Temperate infection in a virus–host system previously known for virulent dynamics

The blooming cosmopolitan coccolithophore Emiliania huxleyi and its viruses (EhVs) are a model for density-dependent virulent dynamics. EhVs commonly exhibit rapid viral reproduction and drive host death in high-density laboratory cultures and mesocosms that simulate blooms. Here we show that this system exhibits physiology-dependent temperate dynamics at environmentally relevant E. huxleyi host densities rather than virulent dynamics, with viruses switching from a long-term non-lethal temperate phase in healthy hosts to a lethal lytic stage as host cells become physiologically stressed. Using this system as a model for temperate infection dynamics, we present a template to diagnose temperate infection in other virus–host systems by integrating experimental, theoretical, and environmental approaches. Finding temperate dynamics in such an established virulent host–virus model system indicates that temperateness may be more pervasive than previously considered, and that the role of viruses in bloom formation and decline may be governed by host physiology rather than by host–virus densities.


Supplementary Note 1: Model equations and description
To understand better the mechanisms underlying the host-viral dynamics we observed experimentally, we studied three versions of a host-virus interaction model: a) Uninfected population growth rate: All versions of the model use a phenomenological implementation of the growth rate.
Using as a reference the experimental data for the uninfected case, in which the host follows an approximately logistic growth, we devised an expression for the growth rate that would produce a logistic curve resembling our population density data in the absence of viruses. The following expression provides a good approximation to how the uninfected population growth rate changed with time (see Supplementary Figure 3a): where [H] represents the density of uninfected hosts, [I] the density of infected hosts (which contribute to resource uptake only before induction, see below), K the carrying capacity (see Supplementary Table 2 for parameter values and units), and: that is, the growth rate stays at a maximum level for two days, then decreases linearly to reach a minimum level at t μ . The parameters of the (decreasing) linear relationship are thus given by: The potential temperate mode for the virus is implemented in the equations above via a switch function: Following the experimental data, in the temperate versions of the model we assumed that the default mode of the virus is temperate, with a physiologically-dependent switch to virulent mode that we modeled in two different ways.

Simple temperate version: data-informed switch
In this version of the model, a data-informed switch determines the change from temperate to virulent. Specifically, we assumed that such a mode change was triggered by the physiological stress of host cells measured in our experiments. Understanding as stress the decline that healthy hosts show in the photosynthetic performance curve (Figure 2c), we imposed in this simple temperate version that induction occur at a particular time, t s , matching the beginning of the decline in the F v /F m curve.
Thus, in this version of the model, r s =1 for t ≥ t s , and zero otherwise. This implicitly assumes that the virus does not switch back to the temperate mode in the duration of the experiment, which is consistent with our experimental results for the phenomenology of interest, namely the initial increase and decline of the host population. The specific times, t s , extracted from the F v /F m curve, depended on initial host density but did not depend considerably on experimental setup. Specifically, these times were: 14 days for initial concentration of 10 1 cells per mL, 11 days for 10 2 cells per mL, 8 days for 10 3 cells per mL, 5 days for 10 4 cells per mL, 2 days for 10 5 cells per mL, and 1 day for higher initial concentrations.  4 show that the phenomenological temperate model describes more closely than the virulent model the host dynamics we observed experimentally. Differences between AICs for the virulent model and the phenomenological temperate model for the three treatments with initial densities 10 1 -10 4 cells per mL were larger than 25, indicating a far superior performance of the temperate model. An exponential transformation of this difference, exp(25 / 2) = 2.7 · 10 5 indicates that the temperate model is 2.7 · 10 5 times more probable to be the one that minimizes information loss in this case, making it dramatically preferred by this metric. In the preinfected treatment with an additional initial viral inoculation, for an initial density of 10 4 cells per mL the phenomenological temperate model has lower AICs by a difference of 19, corresponding to being 1.3 · 10 4 times more probable to minimize information loss relative to the virulent model. In cases with no viruses, and for the 10:1 and preinfected treatments with initial density of 10 5 cells per mL, the virulent model is preferred because it has one fewer parameter than the phenomenological temperate model. For the same initial density in the "preinfected plus additional virus" treatment, the temperate model is preferred but the associated probabilities are not meaningfully different (they are within a factor 5, although the correct choice of likelihood function is not clear). These conclusions are corroborated by the MAE results. For all but one of the experiments (the "preinfected plus additional virus" treatment with an initial density of 10 5 cells per mL, where the virulent model gives different predictions than the temperate model), the residuals of the virulent model are larger, with a median difference of 2.15 (corresponding to a factor of 8.58) compared to the phenomenological temperate model.

Self-regulated temperate version: dynamic switch
The fact that the classic virulent model could not replicate our observed experimental data qualitatively, but the phenomenological temperate modification did replicate the behavior both qualitatively and quantiatively, evidenced the presence of an initial temperate mode for the virus. The fact that the main component differentiating both models is the physiology-informed timing for induction leads to the conclusion that both host density and physiology play a role in the timing of the viral switch to virulence.
Our data, however, did not provide enough information to understand (and therefore include in the model) the exact mechanisms that underlie induction. Thus, we further modified the temperate model to include mechanisms that could explain the timing at which viral pressure significantly decimates and causes declines in host populations. To this end, and based on our observations, we introduced several biologically-reasonable changes/assumptions that aimed at triggering induction through system self-regulation:  The infection mode depends on the time that the virus spends in the extracellular milieu between lysis of prior hosts and finding and infecting the subsequent host (see main text). Specifically, we assumed that the infection is virulent if the typical time between infections is smaller than the average life span of the virus, measured as the typical viral decay rate. Mathematically: or, equivalently, when:  Figure 2 shows that host autophagy co-occurs with induction. This suggests a link between the two that can be use to estimate induction rates. Those estimates need to take into account that induction is triggered when the following expression is minimized: From the point of view of the host, the expression is the result of adding the typical replication time of the infected host and time between infections. Thus, the expression considers the tradeoff between the need to replicate fast and the associated increase in infection risk (due to the consequent increase in the host density, which leads to higher encounter rates). From the point of view of the virus, the expression signifies the overall generation time while temperate (or time between infections, as the replication of the infected cell always translates into "moving" to a new host). Importantly, this expression indirectly takes into account host stress in two ways: through density-dependent factors (selfshading, competition for resources) and other physiological factors including the temperate infection itself.
As mentioned above, we assumed that induction of intracellular temperate viruses occurs when the expression in Equation (9) transitions from decreasing to increasing.
Note that the condition given by Equation (8) is a sufficient condition for the infection to be virulent from the outset, whereas Equation (9) is a sufficient condition for induction. In consequence, infections that should be temperate will immediately after adsorption become virulent if the host is stressed enough for Equation (9) to be fulfilled. The host population typically surpasses the threshold for the infection mode condition (Equation (8)) before the induction condition (Equation (9)) occurs and, therefore, the newly-released viruses will ultimately result in virulent infections.

d) Infected-host replication:
We assume that, while the virus is temperate, infected host cells can continue their usual life cycle and, therefore, continue replicating. Thus, the growth rate of infected hosts is implemented as: that is, infected hosts replicate at the same growth rate as healthy hosts while the virus is temperate, and do not replicate at all when the virus is virulent. The justification for the latter is that, when virulent, the virus utilizes the synthesis machinery of the host, which prevents host replication.
As explained above, we assumed that infected-host replication produces new healthy hosts. In our simulations, distributing these replications between healthy and infected hosts, which is plausible if there is more than one virus per host opeing the possibility of superinfection, introduces some initial lag in the growth of the population. Because we lack information regarding the exact ratio of the population offspring that is represented by cells with complete (temperate) infective viruses, our choice here of assuming a complete healthy offspring is based on the best qualitative match with our experimental data.

e) Further considerations:
Other modeling choices We computationally tested several options for each new mechanism we introduced in our models. For example, before we introduced temperateness, we tested whether the delay in the release of the virus could be explained by explicitly including the viral latent period in our virulent model. Although, for low initial densities, the decline in our experimental host populations occurs several latent periods after the experiments start, a potential accumulation of lags could be an alternative to temperateness when trying to explain our observations. To explicitly introduce the viral latent period, we tested a delayed version of the classic virulent model 5 . The resulting curves, however, show similar limitations to that of the classic virulent model (see Supplementary Table 3). Finally, we considered removing the possibility of attachment by several viruses to the same host, which did not alter qualitatively our results. Removing superinfection entails the second term in Equation (5)

Extrapolation to intermediate initial densities
To extrapolate to initial densities beyond the ones we used for our experiments, we deduced phenomenological expressions that aimed to replicate how several of our parameters depended on the initial densities we sampled with the experiments.
For the timing at which the growth rate reaches its minimum value, t μ , for example, we observed the following approximated behavior:  A combination of host density and physiology triggers induction (either caused by the host alone or facilitated by the virus as well), and the timing is close to that provided by the condition encoded in Equation (9).
 Given the conditions above (and their timing), the switch is effectively unidirectional, going from temperate to virulent but not vice versa.
 Infected cells show more stress than healthy cells, and healthy hosts show more stress in a virus-filled medium than when cultured without viruses, reason why autophagy is seen only in experiments in which viruses are present. The fact that both preinfection treatments show similar host dynamics reinforces this idea.
Future work aims to better understand these potential mechanisms (from both ecological and evolutionary perspectives), and test the hypotheses above in the laboratory.           (Figure 1a) better than the virulent model despite being penalized for having extra parameters. Source data are provided at https://github.com/benjaminwilliamknowles/Coup-de-Grace.   , and pre-infected hosts without extracellular viruses (blue points and LOESS lines) across a range of initial host densities from 10 6 to 10 2 cells per mL from Experiments IV, V, and VI (see Supplementary Table 1). All data points have a > 10 3 cells per mL initial threshold (Supplementary Figure 12). Vertical arrows show average onset of lysis in each treatment. Independent experiments are summarized in Supplementary Table 1  A period of asymptomatic infection (virus-host 'Détente') exists up until host growth peaks from a process like nutrient limitation, at which time the temperate viruses induce and lyse the stressed hosts (the viral-mediated 'Coup de grâce'). Note that carrying capacity (black dashed horizontal line), where uninfected populations (black line and text) would suffer bottom-up restriction of growth, is generally unable to be measured in environmental systems due to the presence of predators, competition, etc., and may only be measurable in laboratory cultures. However, experimental elevation of carrying capacity in the environment (e.g., by adding nutrients to nutrient limited systems) may present a means to determine if viruses are following a temperate or virulent strategy. Virulent killing thresholds will be insensitive to nutrient addition, while temperate killing thresholds will vary as a function of nutrient addition.

Supplementary
Supplementary Figure 12: Schematic summary of flow cytometry gating. (a) Intact Emiliania huxelyi cells were identified and counted via chlorophyll fluorescence (488 nm excitation / 692 ± 40 nm fluorescence; log 10 ) and event size (perpendicular side scatter; log 10 ) gates. Intact cells identified using this gate (red lines and arrows) were then analysed using excitation/fluorescence wavelengths to discern whether cells were positive or negative for the diagnostic markers (b) Sytox (a live/dead stain), (c) Lysotracker (to measure autophagy), and (d) UV autofluorescence (a novel metric likely associated with cellular redox stress). Experiments differed in which markers were used (see Supplementary Table 1 for details). Gates (red boxes) were drawn to minimize false positive signals, allowing ≤ 1 % of event to be counted as positive in negative controls, as shown in the representative sample here. Panels b-d show the percentage of events in each cytogram falling into the gates (i.e., false positive rate).