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

Host cultures

All laboratory experiments were conducted with Emiliania huxleyi strain CCMP374 (https://ncma.bigelow.org/ccmp374) and EhV strain 207 (see below). CCMP374 is a naked strain of E. huxleyi isolated from the Gulf of Maine in 1990, and exhibits rapid growth, high-stationary phase densities (~10⁷ cells per milliliter), and high sensitivity to viral infection^27,63. Cultures were maintained at 5·10⁵ to 1·10⁶ cells per millilier and grown at 18 °C, with a 14 h:10 h light:dark cycle with a light intensity of 125 µmol photons m⁻² s⁻¹. CCMP374 was grown in batch culture conditions with f/2 rich nutrients⁴² added to 0.2 µm pore-size filtered (GE Healthcare USA, filter 6718-9582) autoclaved seawater in either polystyrene 50 mL flasks or 6-well plates or polypropylene 96-well plates (Greiner Bio-One, USA; items 690160, 657185, and 780270, respectively; Supplementary Table 1). Addition of f/2 nutrients increases macronutrient concentrations (e.g., NaNO₃ 882 µM; an ~88-fold enrichment over basal seawater with ~10 µM NaNO₃; other nutrients see similar enrichments). This provides ideal, replete conditions conducive to virulent dynamics in which to probe for the presence of virulent viral behavior.

Virus cultures

EhV207 has commonly been used to elucidate virulent dynamics, as it induces the rapid decline of host populations and concomitant production of high titers of viral progeny under culture conditions^28,36,64. Together with CCMP374, EhV207 comprises a highly virulent host–virus system, strongly predisposing this work towards the execution of virulent activity. Viruses were cultured by adding them to exponentially growing cultures at ~5·10⁵ to 1·10⁶ cells per milliliter in f/2 media at a virus:host ratio of 10:1 MOI. Cultures visibly cleared after approximately three days and viruses were isolated from cellular debris using 0.45 µm pore-size filtration (EMD Millipore, USA; filters SLHV033RS or SVHV01015) and lysates stored in the dark at 4 °C until use within 1 week. This approach yielded viral titers in excess of 10⁸ viruses per milliliter. In experiments where a virus-negative control was required, a heat-killed lysate was produced by incubation at 90 °C for 10–20 min prior to 0.02 µm pore-size filtration (Anotop, Whatman, USA) and cooling to ~18 °C. All infections were conducted in the morning⁴¹. For all experiments, virus infectivity was monitored by running parallel cultures with initial host densities of 10⁵ cells per milliliter coincubated with a MOI of 10 (10:1 viruses:host). These visibly cleared in all cases, showing that our viruses were always infectious in these experiments. All flasks were shaken daily and plates mixed by pipetting to preclude settling and ensure equal exposure to infection. In summary, all experiments were conducted in a manner typically conducive to virulent infection and with viable viruses and sensitive hosts.

Laboratory coincubation experiments

E. huxleyi-EhV virulent infection dynamics were first were studied using coincubation of viruses and hosts at an initial ratio of 10:1 viruses:host (MOI = 10) in laboratory conditions. In experiments without preinfection treatments—Experiments II, III, and VII—viral lysates were added to high-density (~1·10⁶ cells per milliliter; quantified using a Coulter Counter Multi-sizer 3, Beckman, USA) cultures to a final ratio of 10:1 virus:host (MOI = 10; viruses were quantified using an Influx Mariner flow cytometer; BD, USA). Cultures were then serially diluted down to experimental densities; all cells were from the same inoculum within each experiment (see Supplementary Table 1 for densities in each experiment and Supplementary Fig. 3 for experimental rationale). Uninfected controls substituted lysates with heat-killed, filtered lysate. In experiments with preincubation treatments (Experiments I, IV, V, and VI), cultures for 10:1 MOI coincubation treatment were drawn from the uninfected control after centrifugation and washing, so that uninfected controls, 10:1 MOI coincubation, and pre-infected treatments were all subjected to similar centrifugation and washing before lysate/heat-killed viral addition. The initial set of experiments (Experiments I, II, III, and VII) were conducted for approximately a week as we expected lysis to occur at all densities in that time (Supplementary Table 1). These experiments were subsequently repeated due to our initial interpretation that the lack of lysis in scarce densities (<10⁴ cells per milliliter) was spurious and susceptible to resolution with further experiments. Discovering instead that this lack of lysis is robust, we commenced longer experiments to demonstrate that the lack of death is not from declining viral infectiousness or abundances, as death initiated up to 3 weeks into incubations (Experiments IV, V, and VI; Supplementary Table 1).

Laboratory pre-infected and virus addition experiments

Having established that lack of lysis in low-density treatments in f/2 media was a robust phenotype in coincubations, we sought to determine if it arose from viruses either being unable to infect at these densities or from viruses choosing not to kill infected hosts at these densities. To distinguish these scenarios, hosts were pre-infected at high density before dilution (Experiments I, IV, V, and VI; Supplementary Table 1). High density (~1·10⁶ cells per milliliter; quantified using a Coulter Counter Multi-sizer 3, Beckman, USA) host cultures were coincubated with a tenfold higher concentration of virus (~1·10⁷ EhVs per milliliter, final density; quantified using an Influx Mariner flow cytometer; BD, USA) for 2 h in culture flasks (Greiner Bio-One, USA) under standard culture conditions (see above). Uninfected controls and coincubation treatments (see above; these treatments were pooled at this point) received a similar volume of heat-killed, filtered lysate. Cultures were pelleted at speed 7 (30 cm radius, swing bucket rotor; Fisher Scientific Centrific Model 225 centrifuge; ~5000 r.c.f.) for 10 min in 50 mL polypropylene tubes (Corning, USA, item 352070). This was done three times so that samples were “triple washed” of extracellular viruses. Pelleting did not affect cellular health as uninfected controls at the start of experiments (t₀) showed low levels of stress and vigorous growth after resuspension. Supernatants were discarded, and tubes inverted for ~3 min to remove as much supernatant and as many free viruses as possible. Pelleted cells were resuspended in fresh f/2 media, vortexed and transferred to new tubes between spins. After washing, cell densities were quantified (Coulter Counter Multi-sizer 3, Beckman, USA) and serially diluted to experimental densities using fresh media. After dilution down to experimental densities, viruses were also added to a preinfection treatment flasks (10⁶ virus per milliliter; final density). All seawater incubations were preceded by pelleting cells growing in f/2 nutrient-rich media and resuspending them in unamended filtered autoclaved seawater, rapidly transitioning cells from f/2 rich media to seawater.

Flow cytometry setup

Laboratory-based experiments were conducted at the Rutgers University Microbial Flow Sort Facility (https://marine.rutgers.edu/microbial-flow-sort-lab/) using a BD Influx Mariner 209s flow cytometer equipped with 355, 488, and 640 nm excitation lasers. All samples were vortexed immediately prior to being run on the flow cytometer, and flow rates measured repeated throughout counting sessions (every ~20 samples) volumetrically by weight (Fisher Science scale S94793A; USA) before and after running one of the samples (volume and time monitored). Flow rates between ~20 and 150 µL per min were used for dense and sparse host counts and characterization while flow rates of ~10 µL per min were used when counting viruses. Samples were prepared and stored in the dark at ~18 °C during all flow cytometry. Instrument settings were standardized by running Spherotech Ultra Rainbow Fluorescent Particles (3.0–3.4 µm) beads (Spherotech URFP01-30) before and after each session to ensure that all counts were directly comparable. All gates were applied and counts conducted using FlowJo 7.6 (https://www.flowjo.com; Supplementary Fig. 12).

E. huxleyi cell abundance

E. huxleyi were quantified by flow cytomtery using chlorophyll autofluorescence between ~10¹ and 10⁷ cells per milliliter (Supplementary Fig. 13a). E. huxleyi were gated a priori using healthy lab cultures grown in f/2 media gated as log₁₀-transformed 488/692 ± 40 nm excitation/emission plotted against log₁₀-transformed Perpendicular Forward Scatter (Supplementary Fig. 12). Gates were set to optimize capturing healthy E. huxleyi cells while avoiding doublets and false-positive counts from debris in collapsed populations. Finally, gates were tailored in seawater incubations to capture stressed E. huxleyi cells when chlorophyll autofluorescence dropped orders of magnitude after weeks at high host densities. In Experiments I and III, E. huxleyi were counted in samples fixed with glutaraldehyde (0.5% final concentration) at ~18 °C for 30 min and then flash frozen in liquid nitrogen and kept frozen until analysis. In all other experiments, E. huxleyi counts were conducted on fresh, unfixed samples. Counts were then normalized to cell densities (hosts per milliliter) using flow rates calculated circa hourly (above; Fig. 1a).

Determination of dead cells

Dead cells were enumerated by flow cytomtery in Experiments IV, V, VI, and VII using the live-dead stain SYTOX Green (Thermo Fisher S7020, USA; “Sytox”). In this assay, SYTOX (stock concentration: 5 mM) was added to each sample at a final concentration of 1 µM, and incubated in the dark for ~30 ± 10 min prior to flow cytometric analysis²⁸. Events in the E. huxleyi chlorophyll autofluorescence gate (see above) were gated through to these SYTOX gates such that only E. huxleyi cells were analyzed as SYTOX-positive or -negative, meaning that SYTOX-positive cells were recently dead (Supplementary Fig. 12). Routinely used FITC gates were applied to log₁₀-transformed 488/520 ± 15 nm excitation/emission fluorescence plotted against log₁₀-transformed Perpendicular Forward Scatter plots in FlowJo to exclude almost all cells in healthy cultures (<1% false positives were allowed). SYTOX-positive cells in a sample were then calculated as a percentage of the total E. huxleyi population. Host densities below 10³ cells per milliliter yielded noisy and false-positive percent dead rates (Supplementary Fig. 13b), so only values with host densities greater than this threshold were analyzed.

Detection of autophagy

In Experiments IV and V, we probed the lysosomal profile signals of cells, a sensitive indicator of cellular stress and infection, by flow cytomtery using the lysosomal stain Lysotracker Deep Red (Thermo Fisher L12492, USA; “Autophagy”). Lysotracker stain (stock concentration: 1 mM) was added to each sample at a final concentration of 110 nM, and incubated in the dark for 30 ± 10 min prior to flow cytometric analysis. Events in the E. huxleyi chlorophyll autofluorescence gate (see above) were gated through to the autophagy gates such that only E. huxleyi cells were analyzed as autophagy-positive or -negative (Supplementary Fig. 12). Gates were applied to log₁₀-transformed 640/670 ± 30 nm excitation/emission fluorescence plotted against log₁₀-transformed Perpendicular Forward Scatter plots in FlowJo to exclude almost all cells in healthy cultures (<1% false positives were allowed). The percentage of autophagy-positive cells was calculated from the total E. huxleyi population. Host densities below 10³ cells per milliliter were shown (Supplementary Fig. 13c) to yield noisy and false-positive percent autophagy-positive rates, so only values with host densities greater than this threshold were analyzed.

UV-induced autofluorescence

In Experiments IV and VI, we observed increased UV-excited autofluorescence signatures of cells undergoing lytic infection (355 nm/460 ± 50 nm excitation/emission) by flow cytomtery. This signature was observed prior to viral-mediated host collapse and concomitant with viral production in ~500 samples; hence, UV autofluorescence is an inherent cellular characteristic and passive marker of infection. Events in the E. huxleyi chlorophyll autofluorescence gate (see above) were gated through to the UV autofluorescence gates such that only E. huxleyi cells were analyzed as UV autofluorescence-positive or -negative (Supplementary Fig. 12). Gates were applied to log₁₀-transformed 355/520 ± 15 nm excitation/emission fluorescence plotted against log₁₀-transformed Perpendicular Forward Scatter plots in FlowJo to exclude almost all cells in healthy cultures (<1% false positives were allowed). The percentage of UV autofluorescence-positive cells was calculated from the total E. huxleyi population (Fig. 2b). Host densities thresholds similar to Sytox and Lysotracker were applied.

Photochemical quantum yield

We quantified the photochemical quantum yield of photosystem II (F_v/F_m), a sensitive diagnostic marker of photosynthetic stress. F_v/F_m was measured in Experiment IV and VI cultures after ~10 min in darkness using a custom-built mini-FIRe fluorometer⁶⁵ with 100 msec sample delay, 20 independent replicate measures per sample, maximum PAR (µmol photons  m⁻² s⁻¹) of 500 with 10 PAR steps; gains were automatically or manually changed to accommodate different sample densities and filter set accurate to host densities of ≥10³ cells per milliliter. Host density thresholds similar to SYTOX and Lysotracker were therefore applied. Dense cultures were diluted with filtered, autoclaved seawater to ensure accurate readings.

Extracellular virus abundance

The concentration of extracellular viruses was determined by quantitative PCR (qPCR). Samples were fixed with betaine (~7% final concentration) at ~18 °C for 30 min and then flash frozen in liquid nitrogen and kept frozen until analysis. To isolate extracellular viruses, 100 µL subsamples were taken from vortexed betaine-fixed samples that had been defrosted at room temperature and centrifuged in PCR strips (15 min; 10,500 x g; 4 °C; F45-48-PCR rotor in an Eppendorf 5417R centrifuge; Eppendorf, Germany). Then, 50 µL of host-free supernatant was removed and transferred to 96-well PCR plates (Fisherbrand plates 14230232, sealed with Bio-Rad Microseal “B” seals MSB1001). Any free DNA was removed by DNAse I treatment (1 U per 50 µL reaction; 20 U per milliliter) at 37 °C for 30 min. Before and after incubations, all samples and enzymes were gently centrifuged in a salad spinner (OXO, USA; Item 1155901). All molecular biology incubations were conducted in a TGradient Thermocycler (Biometra, Germany). Viruses were lysed by incubation at 95 °C for 60 min (“boil prep” and DNAse denaturation) followed by three freeze/thaw cycles of 0 °C for 10 min to 95 °C for 10 min. Plates were then unsealed, Proteinase K was added at a 0.2 µg µL⁻¹ final concentration, and incubated at 37 °C for 60 min. Proteinase K was then denatured at 95 °C for 20 min after which samples were diluted tenfold with molecular grade water (Invitrogen nuclease-free water; AM9930) and stored at −20 °C. Viral copies were quantified by qPCR targeting the viral major capsid protein (MCP) using a Mx3000P qPCR thermocycler (Strategene, USA) with 10 µL reactions with qPCR plates and caps (Applied Biosystems MicroAmp Optical plates N8010560 with Fisherbrand caps 14230230). Reactions (10 µL total volume) were composed of 5 µL of Power Up SYBR Mix (Applied Biosystems Power Up SYBR Green Master Mix; A25741), 0.3 µL of dimethyl sulfoxide, 0.125 µL (125 nM final concentration) of forward and 0.25 µL (250 nM final concentration) of reverse primer working stocks³⁵ (primers prepared by diluting Integrated DNA Technologies (USA) primers to 100 µM with ~800 µL of molecular water, and diluting again tenfold to 10 µM working stocks), 3.4 µL of molecular water and 1 µL of template. MCP forward primer: 5ʹ-TTC GCG CTC GAG TCG ATC-3ʹ; MCP reverse primer: 5ʹ-GAC CTT TAG GCC AGG GAG-3ʹ³⁵. Primer concentrations were optimized by amplifying known template (~100 copies per reaction) with a matrix of forward and reverse primers from 125 nM to 1 µM and annealing temperate optimized by gradient PCR. Reactions were run at 95 °C for 10 min, then 40 cycles of 53 °C for 1 min, 72 °C for 1 min, 95 °C for 1 min. Products were confirmed by dissociation curves. Amplification curves and cycles to threshold (C_t values) were translated to copies per reaction (and therefore viruses per milliliter of original samples) using an internal standard curve run in each qPCR plate. Standard curves were generated from lysates (~10⁸ viruses per milliliter) processed similar to samples (DNAse, Proteinase K, boil prep, etc.), diluted 100-fold (more concentrated lysates showed qPCR inhibition), and then serial diluted by eight times by half. This gave a standard curve of 3·10³, 1.5·10³, 7.5·10², 3.75·10², 1.87·10², 94, 47, 24, and 12 copies per reaction (Supplementary Fig. 13d). Samples below the range of the standard curve with ≤10 copies per reaction were discarded, effectively giving a detection limit of 10⁵ viruses per milliliter in the original samples. Each plate also had three wells dedicated to no-template controls to detect contamination and non-specific amplification.

Frequency of infected cells

A dilution approach was used to estimate the fraction of cells infected in 10:1 virus:host MOI coincubation and pre-infected treatments (Experiment V; Supplementary Fig. 4). Five hours after first mixing viruses and hosts and ~3 h after cultures were diluted to experimental densities and after the onset of the lytic program⁶⁶, cells were diluted 1000-fold in new f/2 media to preclude subsequent rounds of new infection, and counted after 24 h. While dilution of cultures within ~2 h of viral addition gives the temperate phenotype described in Fig. 1, diluting infected cells after the initiation of the lytic program but before death, occuring at ~5 h after mixing, allows the quantification of infection without encountering subsequent infections consistent with a one-step infection curve. Comparing host densities before and after incubation yielded an estimate of infected cells, which was normalized as a percent of the total host population.

Satellite estimation of E. huxleyi densities

The global distribution of E. huxleyi cell abundance (cells per milliliter) was estimated using satellite ocean color fields of particulate inorganic carbon (PIC)^67,68, together with empirical relationships between PIC, coccolith abundance, and E. huxleyi density. In order to determine the upper bound of observed cell densities, the maximum observed PIC at each pixel during the period 2003-2017 was determined from global Level 3 (~9 km) 8-day composite MODIS-Aqua PIC. Retrieved PIC concentration (milligram per liter) was first converted to an equivalent coccoliths per milliliter, which were subsequently associated with E. huxleyi densities. Specifically, Balch et al.⁶⁹ report values of all three quantities and their inter-relationships measured during a large E. huxleyi bloom in the summertime North Atlantic Ocean. Application of these relationships to our data convey some practical constraints, like a PIC limit below which estimated cell densities become negative, but should not affect our estimate of potential maximum cell concentration.

Field mesocosm experiments

Mesocosm experiments were conducted at the University of Bergen Marine Biological Station in Espegrend, Norway from 3 to 20 June 2008. To stimulate a bloom and drive up E. huxleyi cell densities, mesocosms were enriched with nutrients in Redfield ratio stoichiometry, involving daily additions to triplicate enclosures at 1.5 µM NO₃: 0.1 µM PO₄; N:P = 15³¹. E. huxleyi counts were conducted immediately on site in Espegrend, Norway using methods similar to those above for laboratory studies. Cells were counted on a FACScan flow cytometer (Becton Dickinson, USA) equipped with a 15 mW laser exciting at 488 nm and with a standard filter set up⁵⁴. Samples were analyzed at a high flow rate (~70 μL per min) and specific phytoplankton groups were discriminated by differences in their forward or right angle light scatter. Virus-like particles (c.f., EhVs-only quantified with qPCR above) were enumerated at the Rutgers University Microbial Flow Sort Facility (https://marine.rutgers.edu/microbial-flow-sort-lab/) using a BD Influx Mariner 209s. Briefly, glutaraldehyde-fixed samples (0.5% final concentration) that had been flash frozen after 30 min fixation time were thawed, diluted 50-fold with 0.2 µm filtered 1 part SYBR Gold per 20,000 parts Tris-EDTA, incubated at 80 °C for 10 min, cooled, vortexed, and run on the flow cytometer with routinely used log₁₀-transformed 488 nm/542 ± 27 nm excitation/emission plotted against log₁₀-transformed Perpendicular Side Scatter gates⁷⁰. Intracellular viral transcription activity (relative transcription) was extracted from Fig. 2 in Pagarete et al.⁵⁵ using WebPlotDigitizer (https://automeris.io/WebPlotDigitizer/).

Extracting empirical parameters

Empirical and modeled parameters were compared for “fit” of virulent and temperate models using the density at which viruses initiated lysis (lytic density; Fig. 4b). Lytic densities were defined as the highest observed density in each infected culture that showed viral-mediated declines or where they first diverged from uninfected controls, and was assessed on a flask-by-flask basis (Supplementary Fig. 7). Note that actual maxima may have been missed between sampling periods in lab data points, but not in theoretical prediction points. Carrying capacity was calculated in f/2 systems as the maximum density observed in uninfected cultures that reached stationary phase (6.60·10⁶ ± 3.15·10⁵ cells per milliliter). Carrying capacity was estimated in uninfected seawater cultures in each density and in each experiment independently. Further, seawater showed less well-defined carrying capacities compared to f/2 incubations (Supplementary Fig. 5).

Statistical analyses and graphs

Graphs were plotted using the ggplot2 package in R version 3.4.1 “Single Candle” (https://www.r-project.org/). Locally estimated scatterplot smoothing (LOESS) lines were applied with the ggplot2 stat_smooth function. Plots made in R were combined and finished in Inkscape (https://inkscape.org/).

Quantiative comparison between data and models

The models’ match to the data were evaluated using the AIC⁴⁶ and using the absolute magnitudes of the residuals to calculate the difference between the model predictions and data values. This was done for experiments conducted with f/2 rich media by pooling all data sets generated with this media and comparing to the models. Seawater experiments had different carrying capacities in each experiment, precluding pooling growth curves from different experiments. As a result, we did not apply the AIC analysis to these data sets due to a lack of replication and power without pooling. The AIC was here defined as AIC = 2M + N log(RSS/N), where M is the number of parameters for a given model, RSS is the residual sum of squares, and N is the sample size. We consider residuals of the log-transformed data because the data are logarithmically distributed and because both growth and death are multiplicative processes. The use of the second term on the right hand side of the above equation is in analogy with the case of normally distributed residuals, though we note here that the residuals are in almost all cases not normally distributed according to standard statistical tests (e.g., ref. ⁴⁷). We chose to use the expression, however, in lieu of a better option; this choice does not affect our general message, because the differences between the virulent model and observations are so quantitatively and qualitatively large for most cases. The AIC differences in Fig. 3 show the relative performance of virulent and the phenomenological temperate model, supporting that temperateness explains the behavior observed for sparse host densities, while virulent and temperate dynamics seem mostly indistinguishable for crowded densities.

Nonetheless, due to the non-normality of residuals as an additional test, we further evaluated the closeness of each model to our experimental results by measuring the MAE, the sum of the absolute values of the (log-transformed) residuals divided by N. This statistic penalizes residuals very differently from the AIC, because it is proportional to their amplitude rather than the square of their amplitude. As Fig. 3 shows, the MAEs confirm our conclusion above. See Supplementary Notes 1 and 2 for further details.

Virulent and temperate dynamical models

To better understand the mechanisms underlying the host–virus dynamics observed in our experiments, we compared three versions of a host–virus interaction model (Supplementary Figs. 2 and 5): (i) a classic version in which the virus is purely virulent; (ii) a temperate version of the classic model in which induction occurs at times informed by the host physiological data from our experiments; (iii) an improved version of the temperate model that replaces the pre-set induction times by times that emerge from suggested mechanisms for the self-regulation of induction. The comparison between (i) and (ii) aim to discern whether the behavior observed in the laboratory can be explained with a purely virulent virus or with a temperate one. Further, the introduction of (iii) aims to shed some light onto the mechanisms underlying induction. We summarize here the first two; see Supplementary Table 2 and Supplementary Figs. 2 and 5 for further details (including model parametrization), and Supplementary Notes 1 and 2 for the third version of the model.

Equations (1–3) in Fig. 6 represent model versions (i) and (ii), with the growth of the uninfected population presented in black, the additions for the classic virulent model in red, and the additions to represent temperate dynamics in blue, describing the dynamics of uninfected host [H], free infective virus [V], and infected host [I] concentrations (all in units of individuals per liter, see Supplementary Table 2). In the first equation (dynamics of the uninfected host population), the first term represents population growth; the second term represents natural mortality; the third term represents infection events, which occur at a rate k (viral adsorption rate); the last term assumes that infected hosts can reproduce similarly to uninfected cells if the infecting virus is temperate (which, for simplicity, we assume results in new uninfected hosts). In the second equation (dynamics of the extracellular viral population), the third term represents viral decay in the extracellular milieu; the second term represents infection events (including the possibility of superinfection wherein several viruses attaching to or passively infecting the same host); and the first term represents the viral offspring resulting from lysis (which only occurs if the virus is virulent or is a temperate virus undergoing induction, see below); each virus produces B virions per host, and we assume here that the offspring is released at a lytic rate k_L (inverse of the infection time; latent period, L). In the last equation (dynamics of infected hosts), the first term represents infection events; the second term represents lysis of hosts by virulent viruses (or temperate viruses undergoing induction); and the third term represents host natural mortality.

Based on the experimental data for the uninfected treatment, the models use a phenomenological logistic equation to implement host growth rate. Specifically, the following expression provides a good approximation to the uninfected population growth rate:

where K represents 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. See Supplementary Table 2 for more details, including the values for s_μ, n_μ, and t_μ. Equation (4) aims to replicate as closely as possible the growth conditions for the uninfected host population, including changes in its host growth rate due to unknown/uncharacterized sources of physiological stress for which we may have no information. Note that the term takes into account that the “healthy-like” behavior of infected cells before induction reduces the available nutrient for the total host population. However, our results do not change qualitatively if, for example, we replace Eq. (4) with a standard Monod growth function dependent on, e.g., nitrogen as single source of growth limitation in our simulated batch experiment. We further assume that hosts infected with temperate viruses continue their usual life cycle and, therefore, replicate. Thus, the growth rate of infected hosts is:

Given r_s below (Eq. (7)), 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 or undergoing induction as the virus utilizes the synthesis machinery of the host, precluding host replication. We assumed for simplicity that infected host replication produces only uninfected hosts. See Supplementary Notes 1 and 2 for further details and discussion on other options.

Induction, wherein temperate viruses enter lytic replication, is implemented in the equations above via a switch function:

Following our experimental data, we assumed that the default mode of the virus is temperate, with a physiologically dependent induction switch that we modeled in two different ways. Here, we discuss the phenomenological implementation (model (ii)) whose results are shown in Fig. 3 and Supplementary Fig. 8, but see Supplementary Notes 1 and 2 for the more complete version of the model (model (iii)).

For the phenomenological temperate model, we used the decline in the photochemical quantum yield curve as a quantitative indicator of stress (see F_v/F_m curve, Fig. 2c), by imposing an induction time, t_s, matching the beginning of the decline in that 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 the initial increase and decline of the host population. As shown in Fig. 3 and Supplementary Fig. 5, the resulting behavior obtained with this simple temperate version is qualitatively and quantitatively similar to that from the experiments. As in experiments, the specific time t_s is assumed to depend on initial host density, but not considerably on the treatment (see Supplementary Notes 1 and 2). The virulent, purely lytic mode can be seen as a particular implementation of this case in which induction occurs from the outset, where t_s= 0.

As explained in Supplementary Notes 1 and 2, before we introduced a temperate mode, we tested whether the delay in the release of the virus could be explained by explicitly including the latent period in our virulence model. To that end, we introduced a delayed version of the classic virulent model⁷¹. The resulting curves show a qualitative behavior that is similar to that of the classic virulent virus, including the fact that the host population directly declines for the pre-infected treatment that includes additional viruses from the outset. Only decreasing the probability of successful contacts/infections allowed the host population to grow in this simulated treatment, but with a week-long delay that contrasts with the healthy-like growth of the experimental population observed in this case. Thus, a delayed virulent model cannot explain the behavior observed in the laboratory. We also explored the possibility for host physiology to affect the viral latent period and/or burst size instead⁷², which did not qualitatively alter the behavior of the virulent model. In addition, we considered exclusive infection (as opposed to superinfection) where an infected host cannot be infected by more than one virus. This variation, which can be implemented by replacing the second term in Eq. (2) (Fig. 6) with k[H][V], meaning that free viruses attach and infect only uninfected hosts), did not qualitatively alter our results. Finally, although the parametrization used here is a very conservative representation of EhV trait values (see Supplementary Table 2), other parametrizations (e.g., lower contact rates or longer latent periods) did not qualitatively alter our conclusions, as summarized in Supplementary Table 3.

Spatially explicit encounter rates calculation

We estimated the time for a virus to find a host using the model of the encounter between two particle types⁷³,

where E is the volumetric encounter rate, β is the encounter rate kernel, C_V is the concentration of virus, and C_H is the concentration of host (note the change in notation with respect to the models, to emphasize the fact that these are expected values for concentrations measured in the field). Rearranging Eq. (8) provides the time for a virus to encounter a host cell,

In the dynamic models for the laboratory observations, we assumed that the encounter rate kernel was simply a constant, k, which is a good approximation for our laboratory setup. The more general form of the encounter kernel β, however, differentiates between host–virus encounters due to Brownian motion β_b, differential sinking β_s, and turbulence β_t,

The encounters due to Brownian motion depend on the sizes of virus and host,

where k_B is the Boltzman’s constant, T is absolute temperature, η is dynamic viscosity, r_V is viral radius, and r_H is host cell radius. The encounters due to differential sinking are estimated assuming that viral sinking is negligible,

where w_H is the terminal sinking velocity of the host cell. We calculated w_H using Stokes’ Law for small spheres, assuming that the host cells have a diameter of 5 and 6 µm for naked and calcified cells, respectively, and densities of 1.05 and 1.19 g cm⁻³ for naked and calcified cells⁷⁴, respectively. Finally, the encounters due to turbulence are

where ε is the dissipation rate of turbulent kinetic energy and ν is the kinematic viscosity.

We estimated the time for a virus to encounter a host in relatively calm water (ε = 10⁻⁸ m² s⁻³) and in strong turbulence (ε = 10⁻⁴ m s⁻³), equivalent to near-surface conditions under moderate winds. Depending on the host cell’s calcification state and on dissipation rate, encounter rates are dominated by host cell sinking (β_s) for calcified cells or by turbulence (β_t) for naked cells (see Supplementary Fig. 10b, c).

Encounters between particles are central to many ecological processes, but the β kernels take diverse functional forms. Additive β kernels (Eq. (9)) are widely used to estimate encounter rates among planktonic predators and prey⁷⁵ and in coagulation models⁷³. In viral ecology, however, encounter rates are more often estimated using an advection-diffusion framework based on the Sherwood number Sh⁷⁶, a ratio of the contact rates due to advection and diffusion to the contact rates due to diffusion alone. The Sh framework is particularly appropriate when both particle types are small (~1 µm) and encounter rates are strongly influenced by Brownian motion. For the E. huxleyi-EhV system in nature, however, the host cells sink at speeds that render Brownian motion a negligible contributor to encounters. Moreover, there is no straightforward modification for encounters in turbulence, which is a fundamental condition underlying the infection process. In general, encounter rates are slightly higher when estimated from additive kernels than from Sh-based kernels, and, thus, our use of Eq. (10) provides conservative estimates of the time for a virus to encounter a host (Eq. (9)).

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Source: Ecology - nature.com