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6.11: 6. 11- Microbial Growth in Communities - Biology

6.11: 6. 11- Microbial Growth in Communities - Biology


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6.11: 6. 11- Microbial Growth in Communities

Fermented Foods: Definitions and Characteristics, Impact on the Gut Microbiota and Effects on Gastrointestinal Health and Disease

Fermented foods are defined as foods or beverages produced through controlled microbial growth, and the conversion of food components through enzymatic action. In recent years, fermented foods have undergone a surge in popularity, mainly due to their proposed health benefits. The aim of this review is to define and characterise common fermented foods (kefir, kombucha, sauerkraut, tempeh, natto, miso, kimchi, sourdough bread), their mechanisms of action (including impact on the microbiota), and the evidence for effects on gastrointestinal health and disease in humans. Putative mechanisms for the impact of fermented foods on health include the potential probiotic effect of their constituent microorganisms, the fermentation-derived production of bioactive peptides, biogenic amines, and conversion of phenolic compounds to biologically active compounds, as well as the reduction of anti-nutrients. Fermented foods that have been tested in at least one randomised controlled trial (RCT) for their gastrointestinal effects were kefir, sauerkraut, natto, and sourdough bread. Despite extensive in vitro studies, there are no RCTs investigating the impact of kombucha, miso, kimchi or tempeh in gastrointestinal health. The most widely investigated fermented food is kefir, with evidence from at least one RCT suggesting beneficial effects in both lactose malabsorption and Helicobacter pylori eradication. In summary, there is very limited clinical evidence for the effectiveness of most fermented foods in gastrointestinal health and disease. Given the convincing in vitro findings, clinical high-quality trials investigating the health benefits of fermented foods are warranted.


Experimental warming effects on the microbial community of a temperate mountain forest soil

Soil microbial communities mediate the decomposition of soil organic matter (SOM). The amount of carbon (C) that is respired leaves the soil as CO2 (soil respiration) and causes one of the greatest fluxes in the global carbon cycle. How soil microbial communities will respond to global warming, however, is not well understood. To elucidate the effect of warming on the microbial community we analyzed soil from the soil warming experiment Achenkirch, Austria. Soil of a mature spruce forest was warmed by 4 °C during snow-free seasons since 2004. Repeated soil sampling from control and warmed plots took place from 2008 until 2010. We monitored microbial biomass C and nitrogen (N). Microbial community composition was assessed by phospholipid fatty acid analysis (PLFA) and by quantitative real time polymerase chain reaction (qPCR) of ribosomal RNA genes. Microbial metabolic activity was estimated by soil respiration to biomass ratios and RNA to DNA ratios. Soil warming did not affect microbial biomass, nor did warming affect the abundances of most microbial groups. Warming significantly enhanced microbial metabolic activity in terms of soil respiration per amount of microbial biomass C. Microbial stress biomarkers were elevated in warmed plots. In summary, the 4 °C increase in soil temperature during the snow-free season had no influence on microbial community composition and biomass but strongly increased microbial metabolic activity and hence reduced carbon use efficiency.

Highlights

► No warming effects on microbial biomass C and N. ► No warming effects on major microbial communities. ► Increase of stress biomarker in warmed soil. ► Warming caused a strong increase in microbial metabolic activity (soil respiration per biomass).


6.11: 6. 11- Microbial Growth in Communities - Biology

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Results

Growing a collection of soil microbes in a medium that contains 1% glucose as the main carbon source and 0.8% urea as the main nitrogen source leads to a change of the initial pH for nearly all tested bacteria (n = 119 for phylogenetic identity, see S1 Fig) (Fig 1a). One percent glucose lies within the range of carbohydrates in soil (0.1% [31] to 10% [32]), although the carbohydrates in soil are often more complex. Also, the bacterial densities that are reached in the experiments lie within the range that can be found in soil [33,34], and soil has even a slightly lower buffering capacity than our medium (S2 Fig). Microbial growth modulates the pH, but the pH is also known to strongly affect microbial growth [25,27,35,36]. In this way, microbes feed back on their own growth but also influence the growth conditions of other species that might be present (Fig 1b).

(a) A collection of soil bacteria grown in a medium that contains urea and glucose can lower or increase the pH (initially set to pH 7, dashed line). The soil the microbes were isolated from has a buffer capacity similar to the experimental medium (S2 Fig). Also, growing the soil bacteria in Luria-Bertani medium causes pH changes (S2 Fig). (b) By changing the environment, bacteria influence themselves but also other microbes in the community. (c) Lactobacillus plantarum and Pseudomonas veronii prefer acidic, Corynebacterium ammoniagenes prefers alkaline, and Serratia marcescens has a slight preference towards alkaline environments. Fold growth in 24 h is shown. The bacteria were grown on buffered medium with low nutrients to minimize pH change during growth (Materials and methods and S2 Fig). (d) Starting at pH 7, L. plantarum and S. marcescens decrease and C. ammoniagenes and P. veronii increase the pH. Only little buffering, 10 g/L glucose and 8 g/L urea as substrates were used in (d). (e) Microbes can increase or decrease the pH (blue environment is alkaline, and red environment is acidic) and thus produce a more or less suitable environment for themselves. Blue bacteria prefer and/or tolerate alkaline and red acidic conditions. The soil bacteria in (a) were isolated from local soil, whereas the 4 species in (c) to (e) were obtained from a strain library (see Materials and methods for details). The data for this figure can be found in S1 Data. Ca, Corynebacterium ammoniagenes Lp, Lactobacillus plantarum Pv, Pseudomonas veronii Sm, Serratia marcescens.

Microbes can lower or increase the pH, which may be beneficial or deleterious for their own growth. This leads to 4 possible combinations (Fig 1e), for which we identified an example species of each (Fig 1b, 1c and 1d Materials and methods and S2 and S3 Figs). Lactobacillus plantarum is an anaerobic bacterium that produces lactic acid as metabolic product and thus lowers the pH but also prefers low pH values [37]. Corynebacterium ammoniagenes produces the enzyme urease that cleaves urea into ammonia and thus increases the pH [38] at the same time, it prefers higher pH values. Pseudomonas veronii also increases the pH of the medium but prefers low pH values for growth. Finally, Serratia marcescens strongly lowers the pH [39] but better tolerates comparably higher pH values, with a slight optimum at around pH 8. As expected, the strength of the pH change depends on the amount of glucose and urea (S2 Fig) and can be tempered by adding buffer (S2 and S4 Figs). A pH change can also be first good and then bad for a microbe by first shifting the pH towards the optimum but then keeping on shifting it beyond it (S2 Fig) however, we focus here on the simple cases. Also, oxygen levels are changed by the bacteria but seem not to have a major influence on the system (S5 Fig). In summary, we find that microbial growth often leads to dramatic changes in the pH of the environment, and this pH change can promote or inhibit bacterial growth.

When the pH modification is beneficial for the bacteria, there is a positive feedback on their growth. The more bacteria there are, the stronger they can change the environment and thus the better they do. At adverse pH conditions, a sufficiently high cell density may therefore be needed to survive at all—an effect known as strong Allee effect [40–42]. Indeed, we observe such an effect: C. ammoniagenes promotes its own growth by alkalizing the environment, leading to a minimal starting cell density required for survival under daily batch culture with dilution (Fig 2a). Adding buffer (Fig 2a, right, S2 and S4 Figs) or lowering the nutrient concentration (S2 and S6 Figs) tempers the pH change and thus necessitates an even higher bacterial density for survival. Changes to the pH could therefore be a common mechanism of cooperative growth that leads to an Allee effect and an associated minimal viable population size.

The curves show bacterial density over time, and the color shows the pH. (a) C. ammoniagenes increases the pH and also prefers these higher pH values, leading to a minimal viable cell density required for survival. Increasing the buffer concentration from 10 mM (−buffer) to 100 mM (+buffer) phosphate makes it more difficult for C. ammoniagenes to alkalize the environment and therefore increases the minimal viable cell density. (b) P. veronii also increases the pH yet prefers low pH values. Indeed, P. veronii populations can change the environment so drastically that it causes the population to go extinct. Adding buffer tempers the pH change and thus allows for the survival of P. veronii. An Allee effect can also be found in L. plantarum and ecological suicide in S. marcescens (S8 Fig). Note that buffering often just slightly affects the final pH values (S2 Fig) but saves the population by delaying the pH change (as shown in S4 Fig and discussed in more detail in [35]). Linlog scale is used for the y-axis. The data for this figure can be found in S1 Data. Ca, Corynebacterium ammoniagenes CFU, colony-forming unit Pv, Pseudomonas veronii.

Bacteria can also change the environment in a way that harms themselves, for example, by shifting the pH away from the growth optimum. In the most extreme case, the bacteria may make the environment so detrimental that it becomes deadly for them, an effect we call ecological suicide. Indeed, we find that P. veronii, which prefers lower pH, alkalizes the medium and thus causes its own extinction (Fig 2b). Again, adding buffer (Fig 2b, right) or lowering nutrient concentrations (S7 Fig) tempers the pH change and saves the population. It is therefore not the initial condition that kills the bacteria but the way the population changes the pH, which is further underlined by optical density (OD) measurements and following the colony-forming unit (CFU) over time (S7 Fig). The effect of ecological suicide is investigated in more detail in a separate manuscript [35].

Microbes that modify the environment not only affect their own growth but also other microbial species that may be present. In this way, the environmental modifications could drive interspecies interactions. We described previously (Fig 1) 4 different ways that a single species can change the environment and in turn be affected: lowering and increasing the pH and affecting the growth in positive or negative ways. Accordingly, there exist, in principle, 6 (4 choose 2) pairwise combinations of the 4 types in Fig 1d however, 2 of them are symmetric cases of each other, leaving 4 unique interaction types (S10 Fig). We have seen that the microbial metabolism can determine the fate of a population by changing and reacting to the pH. Therefore, can we, in a similar way, understand and perhaps even anticipate possible outcomes of those 4 interactions based on the properties of the single species? To explore this question, we captured the essential elements of the pH interaction in mono- and coculture via a simple differential equation model (see S1 Text and S11 Fig).

The bacteria densities na/b follow a logistic growth that saturates at the carrying capacity K. However, the overall growth rate also depends on the proton concentration, and growth becomes maximal at a preferred proton concentration, ppref. For the dependence of the growth on the proton concentration, we used a Gaussian function however, the general properties of the system do not depend on the exact choice of this function (S1 Text). The further away the proton concentration is from the optimum of the species, the slower the bacteria grow and finally start to die, whereas δ sets the maximal death rate. The proton concentration p is changed by the bacteria, according to their density na/b and their strength in changing the proton concentration ca/b, which is set to +/− 0.1. Multiplication by a quadratic function ensures that the proton concentration stays within [0, 2b], which takes into account that the pH between inside and outside the bacteria can only be changed until the difference in chemical potential becomes too big [43]. The outcomes of the model should be regarded as qualitative. Stability analysis of this model supports the simulation outcomes shown in S1 Text. Adding a periodic dilution can affect the outcome at high dilution rates but does not qualitatively affect the results at sufficiently low dilution rates (S13 Fig). Moreover, a fuzzy logic–based model—that does not rely on defined functions—leads to very similar results the outcomes are basically the same, but stabilization happens over a wider parameter range (S1 Text and S14 and S15 Figs).

For the single-species cases of L. plantarum and C. ammoniagenes, this model naturally gives an Allee effect—a minimal initial bacterial density is needed for survival depending on the initial pH value (Fig 3 and S11 Fig). In addition, when the species are changing the environment in a way that is bad for them (e.g., P. veronii and S. marcescens), the model yields ecological suicide in which the population dies under all starting conditions (Fig 3 and S11 Fig). Therefore, this simple model can capture the measured outcomes for the single species.

A simple model based on differential equations was set up to qualitatively simulate the bacterial growth (see main text). The survival of the species at the end of the simulation for different initial parameter values are plotted as follows. A species that is extinct at the end of the simulation run either did not grow under these conditions, was outcompeted by another species, or went extinct by ecological suicide. The upper two rows of panels show the simulation outcome for the single species. The third row of panels shows the outcomes of the cocultures, for which representative time series of the phase diagrams marked by the dashed circles are shown in the bottom row. The “pH” scale reaches from low to high, which corresponds to a “proton concentration” of 10 to 0. σ was set to 4 and δ to 0.5. ca/b was set to +/− 0.1, b to 5, and d as described in the S1 Text. (a) L. plantarum and C. ammoniagenes show bistability in coculture depending on the initial fraction and pH. (b) L. plantarum and S. marcescens show successive growth at high initial pH values, for which L. plantarum can only survive if the pH was first lowered by S. marcescens. Note that a high percentage of S. marcescens in the coculture panel (dashed circle) means low S. marcescens and high L. plantarum in the upper panels. (c) If P. veronii lowers the proton concentration by enough, it can kill itself and also L. plantarum, resulting in extended suicide. The coexistence at initial low ratios of P. veronii is caused by oscillatory dynamics as shown in S12 Fig. (d) S. marcescens and P. veronii can protect each other from ecological suicide and coexist, whereas they cannot survive on their own. The effect of varying interaction strength and initial conditions are shown in S11 Fig. We use the words bistability, successive growth, extended suicide, and stabilization merely to characterize the interaction outcomes and not any “intentions” of the bacteria. Linlog scale is used for the y-axis. Ca, Corynebacterium ammoniagenes Lp, Lactobacillus plantarum Pv, Pseudomonas veronii Sm, Serratia marcescens.

We next explored whether the model can provide insight into the two species’ interactions. In particular, there is a question of whether just one environmental parameter—the pH—is sufficient to predict nontrivial outcomes of interspecies competition, neglecting all the other ways in which the species interact. In what follows, we focus on the outcomes predicted by the model that are marked by dashed circles in Fig 3. To test if those 4 outcomes can indeed be found in the experiments, the corresponding interaction pairs were grown with daily dilutions both as single species and in pairs under the conditions suggested from the model (Fig 4).

Four different interaction types can be found depending on how the environmental changes act on the organisms themselves and each other. (a) L. plantarum and C. ammoniagenes produce bistability. (b) S. marcescens and L. plantarum show successive growth. (c) P. veronii commits extended suicide on L. plantarum. (d) S. marcescens can stabilize P. veronii when the medium is sufficiently buffered. For a more detailed description of the different interactions cases, see the main text. The media composition and protocols are slightly different for the different cases. See Materials and methods for details. We use the words bistability, successive growth, extended suicide, and stabilization merely to characterize the interactions outcomes and not any “intentions” of the bacteria. Linlog scale is used for the y-axis. The bacteria were diluted every 24 h into fresh media with a dilution factor of 1/100x (a and b) or 1/10x (c and d). The data for this figure can be found in S1 Data. Ca, Corynebacterium ammoniagenes CFU, colony-forming unit Lp, Lactobacillus plantarum Pv, Pseudomonas veronii Sm, Serratia marcescens.

L. plantarum and C. ammoniagenes each modify the environment in a way that is good for themselves yet bad for the other species. Given this “antagonistic niche construction,” the model predicts that the coculture can yield bistability, in which only one species will survive, whereas the winner depends on the initial species abundances and initial pH (Fig 3a). Consistent with this prediction, we experimentally find bistability in the coculture of L. plantarum and C. ammoniagenes, with the initially abundant species driving the other species extinct (Fig 4a and S11 Fig). As expected, removing glucose and urea from the medium prevents pH changes and thus also removes the forces leading to bistability, which results in coexistence between the two species (S16 Fig). Two species that are attempting to modify the environment in incompatible ways can therefore lead to the emergent phenomenon of bistability.

L. plantarum does not tolerate high pH values, whereas S. marcescens can grow at high pH but subsequently acidifies the environment and kills itself (S8 and S11 Figs). This raises the question of whether S. marcescens can aid L. plantarum by lowering an initially high pH, thus allowing L. plantarum to survive. Indeed, our model suggests that it may be possible to observe successive growth, in which S. marcescens grows first and lowers the pH, thus allowing L. plantarum to survive despite the fact that the starting pH would have been lethal for L. plantarum (Fig 3b and S11 Fig). We can indeed find this interaction motif experimentally. At an initially high pH, L. plantarum can only survive if S. marcescens helps to modify the environment (Fig 4b). However, contrary to the simulation, S. marcescens alone does not experience ecological suicide in the experiment, likely because the high starting pH prevents S. marcescens from lowering the pH too rapidly. Indeed, at lower starting pH values, S. marcescens shows ecological suicide (S8 and S11 Figs). Adding buffer or removing nutrient causes only moderate acidification and thus kills L. plantarum but allows S. marcescens to survive (S17 Fig). In successive growth, L. plantarum can only establish growth after S. marcescens has prepared the ground for it, a well-understood phenomenon in plant ecology [44,45].

Above, we considered the case of a species transiently helping another species to survive, raising the question of whether it might also be possible to observe the opposite situation, in which pH modification leads to ecological suicide and kills the interaction partner with it. Indeed, our model predicts that this “extended suicide” could be present for the L. plantarum/P. veronii pair over a wide range of cell densities and starting pH values (Fig 3c). To explore this prediction of our model experimentally, we utilize P. veronii, which commits ecological suicide via alkalization (Fig 2b), together with L. plantarum, which dies in alkaline conditions (Fig 2a). Once again consistent with the predictions of our simple model, we successfully observed such an extended suicide, in which the extreme alkalization of the media by P. veronii led to the death of both P. veronii and L. plantarum (Fig 4c). The addition of buffer tempers this alkalization sufficiently to stop P. veronii from suicide but still allows it to outcompete L. plantarum (S18 Fig). However, if L. plantarum were more effective at acidifying the media, then coexistence might have been possible (S11 Fig). We therefore find that ecological suicide can also have a negative impact on other present species.

Finally, the model suggests that it may be possible for 2 species to help each other avoid ecological suicide (Fig 3d). This would correspond to an obligatory mutualism, in which the opposing pH changes cancel each other and therefore allow for the stable coexistence of the 2 species in an environment in which neither species could survive on its own. However, this stabilization is only observed in the model in a rather small parameter range, which suggests that finding it experimentally may be difficult. Indeed, experimentally, we could not find conditions in which P. veronii and S. marcescens form the most extreme form of stabilization, in which each species alone results in ecological suicide yet together they survive. However, we did observe a situation in which P. veronii alone causes ecological suicide yet S. marcescens can stabilize the pH and allow both species to survive and coexist (Fig 4d see Materials and methods for details). Species that harm themselves through their environmental modifications can therefore benefit from other species in the environment.


The impact of synthetic biology for future agriculture and nutrition

Synthetic metabolic pathways to improve plant carbon efficiency.

Reducing synthetic fertilizer usage in agriculture by optimizing plant nitrogen and phosphorous utilization.

Engineering strategies to improve the nutritional value of crop plants.

Harnessing the power of photoautotrophic organisms as large-scale production platforms.

Global food production needs to be increased by 70% to meet demands by 2050. Current agricultural practices cannot cope with this pace and furthermore are not ecologically sustainable. Innovative solutions are required to increase productivity and nutritional quality. The interdisciplinary field of synthetic biology implements engineering principles into biological systems and currently revolutionizes fundamental and applied research. We review the diverse spectrum of synthetic biology applications that started impacting plant growth and quality. We focus on latest advances for synthetic carbon-conserving pathways in vitro and in planta to improve crop yield. We highlight strategies improving plant nutrient usage and simultaneously reduce fertilizer demands, exemplified with the engineering of nitrogen fixation in crops or of synthetic plant-microbiota systems. Finally, we address engineering approaches to increase crop nutritional value as well as the use of photoautotrophic organisms as autonomous factories for the production of biopharmaceuticals and other compounds of commercial interest.


Advances in Bacterial Electron Transport Systems and Their Regulation

3.4 Electron Transfer Through the Outer Membrane of Gram-Negative Bacteria

Current research has identified two separate systems by which electrons might pass through the outer membrane of Gram-negative bacteria. The first, the MtrAB porin–cytochrome complex, represents the best characterised of the electron transfer conduits, with representative complexes identified from the iron-reducing Shewanella, Geobacter and lithotrophic iron-oxidising Sideroxydans and Gallionella. It appears a key feature of respiration using the transfer of electrons to and from iron under conditions where iron oxides develop and is important when dealing with insoluble metal oxides. The second system is the Cyc2 fused porin–cytochrome system that is common amongst microorganisms that utilise extracellular soluble Fe(II), such as A. ferrooxidans, this much simpler system is used under acidic conditions when insoluble iron oxides are unlikely to develop. There is also overlap within these systems, S. lithotrophicus contains homologues of both the MtrAB porin–cytochrome complex and the Cyc2 fused porin–cytochrome while certain strains of Geobacter contain homologues of MtrAB, Cyc2 and also generate conductive pili. It is not known whether these systems have overlapping functionality or perhaps work together to create an efficient iron metabolic pathway.

Despite the observation of these conserved pathways for outer membrane electron transfer there are also several organisms that have, as yet, unknown mechanisms for electron transfer through their outer membranes. For example, Rhodobacter ferrooxidans does not contain the genes for porin–cytochromes in their outer membranes, and yet can oxidise metal on the cell surface under neutrophilic conditions ( Hegler, Posth, Jiang, & Kappler, 2008 Saraiva et al., 2012 ) ( Fig. 2 ).


General Overviews

Darwin’s On the Origin of Species contains a good deal about competition, usually competition between species operating as the force of natural selection. There is a good deal about plants and plant ecology in Darwin’s work. Of course, Darwin was greatly influenced by the English economist Thomas Malthus, who wrote about resources and population growth, including the famous Essay on the Principle of Population. The first major work of the 20th century in this area was Weaver and Clements 1938, a volume with a wealth of competition experiments. Perhaps the book is overlooked because of its extensive discussion of succession, as well as the many new terms introduced under this topic (one is advised to try reading the book as a treatise on competition, skipping the other parts). Competition was also included within even the most basic models of ecology, such as the logistic equation, which led to the Lotka-Volterra models for competition, well described in MacArthur 1972. MacArthur’s book also explores how species might escape competition by using different resources (“resource partitioning”), although disagreement remains about how applicable this concept is to plants, which share a common set of resources. Harper 1977 can be considered very influential for refocusing attention upon plant populations and plant life cycles. This book summarizes a vast number of studies on plant populations, including studies in agriculture and forestry. The emphasis on populations and agricultural systems was challenged in the 1970s by Grime, who emphasized that natural habitats lacking in key resources (“stressed” habitats) are very different from the relatively fertile sites favored by agricultural researchers (Grime 2001). Grime introduced the CSR model, which relates plant strategies (competitor, stress-tolerator, ruderal) to two basic gradients: stress and disturbance. The first edition of this book in 1979 was a landmark work, shifting attention away from populations and back to plant traits and environmental gradients. The role of aboveground and belowground resources is explored in Tilman 1982, suggesting that many plants may coexist by exploiting different ratios of above to below ground resources, particularly light and nitrogen. This resource ratio model may be more useful than the Lotka-Volterra model for plants. By 1990 a good deal more thought had been given about how to best explore competition among plants some of the challenges are illustrated by the array of views, ideas, and data sets in Grace and Tilman 1990. As one referee noted, the book shows primarily how little agreement there was about what the word competition meant, how it should be measured, and how even common experimental designs should be interpreted. Keddy 2001 emphasizes that some of the confusion was the result of there being many different components of competition—intraspecific/interspecific, symmetrical/asymmetrical, and diffuse/monopolistic, to name just three. Of course, competition is only one of many factors that affect plant communities: Keddy 2017 provides a shorter introduction to plant competition nested among the other causal factors controlling composition in plant communities.

Grace, James B., and David Tilman, eds. 1990. Perspectives on plant competition. San Diego, CA: Academic Press.

It is instructive to read the book as a historical snapshot. Weaver and Clements, for example, are largely forgotten. Grime is beginning to challenge the status quo—but does not appear as a contributor. It is also useful to compare and contrast the definitions of competition and the sources of evidence used in each chapter.

Grime, J. Philip. 2001. Plant strategies, vegetation processes, and ecosystem properties. 2d ed. Chichester, UK: John Wiley.

An early edition of this book (1979) challenged ecologists to consider mechanisms of plant competition in different environments. Plants must invest resources and forage to obtain resources, and this has consequences ranging from plant traits to ecosystem properties.

Harper, John L. 1977. Population biology of plants. London: Academic Press.

Chapters 6–11 are must reading for someone planning to study plant populations and competition. Most of the other chapters are relevant as well, since competition may occur at different stages in life history.

Keddy, Paul A. 2001. Competition. 2d ed. Dordrecht, The Netherlands: Kluwer.

Chapters 1 and 2 introduce kinds of competition as measured by different kinds of experiments. The book was originally published in 1989 by Chapman and Hall, and many more examples were added to this second edition. Chapter 9 introduces many models, including models by Skellam and Pielou, for competition among patches and along gradients, respectively. Chapters 1 and 9 are available online from the author.

Keddy, Paul A. 2017. Plant ecology: Origins, processes, consequences. Cambridge, UK: Cambridge Univ. Press.

Chapter 4, “Competition” (pp. 123–162), provides a contemporary overview of plant competition, set within the context of other forces in plant communities, such as resources, herbivory, and mutualism. Includes two important older models of plant competition by Skellam and Pielou.

MacArthur, Robert H. 1972. Geographical ecology: Patterns in the distribution of species. New York: Harper & Row.

This book begins with general issues affecting plant and animal distributions. It has a lucid description of the two-species Lotka-Volterra model.

Tilman, David. 1982. Resource competition and community structure. Princeton, NJ: Princeton Univ. Press.

Plants may use different ratios of aboveground and belowground resources, and a critical consideration is the lowest levels to which those resources can be reduced, termed r*. The simplest view is that plants often partition gradients along light to nitrogen ratios.

Weaver, John E., and Frederic E. Clements. 1938. Plant ecology. 2d ed. New York: McGraw-Hill.

A classic that all plant ecologists should own, and read, before planning their own work. Inexpensive copies of this book can still be found second-hand. For the study of competition, it is best to ignore the other main theme of this book, succession, which is an entirely different topic (see also the Oxford Bibliographies entry on Succession). This book also introduces the use of phytometers that is, using an easily grown species to compare habitats from a plant’s perspective.

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Author information

These authors contributed equally: Sonja Blasche, Yongkyu Kim.

Affiliations

European Molecular Biology Laboratory, Heidelberg, Germany

Sonja Blasche, Yongkyu Kim, Daniel Machado, Eleni Kafkia, Alessio Milanese, Georg Zeller, Vladimir Benes & Kiran Raosaheb Patil

Institute of Molecular Systems Biology, ETH Zurich, Zurich, Switzerland

Ruben A. T. Mars & Uwe Sauer

Chr. Hansen A/S, Horsholm, Denmark

Maria Maansson & Rute Neves

The Medical Research Council Toxicology Unit, University of Cambridge, Cambridge, UK

Eleni Kafkia & Kiran Raosaheb Patil

Vrije Universiteit Amsterdam, Amsterdam, the Netherlands

Chalmers University of Technology, Gothenburg, Sweden

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Contributions

S.B. and Y.K. conceived the project, designed and performed the experiments, analysed the data and wrote the paper. R.A.T.M. performed the untargeted metabolomics experiments and data analysis, as well as the quantitative analysis of aspartate and proline. E.K. and M.M. performed the GC–MS and ion chromatography analysis. V.B. contributed to the amplicon, metagenome and messenger RNA sequencing. J.N. and B.T. contributed to the experimental design. R.N. oversaw the targeted metabolomics analysis. D.M. contributed to the amino acid profile analysis and interpretation. A.M., D.M. and G.Z. analysed the RNA-seq data. U.S. oversaw the exo-metabolome analysis. K.R.P. conceived the project, designed the experimental approach, oversaw the project and wrote the paper.

Corresponding author


Mathematical modelling of microbes: metabolism, gene expression and growth

The growth of microorganisms involves the conversion of nutrients in the environment into biomass, mostly proteins and other macromolecules. This conversion is accomplished by networks of biochemical reactions cutting across cellular functions, such as metabolism, gene expression, transport and signalling. Mathematical modelling is a powerful tool for gaining an understanding of the functioning of this large and complex system and the role played by individual constituents and mechanisms. This requires models of microbial growth that provide an integrated view of the reaction networks and bridge the scale from individual reactions to the growth of a population. In this review, we derive a general framework for the kinetic modelling of microbial growth from basic hypotheses about the underlying reaction systems. Moreover, we show that several families of approximate models presented in the literature, notably flux balance models and coarse-grained whole-cell models, can be derived with the help of additional simplifying hypotheses. This perspective clearly brings out how apparently quite different modelling approaches are related on a deeper level, and suggests directions for further research.

1. Introduction

Bacterial growth curves have exerted much fascination on microbiologists, as eloquently summarized by Frederick Neidhardt in his short commentary ‘Bacterial growth: constant obsession with dN/dt’ published almost 20 years ago [1]. When supplied with a defined mixture of salts, sugar, vitamins and trace elements, a population of bacterial cells contained in liquid medium is capable of growing and replicating at a constant rate in a highly reproducible manner. This observed regularity raises fundamental questions about the organization of the cellular processes converting nutrients into biomass.

Work in microbial physiology has resulted in quantitative measurements of a variety of variables related to the cellular processes underlying growth. These measurements have usually been carried out during steady-state exponential or balanced growth, that is a state in which all cellular components as well as the total volume of the population have the same constant doubling time, implying that the concentrations of the cellular components remain constant [2]. The measurements have enabled the formulation of empirical regularities, also called growth laws [3], relating the macromolecular composition of the cell to the growth rate [4,5]. A classical example is the linear relation between the growth rate and the fraction of ribosomal versus total protein, a proxy for the ribosome concentration, over a large range of growth rates [6–9]. The reported regularities between the growth rate and the macromolecular composition of the cell are empirical correlations and should not be mistaken as representing a causal determination of cellular composition by the growth rate [6,10]. In fact, it has been shown that, for certain combinations of media, the same growth rate of E. coli may correspond to different ribosome concentrations [6].

To unravel causal relations, it is necessary to go beyond correlations and consider the biochemical processes underlying microbial growth. These processes notably include the enzyme-catalysed transformation of substrates into precursor metabolites, the conversion of these precursors into macromolecules by the gene expression machinery, the replication of the cell when its macromolecular content has attained a critical mass and the regulatory mechanisms on different levels controlling these processes [11–14]. Moreover, for identifying causality, a dynamic perspective on microbial growth focusing on transitions between different states of balanced growth, and the time ordering of events during the transitions, is more informative than considering a population at steady state [10]. Whereas most measurements have been obtained under conditions of balanced growth, in which experiments are easier to control and reproduce, data on transitions from one state of balanced growth to another are also available in the literature (reviewed in [4]). One classical example is the measurements of the temporal ordering at which RNA, protein and DNA attain their new steady-state concentrations after a nutrient upshift [5,15]. Recent experimental technologies, allowing gene expression and metabolism to be monitored in real time, have opened new perspectives for studying the dynamics of bacterial growth on the molecular level [16,17].

The large and complex networks of biochemical reactions enabling microbial growth have been mapped in great detail over the past decades and, for some model organisms, much of this information is available in structured and curated databases [18,19]. While a huge amount of knowledge has thus accumulated, a clear understanding of the precise role played by individual constituents and mechanisms in the functioning of the system as a whole has remained elusive. For example, it is well known that in the enterobacterium E. coli the concentration of the second messenger cAMP increases when glycolytic fluxes decrease, leading to the activation of the pleiotropic transcription factor Crp. However, the precise role of this mechanism in the sequential utilization of different carbon sources by E. coli remains controversial [20,21].

Mathematical models have great potential for dissecting the functioning of biochemical reaction networks underlying microbial growth [22–24]. To be useful, they need to satisfy two criteria. First, they should not be restricted to subsystems of the cell, but provide an integrated view of the reaction networks, including transport of nutrients from the environment, metabolism and gene expression. In particular, they should account for the strong coupling between these functions: enzymes are necessary for the functioning of metabolism, while the metabolites thus produced are precursors for enzyme synthesis. In the words of Henrik Kacser, one of the pioneers of metabolic control analysis, ‘to understand the whole, you must look at the whole’ [25]. Second, models of microbial growth should be multilevel in the sense of expressing the growth of a population in terms of the functioning of the biochemical reaction networks inside the cells. Growth amounts to the accumulation of biomass, that is proteins, RNA, DNA, lipids and other cellular components produced in well-defined proportions from nutrients flowing into the cells. The two criteria amount to the requirement that models should capture the autocatalytic nature of microbial growth, the production of daughter cells from growth and division of mother cells.

Precursors of such integrated, multilevel models are the simple autocatalytic models of Hinshelwood, capable of displaying steady-state exponential growth and a variety of responses to perturbations reminiscent of the adaptive behaviour of bacteria [26]. Another early example is the coarse-grained model of a growing and dividing E. coli cell [27], which has evolved over the years into a model of a hypothetical bacterial cell with the minimal number of genes necessary for growing and dividing in an optimal environment [28]. In addition, we mention so-called cybernetic models describing growth of microbial cells on multiple substrates [29–31], and the E-CELL computer environment for whole-cell simulation [32]. In recent years, integrated, multilevel models of the cell have received renewed attention with the landmark achievement of a model describing all individual cellular constituents and reactions of the life cycle of the human pathogens Mycoplasma genitalium [33] and other genome-scale models of bacteria [34]. In addition, several coarse-grained models describing the relation between the macromolecular composition of microorganisms and their growth rate have been published [24,35–39].

At first sight, the above-mentioned models of microbial growth are quite diverse, in the sense that they have a different scope and granularity, make different simplifications, use different approaches to obtain predictions from the model structure and originate in different fields (microbiology, theoretical biology, biophysics and biotechnology). The aim of this review is, first, to show how a general framework for the kinetic modelling of microbial growth, including an analytical expression for the growth rate, can be mathematically derived from few basic hypotheses. Second, we show how additional simplifying assumptions lead to approximate kinetic models that do not require the biochemical reaction networks to be specified in full. The resulting models exemplify two widespread modelling approaches, flux balance analysis (FBA) and coarse-grained whole-cell modelling. The discussion of the different hypotheses and assumptions, including those related to the measurement units employed, which are often not explicit and/or buried in the (older) literature, reveals how the models are related on a deeper level. This will be instrumental for identifying their respective strengths and weaknesses as well as for indicating new directions in the study of the biochemical reaction networks underlying microbial growth.

2. Growth of microbial populations

An obvious view on microbial growth starts by considering the individual cells in a growing population (figure 1a). We denote by n(t) the number of cells at time t (h). Individual cells in a temporal snapshot of the population have different sizes, as they are in different stages between birth and division. Moreover, cell sizes at birth and division are different [40–42]. As a consequence, the size of the cells in a population at time t is best described by a statistical distribution. This distribution may change over time and with the experimental conditions. For instance, in conditions supporting a higher growth rate, the average size of the cell in the population is larger [6,43]. Several models of the cell size distribution and its dependence on the experimental conditions have been proposed, based on different hypotheses about the criterion determining when a cell divides (reviewed in [42,44]). When the size distribution is known at every time t, the number of cells in a growing population can be directly used to estimate the volume of the population.

Figure 1. (a) Population of n growing cells with different sizes. (b) Volume Vol of a growing population of cells. (c) Total mass Ci and concentration ci of molecular constituents i in a population with volume Vol (each constituent is indicated by a different colour).

In what follows, however, we will adopt another point of view and ignore the individual cells making up a population. Instead, we directly quantify the growing population in terms of its expanding volume Vol (l) (figure 1b), that is, the sum of the volumes of the cells in the population. This aggregate description is appropriate when one is interested in concentrations of molecular constituents on the population level rather than in individual cells, as in the kinetic models developed below. Moreover, it corresponds to most data available in the experimental literature, obtained by pooling the contents of all cells in a (sample of the) population.

We model the growth of a population of microorganisms by means of a deterministic ordinary differential equation (ODE):

The growth rate as defined by equation (2.1) is sometimes also called specific growth rate, in order to indicate that it concerns the increase in population volume per unit of population volume ( ), instead of the absolute increase in population volume ( ). In what follows, we will drop the qualifier ‘specific’. The growth rate definition of equation (2.1) should be distinguished from another definition of the growth rate as 1/t1/2, that is, the number of doublings of the population volume per time unit. While the two definitions result in a quantity with the same unit, they do not mean the same thing and differ by a factor of ln2 [4]. Below, we use the growth rate definition of equation (2.1).

Models that do not distinguish individual cells but lump them into an aggregate volume have been called non-segregated as opposed to segregated models that do make this distinction [45–47]. If the population is composed of cells with the same growth rate, not much is lost by ignoring individual cells and using the population-level description of equation (2.1) (see the electronic supplementary material). There are situations, however, in which this assumption is not appropriate and in which essential features of the growth kinetics are shaped by the heterogeneity of the population [48–51]. For example, it was recently proposed that the lag observed in diauxic growth of E. coli on a glycolytic and gluconeogenic carbon source (e.g. glucose and acetate) is due to the responsive diversification of the population into two subpopulations upon the depletion of the (preferred) glycolytic carbon source and that only one of these subpopulations continues growth on the gluconeogenic carbon source [49]. Non-segregated models are obviously not suitable for describing such phenomena and models describing the dynamics of the distribution of individual cells in a population or of subpopulations need to be used instead.

3. Volume and macromolecular content of cells

The model of equation (2.1) is unstructured in the sense that it does not take into account the biochemical processes enabling cells to grow. By contrast, so-called structured models [45–47] explicitly describe molecular constituents of the cell and the biochemical reactions in which they are involved. Let Ci (g) be the (dry) mass of molecular constituent i contained in volume Vol (figure 1c). A common assumption supported by experimental data ([52] and references therein) is that the volume of the population is proportional to the biomass, that is, the total mass of the molecular constituents of the cells:

Consistent with the decision above to consider the population as a non-segregated volume, we define the concentration ci (g) of each molecular constituent i in a population as

An immediate consequence of the above definition is the following relation:

The dynamics of each molecular constituent i are modelled by means of an ODE, obtained from equations (2.1) and (3.3):

The growth rate itself is directly connected to the concentrations of the molecular constituents, because

Therefore, while it makes sense for a specific constituent i to dilute out when it is not produced, no growth dilution occurs if the mass of all molecular constituents remains constant ( for all i). In the latter case, it follows from equation (3.6) that the growth rate is 0 by definition.

It is increasingly realized that growth dilution may have important physiological consequences [52,58,59] and therefore cannot be neglected in mathematical models of cellular processes. In particular, the interaction of a synthetic circuit with the growth physiology of the cell, and the changes in the growth rate this entails, may have an unexpected nonlinear feedback on the dilution of transcription factors and thus on the functioning of the circuit. This was illustrated by a synthetic circuit in E. coli in which the alternative T7 RNA polymerase regulates itself and a fluorescent protein. Expression of the fluorescent protein causes a metabolic burden, impairing growth and thus growth dilution of T7 RNA polymerase. The resulting positive feedback was shown to lead to two different phenotypes: growth and growth arrest [59].

An important special case of microbial growth occurs when the growth rate and the concentrations of the individual molecular constituents are constant over time, that is, μ = μ* and ci = c*i, for all i. From ci = Ci/Vol = c*i it follows that a doubling of the volume Vol of the population is accompanied by a doubling of the mass Ci of each molecular constituent, which explains why this situation of steady-state exponential growth is also referred to as balanced growth [2,60].

4. Biochemical reactions underlying microbial growth

The molecular constituents of the cell are continually produced and consumed by biochemical reactions. Many of these reactions are enzyme-catalysed, such as the metabolic reactions involved in the conversion of nutrients from the environment into building blocks for macromolecules (amino acids, nucleotides) and energy carriers (ATP, NADH). The building blocks and energy are consumed in large part by the transcription and translation reactions producing macromolecules. The metabolic reactions together form the metabolic network of the cell [14,61].

The term in equation (3.5) represents the net effect of the biochemical reactions on the concentration of molecular constituent i, separate from growth dilution. Usually, for intracellular reactions, the quantities of molecular constituents are expressed in molar rather than mass units. Hence, we introduce Xi = Ci/αi, with Xi (mol) the molar quantity of constituent i and αi (g mol −1 ) the molar mass of i. The reason for this change in units is that kinetic models of biochemical reactions are based on the physical encounters of molecules in the cell [62,63], which is best expressed in terms of molar quantities. With this unit conversion, and xi = Xi/Vol, equation (3.5) becomes

With the help of the above concepts, the effect of the biochemical reactions on the concentrations of molecular constituents can be rewritten as

As a consequence of the conversion of Ci to Xi and the introduction of reaction stoichiometries, the growth rate becomes,

Combining all of the above, we obtain the following model for a growing microbial population:

We emphasize that the explicit expression for μ in equation (4.6) is not an ad hoc definition, but mechanically follows from the basic modelling assumptions underlying the stoichiometry model of equation (4.5), notably the assumption of constant biomass density. Figure 2a schematically projects the reaction network on a growing microbial population.

Figure 2. (a) Population of cells with volume Vol growing at a rate μ, described by the model of equations (4.5) and (4.6). The reactions fuelling growth involve intracellular constituents with concentrations x. The dots represent the molecular constituents and the arrows biochemical reactions. (b) Idem, but extended with a bioreactor environment from which the cells take up nutrients and into which they excrete by-products (with concentrations y). This extended system is described by equations (5.4)–(5.7). The boundary of the environment is schematized by the pink rectangle.

Textbooks on the modelling of biochemical reaction systems detail the different rate laws that specify how the reaction rates vj depend on the concentrations x [62,64]. A common choice, relying on first principles, is to assume mass–action kinetics for the reactions, based on the random encounter of molecules in a well-mixed volume [62,63]. In many situations, however, it is more convenient to lump individual reactions into aggregate reactions that are described by approximate rate laws such as (reversible and irreversible) Henri–Michaelis–Menten kinetics, Monod–Wyman–Changeux kinetics, Hill kinetics, etc. [62,64]. The Henri–Michaelis–Menten rate law for an irreversible, enzyme-catalysed reaction with substrate concentration x and enzyme concentration e reads: , with , where kcat (min −1 ) is the so-called catalytic constant of the enzyme, quantifying the maximum number of substrate molecules converted per enzyme per minute. This expression, and many other approximate kinetic rate laws, can be derived from mass–action kinetics when making appropriate assumptions on the time scale of the rate of the elementary reaction steps. In the case of the Henri–Michaelis–Menten rate law, this concerns the association/dissociation of enzyme and substrate and the formation of the product [65,66].

5. Growth in a changing environment

Some of the reactions changing the molecular constituents of the cell correspond to exchanges with the environment, that is the uptake of substrates and the excretion of products. The environment is not explicitly modelled by equations (4.5) and (4.6) and the entries in v corresponding to the rates of these exchange reactions are therefore treated as external inputs. For many purposes, however, it is more appropriate to extend the model and include a (simple) representation of the environment. In what follows, we equate the environment with a bioreactor filled by a liquid medium of fixed volume containing the growing population of microorganisms as well as external substrates and products. The substrate and product concentrations in the medium are denoted by the vector y. Usually, external concentrations are expressed in terms of units g l −1 , that is mass in a fixed volume of medium.

The dynamics of the substrate and product concentrations in the medium can be described by the following differential equation:

The above considerations lead to the following extended model, taking into account the dynamics of exchanges with the environment (figure 2b):


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