INVITED REVIEW MICROBIAL GROWTH KINETICS

Enzymatic origin and various curvatures of metabolic scaling in microbes

The famous and controversial power law is a basal metabolic scaling model mainly derived from the “surface rule” or a fractal transport network. However, this law neglects biological mechanisms in the important active state. Here, we hypothesized that the relative metabolic rate and growth rate of actively growing microbes are driven by the changeable rate of their rate-limiting enzymes and concluded that natural logarithmic microbial metabolism (lnλ) and growth (or biomass) (lnM) are both dependent on limiting resources, and then developed novel models with interdependence between lnλ and lnM. We tested the models using the data obtained from the literature. We explain how and why the scaling is usually curved with the difference between microbial metabolic and growth (or biomass’s) half-saturation constants (K_M, K_λ) in the active state and agree that the linear relationship of the power law is a particular case under the given condition: K_M = K_λ, which means that the enzyme dynamics may drive active and basal metabolic scaling relationships. Our interdependent model is more general than the power law, which is important for integrating the ecology and biochemical processes.

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.

Dynamic simulation of an in vitro multi-enzyme system

Parameters often are tuned with metabolite concentration time series data to build a dynamic model of metabolism. However, such tuning may reduce the extrapolation ability (generalization capability) of the model. In this study, we determined detailed kinetic parameters of three purified Escherichia coli glycolytic enzymes using the initial velocity method for individual enzymes; i.e., the parameters were determined independently from metabolite concentration time series data. The metabolite concentration time series calculated by the model using the parameters matched the experimental data obtained in an actual multi-enzyme system consisting of the three purified E. coli glycolytic enzymes. Thus, the results indicate that kinetic parameters can be determined without using an undesirable tuning process.

Toward large-scale modeling of the microbial cell for computer simulation

In the post-genomic era, the large-scale, systematic, and functional analysis of all cellular components using transcriptomics, proteomics, and metabolomics, together with bioinformatics for the analysis of the massive amount of data generated by these "omics" methods are the focus of intensive research activities. As a consequence of these developments, systems biology, whose goal is to comprehend the organism as a complex system arising from interactions between its multiple elements, becomes a more tangible objective. Mathematical modeling of microorganisms and subsequent computer simulations are effective tools for systems biology, which will lead to a better understanding of the microbial cell and will have immense ramifications for biological, medical, environmental sciences, and the pharmaceutical industry. In this review, we describe various types of mathematical models (structured, unstructured, static, dynamic, etc.), of microorganisms that have been in use for a while, and others that are emerging. Several biochemical/cellular simulation platforms to manipulate such models are summarized and the E-Cell system developed in our laboratory is introduced. Finally, our strategy for building a "whole cell metabolism model", including the experimental approach, is presented.

Mathematical modelling of bacterial growth at subinhibitory levels of aminoglycosides

The subinhibitory effect of antibiotics has often been studied without any clear theoretical framework; we have chosen to use mathematical bacterial growth modelling as a useful tool to analyse these biological states in a more rigorous manner. Since their mode of action and molecular target are relatively well known, aminoglycosides were well suited for this more sophisticated study of subinhibitory action. We have shown that two models (the Monod and the logistic models) regularly used in bacteriology, were adequate to describe these effects in a glucose-limited medium. A change of model, according to antibiotic concentration, revealed the existence of two separate actions. At lower concentrations, inhibition affected mainly glucose use, the substrate remained limiting and growth mode did not change. As soon as the concentration exceeded a threshold, growth was totally disturbed, probably through a physiological "catastrophe". This threshold can be used to estimate bacterial susceptibility to these antibiotics.