Individual-based modeling unveils pattern formation and population dynamics in microbial aggregates

Bastiaan Julien Reinaart Cockx

Research output: Book/ReportPh.D. thesis

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Microbes are commonly found in aggregated form, where a community of various microbial species fill a variety of ecological niches. They play an essential role in global nutrient cycles, human and animal health, and in numerous industrial applications. Microbial aggregates, in many cases referred to as bio-films, have a dynamic life cycle. The cycle starts when planktonic cells start attaching to a surface or other cells. In this so called reversible attachment phase microbial surface properties such as the hydrophobicity of the cell play a key role. After this the nascent biofilm enters the irreversible attachment phase, more cells continue to be embedded in the growing aggregate, and phenotypic changes associated with microbial life in a biofilm, including the production of large quantities of Extracellular Polymeric Substances (EPS), start to occur. As the aggregate grows, spatial structures such as microcolonies and stratification start to emerge. Mature biofilms may get into a final phase in which EPS degradation occurs and cells disperse into the environment.

The spatial and community structure of a microbial aggregate result from a combination of physical processes such as matter transport and mechanical stresses acting upon the microbial aggregate, and the individual traits and behavior of the microbes embedded in the aggregate. Due to the complexity of multi-species microbial aggregates and our limited ability to observe the dynamic development of internal structures and biochemical conditions in microbial aggregates, modeling approaches have played a substantial role in biofilm research. The first mathematical and computational biofilm models, developed over half a century ago, clarified how, through diffusion limitation, chemical gradients form within microbial aggregates that can in turn, lead to the stratification of microbial species in the aggregate. Later, Individual-based Models (IbM) showed how individual traits and variability can affect the development of the microbial aggregate and how subtle differences can lead to vastly different outcomes.

Over two decades of IbM assisted biofilm research has proven fruitful and the approach is increasingly being used in contemporary research. An increasing number of modeling platforms facilitate the development of IbMs. However, current drawbacks and limitations restrain us from using the methodology in a broader palette of studies. These drawbacks include the limited scale of computationally feasible model systems, the limited availability of individual based observations required to parameterize the model systems, the expertise required to develop an IbM, and limitations in the ability to accurately represent some important microbial traits or model systems with currently available modeling tools. Recent efforts by multiple research consortia have brought substantial improvements in some of these limitations, but an integrated approach that addresses all these limitations simultaneously is still missing.

Central to my thesis is the development of such an integrated approach, and thereby facilitating a wide range of biofilm research to help explain how individual microbial traits lead to emergent properties of the microbial aggregate. This goal can be subdivided into the following objectives:

1. Enabling a larger range of dynamic individual-based characteristics and behaviors for a better representation of various microbial traits.
2. Widening the range of (bio-)chemical sub-models to provide a better representation of microbial metabolisms.
3. Improving the physical representation and interaction models available.
4. Closing the gap between experimental and modeling work facilitating a better integration of experiments and modeling and reducing the required expertise to construct a model.
5. Facilitating model parameterization where individual based experimental observations may be lacking.
6. Improving computational efficiency to allow for models at larger scales.

To achieve this goal, I have worked with a dedicated group of collaborators on the development of the novel individual-based modeling framework iDynoMiCS 2.0 and the closely related gut modeling software eGUT. The latter expands on iDynoMiCS 2.0 with an epithelium and mucus facilitating gut lumen and mucosa models. iDynoMiCS 2.0 introduces a new structure where modeled microbes, often referred to as agents, can be assembled from orthogonal modules. Any characteristic, including the morphology, biochemical and biophysical behavior, can dynamically change in response to external or internal cues. These cues include solute or signal molecule concentrations, the internal availability of storage molecules, or even stochastic processes. This allows for a better representation of dynamic microbial traits. A new biochemical sub-model allows to express kinetic models through arithmetic functions. These arithmetic functions may include conditions in agent’s local environment such as solute or signal molecule concentrations, and the internal conditions or properties of the agent. This massively expands the range of (bio-)chemical sub-models available as any model that can be expressed arithmetically can be used. The new mechanical interaction and microbial morphology sub-models introduce rod-shaped and filamentous microbes to the modeling platform and, like the (bio-)chemical models, allow the modeler to express these interactions through arithmetic functions.

By removing the necessity to provide abstract software or model parameters and enabling biologists to formulate their system in their own language rather than computer code, the gap between experimental and modeling work is reduced. This was achieved with iDynoMiCS 2.0 by the development of self-analyzing and optimizing algorithms, a set of default parameters where they make sense and relying on understandable parameters with biological meaning where they are needed. A graphical user interface further helps lower the barrier of entry into individual-based modeling. The integration of quantitative tools for spatial structure analysis provides insight into the structural development of microbial aggregates. By quantifying the spatial structure, it becomes easier to compare model results with experimental observations. Sensitivity analysis tools, utilizing Morris screening, reveal what state variables (properties of the modeled biofilm) are sensitive to the model inputs and thus what properties of the biofilm may change resulting from changing properties of individual microbes in the model. In this way it becomes easier to link emergent properties of the biofilm to microbial traits. A genetic algorithm was implemented to help estimate the model parameters. Despite the long evaluation times, stochastic processes, and localized variability, the genetic algorithm proves to be effective in optimizing an individual based biofilm model. The combination of tools facilitates Pattern-Oriented Modeling (POM) with iDynoMiCS 2.0. POM is a modeling approach that aims to identify and replicate the patterns that characterize the modeled system observed at different levels of the system’s organization and scale. With the modeling platforms developed for this thesis, it is now possible to identify these characteristic multi-level patterns, and to infer individual based properties from them. POM can help mitigate the issues caused by the limited availability of individual based observations. In many cases reasonable initial parameter estimation can be made using existing empirical models. A focused effort addressing software bottlenecks enables biofilm simulations with over 10 million agents. This is over two orders of magnitudes more than iDynoMiCS 2.0’s predecessor. A rigorous testing process verifies the effectiveness and numerical accuracy of the solvers and algorithms used in the platforms.

This thesis further includes multiple models utilizing iDynoMiCS 2.0 and eGUT, which provide interesting insights into the ecological processes and the dynamic community development of microbial aggregates. This includes a model studying the interactions of yield- and rate strategists with either filamentous or spherical morphologies. The model reveals a strong competitive advantage for filament forming agents under nutrient limiting conditions. The next model explores spatial pattern formation during the initial aggregation process under various hydrological conditions and shows how differences in agent surface properties can lead to cell sorting. Agents with large Gibbs free energy of adhesion (Δ𝐺𝑎𝑑ℎ) form the center of an aggregate, surrounded by agents with small Δ𝐺𝑎𝑑ℎ. Further, a partial nitritation anammox model was developed. This model was used to identify how the growth characteristics of simulated microbes affect the structure and shape of the emergent biofilm. Finally, a multi-compartment gut model is developed using eGUT. The model simulates the microbial community composition and spatial structure of the proximal, transverse and distal colon. The insights into the spatial structure development of the mucosa are particularly valuable as it is often not possible to obtain this in vivo. Additional models are presented in the included manuscripts and/or available through the open source software repositories. The work presented in this thesis allows for a more accurate representation of microbes embedded in microbial aggregates in computational models. This improved representation enables these models to better capture the processes and interactions within biofilms and thereby predict patterns and phenomena that could not be captured with previous approaches.
Original languageEnglish
Place of PublicationKgs. Lyngby
PublisherTechnical University of Denmark
Number of pages112
Publication statusPublished - 2024


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