Towards predictive models of the human gut microbiome

Abstract

The intestinal microbiota is an ecosystem susceptible to external perturbations such as dietary changes and antibiotic therapies. Mathematical models of microbial communities could be of great value in the rational design of microbiota-tailoring diets and therapies. Here, we discuss how advances in another field, engineering of microbial communities for wastewater treatment bioreactors, could inspire development of mechanistic mathematical models of the gut microbiota. We review the state of the art in bioreactor modeling and current efforts in modeling the intestinal microbiota. Mathematical modeling could benefit greatly from the deluge of data emerging from metagenomic studies, but data-driven approaches such as network inference that aim to predict microbiome dynamics without explicit mechanistic knowledge seem better suited to model these data. Finally, we discuss how the integration of microbiome shotgun sequencing and metabolic modeling approaches such as flux balance analysis may fulfill the promise of a mechanistic model.

Keywords: antibiotic; biofilm; mathematical modeling; metagenomics; network inference.

Figure 1. Analogy between environmental engineering bioreactors and the human intestinal microbiome

Bioreactors, such as the activated sludge (A) use multispecies microbial communities to degrade waste (e.g. C = organic carbon) and other nutrients (e.g. N = nitrogen as ammonia, P = phosphorous) which if untreated can lead to environmental pollution problems. The optimal microbial community is selected by the bioengineer by tuning external parameters such as mixing, aeration, and temperature. Composition shifts due to wrong operational conditions can lead to system failure. (B) The intestinal microbiome is the multispecies microbial communities harbored in the human intestine. Similar to the environmental bioreactors communities, the microbiome degrades nutrients and is susceptible to external perturbations such as diet change and antibiotic application. Its composition shifts due to changes in diet or antibiotic use, and some community alterations have been associated with disease.

Figure 2. Population and individual-level approaches used to model environmental bioreactors microbial communities

(A) Population-level modeling, such as the Activated Sludge Model, considers microbial population as continuous entities. These models do not account for population heterogeneity in parameters and internally stores nutrients and are used to reproduce bulk community measurements. μ_PAO is the maximum growth rate of phosphate accumulating organisms (PAOs), SO₂ represents the oxygen bulk concentration, S_PO4 represents the bulk phosphate concentrations, S_ALK is the alkalinity of the wastewater, S_NH4 represents the bulk ammonia concentrations, X_PHA is the poly-hydroxy-alkanoates internally stored concentration for PAOs and X_PAO is the biomass density of PAOs in the wastewater. K_O2, K_PS, K_ALK, K_NH4 and K_PHA are the half-saturation constants for the respective saturation kinetics. (B) Individual-based modeling has been used to respond to the increasing number of single-cell measurements (e.g. Raman spectroscopy^,). These measurements show that microbial functionally relevant groups in bioreactors are heterogeneous, such that they harbor different level of internally stored nutrients. Fitting single cell observations and bulk community data with individual based modeling lead to a deeper understanding of the system under investigation. In the IbM approach, total PAOs growth is an emergent property of the summation over each individual cell contribution to growth which is dependent on the current state of the individual cell, its parameters and the local concentrations of solutes. With superscript i we indicate the parameters corresponding to individual cell i=1…L and L is the total number of individuals. Example of IbMs are the Framework, IDynoMicS and iAlgae.

Figure 3. Computational analysis and mathematical models of the intestinal microbiome

(A) Example and list of current computational approaches used to analyze community data for microbiome (16s rRNA) studies. (B) Schematic of a model to simulate polysaccharide digestion in the intestine. This model is built in a bottom-up approach, which aims to determine population-level behaviors from detailed biochemical reactions. Parameters are often taken from literature. No comparison with data is provided in the original paper. (C) Conceptual scheme of the approach used in the eGUT simulator under development by Jan Kreft. (D) Generalized Lotka–Volterra system of equation with time-variable perturbations approach. The method uses ecological modeling and machine learning to infer network of microbial interactions, susceptibilities to external perturbations and growth rates. The parameters inferred are used in an ecological community model that can then be used to predict ecosystem dynamics by numerical simulations or to identify steady states. The data shown is an example was obtained by simulation to validate the inference method and shows microbiota dynamics in the presence of three distinct perturbations representing antibiotic admnistration.