# Modeling Virus and Bacteria Populations in Europa’s Subsurface Ocean

^{1}

^{2}

^{3}

^{4}

^{5}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. The Viral Elevator Hypothesis

_{2}by chemosynthetic microorganisms, into suspended DOM. This DOM is then transported upward through the ocean column via circulation and/or diffusion to the sub-ice biosphere, where it is able to be consumed by DOM-limited heterotrophs. This scenario rests on the assumption that Europa’s biosphere is net reductant limited, based on recent estimates showing that O

_{2}fluxes from radiolysis could be comparable to or even overwhelm H

_{2}fluxes from hydrothermal activity [22,27]. Hence, the viral elevator represents the primary mechanism for reduced organic matter to make it to the sub-ice biosphere, promoting the viability of this habitat.

## 3. Methods

#### 3.1. Plausibility of the Viral Elevator

#### 3.2. Model and Parameters

^{4}–10

^{6}mL

^{−1}) and viruses (10

^{5}–10

^{7}mL

^{−1}). Our bacterial values are based on the results of Nguyen and Maranger (2011), who studied bacterial production and respiration rates in the sea ice and underlying waters around Banks Island (Northern Canada) [35]. They found a bacterial abundance of $2.99\times {10}^{5}$ cells mL

^{−1}in the ice, and an abundance of $2.27\times {10}^{5}$ cells mL

^{−1}in the ice-water interface. Typically, in seawater, VBRs can range between 1 and 100 viruses per bacterium [30].

_{10}law based on this temperature range, and both $\alpha $ and the half-saturation constant Q are taken from Showalter (2020). Likewise, the bacterial growth rate ($\mu $) was averaged from the range of values according to Showalter (2020) and varied $\pm $ the geometric mean of the range [30].

_{10}law for Arctic Ocean temperatures [37].

^{4}cm

^{3}sample field, and calculated $m=0.015$ h

^{−1}.

Parameter | Units | Description | Europa-Proxy Value * | Source |
---|---|---|---|---|

${N}_{i}$ | $\frac{\mathsf{\mu}\mathrm{g}}{\mathrm{mL}}$ | Initial amount of DOM (nutrient pool) | $10-50$ | [30] |

${B}_{i}$ | $\frac{\mathrm{cells}}{\mathrm{mL}}$ | Initial bacterial population | $1\times {10}^{4}-1\times {10}^{6}$ | [35] |

${V}_{i}$ | $\frac{\mathrm{cells}}{\mathrm{mL}}$ | Initial viral population | $1\times {10}^{5}-1\times {10}^{7}$ | [30,35] |

$T$ | $\mathrm{C}$ | Temperature | $-4-0$ | [36] |

$\alpha $** | $\frac{\mathsf{\mu}\mathrm{g}}{\mathrm{cell}\cdot \mathrm{hr}}$ | Uptake constant | $\left(1.2\times {10}^{-7}\right)\times \left({3}^{\frac{T-23}{10}}\right)$ | [30] |

$\mu $ | ${\mathrm{hr}}^{-1}$ | Bacterial growth rate | $0.016-0.032$ | [30] |

$Q$ | $\frac{\mathsf{\mu}\mathrm{g}}{\mathrm{mL}}$ | Half-saturation constant | 0.022 | [30] |

$d$ | ${\mathrm{hr}}^{-1}$ | Constant of bacterial death | $0.0002$ | [37] |

$m$ | ${\mathrm{hr}}^{-1}$ | Viral decay rate | $0.015$ | [40] |

$g$ | $-$ | Fraction of uptake material recycled into nutrient pool as exudate | 0.02–0.2 | [38] |

$n$ | $-$ | Fraction of viral lysis material recycling into nutrient pool | 0.99 | [39] |

$\gamma $ *** | $-$ | Lytic vs. lysogenic fraction | $0-1$ | [30] |

$\varphi $ | $\frac{\mathrm{mL}}{\mathrm{cell}\cdot \mathrm{hr}}$ | Adsorption (infection) rate | $1\times {10}^{-11}-1\times {10}^{-9}$ | [41] |

$\beta $ | $\frac{\mathrm{cells}}{\left[\mathrm{burst}\right]\mathrm{cell}}$ | Viral burst size | $10-500$ | [41] |

$f$ | $\frac{\mathsf{\mu}\mathrm{g}}{\mathrm{cell}}$ | Conversion rate between grazed bacteria and DOM | $70-85$ | This study |

_{10}law. *** $\mathsf{\gamma}$ ranges between fully lytic (0) and fully lysogenic (1).

_{B}) was 0.07 d

^{−1}, with a viral concentration (V

_{C}) of approximately $2\times {10}^{7}\frac{\mathrm{cells}}{\mathrm{mL}}$. From these values we calculated an infection rate $\varphi $ of:

^{–11}–10

^{–9}$\frac{\mathrm{mL}}{\mathrm{cell}\cdot \mathrm{hr}}$.

## 4. Results

#### 4.1. Closed System

^{5}; V = 10

^{6}; $T=-2$; $g=0.09$; $\mu $= 0.024; $\gamma =1$; $\varphi $= 10

^{−10}. The burst size $\beta $ has values of 10, 100, and 250, labeled accordingly.

^{−1}and a maximum of ~1 $\times $ 10

^{8}mL

^{−1}. The viral population varies even more, between a minimum of ~0.1 mL

^{−1}and a maximum of 2 $\times $ 10

^{9}mL

^{−1}. The bacterial population at its minimum is therefore a mere 6 $\times $ 10

^{−7}of the population at its peak, while the viral population minimum is 5$\times $ 10

^{−11}of its maximum. This has interesting implications for the search for life on icy ocean worlds. We can use the wildflower blooms of Death Valley as an analogy: if one were to visit and observe for a short period in between blooms, it would seem that the area is devoid of flowering plants, whereas observation over a longer time would show this not to be the case. While bacterial and viral population peaks in our model of Europa’s ocean are functionally different from wildflower blooms, the implications are similar—that observing during a short period between population peaks could result in a false negative for the presence of life. These results suggest that mission longevity and continuous measurements could be important to the success of future life detection missions to icy ocean worlds.

#### 4.2. Open System

^{4}, with lower and upper quartiles at 891 and 5.8$\times $10

^{5}, respectively. The majority of VBR values were around 100 or less. This is in good agreement with terrestrial VBR values for the Arctic [2]. Given that in Earth’s oceans the VBR is ~10 and yet viruses only make up ~5% of the prokaryotic biomass, a VBR of ~200 will result in a roughly equal split of biomass between viruses and bacteria [42]. Our models suggest that for reasonable burst sizes, viruses on icy worlds could outweigh their bacterial hosts in biomass. Thus, our search for life on Europa and other icy ocean worlds should certainly account for viruses. Not only would they be highly abundant, but given the slight time delay in the peak of the viral population after the peak of bacterial population, a bacteria-based search for life could struggle to find positive readings during times where the viral population would still be blooming.

_{2}) flux in $\frac{\mathrm{mol}}{\mathrm{yr}}$, $G$ is the Gibbs free energy for the given metabolic redox reaction in $\frac{\mathrm{kJ}}{\mathrm{mol}}$, and $c$ is the anabolic conversion factor in grams of biomass per kJ of free energy. Vance et al. (2016) gives the flux of H

_{2}from water-rock reactions to be ${10}^{10}\frac{\mathrm{mol}}{\mathrm{yr}}$ and show that this H

_{2}flux is likely matched or exceeded by the O

_{2}flux into Europa’s ocean from surface ice radiolysis [22]. Hence, the dominant geochemical gradient at the Europan seafloor can be considered to be one in which H

_{2}serves as the reductant and O

_{2}serves as the oxidant. The Gibbs free energy for H

_{2}reacting with O

_{2}is $237.13\frac{\mathrm{kJ}}{\mathrm{mol}}.$ Taking the conversion factor $c=\frac{1\mathrm{g}}{4.1868\mathrm{kJ}}$ from Chyba et al. (2001), we get ${B}_{R}~6\times {10}^{8}\frac{\mathrm{kg}}{\mathrm{yr}}$ [15].

^{−15}$\mathrm{kg}$), $n$ is the amount of DOM ($6\times {10}^{-8}\frac{\mathsf{\mu}\mathrm{g}}{\mathrm{cell}}$), $r$ is the radius of Europa ($1.5\times {10}^{6}\mathrm{m}$), and $d$ is the depth of the sub-ice biosphere in mm. The numerator gives a biomass synthesis rate in $\frac{\mathsf{\mu}\mathrm{g}}{\mathrm{hr}}$, while the denominator gives a volume in ml, which results in our viral elevator input rate with units $\frac{\mathsf{\mu}\mathrm{g}}{\mathrm{mL}\cdot \mathrm{hr}}$.

_{R}~6 × 10

^{8}kg/yr) and calculate the viral elevator flux E required to produce sub-ice biofilms of various depths (Figure 8). We overlay the median and interquartile values of the averaged E values from our simulations to indicate the most plausible biofilm depth for a given benthic biomass synthesis rate.

## 5. Discussion

_{2}-limited, we suspect that this is not the case given that CO

_{2}is the most abundant gas in plumes on Enceladus, a similar icy moon to Europa [49]. Regardless, we acknowledge that our open system model is a simplified representation of Europa’s biogeochemical cycles, given the likely flux of reductants from the surface.

_{10}law. However, especially in the case of our closed system model, several parameters are likely affected by temperature, given that temperature affects the relative contact rate (RCR) between bacteria and viruses. Future iterations of this model may include initial values for DOM, bacteria, and viruses as well as viral burst size ($\beta $), bacterial growth rate ($\mu $), and infection rate ($\varphi $) as a function of temperature. Future work may also take into account sporulation and changes to the lytic vs. lysogenic state by making bacterial growth rate ($\mu $), uptake constant ($\alpha )$, and lytic vs. lysogenic fraction $\left(\gamma \right)$ functions of DOM availability and/or other parameters of the model.

## 6. Conclusions

^{−3}–10

^{−1}mm GEL.

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

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**Figure 1.**(

**a**) A simplified model of the viral shunt in Earth’s oceans (after Breitbart et al., 2018) [1]. On Earth, carbon enters the system via photosynthesis at the top of the ocean, eventually settling at the bottom of the ocean as particulate organic matter (POM). The viral shunt assists in keeping organic matter in near-surface waters by creating dissolved organic matter (DOM) for further consumption. (

**b**) A simplified model of the viral elevator in Europa’s ocean—a reverse of the viral shunt process on Earth. Here, carbon enters the system via chemosynthesis, fueled by reductants emitted at hydrothermal vents, at the bottom of the ocean. The viral elevator assists in creating DOM that can be transported from the benthic biosphere to a sub-ice biosphere, which would be much more accessible to near-future missions.

**Figure 2.**Closed-system model results from 300 runs (with 31 outliers removed). Each color represents an individual run. Parameters were randomly seeded where applicable (Table 1), resulting in a wide range of system longevity and VBR ranging between ~10

^{−2}–10

^{6}. All modeled systems trend to zero (i.e., the finite DOM supply is consumed and the system loses viability).

**Figure 3.**Closed-system model results from a single run over 15,000 h, with varying viral burst sizes to show differences in system longevity. Higher viral burst sizes result in greater system longevity. (

**a**) Burst size 10; (

**b**) burst size 100; (

**c**) burst size 250.

**Figure 4.**(

**a**) Bacterial and viral populations with varying burst size over 2000 h. Time between peaks slightly decreases as viral burst size increases, however, for a maximum viral burst size of 500, the time between peaks is still significant (~28 days). (

**b**) Bacterial and viral populations with varying burst size over 25,000 h. For a maximum viral burst size of 500, populations persist for ~3 years.

**Figure 5.**A sample of 4 runs from the open-system model to better demonstrate the behavior of the steady state. Plots show the last 50,000 h (2500 runs in total were done, with 2342 outliers removed). These runs clearly demonstrate a steady state with no significant increase or decrease in each parameter over time.

**Figure 6.**Open system model results showing the last 2000 h for a steady state system. Unlike the closed-system model, open-system runs do not taper off to zero over time.

**Figure 7.**Histogram of average E values with log-normal distribution curve (pdf) and cumulative distribution function curve (cdf) fitted to the model outputs. Based on the cdf, it is 90% likely that E is less than ~1.2 $\times $ 10

^{−3}but above the lower limit of ~1 $\times $ 10

^{−4}.

**Figure 8.**Colormap diagram of abyssal biomass synthesis rate vs. depth of sub-ice biofilm. Solid contours show the median of the averaged E values from Figure 7, while dashed contours represent the interquartile range. Values for biomass and depth that fall within the blue support a steady state system, while values falling in the red do not. Values that support a steady state suggest that a sub-ice biofilm would be no more than 0.1 mm in thickness.

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Gomez-Buckley, A.C.; Showalter, G.M.; Wong, M.L.
Modeling Virus and Bacteria Populations in Europa’s Subsurface Ocean. *Life* **2022**, *12*, 620.
https://doi.org/10.3390/life12050620

**AMA Style**

Gomez-Buckley AC, Showalter GM, Wong ML.
Modeling Virus and Bacteria Populations in Europa’s Subsurface Ocean. *Life*. 2022; 12(5):620.
https://doi.org/10.3390/life12050620

**Chicago/Turabian Style**

Gomez-Buckley, Adriana C., Gordon M. Showalter, and Michael L. Wong.
2022. "Modeling Virus and Bacteria Populations in Europa’s Subsurface Ocean" *Life* 12, no. 5: 620.
https://doi.org/10.3390/life12050620