Metabolic Model-based Ecological Modeling for Probiotic Design James Brunner12and Nicholas Chia34

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Metabolic Model-based Ecological

Modeling for Probiotic Design

James Brunner1,2* and Nicholas Chia3,4*

*For correspondence:

jdbrunner@lanl.gov (JB);

chia.nicholas@mayo.edu (NC)

1Biosciences Division, Los Alamos National Laboratory, Los Alamos, NM, USA; 2Center

for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, NM, USA;

3Microbiome Program, Center for Individualized Medicine, Mayo Clinic, Rochester, MN,

USA; 4Department of Surgery, Mayo Clinic, Rochester, MN, USA

Abstract The microbial community composition in the human gut has a profound eﬀect on

human health. This observation has lead to extensive use of microbiome therapies, including

over-the-counter “probiotic" treatments intended to alter the composition of the microbiome.

Despite so much promise and commercial interest, the factors that contribute to the success or

failure of microbiome-targeted treatments remain unclear. We investigate the biotic interactions

that lead to successful engraftment of a novel bacterial strain introduced to the microbiome as in

probiotic treatments. We use pairwise genome-scale metabolic modeling with a generalized

resource allocation constraint to build a network of interactions between 818 species with well

developed models available in the AGORA database. We create induced sub-graphs using the

taxa present in samples from three experimental engraftment studies and assess the likelihood

of invader engraftment based on network structure. To do so, we use a set of dynamical models

designed to reﬂect connect network topology to growth dynamics. We show that a generalized

Lotka-Volterra model has strong ability to predict if a particular invader or probiotic will

successfully engraft into an individual’s microbiome. Furthermore, we show that the mechanistic

nature of the model is useful for revealing which microbe-microbe interactions potentially drive

engraftment.

Introduction

Microbiome research has come to encompass key areas of disease, ranging from infections (An-

tharam et al., 2013;Honda and Littman, 2012;Battaglioli et al., 2018) and cancer prevention

(Moss and Blaser, 2005;Walther-António et al., 2016;Kim et al., 2020) to systemic immune and

neurological responses (Severance et al., 2016;Kang et al., 2014;Chen et al., 2016). The eﬀect

of the microbiome on health is now undeniable, and every year in the US over 400,000 people

collectively spend $1 billion dollars on over-the-counter probiotics intended to alter their micro-

biome(Kristensen et al., 2016). Many of the purported interactions between microbes and health

involve resident microbiota and their interactions with the host, i.e., the interface between microbial

ecology and human health. The goal of microbiome-targeted interventions is therefore to promote

health by “restoring and maintaining the microbiota and the crucial health-associated ecosystem

services that it provides" (Costello et al., 2012).

Despite the many links between the microbiome and health, our ability to deploy probiotics to

modify the microbiome as intended has been met with relatively little success(Mullard, 2016;Zhu

et al., 2019;Yuan et al., 2017;Zhao et al., 2021;Wu et al., 2017). Studies looking at the ecologi-

cal eﬀects of probiotic administration show that administration of a probiotic is not suﬃcient to

alter the community in the desired way. Speciﬁcally, engraftment of the administered microbial

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arXiv:2210.03198v1 [q-bio.QM] 6 Oct 2022

species is often limited, with only one-third to one-half of patients showing any signs of medium

or long-term engraftment(Maldonado-Gómez et al., 2016;Pudgar et al., 2021). We oﬀer the argu-

ment that probiotic interventions are primarily ecologic in nature; their purpose is to reshape the

complex microbial communities in our body in beneﬁcial ways. Therefore, to predict whether a

probiotic has the desired eﬀects in the gut microbial community, we need more studies examining

the ecology of probiotic interventions(Walter et al., 2018). A mechanistic, personalized approach

to probiotic design—one rooted in empirical metabolic data and ecologic principles—has the po-

tential to propel the ﬁeld forward.

Previous work trying to predict engraftment has been mostly restricted to fecal microbiome

transplant (FMT) studies using non-mechanistic classiﬁers(Smillie et al., 2018;Podlesny et al., 2021).

While potentially predictive, such classiﬁer approaches are sensitive to the underlying assumptions

or conditions in which the study is carried out. Because such models are built using statistical

methods on data that is assumed to be uniformly collected, these models cannot be generalized

to new circumstances. It would be unexpected to see predictions built from patients with diarrhea,

undergoing bowel prep, taking antibiotics, and given an FMT accurately predict what happens in

patients taking orally administered probiotics.

The goal of this work is to examine the use of metabolic modeling-informed population dynamic

approaches. This builds on top of related work in both constraint-based metabolic modeling and

population models such as Lotka-Volterra. It is worth highlighting that the use of dynamic ﬂux

balance analysis for population models has also been a well-published approach. Despite these

successes, there are a number of practical drawbacks for communities of high complexity such as

labor-intensive interpretation and high computational complexity.

Population models such as the generalized Lotka-Volterra model are popular tools for under-

standing microbial community dynamics in a mechanistic manner (Stein et al., 2013;Friedman

et al., 2017;Angulo et al., 2019;Kuntal et al., 2019). However, these models are in general diﬃcult

to parameterize, with state of the art gradient-matching procedures requiring somewhat dense

time-longitudinal data with many replicates Bucci et al. (2016). Furthermore, the authors have pre-

viously shown that parameters ﬁt from data to these models do not extend to novel environmental

situations, and may even change with the addition of a new taxa to the community (Brunner and

Chia, 2019). These drawbacks make such mechanistic population models impractical for predicting

engraftment. However, by leveraging metabolic modeling we are able to parameterize population

models in a way that can be easily adapted to novel environments and does not require dense

time-longitudinal data. This allows us to use these models to predict microbial engraftment into a

community. See ﬁg. 1for a comparison of our method with standard parameter ﬁtting.

In this paper, we present a method to predict engraftment of an invader into a microbial com-

munity in the following manner. First, we construct an interaction network of the microbial taxa

found in a sample from the community using pairwise ﬂux balance analysis with resource allo-

cation constraints (Kim et al., 2022) with genome-scale metabolic models included in the AGORA

database(Magnúsdóttir et al., 2017). We then make a prediction based oﬀ of one or more of six

dynamical systems models parameterized by this network—the generalized Lotka-Volterra (LV)

model Edelstein-Keshet (2005); Stein et al. (2013); Friedman et al. (2017), an adjustment to the

LV model we call the “antagonistic Lotka-Volterra" model (AntLV), another adjustment to the LV

model we call the “inhibitory Lotka-Volterra" model (InhibtLV), a fourth non-linear model based on

the replicator equation Madec and Gjini (2020); Gjini and Madec (2021) which is similar to the LV

model, and two similar linear models based on node balancing (NodeBalance) and random walks

(Stochastic) (see ﬁg. 2).

We test the predictive potential of each dynamical model by predicting the outcomes of micro-

biome invasion experiments (Battaglioli et al., 2018;Maldonado-Gómez et al., 2016;Huang et al.,

2021) from the initial presence/absence of species in each sample. We choose to test all six mod-

els because no deﬁnitive “best model" has been established. The LV model is widely used, but we

found that this model could lead to uncontrolled simulated growth. We developed the AntLV and

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Pairwise GEMs Traditional Model Fitting

Parameter Fitting

Calculation

N2pairwise joint ﬂux balance analysis (linear opti-

mizations)

Gradient matching (quadratic optimization or

Baysian ﬁtting)

Free Parameters 1 joint ﬂux balance analysis meta-parameter + nutri-

ent condition + choice of dynamics

−Ninteractions + choice of dynamics

Data Required Single sample compositional data Dense time-longitudinal data with multiple replicates

Generalizability Can be adapted to nutrient condition Must reﬁt for each experiment

Inherent Assump-

tions

Microbial optimization for growth, constant direct

interactions between microbes

Constant direct interactions between microbes

Convenient As-

sumptions

Uniform intrinsic growth across the community Constraints on possible interactions (e.g. self-

regulation must be negative)

Figure 1. Population models such as Lotka-Volterra generally require dense time-longitudinal data to

accurately parameterize. In this work, we leverage genome-scale metabolic modeling to parameterize

population models with only genomic data from a single time-point. We are unable to parameterize these

models using standard techniques due to the sparsity of the data.

InhibitLV models in order dampen the numerical instability of the LV model. We also include the

replicator model because has recently been shown to provide insight into microbial population

dynamics (Madec and Gjini, 2020). Finally, we include the two linear models because they provide

a substantial reduction in computational complexity, and so are more practical to use as long as

they provide adequate predictive power.

Because the speciﬁc invasion experiments involved invader strains not present in the AGORA

database, we repeated the experiment for each species-level match to the invader in the database.

We show that this method has good predictive potential depending on the choice of dynamical

system used to score the sub-graphs and choice of AGORA database match to the invader strain.

Furthermore, we perform two types of sensitivity analysis to demonstrate that the mechanistic

nature of the model provides additional insight into the impact of the various components of the

network. We perform simulated knock-out experiments to test how sensitive engraftment is to

each community member, and we use parameter sensitivity analysis to test how sensitive engraft-

ment is to each network connection.

Results

We ﬁrst examine the ability of our metabolic modeling-based approach to successfully predict en-

graftment versus non-engraftment for diﬀerent microbial species introduced orally across diﬀer-

ent experimental or clinical trial settings. The three studies we use to test predictive power all

involved the introduction of an invading taxa into an established microbial community. Two of

these studies examine the introduction of candidate probiotics, B. longum and L. plantarum, re-

spectively, into human subjects (Maldonado-Gómez et al., 2016;Huang et al., 2021). The third

examines the introduction of the pathogen C. diﬃcile (Battaglioli et al., 2018) into mice that had

been inoculated with microbial communities from healthy and disbiotic human donors. Note that

while this study introduces a pathogen rather than a probiotic, the ecological principle of engraft-

ment into an existing community is the same. All three studies include microbiome samples from

prior to introduction of the invader, which we use to generate predictions, as well as samples from

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Predictions are made for each sample using 6 diﬀerent dynamical models

Four quadratic models.

Generalized Lotka-Volterra

Each microbe grows exponentially

modiﬁed by positive and negative

interactions determined by joint FBA

Antagonistic Lotka-Volterra

Each microbe grows exponentially

modiﬁed by negative interac-

tions determined by joint FBA

Inhibitory Lotka-Volterra

Each microbe grows logistically

modiﬁed by positive and negative

interactions determined by joint FBA

Replicator

Community Eﬀect

Each microbe grows exponentially

modiﬁed by positive and negative

interactions and a community wide in-

teraction term determined by joint FBA

Two linear models.

Node Balance

Biomass ﬂows linearly through the network

with conductance determined by joint FBA.

Stochastic

Biomass behaves as a random walk with tran-

sition probabilities determined by joint FBA.

Figure 2. We used six dynamical systems to assess the engraftment potential of an invading taxa. All six are

parameterized based on a set of network connections 𝑤𝑖𝑗 derived from metabolic modeling. The four

quadratic models are variations on the generalized Lotka-Volterra model. The two linear models are related

to diﬀusion on the graph.

after the community was allowed to reform, which we use to score our predictions.

As a metric of classiﬁcation success for the C. diﬃcile and B. longum data-sets, we use the area

under the curve of the receiver-operator characteristic (AUC-ROC). This metric provides a measure

of performance based on the model’s ability to identify true positives while avoiding false positives,

so that 1is perfect classiﬁer performance and 0.5is equivalent to random classiﬁcation (i.e. ﬂipping

a coin for each sample). We use Kendall-tau rank correlation as a metric of classiﬁer success for the

L. plantarum data-set, comparing our test-score with the observed abundance. This is necessary

because AUC-ROC requires binary classiﬁcation of the test data, which was unavailable for this

data-set.

In ﬁgs. 3to 5, we report the AUC-ROC of each dynamical model for each experiment, as well

as the AUC-ROC for support vector machine and random forest classiﬁcation or regression (see

ﬁg. 2for the dynamics used). Tables of these results and associated estimated p-values can be

found in the supplementary ﬁle supp_tables.pdf, (results in Tables 1,3 and 6, p-values in Tables

2,4,7, and standard machine learning’s performance in Tables 5 and 8). Study data from (Battagli-

oli et al., 2018) displayed clear diﬀerences between engrafter and non-engrafter samples in both

species composition and 𝛼-diversity (see Supplementary Figure 3 in supp_figures.pdf). For this

reason, any reasonable classiﬁer should be expected to diﬀerentiate the two groups. Indeed, our

method produced perfect classiﬁcation on the C. diﬃcile data-set for every of choice of dynamics

or GEM representing the invading C. diﬃcile. We may consider this performance a necessary, but

not suﬃcient criteria for the quality of the method.

On the other hand, data from the studies (Maldonado-Gómez et al., 2016;Huang et al., 2021)

was much more muddled. In both of these studies, our method generally outperforms the classical

machine-learning techniques to which we compared it. The Lotka-Volterra dynamics performed

the best, especially when modiﬁed to be made antagonistic or inhibitory. Inspection of individual

simulations revealed that this improvement is due to those modiﬁcations preventing ﬁnite-time

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MetabolicModel-basedEcologicalModelingforProbioticDesignJamesBrunner1,2*andNicholasChia3,4**Forcorrespondence:jdbrunner@lanl.gov(JB);chia.nicholas@mayo.edu(NC)1BiosciencesDivision,LosAlamosNationalLaboratory,LosAlamos,NM,USA;2CenterforNonlinearStudies,LosAlamosNationalLaboratory,LosAlamos,NM,USA;3Mi...

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