When we think about viruses we tend to consider ones that afflict humanssuch as those that cause influenza, HIV, and Ebola. Yet, vastly more viruses infect single-celled microbes. Diverse and abundant, microbes and the viruses that infect them are found in oceans, lakes, plants, soil, and animal-associated microbiomes. Taking a vital look at the "microscopic" mode of disease dynamics, Quantitative Viral Ecology establishes a theoretical foundation from which to model and predict the ecological and evolutionary dynamics that result from the interaction between viruses and their microbial hosts.
Joshua Weitz addresses three major questions: What are viruses of microbes and what do they do to their hosts? How do interactions of a single virus-host pair affect the number and traits of hosts and virus populations? How do virus-host dynamics emerge in natural environments when interactions take place between many viruses and many hosts? Emphasizing how theory and models can provide answers, Weitz offers a cohesive framework for tackling new challenges in the study of viruses and microbes and how they are connected to ecological processesfrom the laboratory to the Earth system.
Quantitative Viral Ecology is an innovative exploration of the influence of viruses in our complex natural world.
About the Author
Joshua S. Weitz is associate professor of biology at the Georgia Institute of Technology.
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Quantitative Viral Ecology
Dynamics of Viruses and Their Microbial Hosts
By Joshua S. Weitz
PRINCETON UNIVERSITY PRESSCopyright © 2015 Princeton University
All rights reserved.
What Is a Virus?
1.1 WHAT IS A VIRUS?
Efforts to define a virus inevitably raise the question of exceptions. Nonetheless, a definition or two can help guide us in identifying what is common to all viruses.
Merriam-Webster's Online Dictionary: an extremely small living thing that causes a disease and that spreads from one person or animal to another.
Introduction to Modern Virology: submicroscopic, parasitic particles of genetic material contained in a protein coat (Dimmock et al. 2007).
These two definitions are useful, as they reflect the difference in perception as well as current understanding of what a virus is. In that respect, the roots of the term virus are also revealing:
Oxford English Dictionary: late Middle English (denoting the venom of a snake): from Latin, literally "slimy liquid, poison."
Irrespective of source, it would seem that viruses have a bad reputation. Informal surveys tend to yield similar results. For example, when I ask undergraduates to name a virus, some of the most common answers are HIV, influenza, Ebola, chickenpox, herpes, rabies — not a friendly one in the bunch. The answers represent a typical conflation of the disease with the virus. Nonetheless, this conflation is not entirely inappropriate, as viruses do often negatively affect their hosts, whether by causing disease in humans, plants, or animals or killing their microbial hosts.
In fact, one version of the history of viruses begins more or less as follows (Dimmock et al. 2007) — with smallpox. Smallpox is one of the most vicious of diseases, with historical estimates of mortality rates on the order of 30%. Smallpox is caused by a virus, so-called variola, from the Latin varius or varus meaning "stained" or "mark on the skin," respectively (Riedel 2005). In 1796, Edward Jenner, a surgeon and scientist, made a bold hypothesis based on the common lore that dairymaids did not suffer from smallpox, perhaps because they had been exposed to an apparently similar disease that affected cows, that is, cowpox. Jenner hypothesized that exposure to cowpox led to protection against smallpox. To test this hypothesis, he transferred material from a fresh cowpox lesion of a dairymaid to an 8-year-old boy who had no prior signs of having been exposed to either cowpox or smallpox. The transfer was likely done with a lancet, directly into the arm of the young boy, who then had a mild reaction — similar to the side effects of modern vaccines — but quickly recovered. Then, Jenner did something remarkable, ghastly, but ultimately providential: two months later he returned and inoculated the same boy with material taken from a new smallpox lesion! Remarkably, the boy did not get sick. This event was widely credited, after Jenner's death, as being the first example of a successful vaccination — as it turns out, a vaccination against what later became known as the smallpox virus.
Viruses as agents of disease and death seem to be the common theme, both in the popular and historical understanding. This bad reputation is similar to that ascribed to bacteria, that is, until recently. Bacteria, which were once considered exclusively "bad" because they cause such diseases as cholera, meningitis, gonorrhea, and chlamydia have had their image redeemed, at least in part. That yogurt companies can market the benefits of products enriched with additional naturally occurring Lactococcus cells, that fecal transplants are being considered as a means to stimulate normal digestive tract function, and that the American Society of Microbiology now regularly convenes a meeting on beneficial microbes suggests a reformation in both the scientific and popular opinion of bacteria.
Now, imagine for a moment a yogurt enriched with viruses. This does not seem like a good sales pitch. Or imagine instead, an ocean of viruses. Do you want to go swimming? In fact, a swimmer entering coastal waters for a dip could fill up a single liter bottle and find more than 10 billion, if not 100 billion, virus-like particles. This swimmer is unlikely to get sick, at least not from the viruses. The reasons include the strength of the human immune system and the type of viruses that are found in seawater. Ocean viruses are predominantly viruses of microorganisms and do not have direct effects on human cells. What they do to associated microbes remains an important but ongoing question. Indeed, an alternative history of viruses begins with the viruses of bacteria and constitutes the basis for a far more nuanced view of the range of effects that viruses may have than what is now considered the norm.
This history begins in the late nineteenth/early twentieth century, when microbiologists — also known as "microbe hunters" — such as Louis Pasteur and Robert Koch were trying to identify the causative agents of disease and to find cures for them (de Kruif 2002). Two microbiologists of the next generation of microbe hunters, Frederick Twort, a British microbiologist, and Felix d'Herelle, a French physician, independently observed a curious phenomenon of clearing in solutions and on plates otherwise replete with bacteria (Twort 1915; d'Herelle 1917). Both Twort and d'Herelle passed the material through a series of filters and chemical preparations that should have eliminated any bacterial or predatory organisms like protists. The filtered material derived from the remains of killed bacteria continued to kill newly grown cultures of cells. Twort thought it was an enzyme that killed bacteria, whereas d'Herelle speculated that a small organism was responsible. He called the small, unseen organism a bacteriophage or "bacteria eater," from the Greek word phagos meaning "to devour." The notion that viruses could kill bacteria suggested the possibility of phage therapy — the application of viruses to treat human diseases caused by bacterial pathogens. Phage therapy was championed by d'Herelle and became a focus of scientific investigation and a subject of public discourse. Indeed, Dr. Arrowsmith, the protagonist of Sinclair Lewis's Arrowsmith, published in 1925, discovers a phage capable of killing the microbe that causes bubonic plague. It would seem that viruses, at least those that infect bacteria, could be forces of good.
Despite these advances, neither Twort nor d'Herelle had seen a virus. This happened later, after the electron microscope was developed and applied to the study of bacteria and viruses in the late 1930s. Mice-associated pox viruses (Von Borries et al. 1938) and the tobacco mosaic virus (Kausche et al. 1939) were two of the first viruses analyzed with an electron microscope. Similar visualizations of bacteriophage followed in 1940 (see discussion in Ackermann 2011). In the debate over whether viruses of bacteria were enzymes or distinct particles, the latter camp ruled the day, helped by the direct observations of viruses. In summary, d'Herelle had been prescient in one significant respect: bacteriophage are a kind of virus — the kind that infects bacteria. But not all the early predictions were realized. Phage therapy is not nearly as commonplace as is the application of antibiotics to treat illness. The reasons for this are treated wonderfully in a book on d'Herelle and the origins of modern molecular biology (Summers 1999). Nonetheless, the promise of phage therapy and phage-enabled therapeutics remains (Sulakvelidze et al. 2001; Merril et al. 2003; Fischetti et al. 2006; Abedon et al. 2011). To the extent that phage therapy can work, it does so because of virus-host dynamics. Similarly, it fails because virus-host dynamics also include evolution (Levin and Bull 2004). Mathematical models that underpin phage therapy models will be introduced and analyzed in Chapters 3–5.
Uncharacteristically for biology, mathematical models were very much part of the formative studies of phage that were designed and executed by luminaries such as Emory Ellis, Max Delbrück, and André Lwoff. Of these, Delbrück was a physicist, and papers from the early days of phage biology (certainly those with his name attached) reveal quantitative thinking that helped build intuition regarding the dynamics that could be seen only at scales far larger than those at which the actual events were unfolding. These early studies provided the foundation for subsequent diversification of the study of phage: the basic concepts of what happens subsequent to infection, experimental protocols for inferring quantitative rates from time-series data, and methods for interpreting and disentangling alternative possibilities underlying the as-yet-unseen actions taking place at micro- and nanoscales Delbrück 1946; Lwoff 1953). Two recent books revisit these early days, including one written by Summers (1999), mentioned previously, and another by Cairns et al. (2007), Origins of Molecular Biology. Both place phage and phage biologists where they deserve to be: at the center of the historical development of molecular biology. These early studies also provided another output: raw material. Phage biologists isolated many of the phage and bacterial strains that have since been disseminated globally for use in many branches of biology (Abedon 2000; Daegelen et al. 2009).
Finally, there is a third story of viruses to tell, one that began only in recent years. It reveals how fraught with difficulties efforts are to define what a virus is and how important it is to think carefully about this seemingly semantic question. In 1992, a French research team identified a previously unknown parasitic organism that infected amoeba. The organism had been observed at least a decade earlier but had not been characterized (for more discussion of this history refer to Wessner (2010)). Each particle was nearly 0.5 µm in size, with a large genome approximately 10 bp (base pairs) in length, encapsulated in a membrane vesicle that was itself encapsulated by a protein shell and was further surrounded by fibers. Morphologically the organism had much in common with bacteria, or should have had. As it turned out, this organism is a virus — a giant virus. The virus was called a "mimivirus," because of features that suggested it was a mimicking microbe virus (la Scola et al. 2003). Previous research on giant viruses, for example, that by James Van Etten and colleagues, had characterized large Chlorella viruses with genomes exceeding 300,000 bp (Van Etten et al. 1991). What made these giant mimiviruses even more remarkable, beyond their size, was that they seemed to constitute a hybrid, chimeric, or seemingly new form of life. Once they infected amoeba cells, these viruses did not depend exclusively on host machinery to produce their component parts. Instead, they carried with them nearly all the genes to do so themselves. We are now, it seems, at a moment where discoveries call into question the long-standard definition of viruses — these things that live, die, and multiply, just like other organisms.
What, then, is a virus? There are those who say viruses are not alive and others who argue that they are. In the present context, I would prefer to focus attention on ecologically relevant questions, for example, what do viruses do to the hosts and host populations they infect? This question has implications for how entire microbial communities change and function, in part because viruses infect microbial (and metazoan) hosts from the three kingdoms of life (see Figure 1.1). To understand the effect of viruses on microbes and microbial communities it is important to first ask, what are the physical, chemical, and biological dimensions across which viruses differ? These dimensions of viral biodiversity are crucial to understanding viral life history traits and, ultimately, the effects that viruses have on shaping the microbes and the environments in which they persist.
1.2 DIMENSIONS OF VIRAL BIODIVERSITY
Tobacco mosaic virus, one of the first viruses viewed under an electron microscope, is a rodlike virus approximately 300 nm in length and 20 nm across. In contrast, phage λ, a subject of formative studies of gene regulation (Ptashne 2004), has a capsid approximately 50 nm in diameter with a tail fiber extending approximately 150 nm. Although viruses are "small," their range of sizes is larger than is widely recognized, spanning at least one, if not two, orders of magnitude, with significant morphological variation when considering viruses that infect all kingdoms of life (Figure 1.1). That size varies by two orders of magnitude is due to the recent discovery of "giant" viruses that can reach 0.5 µm in size that infect amoeba, ciliates, and perhaps other eukaryotes (Van Etten et al. 2010).
The physical disparity in size might seem curious, or simply a curiosity (akin to the "Rodents of Unusual Size" from The Princess Bride). However, differences in the physical size of virus particles are linked to many aspects of viral life-history traits. The study of the relationship between size and function is one of the oldest in science. Leonardo da Vinci is considered the first to develop an argument for allometric scaling in biology (see discussion in Brown and West (2000)). Da Vinci hypothesized that the sum of cross sectional areas of tree limbs should be equal before and after branching and, further, that limb lengths scale with limb diameter. This isometric change in limb component size is not quite accurate, given that limb widths increase in size faster than do limb lengths (McMahon 1973). The modern history of the study of allometry, the change of organismal structure and function with body size, has its origins in the late 1800s. In 1883, the German physiologist Max Rübner claimed that the metabolic rate of dogs could be estimated accurately based on knowledge of their size alone (see discussion in Kleiber (1947)). The reasoning assumed that an organism's metabolic rate was mediated via exchange with the surroundings. Organismal surfaces were hypothesized to scale with body size to the 2/3 power, scaling in some sense like spheres. If exchange area scaled to the 2/3 power, then so, too, would metabolic rate. This simple hypothesis is not that far off, though how far off such a prediction is depends on whether mice or elephants are being considered. The analysis of the scaling of metabolic rate is a matter of long-standing scrutiny and debate (Kleiber 1961; McMahon 1973; Peters 1983; Schmidt-Nielsen 1984; Brown and West 2000). Indeed, linking organismal body size to organismal function, such as rates of locomotion, predation, and even death, is the basis for the study of macroecology (Brown 1995).
What is the analogous link between size and function in the case of virus–microbe interactions? Here, there are two sizes to consider: the size of the virus and the size of its host. This chapter largely focuses on virus size, which has two key components: the size of the virus particle and the length of the virus genome. These two sizes are interrelated. Viral genomes are packed under pressure inside a protein capsid. In the case of dsDNA nonlipid-containing phage, the genome is highly organized; for example, there is evidence that DNA can be coiled (Purohit et al. 2005) or even folded toroidally (Petrov and Harvey 2007). The total volume of the genome can be approximated as the sum of the volumes of the nucleotides. The available volume inside the capsid is 4πr3/3, where r is the internal radius of the capsid. How does the realized volume of the genome change as the available volume increases?
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Table of Contents
I VIROLOGY: AN ECOLOGICAL PERSPECTIVE 1
1. What Is a Virus? 3
1.1. What Is a Virus? 3
1.2. Dimensions of Viral Biodiversity 7
1.3. Summary 22
2. Viral Life History Traits 24
2.1. Life History Traits in Ecology 24
2.2. Viral Life Cycle 25
2.3. Traits Associated with Lysis 28
2.4. Traits Associated with Lysogeny 39
2.5. Extracellular Traits 46
2.6. Summary 52
II POPULATION AND EVOLUTIONARY DYNAMICS OF VIRUSES AND THEIR MICROBIAL HOSTS 55
3. Population Dynamics of Viruses and Microbes 57
3.1. On Measurements and Models 57
3.2. Viruses and the “Control” of Microbial Populations 58
3.3. Viruses and Oscillatory Dynamics 74
3.4. Linking Microscopic Details with Dynamics 84
3.5. Summary 88
4. Evolutionary Dynamics of Viruses or Microbes, but Not Both 89
4.1. Viruses and the Nature of Mutation 89
4.2. The Effects of Viruses on Host Evolution 98
4.3. The Effects of Hosts on Viral Evolution 110
4.4. Summary 123
5. Coevolutionary Dynamics of Viruses and Microbes 125
5.1. From Sensitivity Relations to Coevolution 125
5.2. Toward “Novel” Coevolution: On the Probability of Compensating Mutations 129
5.3. The Effect of Coevolution on Host and Viral Population Dynamics 137
5.4. Ecological Effects on the Coevolutionary Dynamics of Types and Traits 146
5.5. Summary 159
III VIRAL ECOLOGY IN THE OCEANS: A MODEL SYSTEM FOR MEASUREMENT AND INFERENCE 161
6. Ocean Viruses: On Their Abundance, Diversity, and Target Hosts 163
6.1. Ways of Seeing 163
6.2. Counting Viruses in the Environment 165
6.3. Estimating Viral Diversity 175
6.4. Virus-Microbe Infection Networks 186
6.5. Summary 199
7. Virus-Host Dynamics in a Complex Milieu 201
7.1. Rosenblueth and Wiener’s Cat 201
7.2. Many Viruses and Many Hosts 203
7.3. Nutrients and the Viral “Shunt” 213
7.4. Viruses and Grazers 219
7.5. Summary 235
8. The Future of Quantitative Viral Ecology 236
8.1. Current Challenges, in Theory 236
8.2. On the Future of Quantitative Viral Ecology 239
TECHNICAL APPENDIXES 245
A. Viral Life History Traits 247
A.1. Measuring Viral Life History Traits: A Quantitative Perspective 247
A.2. A Core Technique: The Plaque Assay 248
A.3. Protocols for Life History Trait Estimation 254
B. Population Dynamics of Viruses and Microbes 258
B.1. Host-Associated Life History Traits 258
B.2. Linear Stability Analysis of a Nonlinear Dynamical System 259
B.3. Implicit Resource Dynamics as a Limit of Explicit Resource Dynamics 269
B.4. On Poisson Processes and Mean Field Models 270
B.5. A Note on Simulating Dynamical Systems 272
B.6. Analysis of a Population Dynamics Model with Reinfection of Infected Hosts 276
C. Evolutionary Dynamics of Viruses or Microbes, but Not Both 278
C.1. Models of Independent Mutations Arising in the Growth of Populations 278
C.2. Invasion Criterion for Mutant Viruses with Distinct Life History Traits 280
C.3. Deriving the Canonical Equation of Adaptive Dynamics 281
C.4. Simulating Evolutionary Dynamics 283
D. Ocean Viruses: On Their Abundance, Diversity, and Target Hosts 286
D.1. Protocol for Automatic Estimation of Virus-Like Particles from Digital Images Derived from Epifluorescence Microscopy 286
E. Virus-Host Dynamics in a Complex Milieu 288
E.1. A Multitrophic Model to Quantify the Effects of Marine Viruses on Microbial Food Webs and Ecosystem Processes 288