Article series: New technologies: methods and applications

Advancing microbial sciences by individual-based modelling

Journal name:
Nature Reviews Microbiology
Volume:
14,
Pages:
461–471
Year published:
DOI:
doi:10.1038/nrmicro.2016.62
Published online

Abstract

Remarkable technological advances have revealed ever more properties and behaviours of individual microorganisms, but the novel data generated by these techniques have not yet been fully exploited. In this Opinion article, we explain how individual-based models (IBMs) can be constructed based on the findings of such techniques and how they help to explore competitive and cooperative microbial interactions. Furthermore, we describe how IBMs have provided insights into self-organized spatial patterns from biofilms to the oceans of the world, phage–CRISPR dynamics and other emergent phenomena. Finally, we discuss how combining individual-based observations with IBMs can advance our understanding at both the individual and population levels, leading to the new approach of microbial individual-based ecology (μIBE).

At a glance

Figures

  1. Simplified overview of approaches that are useful for modelling communities and single cells.
    Figure 1: Simplified overview of approaches that are useful for modelling communities and single cells.

    Representative volume elements of ecosystems, such as the surface of oceans or the mouse gut, can be modelled using various approaches, which include population-level models (PLMs) and individual-based models (IBMs). PLMs describe the rates of change in populations (X) and/or resources (R) directly (that is, the level of individuals is absent). PLMs can be applied to spatially homogenous environments, using ordinary differential equations (ODEs), or spatially structured environments, using partial differential equations (PDEs); comparing the non-spatial ODEs with the spatially explicit PDEs highlights the effect of spatial structure. IBMs describe the activities of individuals, whereas changes at the population level are not directly described because they emerge from individual behaviour. Consequently, IBMs can make use of data on both levels: individual-level data as input and population-level data to compare with simulation output. Comparing PDEs with IBMs elucidates the effect of individuality and adaptive behaviour. Therefore, combining all three approaches is best practice. To date, most IBMs include only simple kinetic models of growth and rules for cell division, but as IBMs treat individuals as discrete agents, they enable the incorporation of intracellular dynamics as modelled in systems biology — bridging the scales from intracellular reactions to ecosystem function. Only two major types of model for intracellular dynamics are shown: dynamic kinetic models use full kinetic equations that are only known for a select number of enzyme reactions, whereas flux balance models only require the stoichiometry of the reactions and constraints, which enables a genome-wide prediction of metabolic fluxes at steady state77.

  2. Using individual-based models to predict complex systems.
    Figure 2: Using individual-based models to predict complex systems.

    a | The observed cellular phosphorous content93 (quota q) in the marine cyanobacterium Synechococcus WH8103 and the rate of photosynthesis (μ) calculated using nonlinear Droop kinetics (shown as a black line)41. Calculating the rate for each individual based on its quota (full circles) and averaging over individuals (red line: ave[μ(q)]) gives a lower population productivity than first averaging the quotas and calculating the rate based on that average quota (blue line: μ(ave[q])). b | Growth kinetics that are parameterized from chemostat experiments can be used in partial differential equations (PDEs) or individual-based models (IBMs) to predict biofilm structure, growth rate and concentration gradients. IBMs could include adaptations in kinetics or heterogeneity in the population, such as persisters. c | Predicting feedbacks between developing biofilm structure and metabolic interactions. Once clusters of red cells that consume resources economically have formed by chance, they grow faster than clusters of the blue, fast growing cells, because their economy sustains higher substrate concentrations locally60. d | Members of a microbial community may be engineered to depend on each other for growth, which is referred to as synthetic obligate cross-feeding. A cheating strain that receives secreted nutrients but does not produce any is excluded by spatial self-organization of the cooperators; this is shown both experimentally, in which strains are fluorescently tagged, and in an IBM of the system61. e | Verifying IBM predictions for a nitrifying food-web in a laboratory scale aerobic upflow fluidized bed reactor with microelectrodes and microscopy. Based on standard literature parameters for nitrifiers rather than fitting the model to data, an IBM can predict the measured solute profiles and biomass distributions of the autotrophic ammonia-oxidizing bacteria (AOB) and nitrite-oxidizing bacteria (NOB), and of exopolysaccharide (EPS), reasonably well (simulated profiles were averaged over concentric layers). The images in the top row of part d courtesy of B. Momeni, Boston College, Chestnut Hill, Massachusetts, USA. The images in the bottom row of part d are adapted from Ref. 61. The images in part e are adapted with permission from Ref. 68, Wiley.

  3. Using individual-based models to predict evolution.
    Figure 3: Using individual-based models to predict evolution.

    a | Many of the processes that are observed in real-life microbial ecology and evolution can be mapped directly to those that are modelled in individual-based models (IBMs). These include growth, division, death, individual–individual interactions, resource competition and other indirect interactions. A digital genome that directly encodes phenotypic traits can be used when the genotype-to-phenotype mapping is unknown. During division, the digital genome is inherited, but chance mutations during reproduction might result in new phenotypes (for example, an increase in the rate of a particular metabolic reaction) with different fitness in a given environment. Differential survival and reproduction then result in evolution by natural selection. b | Spatial and temporal patterns in cyanobacterial biomass and cell size distribution emerge in an evolutionary IBM that is based on a generic, cell-based model for cyanobacteria and coupled to a hydrodynamic model of vertical transport. As the water column stratifies when entering into summer, the model predicts that small high-light-adapted cyanobacterial cells will begin to dominate in well-lit but nutrient starved surface waters, whereas larger low-light-adapted cyanobacterial cells will begin to dominate at greater depths. c | IBMs can be used to predict phage–host co-evolution. In this model, phages mutate and hosts have innate immunity and adaptive immunity based on CRISPR–Cas. The host can acquire and lose single spacers and the entire cassette. This IBM predicts that increased immune evasion by mutant phages will, counterintuitively, decrease overall phage population size and diversity despite an increased number of phages per host cell as the host population declines. The images in part b are adapted with permission from Ref. 70, Wiley. Data in part c from Ref. 28.

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Affiliations

  1. Department of Civil and Environmental Engineering, Northeastern University, 360 Huntington Avenue, Boston, Massachusetts 02115, USA.

    • Ferdi L. Hellweger
  2. Centre for Computational Biology & Institute of Microbiology and Infection, School of Biosciences, University of Birmingham, Birmingham B15 2TT, UK.

    • Robert J. Clegg &
    • Jan-Ulrich Kreft
  3. Plymouth Marine Laboratory, Prospect Place, Plymouth, PL1 3DH, UK.

    • James R. Clark
  4. Laboratory of Microbiology, Wageningen University, 6708 WE Wageningen, The Netherlands.

    • Caroline M. Plugge

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The authors declare no competing interests.

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Author details

  • Ferdi L. Hellweger

    Ferdi L. Hellweger is an associate professor in the Department of Civil and Environmental Engineering at Northeastern University, Boston, Massachusetts, USA. He received his Ph.D. in earth and environmental engineering from Columbia University, New York, USA. His research interests are in the ecology of microorganisms in surface water systems, including harmful algal blooms in lakes and the evolution of marine bacteria. He specializes in the development and application of mathematical models, with a focus on agent-based techniques. During the past 10 years, a unifying theme of his research has been the combination of systems biology and systems ecology, a concept he refers to as systems bioecology. Ferdi L. Hellweger's homepage

  • Robert J. Clegg

    Robert J. Clegg is a mathematician by training, and his interest in population dynamics led him to complete a Ph.D. in modelling the ecology and evolution of microorganisms under the supervision of Jan-Ulrich Kreft at the University of Birmingham, UK. Now a postdoctoral research fellow, he is currently developing an individual-based modelling platform for research into the host–microbiome interactions in the gut (eGUT) and is also the lead developer of iDynoMiCS. Robert J. Clegg's homepage

  • James R. Clark

    James R. Clark is a research scientist at the Plymouth Marine Laboratory (PML), UK. He received his Ph.D. in environmental science, in 2011, from the University of East Anglia, Norwich, Norfolk, UK. Following his Ph.D., he took up a postdoctoral position at the University of Exeter, Devon, UK, prior to starting at PML in 2013. He has extensive experience in developing and using both individual-based models (IBMs) and more traditional modelling approaches to study spatial and temporal patterns in marine microbial populations.

  • Caroline M. Plugge

    Caroline M. Plugge is an associate professor at the Laboratory of Microbiology, Wageningen University, the Netherlands. She received her Ph.D. from Wageningen University, where she studied the physiology of thermophilic syntrophic methanogenic communities. Since her Ph.D., she has become a staff member of the Laboratory of Microbiology at Wageningen University. Her main research interests are the physiology and biochemistry of anaerobic microorganisms. Her current interest is in microbial communities from anaerobic methanogenic ecosystems. She specializes in the interaction and communication in syntrophic communities.

  • Jan-Ulrich Kreft

    Jan-Ulrich Kreft is a microbiologist turned mathematical modeller. He received his Ph.D. from the University of Konstanz, Germany, where he studied the degradation of methylated aromatic compounds by an anaerobic bacterium. He decided to apply individual-based modelling to microorganisms as a postdoctoral researcher at Cardiff University, Wales, to ask bigger questions. At the University of Bonn, Germany, and now as lecturer at the University of Birmingham, UK, he continues to develop and apply individual-based models to understand competition, cooperation, communication, plasmid transfer or any other interesting interactions between microorganisms. Increasingly, he is combining individual-based models with other modelling and experimental approaches. Jan-Ulrich Kreft's homepage

Supplementary information

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  1. Supplementary information 1 (box) (167 KB)

    Primer of some modelling approaches used in microbial ecology

  2. Supplementary information 2 (box) (116 KB)

    Software for individual-based modelling in microbial ecology

  3. Supplementary information 3 (table) (145 KB)

    Generic open source platforms for individual-based modelling in microbial ecology

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