Mathematical modelling of microbes: metabolism, gene expression and growth

Abstract

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.

Elementary Growth Modes provide a molecular description of cellular self-fabrication

“…Elementary Growth Modes are still the minimal building blocks, and the above-mentioned maximiser theorems still hold. A commonly used simplification is to consider a small coarsegrained whole-cell model (Scott and Hwa, 2011;Molenaar et al, 2009;Weiße et al, 2015;de Jong et al, 2017). These models become computationally feasible because of their small size, such that no further simplifications have to be made; EGM-theory is directly applicable to this type of models.…”

“…In our derivation, we assumed that V (t) = V (n(t)), which means that the contents of a cell is approximated by an ideal solution (Dill and Bromberg, 2012). We realise that this is likely an oversimplifying assumption (McGuffee and Elcock, 2010;Parry et al, 2014)), but one that underlies many models of cell growth (de Jong et al, 2017;Schaechter, 2015). We note that balanced growth becomes much harder to rationalise when the assumption V (t) = k ρ k n k (t) is invalid.…”

An analytical theory of balanced cellular growth

“…We term this general modeling scheme Growth Balance Analysis (GBA); below, we develop an 2/45 analytical theory for GBA of arbitrarily complex cellular systems. FBA and its extensions can be viewed as linearizations of the GBA scheme 15 . Fig.…”

gapseq: Informed prediction of bacterial metabolic pathways and reconstruction of accurate metabolic models

“…Mathematical analysis has shown great potential for dissecting the functioning of metabolic networks on the level of topological, stoichiometric, and kinetic models [79], which together provide a wide array of methods [47]. Although different microbial metabolic modelling approaches exist, they can be summarised by a theoretical framework that provides a unifying view on microbial growth [38]. Metabolic models not only have demonstrated their ability to predict phenotypes on the level of cellular growth and gene knockouts, but also provide potential molecular mechanisms in form of gene and reaction activities, which can be validated experimentally [87].…”

“…The habitat of the diverse group of soil microorganisms more likely represents an open ecosystem, whereas the gut microbiome is directly constraint by a multi-cellular host that potentially controls microbial traits [22]. In general, metabolic modelling should be accompanied by the analysis of pathways based on statistical methods [25] to compensate for additional assumptions, which are introduced in constraint-based metabolic flux modelling [38].…”