Impact Factor 4.076

The 3rd most cited journal in Microbiology

Opinion ARTICLE

Front. Microbiol., 01 March 2018 | https://doi.org/10.3389/fmicb.2018.00358

Marine Virus-Like Particles and Microbes: A Linear Interpretation

  • 1Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Cambridge, MA, United States
  • 2Woods Hole Oceanographic Institution, Woods Hole, MA, United States
  • 3Faculty of Biology, Technion, Israel Institute of Technology, Haifa, Israel

Viruses are key players in ocean ecology and biogeochemistry, not only because of their functional roles but also partially due to their sheer abundance (Fuhrman, 1999; Wilhelm and Suttle, 1999). Because viruses cannot replicate without their hosts' machinery, their abundance is inextricably related to that of their (mostly microbial) hosts. The relationship between viral and microbial abundances is thus of great interest.

It is often assumed that the abundance of virus-like particles (V, mL−1) and microbial cells (M, mL−1) are approximately proportional. A rule-of-thumb “virus-to-microbe” ratio of 10 has been used (Thingstad, 2000) as measurements of V are frequently an order of magnitude larger than those of M. However, V/M is known to vary substantially (Maranger and Bird, 1995; Knowles et al., 2016; Wigington et al., 2016; Parikka et al., 2017).

Wigington et al. (2016) presented an alternative paradigm. They compiled 5,671 V and M measurements from 25 studies spanning diverse marine environments, an order of magnitude larger than any previous data compilation of its kind. They definitively showed that a power-law relationship V = αMβ is a better statistical model than a proportionality V = αM, in terms of the proportion of variance explained by each. They found β < 1 in most cases, meaning V/M decreases as M increases. If V does scale nonlinearly with M this has broad implications for the characterization of marine viruses' abundance and influence (Wigington et al., 2016), so it is important to be certain that a nonlinear model is superior to a linear description. It also raises questions as to how this nonlinear scaling emerges, and what determines α and β.

While several studies (Maranger and Bird, 1995; Danovaro et al., 2011; Knowles et al., 2016; Wigington et al., 2016) have tested the model V = αMβ by performing ordinary least-squares (OLS) regression on log-transformed V and M data, to our knowledge none have tested the linear model V = aM+b. Unlike V = αM, the linear model V = aM+b has the same number of parameters as the nonlinear model V = αMβ, is consistent with a decreasing V/M as M increases, and is not a special case of the nonlinear model. We interpret V = aM+b to consider V as the sum of two pools—a pool of viruses whose abundance is proportional to microbial abundance (aM), and a background pool of other viruses and virus-like particles whose abundance is unrelated to microbial abundance (b). Because this model is simple and its parameters are comparatively straightforward to interpret and possibly predict, its ability to explain observations should be evaluated before concluding that V and M are nonlinearly related.

Here we evaluate the ability of the linear model V = aM+b to explain the relationship between V and M in the marine datasets considered by Wigington et al. (2016), Knowles et al. (2016), and Parikka et al. (2017). We show that the linear model's performance is never significantly different from that of the nonlinear model, and therefore that the linear model is a tenable description of the relationship between V and M.

We first reanalyzed the datasets considered in Wigington et al. (2016). They analyzed data from 25 studies, and also aggregated surface (z ≤ 100 m; n = 2, 921) and subsurface (z > 100 m; n = 2, 750) samples, totaling 27 datasets. We repeated their OLS regression of log10-transformed V and M data (see Supplementary Material for MATLAB R2017a code). We also fit the model V = aM+b after log-transformation:

log10V=log10(a10log10M+b)

to the log-transformed data via nonlinear least-squares regression. Note that a linear relationship appears curved after log-transformation, asymptoting to V = b as M → 0 and to V = aM as M → ∞. We analyzed log-transformed data to be consistent with Wigington et al. (2016) and others (Maranger and Bird, 1995; Danovaro et al., 2011; Knowles et al., 2016), and because M and V span multiple orders of magnitude.

As the models have the same number of free parameters, we compared the two models by their coefficients of determination (rl2 and rn2 for the linear and nonlinear models respectively). We contend that if one model can be judged superior to the other based on these data alone, its superiority should be apparent even in the simplest statistical analyses.

Figure 1 shows rl2 vs. rn2 for all 27 datasets; neither model consistently outperforms the other and often their coefficients of determination are virtually the same1 (Table S1). The striking similarity between the models' performance suggests that one cannot discriminate between them based on these data alone.

FIGURE 1
www.frontiersin.org

Figure 1. (Left) Example of linear model V = aM+b (dotted purple curve) compared to nonlinear model V = αMβ (solid red curve) for viral (V) and microbial (M) abundance data. Data are the subsurface samples (z > 100 m) from Wigington et al. (2016); compare to their Figure 3b. (Right) Coefficient of determination for linear model V = aM+b (rl2) vs. nonlinear model V = αMβ (rn2) for the 29 datasets considered in the text. Dashed red line corresponds to rl2=rn2. Scatterpoints are sized by the logarithm of the number of samples in each dataset. For each point, the difference between it and the red dashed line is not statistically significant at the 90% confidence level, as estimated by the bootstrap analysis described in the text.

To quantify the similarity of rl2 and rn2, we estimated their confidence intervals with a bootstrap analysis (Efron, 1979). For each of the 27 datasets, we generated 10,000 replicate datasets via resampling with replacement, repeated the above analysis on each replicate, and estimated the 90% confidence intervals of rl2 and rn2 for each dataset by the 5 and 95th percentiles of their bootstrap distributions (Table S1). For all 27 datasets the 90% confidence intervals for rn2 and rl2 overlap, indicating that the difference between the two is not statistically significant, even at the nonconservative 90% confidence level.

Knowles et al. (2016) and Parikka et al. (2017) also compiled V and M data from different environments, including marine environments. We repeated the above analyses on the marine data from both studies, and found that they corroborate our findings above. For the “Pelagic Marine” data from Parikka et al. (2017) (n = 221) we found rl2=0.59 and rn2=0.57 with overlapping 90% confidence intervals; for the “Deep Ocean” data2 from Knowles et al. (2016) (n = 18) we found rl2=0.91 and rn2=0.87 with overlapping 90% confidence intervals (Table S1).

Two earlier studies further corroborate that statistically a linear model is a tenable explanation of the V-M relationship. Maranger and Bird (1995; their Figure 2) (n = 149), and Danovaro et al. (2011; their Figure 1a) [n = 631, including the data from (Maranger and Bird (1995)] also performed OLS regression of aggregated and log-transformed marine V and M data. Both studies estimated β≈1 – Maranger and Bird (1995) found β = 0.93, and Danovaro et al. (2011) found β = 1.03—though neither study's data were available to reanalyse and uncertainties on their estimates for β were not reported. The closeness of β to 1 is consistent with a linear relationship; nonlinearity requires β ≠ 1.

Thus, we conclude that the linear model V = aM+b and the nonlinear model V = αMβ fit this series of datasets of marine viral and microbial abundance equivalently well. This raises the questions of how each model should be interpreted as a description of the relationship between viral and microbial abundances.

The linear model can be interpreted as decomposing virus-like particle abundance into two terms: V = aM+b = Va+Vb. In this interpretation, the first term Va is the abundance of viruses that infect organisms included in M, and it is assumed that VaM as captured by the parameter a. In marine systems, M is dominated by the abundance of prokaryotes, thus Va can be considered to generally represent the abundance of bacteriophage (Suttle, 2007). a can then be considered a characteristic virus-to-microbe ratio, and can be understood in the context of dynamical models. For example, consider arguably the simplest model for virus-microbe dynamics (Lotka, 1920; Volterra, 1928; Lauro et al., 2011; Yau et al., 2011),

dVdt= γφVMλV, dMdt= μMφVM

where (γ, φ [mL s−1], λ [s−1], μ [s−1]) represent burst size, virus-microbe interactions, viral decay, and microbial growth respectively (Record et al., 2016). At steady state, this model predicts V/M = γμ/λ. Predictions for a can therefore be derived from such models. In the above model, a is the product of the viral burst size, the host growth rate, and the viral decay timescale—though most of these are poorly parameterized in environmental populations. Across the 29 datasets we considered, our estimates of a ranged from 0 to 92, with a median of 8.2 (Table S1). This large variation is similar to that of α and β (Table S1; Knowles et al., 2016; Wigington et al., 2016), and is also consistent with the large range in virus-to-microbe ratios observed across marine environments (Parikka et al., 2017). In a majority of cases a was within a factor of two of the “rule of thumb” virus-to-microbe ratio of 10.

The second term Vb is an additional “background pool” of virus-like particles, whose abundance is assumed to be unrelated to microbial abundance. Different types of particles other than infective bacteriophage may be present in this background pool, which could plausibly be variable and non-negligible. Virus-like particles are operationally defined as particles <0.2 μm in size containing nucleic acids; their abundance is measured by treating samples with a fluorescent nucleic acid stain, then counting fluorescing particles with epifluorescence microscopy (Noble and Fuhrman, 1998; Patel et al., 2007). Several non-viral sources are known to be captured by these methods whose contribution to total counts can be large, such as free nucleic acids (Bettarel et al., 2000), DNA-containing extracellular vesicles that are secreted by numerous marine microbes (Soler et al., 2015; Biller et al., 2017), gene-transfer agents (Biers et al., 2008), and decomposing viral material (Wommack et al., 1996). Additionally, while the relationship between microbes and viruses is generally thought to be dominated by prokaryotes and bacteriophage, eukaryote-infecting viruses (Nagasaki and Bratbak, 2010), zooplankton-infecting viruses (Fischer et al., 2010), and virophage (La Scola et al., 2008) may also contribute to V without their corresponding hosts contributing to M. Finally, virus-like particles and microbes have overlapping sizes and counting each population has a significant degree of subjectivity. Therefore, many different kinds of particles might be subsumed into Vb; this background pool could change across environmental gradients (Biller et al., 2017) and with host types in ways unrelated to microbial density. Predictions for b could be made depending on which combination of these particle types b is assumed to represent. Across the 29 datasets we considered, our estimates of b also ranged substantially, from 0 to 6 × 107 mL−1, with a median of 6 × 105 mL−1. Biller et al. (2014) reported vesicle abundances of 3 × 105 and 6 × 106 mL−1 for coastal surface water and Sargasso Sea samples; interestingly, a majority of our estimates for b were between these two values (Table S1).

Interpreting the nonlinear model is less straightforward. Knowles et al. (2016) developed a theory of viruses switching from lytic to lysogenic lifestyles to explain the sublinear scaling relationships they observed, but their theory has been disputed (Weitz et al., 2017) and broadly speaking the relationships between viral and microbial abundances they find tend to be weak or have β≈1 (not indicative of nonlinearity); see their Figures 1a, 2. Empirical sublinear relationships are ubiquitous in biology (Hatton et al., 2015), but the underpinnings of the metabolic theory commonly invoked to explain these relationships have also been disputed (Dodds et al., 2001). It is unclear how the nonlinear model would account for virus-like particles other than bacteriophage, or how α and β would be interpreted and predicted.

These analyses highlight the need for alternative methods to quantify viruses in the environment relative to their hosts. Measurements from marine environments with extremely low microbial densities (because the two models diverge for low values of M), novel experiments with model systems, or other types of data that improve upon the indiscriminant measure of virus-like particles may help answer this question (Baran et al., 2018), and may also be useful for making accurate estimates of b. For now, we contest that a linear model remains plausible.

Author Contributions

BC conceived the research, performed the analyses, and wrote the paper. MC, CF, and MF assisted in the writing process and revised the manuscript.

Funding

The National Science Foundation (GRFP-2388357, OCE-1315201), the National Aeronautics and Space Administration (NNX16AR47G), and the Simons Foundation (SCOPE Award 329108, CBIOMES Award 553242) supported this work.

Conflict of Interest Statement

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.

Acknowledgments

We thank Maureen L. Coleman for productive discussions and suggestions.

Supplementary Material

The Supplementary Material for this article can be found online at: https://www.frontiersin.org/articles/10.3389/fmicb.2018.00358/full#supplementary-material

Footnotes

1. ^The large fluctuations evident in V compared to the range of M helps explain the models' equivocal performance and can yield correlations between V and V/M (Parikka et al., 2017).

2. ^These are compiled from Muck et al. (2014); the other marine dataset considered by Knowles et al. (2016) is taken from Parsons et al. (2012) and is included in the Wigington et al. (2016) dataset and therefore in our analyses above.

References

Baran, N., Goldin, S., Maidanik, I., and Lindell, D. (2018). Quantification of diverse virus populations in the environment using the polony method. Nat. Microbiol. 3, 62–72. doi: 10.1038/s41564-017-0045-y

PubMed Abstract | CrossRef Full Text | Google Scholar

Bettarel, Y., Sime-Ngando, T., Amblard, C., and Laveran, H. (2000). A comparison of methods for counting viruses in aquatic systems. Appl. Environ. Microbiol. 66, 2283–2289. doi: 10.1128/AEM.66.6.2283-2289.2000

PubMed Abstract | CrossRef Full Text | Google Scholar

Biers, E. J., Wang, K., Pennington, C., Belas, R., Chen, F., and Moran, M. A. (2008). Occurrence and expression of gene transfer agent genes in marine bacterioplankton. Appl. Environ. Microbiol. 74, 2933–2939. doi: 10.1128/AEM.02129-07

PubMed Abstract | CrossRef Full Text | Google Scholar

Biller, S. J., Schubotz, F., Roggensack, S. E., Thompson, A. W., Summons, R. E., and Chisholm, S. W. (2014). Bacterial vesicles in marine ecosystems. Science 343, 183–186. doi: 10.1126/science.1243457

PubMed Abstract | CrossRef Full Text | Google Scholar

Biller, S. J., McDaniel, L. D., Breitbart, M., Rogers, E., Paul, J. H., and Chisholm, S. W. (2017). Membrane vesicles in sea water: heterogeneous DNA content and implications for viral abundance estimates. ISME J. 11, 394–404. doi: 10.1038/ismej.2016.134

PubMed Abstract | CrossRef Full Text | Google Scholar

Danovaro, R., Corinaldesi, C., Dell'Anno, A., Fuhrman, J. A., Middelburg, J. J., Noble, R. T., et al. (2011). Marine viruses and global climate change. FEMS Microbiol. Rev.35, 993–1034. doi: 10.1111/j.1574-6976.2010.00258.x

PubMed Abstract | CrossRef Full Text | Google Scholar

Dodds, P. S., Rothman, D. H., and Weitz, J. S. (2001). Re-examination of the “3/4-law” of metabolism. J. Theor. Biol. 209, 9–27. doi: 10.1006/jtbi.2000.2238

PubMed Abstract | CrossRef Full Text | Google Scholar

Efron, B. (1979). Bootstrap methods: Another look at the jackknife. Anna. Statist. 7, 1–26. doi: 10.1214/aos/1176344552

CrossRef Full Text

Fischer, M. G., Allen, M. J., Wilson, W. H., and Suttle, C. A. (2010). Giant virus with a remarkable complement of genes infects marine zooplankton. Proc. Natl. Acad. Sci. U.S.A. 107, 19508–19513. doi: 10.1073/pnas.1007615107

PubMed Abstract | CrossRef Full Text | Google Scholar

Fuhrman, J. A. (1999). Marine viruses and their biogeochemical and ecological effects. Nature 399, 541–548. doi: 10.1038/21119

PubMed Abstract | CrossRef Full Text | Google Scholar

Hatton, I. A., McCann, K. S., Fryxell, J. M., Davies, T. J., Smerlak, M., Sinclair, A. R., et al. (2015). The predator-prey power law: Biomass scaling across terrestrial and aquatic biomes. Science 349:aac6284. doi: 10.1126/science.aac6284

PubMed Abstract | CrossRef Full Text | Google Scholar

Knowles, B., Silveira, C. B., Bailey, B. A., Barott, K., Cantu, V. A., Cobian-Guemes, A. G., et al. (2016). Lytic to temperate switching of viral communities. Nature 531, 466–470. doi: 10.1038/nature17193

PubMed Abstract | CrossRef Full Text | Google Scholar

La Scola, B., Desnues, C., Pagnier, I., Robert, C., Barrassi, L., Fournous, G., et al. (2008). The virophage as a unique parasite of the giant mimivirus. Nature 455, 100–104. doi: 10.1038/nature07218

PubMed Abstract | CrossRef Full Text | Google Scholar

Lauro, F. M., DeMaere, M. Z., Yau, S., Brown, M. V., Ng, C., Wilkins, D., et al. (2011). An integrative study of a meromictic lake ecosystem in Antarctica. ISME J. 5, 879–895. doi: 10.1038/ismej.2010.185

PubMed Abstract | CrossRef Full Text | Google Scholar

Lotka, A. J. (1920). Analytical note on certain rhythmic relations in organic systems. Proc. Natl. Acad. Sci. U.S.A. 6, 410–415. doi: 10.1073/pnas.6.7.410

PubMed Abstract | CrossRef Full Text | Google Scholar

Maranger, R., and Bird, D. F. (1995). Viral abundance in aquatic systems: a comparison between marine and fresh waters. Marine Ecol. Progr. Ser. 121, 217–226. doi: 10.3354/meps121217

CrossRef Full Text | Google Scholar

Muck, S., Griessler, T., Köstner, N., Klimiuk, A., Winter, C., and Herndl, G. J. (2014). Fracture zones in the Mid Atlantic Ridge lead to alterations in prokaryotic and viral parameters in deep-water masses. Front. Microbiol. 5:264. doi: 10.3389/fmicb.2014.00264

PubMed Abstract | CrossRef Full Text | Google Scholar

Nagasaki, K., and Bratbak, G. (2010). “Isolation of viruses infecting photosynthetic and nonphotosynthetic protists,” in Manual of Aquatic Viral Ecology, eds, S. W. Wilhelm, M. G. Weinbauer, and C. A. Suttle (ASLO), 92–101. doi: 10.4319/mave.2010.978-0-9845591-0-7.92

CrossRef Full Text

Noble, R. T., and Fuhrman, J. A. (1998). Use of SYBR Green I for rapid epifluorescence counts of marine viruses and bacteria. Aquat. Microb. Ecol. 14, 113–118. doi: 10.3354/ame014113

CrossRef Full Text | Google Scholar

Parikka, K. J., Le Romancer, M., Wauters, N., and Jacquet, S. (2017). Deciphering the virus-to-prokaryote ratio (VPR): insights into virus-host relationships in a variety of ecosystems. Biol. Rev. 92, 1081–1100. doi: 10.1111/brv.12271

PubMed Abstract | CrossRef Full Text | Google Scholar

Parsons, R. J., Breitbart, M., Lomas, M. W., and Carlson, C. A. (2012). Ocean time-series reveals recurring seasonal patterns of virioplankton dynamics in the northwestern Sargasso Sea. ISME J. 6, 273–284. doi: 10.1038/ismej.2011.101

PubMed Abstract | CrossRef Full Text | Google Scholar

Patel, A., Noble, R. T., Steele, J. A., Schwalbach, M. S., Hewson, I., and Fuhrman, J. A. (2007). Virus and prokaryote enumeration from planktonic aquatic environments by epifluorescence microscopy with SYBR Green I. Nat. Protocols 2, 269–276. doi: 10.1038/nprot.2007.6

PubMed Abstract | CrossRef Full Text | Google Scholar

Record, N. R., Talmy, D., and Våge, S. (2016). Quantifying tradeoffs for marine viruses. Front. Mar. Sci. 3:251. doi: 10.3389/fmars.2016.00251

CrossRef Full Text | Google Scholar

Soler, N., Krupovic, M., Marguet, E., and Forterre, P. (2015). Membrane vesicles in natural environments: a major challenge in viral ecology. ISME J. 9:793. doi: 10.1038/ismej.2014.184

PubMed Abstract | CrossRef Full Text | Google Scholar

Suttle, C. A. (2007). Marine viruses-major players in the global ecosystem. Nat. Rev. Microbiol. 5, 801–812. doi: 10.1038/nrmicro1750

PubMed Abstract | CrossRef Full Text | Google Scholar

Thingstad, T. F. (2000). Elements of a theory for the mechanisms controlling abundance, diversity, and biogeochemical role of lytic bacterial viruses in aquatic systems. Limnol. Oceanogr. 45, 1320–1328. doi: 10.4319/lo.2000.45.6.1320

CrossRef Full Text | Google Scholar

Volterra, V. (1928). Variations and fluctuations of the number of individuals in animal species living together. ICES J. Marine Sci. 3, 3–51.

Google Scholar

Weitz, J. S., Beckett, S. J., Brum, J. R., Cael, B. B., and Dushoff, J. (2017). Lysis, lysogeny and virus-microbe ratios. Nature 549, E1–E3. doi: 10.1038/nature23295

PubMed Abstract | CrossRef Full Text | Google Scholar

Wigington, C. H., Sonderegger, D., Brussaard, C. P., Buchan, A., Finke, J. F., Fuhrman, J. A., et al. (2016). Re-examination of the relationship between marine virus and microbial cell abundances. Nat. Microbiol. 1:15024. doi: 10.1038/NMICROBIOL.2015.24

PubMed Abstract | CrossRef Full Text | Google Scholar

Wilhelm, S. W., and Suttle, C. A. (1999). Viruses and nutrient cycles in the sea: viruses play critical roles in the structure and function of aquatic food webs. Bioscience 49, 781–788.

Google Scholar

Wommack, K. E., Hill, R. T., Muller, T. A., and Colwell, R. R. (1996). Effects of sunlight on bacteriophage viability and structure. Appl. Environ. Microbiol. 62, 1336–1341.

PubMed Abstract | Google Scholar

Yau, S., Lauro, F. M., DeMaere, M. Z., Brown, M. V., Thomas, T., Raftery, M. J., et al. (2011). Virophage control of antarctic algal host-virus dynamics. Proc. Natl. Acad. Sci. U.S.A. 108, 6163–6168. doi: 10.1073/pnas.1018221108

PubMed Abstract | CrossRef Full Text | Google Scholar

Keywords: marine viruses, virus, virioplankton, viral abundance, virus-like particles, virus to microbe ratio, virus to bacterium ratio, virus-microbe relationship

Citation: Cael BB, Carlson MCG, Follett CL and Follows MJ (2018) Marine Virus-Like Particles and Microbes: A Linear Interpretation. Front. Microbiol. 9:358. doi: 10.3389/fmicb.2018.00358

Received: 14 November 2017; Accepted: 15 February 2018;
Published: 01 March 2018.

Edited by:

Ian Hewson, Cornell University, United States

Reviewed by:

Stéphan Jacquet, Institut National de la Recherche Agronomique (INRA), France
Gian Marco Luna, Consiglio Nazionale Delle Ricerche (CNR), Italy

Copyright © 2018 Cael, Carlson, Follett and Follows. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) and the copyright owner are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.

*Correspondence: B. B. Cael, snail@mit.edu