factors that change sporulation patterns in the host, potentially to circumvent host defense and lead to entrapment of viruses in spores [27–32]. Viral genomes can be translocated into the developing forespore and form a “virospore.” This translocation can occur with assistance of host-derived chromosomal segregation genes acquired by the phage [33, 34] leading to the formation of a virospore. Within a virospore, the phage genome is not integrated as a prophage and the infection can resume upon resuscitation [35]. Altogether, there is growing evidence dormancy initiation and revival at cellular scales is modulated as part of coevolved defense and counterdefense systems.

Scaling up the interplay of viral infection and dormancy from cellular to population scales requires accounting for feedback with the environment. Although many phage-bacteria studies are conducted in vitro in shaken flasks, phage infection of bacteria also occurs in soils, on surfaces and/or particles, and within metazoan hosts with distinct selection criteria induced by the spatial structure of the environment [36–39]. First, adjacent cells are more likely to be more closely related than if selecting cells from a population at large [40]. Second, resource environments can be patchy with variation in local availability of resources that differ substantially from the average, impacting the outcome of phage-bacteria interactions [41]. Third, lysis will not impact all other bacteria equally; instead, the local propagation of phage (along with cellular debris and signals associated with infection and lysis) has the potential to influence cell fates close to sites of viral infection [18, 42–46]. All of these factors present new challenges in developing predictive models of eco-evolutionary phage-host dynamics in structured environments.

Here, we explore the interplay between dormancy and viral growth in a spatially structured environment as a means to address if and how dormancy modulates the spread of viruses within B. subtilis populations. To do so, we used conventional plaque assays to evaluate viral growth on a lawn of spore-forming and non-spore-forming hosts. Phage plaques grew at the same rate initially yet produced significantly different final plaque sizes: smaller plaques in spore-forming hosts relative to those in non-spore-forming hosts. Subsequent microscopic imaging revealed that plaques in the spore-forming host were surrounded by a ring of mature endospores well before the appearance of endospores far from plaque centers. This observation catalyzed the integrated development of experiments and mathematical models to explore how dormancy buffers the impact of phage propagation at population scales and enables a potential escape route for phage that can be encapsulated into endospores and re-emerge when conditions improve.

Materials and methods

Experimental setup

Bacterial strains and growth conditions

We used two 168 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \Delta 6\end{document}  Bacillus subtilis strains: a wild type which can sporulate (referred to as the spore-forming strain), and a SPOIIE mutant in which the SPOIIE gene has been deleted ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \Delta \end{document} SPOIIE, further referred to as the non-spore-forming strain). This mutation prevents the cell from sporulating at the asymmetrical division stage \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} II\end{document} , which is early in the sporulation process [47], without changing the fitness or phage infection dynamics compared to the spore-forming strain [22]. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \Delta 6\end{document}  B. subtilis strain has a reduced genome, lacks prophages, is immotile, and has reduced biofilm-forming capacity [48]. The \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \Delta 6\end{document}  B. subtilis strain is also resistant to chloramphenicol (shown as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} Cm^{R}\end{document} in Table SI).

To assist with visualization of spore development, we used a fluorescent sporulation reporter, green fluorescent protein (GFP) fused to a spore coat protein, under its native promoter (amyE::PcotYZ-gfp-cotZ) into both the spore-forming and non-spore-forming strains. This reporter expresses relatively late in sporulation [49]. For detailed strain construction information, please consult SI Section IV A. GFP is only expressed in the spore-forming strain given that it is controlled by a sporulation-specific promoter.

Bacterial cultures were grown in Difco Sporulation Medium (DSM), supplemented with 5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} g/ml chloramphenicol. DSM is a rich media i.e. used to obtain high sporulation rates [50, 51]. The cells were streaked from glycerol stock and grown at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 37^\circ \end{document} C overnight in a shaking incubator (200 RPM) to ensure aeration of the culture. After overnight growth, cells were inoculated from a singular colony and grown under identical conditions for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \approx \end{document} 5 h until they reached OD \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \approx \end{document} 0.5.

Phage strains and plaque assay

We used two wild-type bacteriophages of B. subtilis: SPO1 and SPP1 (see Table SI for more details on phage strains). The plaque assay protocol was adapted from the “tube free agar-overlay” protocol [52]. In brief, 100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu } \textrm{l}\end{document} of cell culture at OD 0.5, 100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu } \textrm{l}\end{document} of viral solution, and 2.5 ml of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 0.3%\end{document} agar soft overlay at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 55^\circ \end{document} C were spotted directly on the DSM 1.5% agar. Immediately after the overlay was poured, the plates were homogenized to help ensure that bacteria and viruses were evenly distributed. After the overlay set at room temperature for 10 min, the plates were moved to a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 37^\circ \textrm{C}\end{document} incubator to grow overnight.

To acquire time-lapse imaging of plaque development, the plates were placed on top of a white LED screen in a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 37^\circ \textrm{C}\end{document} room. Top-down images were captured every 5 min for 15 h. The imaging protocol was the same for end-point images in that plates were set on top of a white LED screen and a top-down image was acquired. The end-point images were taken once the plaques reached a stable state, after 15 h at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 37^\circ \textrm{C}\end{document} .

Micro plaque assay

We developed a “micro” plaque assay to examine the microscale features of viral plaques. Bacterial cultures were grown to reach exponential phase as described in Section (Bacterial strains and growth conditions). We then prepared a viral dilution series to reach a concentration of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sim 4\cdot 10^{4}\end{document} PFU/ml. Concurrently, agar pads were prepared by pouring 6 ml of DSM medium with a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 2%\end{document} agarose concentration on a 60 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \times \end{document} 15 mm Petri dish (based on protocol 3.3 from [53]). Using aseptic technique, the agar was cut with a scalpel into nine squares (1 cm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \times \end{document} 1 cm) (Fig. S1 panels A–D). Once the bacterial cultures reached OD \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sim 0.5\end{document} , 1 ml of culture was concentrated by centrifugation at 15000 rpm for 5 min. 900 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu } \textrm{l}\end{document} of supernatant was removed and the remaining 100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu } \textrm{l}\end{document} before tubes were mixed in a vortex and spun down via centrifugation. The remaining 100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu } \textrm{l}\end{document} of concentrated culture was mixed with 50 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} l of viral solution. Immediately afterward, 2 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu } \textrm{l}\end{document} of the bacteria-virus mixture was spotted onto a 50 mm glass-bottom Petri dish (prod no 14027-20 Ted Pella). These smaller plates have a 50 mm glass bottom compatible with microscopy. A 1 cm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \times \end{document} 1 cm agar pad was placed on top of each droplet, enabling four experiments for each glass-bottom Petri dish. We then incubated the Petri dish at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 37^{\circ } \textrm{C}\end{document} for 8–12 h before imaging (Fig. S1 panel E).

Virospore quantification

We performed a plaque assay with SPO1 phage and spore-forming host as described in Section (Phage strains and plaque assay). Following incubation, we quantified the abundance and spatial distribution of virospores across three replicate SPO1 plaques (0.15 cm radius) on the spore-forming lawn. We sampled along a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sim \end{document} 0.15 cm transect extending from the center of each plaque (0, 0.05 cm) into the annulus (0.075, 0.1 cm) and adjacent bacterial lawn (outside periphery of plaque, 0.15 cm). Samples were taken using a sterile 10 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} l pipette tip (circular area of 0.785 mm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ^{2}\end{document} ) and suspended in 1.5 ml of 1X phosphate-buffered saline (PBS, pH 7.4) and heat-treated at 80 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ^{\circ }\end{document} C for 20 min to kill free phage and vegetative (i.e. non-spore) cells. Following heat-treatment, we performed plaque assays with spore-forming B. subtilis 168 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \Delta \end{document} 6 in the aforementioned manner and incubated plates overnight at 37 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ^{\circ }\end{document} C. Resulting plaques are counted as viral (vPFUs) or virospores. Data were analyzed and plotted in R using ‘’ggplot2” (R version 4.3.3 [54]).

Image analysis

Time-lapse and final point image analysis

We differentiated plaques from bacterial lawns using a binarization method. Plaque centers were identified as the centroid of the largest connected component. We then iterated backwards in time to determine the centroid and plaque size in previous frames. Full details of the inward-moving plaque identification algorithm with intermediate images are reported in SI Sections IV D 1 and IV D 2.

GFP image analysis

We subtracted background fluorescence to compute the average GFP intensity relative to the center of the plaque. The corrected image was used to identify the center of the plaque. Finally, the distance between each pixel and the center was used to calculate a GFP intensity profile; full description provided in SI Section IV D 4.

Mathematical models and simulations

Mathematical modeling

We developed a series of nonlinear partial differential equation (PDE) models of phage-bacteria interactions in a spatially explicit context, building upon mechanisms described in well-mixed [55] and structured [45] populations. In this model, susceptible bacteria \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} S\end{document} grow on resources \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} R\end{document} and can be infected by viruses \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} V\end{document} yielding infected cells \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} I\end{document} . Infected cells can lyse releasing new viruses. Susceptible cells can also transition to dormant spores \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} D\end{document} —phage cannot adsorb to spores [22]. To account for different modes of dormancy initiation, we developed three different model variants: Model R, Model V, and Model M that differentiate the mechanism underlying dormancy initiation: R—depletion of resources; V—interaction with virus particles and, separately, resource depletion; M—interaction with lysis-associated molecules and, separately, resource depletion. Initially, susceptible cells and resources are uniformly distributed and viruses are concentrated at the central point. There are no dormant or infected cells at the beginning of a simulation. In all model variants, we explicitly account for the spatiotemporal dynamics of populations.

Model R—resource-only dependent dormancy

Model R assumes that sporulation in B. subtilis is triggered by starvation [3, 47, 56], specifically, dormancy is initiated at a low rate when resources are high and at a much higher rate when resources are depleted [57, 58]. The associated PDEs are as follows:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial \tilde{R}}{\partial t} &= -\underbrace{g(\tilde{R}) S}_{\textrm{cell growth}}+ \underbrace{D_{R} \nabla^{2} \tilde{R}}_{\textrm{resource diffusion}} \nonumber\\ \frac{\partial S}{\partial t} &= \underbrace{ g(\tilde{R}) S} _{\textrm{cell growth}} - \underbrace{\phi SV}_{\textrm{viral infection}} - \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}}\nonumber\\ \frac{\partial I_{1}}{\partial t} &= \underbrace{\phi SV}_{\textrm{viral infection}} - \underbrace{\eta(\tilde{R}) n_{I} I_{1}}_{\textrm{to next infected state}}\nonumber\\ \frac{\partial I_{i}}{\partial t} &= \underbrace{\eta(\tilde{R}) n_{I} I_{i-1}}_{\textrm{from previous infected state}} - \underbrace{\eta(\tilde{R}) n_{I} I_{i}}_{\textrm{to next infected state or viral lysis}}\nonumber\\ \frac{\partial V}{\partial t} &= \underbrace{\beta \eta(\tilde{R}) I_{n_{I}}}_{\textrm{viral lysis}} - \underbrace{\omega V}_{\textrm{viral decay}} - \underbrace{\phi (S+I_{total})V}_{\textrm{viral infection}} + \underbrace{D_{V} \nabla^{2} V}_{\textrm{viral diffusion}}\nonumber\\ \frac{\partial D}{\partial t} &= \underbrace{f(\tilde{R})S.}_{\textrm{dormancy initiation}}\end{align*}\end{document}

where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \tilde{R}(\textbf{x},t)\end{document} is the rescaled density of resources, expressed in units of cells/ml. The rescaling is performed as [ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \tilde{R}\end{document} ] = [ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} R/\epsilon \end{document} ] = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \frac{\frac{{\mu } \textrm{g}}{\textrm{ml}}}{\frac{{\mu } \textrm{g}}{cells}}\end{document} = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \frac{cells}{\textrm{ml}}\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \epsilon \end{document} denotes the rate of resource to bacteria conversion measured in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} g/cells (see Table SII and Parameter estimations for details). Similarly, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} S(\textbf{x},t), I(\textbf{x},t)\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} D(\textbf{x},t)\end{document} are the densities of susceptible, infected, and dormant bacteria (i.e. spores), respectively, each in units of cells/ml. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} V\end{document} designates the density of phage in viruses/ml. Here, immotile bacteria grow by consuming resources even though resources and viruses diffuse at distinct rates. Susceptible cells can be infected by virulent phage with infection rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \phi \end{document} or become dormant if the density of the resources is sufficiently low. Once infected, the cells go through a series of sequential stages \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} n_{I}\end{document} of infected states \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} I_{i}\end{document} (the sum of which is given by \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} I_{total} = \sum {i=1}^{n{I}} I_{i}\end{document} ), resulting in an effective latent time delay that follows an Erlang distribution. After the latency period, the infected cells burst, yielding new free viruses with burst size \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \beta \end{document} . Virus particles can adsorb to cells at a rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \phi \end{document} and decay with rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \omega \end{document} . The bacterial growth rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} g(\tilde{R})\end{document} , dormancy rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} f(\tilde{R})\end{document} and latent time \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \eta (\tilde{R})\end{document} are dependent on available resources and are given by:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} g(\tilde{R}) &= r_{max} \frac{\tilde{R}}{\tilde{K_{g}} + \tilde{R}} \end{align*}\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} f(\tilde{R}) &= \frac{d_{max}}{1+e^{s(\tilde{R}-\sigma)}} \end{align*}\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \eta(\tilde{R}) &= \eta_{max} \frac{g(\tilde{R})}{g(\tilde{R_{0}})}. \end{align*}\end{document}

The growth rate function follows the Monod equation where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} r_{max}\end{document} is the maximum bacterial growth rate and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \tilde{K_{g}}\end{document} the rescaled Monod constant (similarly to R, [ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \tilde{K_{g}}\end{document} ] = [ \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} K_{g}/\epsilon \end{document} ] = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \frac{\frac{{\mu } \textrm{g}}{\textrm{ml}}}{\frac{{\mu } \textrm{g}}{cells}}\end{document} = \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \frac{cells}{\textrm{ml}}\end{document} ). The dormancy rate function is assumed to be solely dependent on resources but with sporulation starting effectively only when the resource density is close to a fraction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma \end{document} of the Monod constant (for Model R \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma \approx 0.28 \tilde{K_{g}}\end{document} ). The “sharpness” of the transition to dormancy is determined by the value of parameter \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} s\end{document} . Finally, we chose a resource dependent lysis rate i.e. proportional to the growth rate \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} g(R)\end{document} [59, 60]. This choice is justified by the fact that the plaques stop growing as bacteria have exhausted the available resources. Full details of parameter estimation are in Section IV E 2 and model parameters are in Table SII.

Model V—virus-associated dormancy

In Model V, dormancy can be initiated via starvation or with a probability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} f_{V}(\tilde{R}) = \frac{pd_{max}}{1+e^{s(\tilde{R}-\sigma {p})}}\end{document} with \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} p\in (0,1)\end{document} upon interacting with a virus particle. For the dependence of the probability of virally induced dormancy on the resource level \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \tilde{R} \end{document} , we select a function similar to that used for starvation-induced dormancy, but with a switch centered at a threshold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma {p} \end{document} instead of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma \end{document} . When \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma {p} = \sigma \end{document} , the resource dependence of Model V is equivalent to Model R. In contrast, a high threshold \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma {p} \gg \sigma \end{document} allows phage to trigger dormancy even in resource-rich cells, resulting in a nearly constant probability \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} p \end{document} and rendering the transition largely independent of resource availability. A low \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma {p} \end{document} , slightly above the starvation threshold (e.g. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma {p} = 0.28\tilde{K}{g}> \sigma = 0.2\tilde{K}{g} \end{document} ), restricts virus-associated dormancy to near resource-depleted conditions, coupling the transition more tightly to the local metabolic state of the host. In order to account for a time delay for spore formation, we introduce a series of multiple sequential stages \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} n{E}\end{document} to become dormant [58]. Hence, the dormancy initiation time follows an Erlang distribution. The transition to dormancy is immediate for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} n{E} = 0\end{document} , and a delay is introduced for \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} n{E}>0\end{document} ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} E{total} = \sum {i=1}^{n{E}} E_{i}\end{document} ). For our simulations, we select \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} n_{E} = 10\end{document} without loss of generality (see [45]). The net transition rate between the E-states is \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \lambda n_{E}\end{document} , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \lambda = \frac{4}{3} \textrm{h},\textrm{s}^{-1}\end{document} , so that the mean transition rate remains constant with varying number of states. In this model formulation, cells transitioning to dormancy can become infected by phage, whereas spores cannot be infected (see Discussion for elaboration on the consequences of relaxing this assumption). All other parameter values are retained across Models R and V (Table SII). The new terms in Model V are listed in red text, the remainder are shared with Model R:

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial \tilde{R}}{\partial t} &= -\underbrace{g(\tilde{R}) (S+{\color{red}{E_{total}}})}_{\textrm{cell growth}} + \underbrace{D_{R} \nabla^{2} \tilde{R}}_{\textrm{resource diffusion}}\end{align*}\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial S}{\partial t} &= \underbrace{ g(\tilde{R}) S}_{\textrm{cell growth}} - \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} - \underbrace{{\color{red}{(1-f_{V}(\tilde{R}))}}\phi SV}_{\textrm{viral infection}} - \underbrace{{\color{red}{f_{V}(\tilde{R})}}\phi SV}_{\textrm{dormancy initiation}}\nonumber \\ \frac{\partial I_{1}}{\partial t} &= \underbrace{{\color{red}{(1-f_{V}(\tilde{R}))}}\phi (S+{\color{red}{E_{total}}})V}_{\textrm{viral infection}} - \underbrace{\eta(\tilde{R}) n_{I} I_{1}}_{\textrm{to next infected state}}\nonumber \\ \frac{\partial I_{i}}{\partial t} &= \underbrace{\eta(\tilde{R}) n_{I} I_{i-1}}_{\textrm{from previous infected state}} - \underbrace{\eta(\tilde{R}) n_{I} I_{i}}_{\textrm{to next infected state or viral lysis}}\nonumber \\ \frac{\partial V}{\partial t} &= \underbrace{\beta \eta(\tilde{R}) n_{I}I_{n_{I}}}_{\textrm{viral lysis}} - \underbrace{\phi (S+I_{total}+{\color{red}{E_{total}}})V}_{\textrm{viral infection}} - \underbrace{\omega V}_{\textrm{viral decay}} + \underbrace{D_{V} \nabla^{2} V}_{\textrm{viral diffusion}} \nonumber \\{\color{red}{\frac{\partial E_{1}}{\partial t}}} &= \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} + \underbrace{{\color{red}{f_{V}(\tilde{R})}}\phi SV}_{\textrm{dormancy initiation}} - \underbrace{{\color{red}{\lambda n_{E} E_{1}}}}_{\textrm{dormancy process}}\nonumber \\&\quad - \underbrace{{\color{red}{(1-f_{V}(\tilde{R}))\phi E_{1}V}}}_{\textrm{infection of exposed transitioning cells}}\nonumber \\{\color{red}{\frac{\partial E_{i}}{\partial t}}} &= \underbrace{{\color{red}{\lambda n_{E} E_{i-1}}}}_{\textrm{from previous transitioning state}} - \underbrace{{\color{red}{\lambda n_{E} E_{i}}}}_{\textrm{to next transitioning state or to dormancy}}\nonumber \\&\quad - \underbrace{{\color{red}{(1-f_{V}(\tilde{R}))\phi E_{i}V}}}_{\textrm{infection of exposed transitioning cells}}\nonumber \\ \frac{\partial D}{\partial t} &= \left\{ \begin{array}{@{}ll} \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} + \underbrace{{\color{red}{f_{V}(\tilde{R})}}\phi SV}_{\textrm{dormancy initiation}} & {\qquad, n_{E} = 0} \\ \underbrace{{\color{red}{\lambda n_{E} E_{n_{E}}}}}_{\textrm{transition to dormancy}} & {\qquad, n_{E}> 0}. \end{array}\right.\end{align*}\end{document}

Model M—dormancy mediated by lysate-associated molecules

Model M represents a scenario where sporulation can be triggered by diffusible molecules released upon cell lysis. Additional parameters include the rate at which these lysate-associated molecules trigger a susceptible cell to become dormant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu } = 5 \cdot 10^{-11}\end{document}   \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\textrm{ml}}/\end{document} [h \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \cdot \end{document} (cells)], the number of molecules released upon lysis \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} m = 10^{4}\end{document} molecules/cell, and the diffusion constant \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} D_{M} = 4\cdot 10^{5}\end{document}   \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu m}^{2}\end{document} /h. The parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma = 0.2\tilde{K_{g}}\end{document} and molecular concentrations are in cells/ml—representing the equivalent density of cell-to-spore transitions that molecules can trigger. The following system of equations expands Model R and Model V [see equations sets (1) and (5) for comparison with the black and red elements in Model V respectively] with the blue terms that are introduced in Model M.

\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial \tilde{R}}{\partial t} &= -\underbrace{g(\tilde{R}) (S+{\color{red}{E_{total}}})}_{\textrm{cell growth}} + \underbrace{D_{R} \nabla^{2} \tilde{R}}_{\textrm{resource diffusion}} \nonumber\\ \frac{\partial S}{\partial t} &= \underbrace{ g(\tilde{R}) S}_{\textrm{cell growth}} - \underbrace{\phi SV}_{\textrm{viral infection}} - \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} - \underbrace{{\color{blue}{{\mu} MS}}}_{\textrm{dormancy initiation}}\nonumber\\{\color{blue}{\frac{\partial M}{\partial t}}} &= \underbrace{{\color{blue}{m\eta(\tilde{R}) n_{I} I_{n_{I}}}}}_{\textrm{molecule from lysate}} - \underbrace{{\color{blue}{{\mu} MS}}}_{\textrm{dormancy initiation}} + \underbrace{{\color{blue}{D_{M} \nabla^{2} M}}}_{\textrm{molecule diffusion}} \nonumber\\ \frac{\partial I_{1}}{\partial t} &= \underbrace{\phi (S+{\color{red}{E_{total}}})V}_{\textrm{viral infection}} - \underbrace{\eta(\tilde{R}) n_{I} I_{1}}_{\textrm{to next infected state}}\end{align*}\end{document} \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \begin{align*} \frac{\partial I_{i}}{\partial t} &= \underbrace{\eta(\tilde{R}) n_{I} I_{i-1}}_{\textrm{from previous infected state}} - \underbrace{\eta(\tilde{R}) n_{I} I_{i}}_{\textrm{to next infected state or viral lysis}}\nonumber\\ \frac{\partial V}{\partial t} &= \underbrace{\beta \eta(\tilde{R}) n_{I} I_{n_{I}}}_{\textrm{viral lysis}} - \underbrace{\phi (S+I_{total}+{\color{red}{E_{total}}})V}_{\textrm{viral infection}} - \underbrace{\omega V}_{\textrm{viral decay}} + \underbrace{D_{V} \nabla^{2} V}_{\textrm{viral diffusion}}\nonumber\\{\color{red}{\frac{\partial E_{1}}{\partial t}}} &= \underbrace{f(\tilde{R}) S}_{\textrm{dormancy initiation}} + \underbrace{{\color{blue}{{\mu} MS}}}_{\textrm{dormancy initiation}} - \underbrace{{\color{red}{\lambda n_{E} E_{1}}}}_{\textrm{dormancy initiation}} \nonumber \\&\quad- \underbrace{{\color{red}{\phi E_{1}V}}}_{\textrm{infection of exposed transitioning cells}}\nonumber\\{\color{red}{\frac{\partial E_{i}}{\partial t}}} &= \underbrace{{\color{red}{\lambda n_{E} E_{i-1}}}}_{\textrm{from previous transitioning state}} - \underbrace{{\color{red}{\lambda n_{E} E_{i}}}}_{\textrm{to next transitioning state or to dormancy}}\nonumber \\&\quad - \underbrace{{\color{red}{\phi E_{i}V}}}_{\textrm{infection of exposed transitioning cells}}\nonumber\\ \frac{\partial D}{\partial t} &= \underbrace{{\color{red}{\lambda n_{E} E_{n_{E}}}}.}_{\textrm{transition to dormancy}}\end{align*}\end{document}

Results

Plaque growth dynamics in spore-forming vs. non-spore-forming hosts

We performed standard plaque assays of phage SPO1 with spore-forming and non-spore-forming hosts as described in Section (Phage strains and plaque assay). In both cases, phages proliferated and generated macroscopic zones of clearance (i.e. plaques). On average, the radius of plaques on the non-spore-forming host was \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sim 2.2\end{document} -fold greater than the radius of plaques on the spore-forming host (Fig. 1A). Non-spore-forming plaque radii were \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 1.43\end{document} mm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \pm \end{document} 0.33 mm, and spore-forming plaques were 0.64 mm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \pm \end{document} 0.2 mm (t-test, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} P<10^{-3}\end{document} ). We assessed the generality of this finding by comparing plaque sizes on spore-forming vs. non-spore-forming hosts using a different bacteriophage, SPP1. In this case, we observed a 3.5-fold plaque radius reduction for bacteriophage SPP1 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} P<10^{-3}\end{document} , given non-spore-forming plaque radii of 1.22 mm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \pm \end{document} 0.15 mm and spore-forming plaque radii of 0.35 mm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \pm \end{document} 0.12 mm (Fig. S2). Overall, a similar phenomenon is observed across multiple phage types: plaque size is reduced by 2–4-fold in a population of spore-forming bacteria vs. non-spore-forming bacteria (corroborating early observations [33]).

Plaque sizes of phage SPO1 with non-spore-forming mutant and spore-forming wild-type host. (A) Square cropped sections of size 2 cm \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\times$\end{document} 2 cm from non-spore-forming mutant (left) and spore-forming wild type (right) plaque assays are shown. Both plaque assays were carried out as described in Section (Phage strains and plaque assay) and prepared in parallel with the same initial and growth conditions. (B) Final plaque size of the two plaque assays shown in panel A. The images were analyzed using binarization and watershed algorithm (see SI Section IV D 1). The plaque sizes (98 plaques for non-spore-forming mutant and 137 for spore-forming wild-type) were plotted using a violin plot and individual points are shown as a scatter plot. The median non-spore-forming mutant and spore-forming wild-type plaque sizes are shown through the horizontal bold lines. Mutant plaques have a radius of 1.43 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\pm$\end{document} 0.33 mm, and wild-type plaques have a radius of 0.64 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\pm$\end{document} 0.2 mm. A two sample t-test rejected the hypothesis that the two distributions have equal means (P < 10−3).

In order to further quantify plaque growth dynamics on spore-forming vs. non-spore-forming hosts, we recorded a time-lapse of the SPO1 plaques. We extracted the plaque sizes every 5 min over 15 h (Materials and methods Section Image analysis and SI Section IV D 2), Fig. 2). Plaques on both spore-forming and non-spore-forming lawns began to grow at the 3-h mark and continued expanding for approximately 2 h thereafter. The plaques on spore-forming hosts reached a plateau shortly after 5 h, whereas plaques on non-spore-forming hosts continued to grow until reaching maximum size at approximately 13 h (Fig. 2). We classify plaque growth in terms of a lag phase in which plaques are not visible, an enlargement phase in which plaques appear to be growing at a constant rate, and a termination phase in which plaques stop growing, presumably due to a halt in phage replication [42]. The mean plaque size on spore-forming vs. non-spore-forming hosts is 0.43 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \pm \end{document} 0.12 mm vs. 1.28 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \pm \end{document} 0.24 mm. The reduction of plaque size on spore-forming hosts across different phages (Figs 1 and 2) are robust to experimental conditions required for both time-lapse and endpoint measurements.

Time lapse of plaque growth for non-spore-forming mutant and spore-forming wild-type host. A traditional plaque assay was performed at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $37^\circ$\end{document} C and images were captured every 5 min over a period of 15 h. The plaque sizes were estimated for each time point (46 plaques for the non-spore-forming mutant and 100 plaques for the spore-forming wild type) using image analysis techniques summarized in Section (Image analysis) and described in detail in SI Section IV D 2. Cropped sections from the time-lapse are shown at 5 and 13 h for parts of the non-spore-forming mutant and spore-forming wild type plates. The mean of all plaques is shown in the solid line, and the standard deviation is shown in the shaded area. Intermediate images of the independent plaque trajectories are shown in Fig. S5.

Differences in plaque sizes could potentially be ascribed to differences in plaque growth rate or the duration of the enlargement phase. To test this, we fit a linear function to the enlargement phase for each non-spore-forming and spore-forming trajectory to obtain 46 growth rates for phage on non-spore forming hosts and 100 growth rates for phage on spore-forming hosts. The non-spore-forming mean growth rate is 117 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \pm \end{document} 26 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} m/h and the mean plaque growth rate on spore-forming hosts was 136 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \pm \end{document} 69 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} m/h. Using bootstrap resampling of growth rates, we found that in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 10^{5}\end{document} randomized groupings, a fraction \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} P = 0.066\end{document} of slope differences exceeded the observed difference of 19 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} m/h (Fig. S6). We conducted a bootstrap resampling of plaque growth rates to assess the significance of observed differences on spore-forming vs. non-spore forming hosts. We find that a \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} P=0.066\end{document} of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} 10^{5}\end{document} resampled plaque growth rate differences exceed the observed difference of 19 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} m/h (Fig. S6). We interpret this to mean that the observed difference in plaque growth rate on spore-forming vs. non-spore-forming hosts are not significantly different. In other words: differences in plaque sizes on different hosts cannot be ascribed to differences in plaque growth rates. We hypothesize that plaque size differences are due, instead, to early cessation of plaque growth.

Sporulation analysis across plaque transects

In order to explore the early cessation of plaques in sporulating hosts, we developed a microscopic plaque assay to quantify the levels and locations of mature endospores relative to plaque centers. Figure 3 contrasts the bright-field image with the resulting microscopic plaque assay (Section Micro plaque assay). The bright-field image of a plaque is shown in panel A; it resembles a traditional viral plaque with a clearing in the middle surrounded by a bacterial lawn. However, spores are absent near the plaque center and enhanced around the edge of the plaque compared to the rest of the bacterial lawn (Fig. 3B). The enhancement of spore density near plaque edges relative to the rest of the bacterial lawn was captured 8 h after the initiation of the experiment that would otherwise be missed in end-point analysis. Indeed, after a prolonged time period of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sim 16\end{document} h, sporulation levels in the bacterial lawn were similar to those found around the plaque edge (Fig. 3F). This suggests that sporulation is triggered earlier in cells that are close to regions with enhanced viral-induced lysis. The enhancement of sporulation around plaque edges is robust and consistently observed across multiple plaques in multiple experiments. The enhancement of spores is pronounced around plaque edges and increases in intensity over time (Fig. 3D–F), including at a later stage where cell densities at plaque edges approximate background intensities (Fig. S7).

Sporulation is enhanced around plaque edges. A Bright-field image of microplaque assay is shown in panel A and fluorescent images are shown in panels B, D, E, and F. Images A, B, D, and E were taken at 40\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\times$\end{document} magnification and image F at 20\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $\times$\end{document} magnification. The microplaque assay was carried out with phage SPO1. The GFP image was adjusted to remove background fluorescence and enhance contrast (see Section IV D 4). (C) GFP analysis of image in panel B. An averaging filter is applied on the image in panel B to obtain an adjusted GFP image. The green component in every pixel is then computed based on the distance to the center of the plaque (see SI Section IV D 4). Distance to the center of the plaque is shown on the x-axis in \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ${\mu } \textrm{m}$\end{document} and GFP intensity in the adjusted image is shown on the y-axis. The solid line represents the mean and the shaded area is the standard deviation. Panels D, E, and F show microplaque assays at different time points, from earliest in panel D to latest in panel F. The image in panel D was taken within the first 8 h when only cells in the vicinity of the plaque were sporulating. The image in panel F was taken after 12 h when most of the cells have transitioned to spores.

We quantified the distribution of spores relative to plaque centers by measuring the GFP intensity as a function of the distance to the center of the plaque (Fig. 3C). The GFP is tagged to a late-stage sporulation gene giving us a direct and complementary single-cell estimate of sporulation. In each case, we identified plaque centers and then averaged GFP intensity in an annulus of a fixed distance from the center. The lowest GFP level was obtained when the distance to the plaque center was less than \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sim 25\end{document}   \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} m. GFP expression increased between \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sim 15\end{document}   \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} m and 100 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} {\mu }\end{document} m before decreasing to background levels far from plaque centers. This quantitative enhancement of GFP intensity associated with the early emergence of spores is localized to the edge of plaques. This finding is consistent with a potential dynamical feedback between a spreading viral population, localized lysis, and the early onset of endosporulation.

Modeling plaque growth given dormancy initiation by resource depletion

Multiple candidate mechanisms could underlie the emergence of a ring of endospores outside plaque edges associated with early plaque termination. To better understand what factors affect plaque growth and early termination, we developed and analyzed a mathematical model of phage spreading across a lawn of either spore-forming ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} S^{+}\end{document} ) or non-spore-forming ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} S^{-}\end{document} ) bacteria (Fig. 4). The initial mathematical model included bacteria growth, viral infection and lysis, the potential diffusion of virus particles and resources, as well as the initiation of cellular dormancy due to resource depletion (full details in Section Mathematical modeling). Our objective was to compare simulated plaque spreading dynamics with observations arising from both macroscopic and microscopic plaque assay experiments. In developing this PDE model, we first evaluated the scenario where starvation alone induces dormancy. This resource-dependent model (Model R) assumes that sporulation is enhanced at low resource concentrations and suppressed at high resource concentrations consistent with long-standing observations [3, 47, 56].

Schematic comparison of Models R, V, and M. Each shape represents a specific element in the system. Squares correspond to explicit limited resources (R), susceptible bacteria (S), infected bacteria (I), dormant bacteria (D), bacteria transitioning to dormancy while exposed to viruses (E), free viruses (V), and signaling molecules (M). In the E and I boxes, the smaller boxes signify the potential number of E and I states, denoted as \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $n_{E}$\end{document} and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $n_{I}$\end{document} respectively. The number of states defines the duration that cells spend in that state (see Methods-Mathematical modeling). For the E states, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $n_{E}$\end{document} can be set equal to zero, which corresponds to a direct transition from the susceptible state to the dormant state. The arrows indicate interactions, with their direction showing causal effects. The central elements of Model R, Model V, and Model M are highlighted. The three letters denote Resource for Model R, where we assume resource-only dependent dormancy; the Virus for Model V, where dormancy can be triggered by viral contact aside from starvation; and the Molecule for Model M, where we assume an infection-associated molecule is an additional, potential initiator for dormancy. Elements with solid lines are shared across all models, whereas elements with dashed lines are unique to specific models.

The baseline PDE model of phage-bacteria interactions in a depleting resource environment generates a spreading wave of phage infection and lysis. Model R reproduces the macroscale observation of reduced plaque size in spore-forming vs. non-spore-forming hosts (contrast Fig. 1, experimental results with Fig. 5A, simulation results). The underlying reason is that phage spreading on a lawn of the spore-forming host have fewer available cells to infect compared to those on a lawn of the non-spore-forming host. Furthermore, Model R also reproduces the early, equivalent plaque growth dynamics and the early cessation of expansion observed in plaques associated with the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} S^{+}\end{document} vs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} S^{-}\end{document} strain (Fig. 5A). In a model with starvation-induced sporulation, dormancy typically starts from the exterior part of the plate where bacteria growth is not controlled by phage. Therefore, outside the plaque, resources are abruptly depleted sooner, triggering dormancy in a large fraction of cells uniformly distributed out of the reach of phage activity (i.e. outside the plaque). Phage originating from the plaque’s center will eventually reach a region with dormant cells present at relatively higher densities, which prevents further infection and amplification of plaque spread leading to smaller plaques for the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} S^{+}\end{document} strain.

Impact of sporulation on plaque dynamics for Model R. (A) Overlay of experimental data and computational simulations shows the time evolution of the mean plaque radius for the S− and S+ strains in Models R. In the simulations, a plaque is defined as the area where cell density is less than 10% of the maximum density at that time point. The results exhibit robustness to variations in that threshold, attributed to the abrupt density changes at plaque boundaries. The inset panels show a snapshot from the spatial simulation of bacterial densities in Model R, taken at 15 h, corresponding to the terminal point of the time series, using parameters from Table SII. (B and C) The distribution of dormant cells for the S+ host. The arrangement of the simulation results aligns with that presented in Fig. 3B and C. Panel B shows the two-dimensional spatial distribution of dormant cells at t = 5 h after phage addition, while panel C displays the distance profile of dormant cells distribution starting from the center of the plaque. The solid line (primary y-axis) corresponds to results at time = 5 h and is effectively a 1D slice of the left panel at the same row, showing the radial distribution of dormant cells starting from the center of the plaque and moving outwards. The dashed line, plotted on the secondary y-axis, represents the progression of the solid line at 15 h.

Despite agreement with macroscale observations of plaque dynamics, Model R incorrectly predicts that sporulation density should continue to increase away from plaque centers into the bulk bacterial lawn in contrast to micro plaque assays (Fig. 5B and C). This increase in spore density occurs because resources are consumed equally in the absence of phage, triggering a uniformly distributed background of dormant cells. With increasing proximity to the plaque there are fewer susceptible bacteria due to lysis, leading to higher resource availability and lower dormant cell densities. At the edge of the plaque there is a precipitous decrease in bacterial density as all cells are killed, corresponding to a sharp decrease in dormant cells (Fig. 5B and C). Therefore, in this model, the decrease in resources is fastest further from regions of viral infection and lysis (i.e. from the edge of the plate towards the phage-occupied center). The incompatibility of Model R spore density dynamics with observations suggests that processes beyond starvation induce spore formation in the presence of lytic phage infection.

Modeling phage plaque growth given viral-induced sporulation

We hypothesized that viral infection and/or lysis is linked to the emergence of sporulation, given the failure of the resource-depletion Model R to explain the emergence of an annulus of spores around the edge of a growing plaque. In doing so, we consider two alternative hypotheses: (i) sporulation is preferentially induced in cells that interact with molecules released during viral infection and lysis, (i.e. lysis-induced dormancy); (ii) sporulation is preferentially induced in virally-infected cells (i.e. infection-induced dormancy). In both cases, we assume that viral-induced sporulation mechanisms operate in addition to conventional, resource-depletion mechanisms.

There is precedent for linking the viral-induced lysis of cells with changes in uninfected cell fate. Prior work has shown that small peptides released as a result of lytic infection can be taken up by uninfected cells, subsequently modulating cell fate [61]. Here, phage infection may lead to the release and uptake of host metabolites, cellular components (like cell wall fragments, including peptidoglycan), host lysis signals, and/or viral proteins associated with viral infection and/or lysis that diffuse through the environment faster than virions. We hypothesize that dormancy may be initiated in response to lysate-associated molecules. To evaluate this possibility, we developed an alternative Model M (short for lysate-associated “molecules”) which expands Model R such that dormancy can be initiated through uptake of diffusible molecules associated with viral lysates (Methods contain the full model description). Like a resource-driven dormancy initiation model, simulations of Model M reproduce the observed reduction of the plaque size in systems with spore-forming vs. non-spore-forming cells as well as quantitative plaque growth dynamics (Fig. 6G). Unlike Model R, Model M can also reproduce the microscopic observations of a ring of spores surrounding the central region of the plaque (Fig. 6H and I) as observed experimentally (Fig. 3). This finding depends on the assumption that sporulation-inducing molecules diffuse faster than phage. As a result, cells encountering the molecule initiate and differentiate into mature endospores recalcitrant to phage infection. Without a viable path for infection, phage replication and plaque expansion are halted. This explains why, in Model M, plaques progress at the same velocity and then stop abruptly as the plaque front encounters the sporulation ring. Towards the center, viral infections kill vegetatively growing cells that have not yet transitioned to spores, reducing their density. Farther from the plaque front, the spore density eventually decreases given that small molecules in the viral lysate linked to sporulation decrease in density.

Simulated plaque growth dynamics and distribution of dormant cells for Models V and M. The layout follows the same structure per model as in Fig. 5 (Model R) and Fig. 3B and C (experimental results), allowing for straightforward comparisons between the models. Rows are organized by model type, presenting results for Models V and M. The first two rows correspond to two indicative parameter sets for Model V, each representing one of the two qualitatively distinct behaviors that can reproduce the plaque growth dynamics (see Fig. S9). In this model, sp denotes the resource threshold at which direct viral interaction can trigger dormancy, while \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} $p$\end{document} represents the probability that such an interaction leads to dormancy initiation rather than lytic infection. The third row presents the results for Model M. Similarly to the organization in Fig. 5, the left column (panels A, D, and G) depicts an overlay of experimental data and computational simulations showing the time evolution of the mean plaque radius for the S− and S+ strains. The middle column (panels B, E, and H) and the right column (panels C, F, and I) display the 2D spatial distribution and the 1D radial profile, respectively, of the dormant cell density for the S+ strain. The results shown in the middle column panels and the solid line in the right column panels correspond to t = h after phage addition, which lies within the time window of approximatelyt ≈ 3–7 h during which a transient peak in sporulation around the plaque emerges in our simulations. The simulations for both Model V and Model M are performed with nE = 10 as in [45] to introduce the experimentally observed delayed transition to dormancy (see Methods, Model V).

We evaluated whether bacterial dormancy can be triggered by phage infection rather than diffusible molecules associated with lysis. As in the case of Model M, we extended the nonlinear PDE model of plaque expansion given explicit resources to include the potential that virally-infected cells preferentially initiate dormancy (full equations in Methods). In doing so, we assume that infection-induced dormancy is resource-dependent. This “Model V” can represent a continuum of mechanisms spanning fixed traits (i.e. the probability of dormancy is constant for each viral infection) to plastic traits (i.e. the probability of dormancy is a function of resources for each viral infection). For both fixed and plastic traits, Model V reproduces quantitative observations of plaque growth dynamics in which plaques grow at the same speed on both spore-forming and non-spore-forming hosts and yet plaques stop earlier on spore-forming hosts vs. non-spore-forming hosts (Fig. 6A and D).

Despite generating similar plaque growth profiles, simulations of Model V assuming fixed vs. plastic traits generate qualitatively different spore density profiles. A fixed trait model does not generate a sporulation ring. Instead, assuming fixed traits leads to spore density profiles that increase away from the plaque centers at both early and late times (see Fig. 6B and C). Although viral spread may decrease, the net result is—like Model R—that resource scarcity becomes the primary driver of dormancy, and the spatiotemporal profiles of spores are incompatible with the experimental observations from microscale plaque assays. In contrast in a plastic trait model, viral infection can trigger sporulation in moderately resource-limited (but not starved) cells. As the plaque expands, the front will encounter cells in a zone where resources are partially depleted. At this point, newly infected cells are more likely to initiate dormancy well before cells far from the plaque centers. Then, the plaque will halt rapidly given the decrease in productive infections and sporulation will increase locally, reproducing the experimental peak in microscale plaque assays observed at the edge of the plaque (Fig. 6E and F). Consistent with experimental observations (Fig. 3D–F), the radially dependent peak in spore density generated by plastic trait Model V simulations is transient, emerging at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \approx \end{document} 3 h and persisting until \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} t\end{document}   \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \approx \end{document} 7 h. Given that there is a 4–5 h interval between the transition to dormancy and the expression of GFP, this simulated onset at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} t \approx \end{document} 3 h closely aligns with our experimental observations, which show the peak at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} t \approx \end{document} 8 h. The localized sporulation peak around plaque edges is transient given that dormancy is initiated in “far-field” cells distant from plaque centers as a result of resource depletion (contrast \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} t=5\end{document} h vs. \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} t=15\end{document} h result observed experimental (Fig. 3) via simulations of Model V (Fig. 6C and D).

Experimental tests of viral-associated dormancy initiation

We set out to experimentally evaluate alternative hypotheses for the initiation of viral-associated dormancy. One hypothesis is that molecules within phage lysates (as evaluated via Model M) accelerate the onset of host sporulation. To test this, we measured the abundance of mature spores that resulted from exposure to 10 kDa-filtered phage lysates via flow cytometry with cell staining (Fig. S10A). We found no significant differences in spore yield (Fig. S10B) and no evidence for the acceleration of spore development (Fig. S10C) in control vs. phage lysate treated cells. Next, we used a fluorescent reporter strain (GFP fused to Spo0A, the master regulatory protein of sporulation, which is expressed early in spore development) to more sensitively detect the onset of sporulation. We spotted the reporter strain with and without lysate treatments on a square Petri dish (Fig. S11A) and visualized the expression of GFP, again finding no significant differences in GFP intensity over time (Fig. S11B) and further no significant differences in the onset of sporulation among treatments (Fig. S11C). Although phage-associated molecular triggers may exist in this system, we find an absence of evidence that phage lysates differentially increase dormancy initiation through an indirect trigger mechanism.

Viral infections themselves could preferentially initiate dormancy, leading to early plaque cessation and the formation of an annulus of spores around the edge of plaques. To test this hypothesis, we focused on viral entrapment, a process in which the lytic cycle is suppressed and the phage genome is translocated from the mother cell into the developing forespore. Based on previous work linking the appearance of turbid plaque morphology to entrapment [62, 63], we screened for virospore densities in transects from the center to beyond the margins of multiple plaques. As described in the Methods, samples were heat-treated to kill free phage and vegetative cells and then replated on spore-forming B. subtilis 168 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \Delta 6\end{document} to quantify the number of virospore plaque-forming units. Virospores were present in all samples, albeit with highly varying densities. We hypothesized based on our simulation findings that virospore densities would exhibit a peak at the edge of plaques (Fig. 7B–F). Mechanistically, plaque expansion requires replication on vegetative cells. As such, early infections should lead to production of viral progeny and plaque expansion. As resources decrease, new phage infections increase the probability of endospore formation and, potentially, phage genome entrapment. We expect the virospore annulus signal to appear transiently (Fig. 7B–D) and remain durable (Fig. 7E–F). Experimental transects revealed that the turbid annulus region around plaques of spore-forming hosts was enriched in virospores after 18 h. Enrichment was highest at a distance from 0.05 to 0.01 cm from the plaque center, corresponding to a region outside the phage plaque core (Fig. 7A). This finding is consistent with simulations of Model V in which the virospore peak at \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} t=15\end{document} h occurs at a distance slightly above \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sim \end{document} 0.05 cm from the plaque center (Fig. 7). This finding provides direct, mechanistic support for a link between viral infections, dormancy, and the early cessation of phage plaques.

Virospore distribution profile. Comparison between experimental observations and model predictions for the spatial distribution of virospores. (A) Experimental measurements of virospore density as a function of distance from the center of the plaque, taken at time t = 18 h. (B–G) Simulation results from Model V. Panels in the middle row correspond to t = 5 h, and those in the bottom row to t = 15 h. Each column represents a different output: the left column (panels B and E) shows the 2D distribution of all dormant cells, the center column (panels C and F) shows cells that entered dormancy due to direct viral interaction (excluding starvation) which serve as a proxy for virospores, and the right column (panels D and G) compares radial profiles of total dormant cells and virus-induced dormant cells. A clear outward shift in the peak virospore density is observed, from the inner region (0–0.05 cm) at t = 5 h to a broader peripheral band (0.05–0.1 cm) at t = 15 h approximating the peak position of our experimental results. In both experimental and modeled profiles, virospores accumulate at the edge of the plaque, suggesting a consistent spatial pattern of dormancy induction.

Discussion

In this study, we tested the effect of sporulation on phage plaque formation within B. subtilis populations. Macroscopic analysis revealed that phage plaques grow at indistinguishable rates on spore-forming vs. non-spore-forming strains. However, plaques grown on sporulating host populations exhibit rapid and earlier cessation of growth compared to those grown on non-sporulating host strains, leading to 2–3-fold smaller plaque sizes. Via a microscopic imaging assay of the interior and boundary of plaques, we found that sporulation is enhanced around plaque edges well before resource depletion leads to the emergence of spores in the population as a whole. The observation that phage infection generates smaller plaques in sporulating vs. non-sporulating hosts suggests a link between lysis and self-limitation of spatial infection. But the spatiotemporal patterns of plaque growth and virospore appearance alone cannot resolve whether early sporulation was the cause of early plaque cessation or a consequence.

We developed two alternative mathematical models of viral-induced sporulation as a means to assess the link between process and spatiotemporal pattern. First, we hypothesized that phage lysis might generate diffusible (small) molecules that modulate the dormancy pathway of uninfected hosts. Because these molecules should reach hosts significantly earlier than (larger) virus particles, it is possible that sporulating hosts could preemptively initiate dormancy before infection. Spatial models of plaque expansion dynamics incorporating lysate-induced sporulation could recapitulate the macroscopic features of early plaque cessation and the appearance of an annulus of spores around plaque edges. We were unable to experimentally corroborate a direct, mechanistic link between phage lysates and early sporulation. Instead, additional experiments showed that both spores and virospores were enhanced around the edges of plaques. Virospores are mature endospores that include a lytic phage in a pseudolysogenic state, capable of completing the lytic cycle following spore germination. The finding of spatially localized virospore enhancement is consistent with a self-limiting, infection-induced sporulation hypothesis. Spatial models of plaque expansion dynamics assuming infection-induced sporulation recapitulate macroscopic features of early plaque cessation, enhancement of spores around plaque edges, and enhancement of virospores around plaque edges. Together, our experimental and simulation results indicate that phage infections can increase spore formation and viral genome entrapment inside the developing forespore. This limits the production of viable phage progeny and plaque growth. As a result, sporulation serves as a collective defensive feature in the short-term, limiting the spatial spread of phage to the wider host population, even though it enables the long-term survival of phage via dormancy in mature endospores that can then revive and proliferate on sensitive hosts when conditions change.

This study focused on a particular scenario in which B. subtilis was grown on agar plates with rich media that facilitates sporulation when resources are depleted. In this context, our combined experimental and theoretical findings reveal an ecologically relevant link between viral infection and sporulation. Limitation of viral dispersion by sporulating cells has key implications for the eco-evolutionary dynamics of phages and bacteria. For instance, early sporulation reduces the number of productive infections and the potential for the generation of phage progeny, including host-range mutants. The rapid dispersal and spatial localization of lysis-associated signals could limit phage spread, even in the absence of the evolution of phage-resistant bacterial mutants [22].

Sporulation may not always provide long-term protection against phage infection. Phage genomes can become entrapped within endospores, allowing infection to resume once the host undergoes germination. Although entrapment depends on the timing of phage infection relative to host sporulation [64], entrapment is thought to involve an arrest of the lytic reproductive cycle. This interruption occurs when Spo0A, a key host protein involved in spore development, binds to short DNA motifs (5 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ^\prime \end{document} -TGTCGAA-3 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} ^\prime \end{document} ) known as 0A boxes that are present within the genomes of some phages [33]. These motifs are widespread and well characterized in the genomes of spore-forming bacteria, where they play essential roles in transcriptional regulation under unfavorable conditions. The presence of 0A boxes in phage genomes suggests that viruses may modulate infection in a Spo0A-dependent manner that promotes entrapment [33]. The phage examined in this study, SPO1, contains four 0A boxes located within middle and late genes. One 0A box is found within gene 16.2, which encodes a viral tail protein necessary for proper phage development. The remaining 0A boxes occur within genes encoding a dUMP hydroxymethylase (gene 29), a primase (gene 34.11), and a protein of unknown function (gene 18.2).

The probability of entrapment may be further influenced by phage acquisition of host sequences involved in chromosomal segregation [33]. For example, SPO1 contains two Par-like elements within its genome: a ParB-like partition nuclease (gene 2.12) and a ParM partition protein (gene 27.9) [65]. The recovery of 0A boxes and Par-like elements, along with other sporulation-related genes [31], suggests that phages have the potential to exploit host dormancy pathways in ways that may influence their fitness.

Our study did not identify the particular intracellular mechanisms by which viral infection accelerates sporulation nor does it rule out the possibility that certain molecules in phage lysates could—in other ecological contexts—accelerate sporulation. There are multiple classes of cellular mechanisms that could give rise to enhanced sporulation around plaques. First, it has recently been shown that a specific type of siderophore (coelichelin) released by a competitor Streptomyces strain can reduce iron availability within B. subtilis populations, which in turn limits sporulation [66]. Although this interspecies effect alters the outcome of competition, iron availability may also influence spore initiation with implications for phage infection. For example, viral lysis within a developing plaque may increase the local concentration of bioavailable iron, which is then used by B. subtilis to make endospores—leading to a strong, self-limiting plaque. Second, in another study, an extracytoplasmic sigma factor ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma \end{document} X) was shown to remodel the cell wall components of B. subtilis in a way that confers phage tolerance in a sporulation-independent manner [67]. Specifically, a stress-response RNA polymerase ( \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{upgreek} \usepackage{mathrsfs} \setlength{\oddsidemargin}{-69pt} \begin{document} \sigma \end{document} X) activates enzymes that remodel the cell wall, including teichoic acid receptors that are involved in phage adsorption and plaque kinetics. As a result, a transient phage tolerance response restricts the lysis-induced proliferation of viruses as transcription factors released by infected neighboring cells contact uninfected bacteria. Third, the release and uptake of small peptides can also alter viral-associated cell fate in B. subtilis. For example, when infected by SPbeta phages, there is a shift from lysis to lysogeny as the concentration of the communication peptide arbitrium increases during a population-wide infection [61, 68, 69]. Future work that explores the resource and signaling landscape modulated by lysis and the relative concentration of viral genomes within spores (i.e. virospores) would provide further insights into the causes and consequences of sporulation-virus feedback in spatially structured habitats across multiple scales.

Altogether, our findings reveal a mechanism by which phage infections can be self-limiting at short time-scales while enhancing dispersal at long time-scales. The accelerated, viral-induced initiation of dormancy restricts phage spatial spread even when nearby hosts remain available, albeit inaccessible. However, early plaque cessation may enable viruses to infect developing endospores or accelerate encapsulation thereby forming virospores that can then later be revived and generate plaque centers elsewhere. This coupling between short- and long-term dynamics presents challenges in the study of eco-evolutionary dynamics of sporulation given the link between cellular, viral, and population fates. Moving forward, it will be essential to consider the consequences of limitations of viral infections across scales including the possibility that collective defense in the near-term may lead to vulnerabilities in the long-term as spores and their entrapped viral genomes re-encounter favorable conditions.

Supplementary Material

magalie_updated_si_030126_wrag023