Metabolite-mediated modelling of microbial community dynamics captures emergent behaviour more effectively than species–species modelling

Abstract

<jats:p>Personalized models of the gut microbiome are valuable for disease prevention and treatment. For this, one requires a mathematical model that predicts microbial community composition and the emergent behaviour of microbial communities. We seek a modelling strategy that can capture emergent behaviour when built from sets of universal individual interactions. Our investigation reveals that species–metabolite interaction (SMI) modelling is better able to capture emergent behaviour in community composition dynamics than direct species–species modelling. Using publicly available data, we examine the ability of species–species models and species–metabolite models to predict trio growth experiments from the outcomes of pair growth experiments. We compare quadratic species–species interaction models and quadratic SMI models and conclude that only species–metabolite models have the necessary complexity to explain a wide variety of interdependent growth outcomes. We also show that general species–species interaction models cannot match the patterns observed in community growth dynamics, whereas species–metabolite models can. We conclude that species–metabolite modelling will be important in the development of accurate, clinically useful models of microbial communities.</jats:p>

Modeling microbial cross-feeding at intermediate scale portrays community dynamics and species coexistence

“…Inspired by the classical MacArthur’s CR models [ 23 ] and many follow-ups [ 17 , 24 – 26 ], we propose to integrate CR models with a coarse-grained yet mechanistic description of cell metabolism. Metabolic reactions can be broadly classified as catabolic and anabolic, where catabolic reactions break down complex substrates from culture media into smaller metabolic intermediates that can be used to build up biomass components by anabolic reactions.…”

Minimizing the number of optimizations for efficient community dynamic flux balance analysis

“…Various dynamical models have been proposed to explain and predict microbial community population dynamics [8][9][10][11][12]. Among these are models which propose that interactions between species are mediated by the metabolites that each species produces and consumes [13,14], and there is significant evidence that these models perform better than models which depend on direct interaction between species [15,16].…”

“…However, as we will demonstrate with 1, the choice of basis of a degenerate solution is important in a dynamic problem. In fact, if the system given in Eqs (14) and (15) is evolved forward until w I i ðc i ðtÞÞ becomes infeasible, the time at which the system becomes infeasible is the time at which we have some ðw I i Þ j ¼ 0 for j 2 I i . Thus, we need to resolve Eq (10) whenever w I i ðc i ðtÞÞ becomes degenerate, which will be the final time-point at which the w I i ðc i ðtÞÞ is feasible.…”

“…Of course, this assumes that the linear ODE solved in these intervals is solved exactly rather than numerically. Precisely, there exits some sequence t 0 = 0 < t 1 < � � � < t n−1 < t n = T such that if we know the optimal flux vectors w i (t l ) at time t l , then Lemma 1 implies the existence of a set of invertible matrices B l i such that solutions to Eqs (14) and (15) are solutions to Eqs (6), (7) and (10) for t 2 [t l , t l+1 ]. Therefore, if we are able to identify the t l exactly, then Algorithm 1 provides exact solutions to the dynamic FBA problem Eqs (6), (7) and (10).…”

“…We rewrite Eq (4) using Eq (5) and combine with Eqs ( 2 ) and ( 3 ) to form the differential algebraic system where each ϕ i is determined by the optimization Eq (8) , all carried out separately. Note that this is a metabolite mediated model of community growth as defined in [ 15 ]. That is, the coupling of the growth of the separate microbes is due to the shared pool of metabolites y .…”