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How can we predict the ecologic impact of an antimicrobial: the opinions of a population and evolutionary biologist

2001; Elsevier BV; Volume: 7; Linguagem: Inglês

10.1046/j.1469-0691.2001.00070.x

1469-0691

Bruce R. Levin,

Evolution and Genetic Dynamics

A number of years ago, while skiing across from my house in western Massachusetts, I went though a pasture into a Hemlock wood and finally into a mature 'climax' forest. It looked like the forest primeval; tall sugar maples, oaks and beeches surrounded the trail on which I was skiing. It could have been 1000 years ago, 10 000 even, or so I thought. Save for the narrow trail, the forest appeared to be untouched by man; what a delight, a bright clear day, shafts of sunlight reflecting off the fresh, powdery snow. There was no sound, save for that of my skis moving through the snow. And there it was, right across the middle of the trail. There in the forest primeval lies a stone fence. Like much of New England, the area in which I lived and the land on which I was now cross-country skiing had been farmland less than 200 years earlier. Through the considerable efforts of the settlers, with the aid of their draft horses and oxen, the trees were cut down and the stumps removed. The larger stones were pulled out of the earth and made into fences and the foundations for houses and barns. They cultivated the land they cleared – maize, beans, squash, barley, oats and wheat – and let their cattle, sheep and horses graze on the fields that were left fallow. It was a hard life, and soon after the territories to the west opened and the thick, rich soils of Ohio, Illinois, Iowa and Kansas became available, the descendants of settlers of New England left the rocky thin soil of their homeland and moved on. Ecologic succession did its job. The land they left returned to what it had been, mature forests. The only signs of their having been there were the stones of their fences and the foundations of the houses and barns they built. Could we have predicted the ecologic consequences of clearing the land and the years of cultivation and grazing? Could we have predicted what would happen to that land when those enterprises stopped? I do not believe we could have made those predictions 200 years ago, or for that matter, would have had all that much inclination or time at our disposal to do so. We could make those predictions now, but not because we know all that much about the processes that determine the structure of forest communities. We do not and perhaps we cannot. The complexity of interactions between the thousands of species of plants, animals and microbes in these forest and agricultural ecosystems and the relationship between these organisms and their physical environment is mind-boggling. These biotic interactions and physical relationships are what determine the distribution and abundance of the vast array of organisms present in these and every other ecosystem. Our predictions would be based primarily on experience, history as it were, and observations from extant land that are in various stages of clearance, cultivation, grazing and the succession process. At an ecologic level, the use of an antimicrobial agent for chemotherapy and prophylaxis is analogous to clearing land. Not only are the populations of the target microbes denuded, the extensive use of even a narrow-spectrum antimicrobial could make profound changes to the microbial flora of not only individual patients but the treated population at large. In the main, the effect of these agents would be to reduce the diversity of that flora and the relative distributions of the different members of the community. The magnitude of the change in that flora would be even greater with a broad-spectrum antimicrobial, because that many more members of the existing community would be affected. To be sure, the commensal ('normal') microbial communities of the human intestinal tract and skin, and that of the mucosa of the nasal, oral and vaginal orifices, are vastly less complex than that of the plant, animal and microbial flora of a forest or even a cultivated field. Nevertheless, the complexity of these commensal microbes remains well beyond the level that we can use existing ecologic theory to predict with any precision the ecologic consequences of changes in the densities of one or more member species. On the other hand, I believe mathematical models could facilitate these predictions, if not in general, at least with respect to the practical concern of predicting the major consequences of the ecologic disturbance resulting from the introduction of an antimicrobial agent into an established community of microbes (read 'bacteria'). To a population and evolutionary biologist, mathematical models are tools to unambiguously (or at least less ambiguously than purely verbal considerations) define problems and, in a quantitative way, evaluate the contribution of different factors to the processes under consideration. Mathematical models have been used to develop a general theory of the structure of ecologic communities and the relationship between the complexity and diversity of these communities [1May RM Stability and Complexity in Model Ecosystems. Princeton University Press, Princeton, New Jersey1973Google Scholar]. Steven Hubbell's book presents a new and, I believe, very promising approach to a formal theory of the ecology of natural communities [2Levin BR Stewart FM Chao L Resource-limited growth, competition, and predation: a model and experimental studies with bacteria and bacteriophage.Am Naturalist. 1977; 977: 3-24Crossref Google Scholar]. However, this kind of theory is not specific enough to make useful predictions about the consequence of a specific intervention in a microbial community of the sort we are concerned with here. One could construct relatively specific mathematical models of the changes in the densities of multiple interacting populations at different trophic levels and use those models to evaluate the consequences of changes in the density of one or more of the interacting populations due to the introduction of a new antimicrobial. To illustrate this, I consider simple extensions of a model we developed ages ago to study the population biology of bacteria, their primary resources and their viruses, bacteriophage [3Lenski RE Hattingh SE Coexistence of two competitors on one resource and one inhibitor: a chemostat model based on bacteria and antibiotics.J Theoret Biol. 1986; 122: 83-93Crossref PubMed Scopus (109) Google Scholar]. In this model there are K distinct resources upon which the bacteria grow, I distinct populations of bacteria and J distinct populations of phage. The variables rk, ni and pj are, respectively, the densities and designations of the rth resource, ith distinct population of bacteria and jth population of phage (or other predators). We assume the bacteria of population i grow at a rate directly proportional to the concentrations of the different resources, Φi(r1, r2, …, rK), monotonically increasing functions of the rs terms, and that each resource enters the habitat at a constant rate, ρ, from reservoirs where it is present at concentrations Rk. We assume the habitat is in steady state in the sense that the rate at which excess resource, bacteria and phage are removed is also equal to ρ. Individual bacteria of population i take up the resource at a rate proportional to the concentration of that resource concentration, Λik(rk). Phage adsorb to sensitive bacteria of population i at a rate proportional to their density and an adsorption rate parameter δij. In this model, we assume all these phage are lytic and each infection kills the bacteria and produces βij infective phage particles. For this consideration, we neglect the latent period and other time delays associated with phage reproduction. With these definitions and assumptions, the rates of change in the densities of the resources and component populations would be given by a series of differential equations, drk/dt=ρ(Rk−rk)−∑iΛik(rk)nkdni/dt=niΦiI(r1,r2,…, rK)−ni∑jpjδij−ρnidp/dt=pj∑iδijniβij−ρpj To this simple model of the population dynamics of bacteria and phage we can add an additional series of equations for an array of Z different antimicrobial agents, each at concentration az. Individually and collectively, these antimicrobials reduce or kill susceptible bacteria at rates directly proportional to their concentrations Γi(a1, a2, …, aZ). If in combination they are bactericidal, the inhibition function would be greater than their growth rate, Γi(a1, a2, …, aZ). > Φi(r1, r2, …, rK). We can make many different assumptions about how these antimicrobial agents enter the community and how their concentrations, the ak terms, change in the course of time. In the simplest case, their concentration remains constant. Under these conditions, the rates of change in the densities of the different bacterial and phage populations and the concentration of the limiting resource would be given by drk/dt=ρ(Rk−rk)−∑iΛik(rk)nIdni/dt=niΦiI(r1,r2,…, rK)−ni∑jpjδij−Γi(a1,a2,…aZ)−ρnidp/dt=pj∑iδijniβij−ρpkwhere the az terms, z = 1, 2, …, Z, are constant. By adding a fourth set equation for the antimicobials daz/dt=ρ(Az,−az)where Az is the concentration of the zth antimicrobial in some reservoir, we could allow the concentration of the antimicrobial agents to vary in time, e.g. doses taken at specific intervals. We could even make their concentration change as a function of the density of one or more bacterial populations, as would be the case if detoxification took place [3Lenski RE Hattingh SE Coexistence of two competitors on one resource and one inhibitor: a chemostat model based on bacteria and antibiotics.J Theoret Biol. 1986; 122: 83-93Crossref PubMed Scopus (109) Google Scholar], e.g. a β-lactamase-determined resistance to β-lactam antibiotics. If bacteria of a strain or species i is resistant to a phage j, δij = 0. Resistance to an antimicrobial would be reflected in the magnitude of Γi(a1, a2, …, aZ) such that for a fully resistant strain of bacteria i, Γi(a1, a2, …, aZ) = 0. By adjusting the values of the growth rates, Φi(r1, r2, …, rK), we can account for variation in the intrinsic fitness of these different populations of bacteria. We can promote the stable coexistence of these bacteria by having them utilize the different resources at different rates, and by being susceptible to different phages. In the absence of antimicrobials, the necessary (but not sufficient) condition for stable coexistence of different species of bacteria and phage in this model is that the number of distinct populations of phage, J, be less than or equal to the number of distinct populations of bacteria, and that the number of bacterial populations be less than or equal to the sum of the number of distinct resources and phages, J ≤ I ≤ J+K [2Levin BR Stewart FM Chao L Resource-limited growth, competition, and predation: a model and experimental studies with bacteria and bacteriophage.Am Naturalist. 1977; 977: 3-24Crossref Google Scholar]. One implication of this is that even in the very simple habitat specified by this model, a very diverse and complex community could persist in a stable state. The introduction of an antimicrobial would upset this equilibrium, but in theory, if not in practice, it could expand as well as reduce the potential diversity of the community. Constructing these simple population dynamic models of the bacterial (or other microbial) communities is, obviously, not very difficult. It is also a rather pleasant job that gives the model builder the illusion of working, doing science even. These models can easily be extended to account for other kinds of interactions between the microbial populations, like allelopathy such as that resulting from the release of bacteriocins [4Chao L Levin BR Structured habitats and the evolution of anticompetitor toxins in bacteria.Proc Natl Acad Sci USA. 1981; 78: 6324-6328Crossref PubMed Scopus (377) Google Scholar, 5Levin BR Frequency-dependent selection in bacterial populations. Phil Trans Royal Soc London – Series B.Biol Sci. 1988; 319: 459-472Crossref Scopus (182) Google Scholar] and even the host immune response [6Levin BR Bull JJ Phage therapy revisited: the population biology of a bacterial infection and its treatment with bacteria and antibiotics.Am Naturalist. 1996; 147: 881-898Crossref Scopus (133) Google Scholar]. Temporal and physical heterogeneity could also be built into these models, like variation in the dosing of the antibiotics, as could stochastic processes like mutation and the invasion of new species and lineages and the random losses of existing ones. There is no limit to the complexity that one can build into these models. The problem comes in the analysis of their properties and the interpretation of the results of those analyses. To be sure, if one is willing to give up on the aesthetics of analytical solutions and accept the practicality and insecurity of numerical solutions, *Numerical solutions (computer simulations) are very much like experiments. With even relatively few parameters, one could miss important properties of the model by not considering specific interactions between different parameters and by exploring only limited ranges of parameter values. There are ways to reduce the likelihood of this occuring, like randomly sampling arrays of parameter values and combinations thereof, like the 'Latin Hypercube' method developed by Sally Blower. One could also limit the ranges of the parameters (and variables) of the model to those that are realistic, by designing the models so that independent estimates of their parameters can be obtained in populations, and of course, obtaining those estimates. Finally, with a large and complex computer simulation there is always the potential for programming errors or logical errors in the design and construction of the model. For this reason, I believe it is essential that computer simulation (as well as data analysis) programs be made available to the reader, as would (or should) be the case with experimental organisms or materials. with computers one can solve these equations and do so even with a model far more complex than that described, maybe even to the point of approaching the reality of a microbial ecosystem. In that way, one could evaluate the consequences of introducing antimicrobials with different spectra of activity on the distribution and abundance of bacterial strains and species in the community. Being able to do this, however, does not necessarily make it worthwhile. Would we learn something new and worth knowing from this kind of study? And, most importantly for the present consideration, would it be possible to make practical and reliable predictions about the ecologic consequences of introducing an antimicrobial agent into a community? With all the caveats implicit in the above, and more, I believe that mathematical models of this sort and numerical solutions to explore their properties could well be used to evaluate the effects of antimicrobials on the ecology of relatively simple microbial communities. One practical way of doing this is by restricting the consideration to the deleterious (pathological) effects an antimicrobial would have by modifying the ecology of the existing flora of treated patients. 2One favorable thing about this issue is that microbes do not have Rights Groups and human society cares little about the esthetics of their distributions, unless they lead to health, agricultural, industrial or olfactory problems. Indeed, we would mourn little if a microbial species or two were driven to extinction, as long as their demise had little affect on what we care about, our health, agriculture, industry and our noses. However, addressing even this restricted question would require a great deal of effort, of which the construction and analysis of mathematical models would be a minor part. The far more difficult part would be the following: 1Identifying the species and strains of bacteria that play the most prominent role in maintaining the stability of the affected communities. A critical role of a stable commensal flora is to prevent either the invasion of new pathogens or the ascent of normally rare species and strains to densities where they become virulent, like Clostridium difficile in the intestinal tract.2Exploring the generality of these major players. Are the same species (and strains) of bacteria playing the same role in all human hosts and how much variation exists in the communities of commensal microbes among hosts?3Determining in treated and untreated hosts the validity of the assumptions about the habitat, resources and other features of the models and modifying the models to make them more realistic.4Obtaining realistic estimates of the values of the parameters of the model for these key species in treated and untreated hosts and estimates of the absolute densities of these players. With a realistic model and estimates of the values of its parameters and variables, one could use numerical solutions (computer simulations) to explore the effects of treating patients with a new antimicrobial or using that agent for prophylaxis. With estimates of the rates of mutation to resistance in the target pathogen and key members of the bacterial flora and/or the likelihood of resistance being acquired by horizontal transfer, one could use the same models to examine the evolution of resistance in treated hosts and the consequences of that evolution. How can we evaluate the effects of an antimicrobial agent on the ecology of the microbial flora of the community of the human host? As it stands now, the above model is for the ecology of a single community of bacteria a single host. One could expand this kind of model to consider the ecologic consequences of antimicrobial chemotherapy in a community of treated and untreated hosts by tying together these individual host models. For this, it will be necessary to make specific assumptions about how the target microbe and the key players that determine the stability of the communities of individual humans are transmitted between hosts. It will then be necessary to estimate the infectious transmission and colonization parameters that govern the dissemination of these microbes in a community of treated and untreated hosts. Of course, writing this protocol is even easier than building models and far easier than analyzing the properties of these models. The really hard, time consuming and expensive part is the empiric work. Save for the wonderful investigations of Rolf Freter and his colleagues, who used anerobic chemostats to study the ecology of the enteric flora of mammals [7Freter R Jones GW Models for studying the role of bacterial attachment in virulence and pathogenesis.Rev Infectious Dis. 1983; 5: S647-S658Crossref PubMed Google Scholar, 8Wilson KH Freter R Interaction of Clostridium difficile and Escherichia coli with microfloras in continuous-flow cultures and gnotobiotic mice.Infection Immunity. 1986; 54: 354-358PubMed Google Scholar, 9Wilson KH Sheagren JN Freter R Population dynamics of ingested Clostridium difficile in the gastrointestinal tract of the Syrian hamster.J Infectious Dis. 1985; 151: 355-361Crossref PubMed Scopus (76) Google Scholar], I do not know of any studies that have even come close to exploring the community ecology of the mammalian commensal flora in the quantitative way considered here. While we have been reasonably successful in applying an analogous jointly theoretical and experimental approach to studying the population dynamics of phage, plasmids, bacteriocins and transposons [2Levin BR Stewart FM Chao L Resource-limited growth, competition, and predation: a model and experimental studies with bacteria and bacteriophage.Am Naturalist. 1977; 977: 3-24Crossref Google Scholar, 4Chao L Levin BR Structured habitats and the evolution of anticompetitor toxins in bacteria.Proc Natl Acad Sci USA. 1981; 78: 6324-6328Crossref PubMed Scopus (377) Google Scholar, 10Chao L Levin BR Stewart FM A complex community in a simple habitat: an experimental study with bacteria and phage.Ecology. 1977; 58: 369-378Crossref Google Scholar, 11Condit R The evolution of transposable elements: conditions for establishment in bacterial populations.Evolution. 1990; 44: 347-359Crossref Google Scholar, 12Condit R Stewart FM Levin BR The population biology of bacterial transposons: a priori conditions for maintenance as parasitic DNA.Am Naturalist. 1988; 132: 129-147Crossref Google Scholar, 13Levin BR Stewart FM Rice VA The kinetics of conjugative plasmid transmission: fit of a simple mass action model.Plasmid. 1979; 2: 247-260Crossref PubMed Scopus (130) Google Scholar, 14Lundquist PD Levin BR Transitory derepression and the maintenance of conjugative plasmids.Genetics. 1986; 113: 483-497PubMed Google Scholar, 15Schrag S Mittler JE Host parasite coexistence: the role of spatial refuges in stabilizing bacteria–phage interactions.Am Naturalist. 1996; 148: 438-477Crossref Scopus (121) Google Scholar], these studies were done in vitro and did not even come close to addressing the complexity of natural communities of bacteria. Their goal was to elucidate the ecologic and genetic conditions for existence and persistence of bacteriophages and accessory genetic elements in bacterial populations. Saying this another way, it is my impression that the data needed to build these models and analyze their properties do not exist. For the most part, medical microbiology has focused on pathogenic microbes. Although many of these pathogens are commensals that occasionally go bad, like Neisseria meningitidis, Staphylococcus aureus, Escherichia coli and Streptococcus pneumonae, for the most part these investigations have been qualitative rather than quantitative. They also tend to focus on the factors (determinants) responsible for the virulence of these organisms, rather than their population dynamics in their commensal or even pathogenic modes. A quantitative study of the sort described above would provide much needed information about the conditions under which these would-be pathogens can colonize human hosts, and when and how they go bad, i.e. invade and establish populations and proliferate in sites where they should not be, like the CNF. 3It should be of interest to the reader that mathematical models of a similar ilk are already being employed to evaluate the ecologic consequences of vaccines [16Lipsitch M Vaccination against colonizing bacteria with multiple serotypes.Proc Natl Acad Sci USA. 1997; 94: 6571-6576Crossref PubMed Scopus (194) Google Scholar, 17Lipsitch M Dykes JK Johnson SE et al.Competition among Streptococcus pneumoniae for intranasal colonization in a mouse model.Vaccine. 2000; 18: 2895-2901Crossref PubMed Scopus (94) Google Scholar]. These studies would be particularly useful if, in addition to considering the population dynamics and interactions among the populations of bacteria, these models also considered the population dynamics of the constitutive and inducible immune defenses that normally control the dissemination and proliferation of these bacteria. So, my answer to the question posed in the subheading is yes, I do believe it is worth doing. I believe a jointly theoretical and experimental approach similar to that outlined above is the most general, and in the long term, the most useful way of addressing questions of the ecologic impact of antimicrobials. On the other hand, I would be hard pressed to argue that it is the most efficient or most cost effective way to go about addressing this issue for a single new (or old) antimicrobial. The most straightforward way to explore that question is empiric, but still quantitative: treat experimental animals, and then humans, with antimicrobials and follow the changes in the densities and distributions of existing microbial flora to ascertain whether individual animals or human subjects have symptoms that can be attributed to the changes in their microbial flora resulting from the use of these agents. One can also assay the major players in the flora as well. It would not be as elegant or as general as the mathematical modeling and heavy-duty experimental study described above, but it would probably do the job.