cMFA for multi-omics data integration in microbial
community models

Sthyve Junior Tatho Djeanou, Simon Labarthe, Valentina Baldazzi

► To cite this version:

Sthyve Junior Tatho Djeanou, Simon Labarthe, Valentina Baldazzi. cMFA for multi-omics data integration in microbial community models. Population Dynamics: From Data to Models 2025, Mar 2025, Sophia Antipolis, France. hal-04996135

HAL Id: hal-04996135

https://inria.hal.science/hal-04996135v1

Submitted on 18 Mar 2025

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Distributed under a Creative Commons Attribution 4.0 International License
# cMFA for multi-omics data integration in microbial community models

Sthyve Tatho, Simon Labarthe, Valentina Baldazzi

Biogeco (Inrae), Pleiade (Inrae/Inria), France, sthyve.tatho@inria.fr

## INTRODUCTION

### Biology-informed inference from multi-omics data

Understanding natural microbial communities presents significant challenges due to the complex interactions and metabolite exchanges between microorganisms. To gain deeper insights into these dynamics, we are focusing on:

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Population count data

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Metabolomics data

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Metatranscriptomic data

Biological Prior

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Metabolic network

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$f(x)$

Biology
Inform
Inference
Problem

modelling

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Interpretation

Microbial Community

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* Developing mathematical models based on metabolic networks.

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* Inferring metabolic fluxes using biology-informed high-dimensional analysis methods to integrate multi-omics data.

### Scientific Question:

How can mathematical models help us better understand the functioning of microbial communities ?

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* Internal flux reconstruction based on some external reaction rates.

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* Estimating the contribution of each microorganism to the community.

## COMMUNITY METABOLIC FLUX ANALYSIS (CMFA)

### METABOLIC NETWORK

A metabolic network refers to the interconnected set of biochemical reactions and pathways that occur within a cell or organism.

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### INPUT DATA DESCRIPTION

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Time-series of:

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* Targeted metabolomic data.

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* Microbial counts.

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* Metatranscriptomic (expressed metabolic reactions).

### METABOLIC FLUX ANALYSIS (MFA)

Experimental technique used to estimate intracellular metabolic fluxes by analyzing metabolite production and consumption rates in a biological system, providing insights into the cell's core metabolism

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### COMMUNITY MFA (cMFA)

Find, for $t \ge 0$, for a set $\mathcal{M}$ of $N_m$ metabolites and for a set $\mathcal{B}_m$ of $N_b$ micro-organisms the flux vector

$$ \hat{v}(t) = (\nu^{(\hat{b}_1)}(t), \dots, \nu^{(\hat{b}_{N_b})}(t)) \quad \text{of dimension } N_r $$

such that

$$ \hat{v}(t) := \arg \min \sum_{m \in \mathcal{M}} \left\| R_{m,t} - \sum_{b \in \mathcal{B}_m} \chi_t^{(b)} \nu_{m,t}^{(b)} \right\|_2 + \lambda \mathcal{R}(\nu) $$

$$ \text{ST} : \begin{cases} S^{(b)} \cdot \nu^{(b)} = 0, & \text{for } b \in \mathcal{B}_m \\ C_{\min}^{(b)} \le \nu^{(b)} \le C_{\max}^{(b)}, & \text{for } b \in \mathcal{B}_m \end{cases} $$

Regression problem is:

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* High-dimensional ($N_r \sim 5000$)

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* Highly-underdetermined ($N_r \gg N_m$)

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* Biology-informed ($S^{(b)}$)

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* Constrained by metatranscriptomics (where $C_{\min}^{(b)} = C_{\max}^{(b)} = 0$)

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* Regularized by ridge ($\mathcal{R}(\nu) = \|\nu\|_2^2$) or lasso ($\mathcal{R}(\nu) = \|\nu\|_1$) penalty

### CO-CULTURE DEFINITION

Biological situation of E. coli to produce amine acids and ALA super producer

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Co-consumption

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Individual + Co-consumption and Co-production

### BENCHMARK METHODOLOGY

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### GENERATING DATA: dFBA

Dynamic Flux Balance Analysis (DFBA) is an extension of traditional Flux Balance Analysis (FBA), which is a mathematical modeling approach used in systems biology to predict the flow of metabolites through metabolic networks.

$$ \begin{align*} \partial_t b_i &= B \hat{v}_i (M, b) b_i \\ \partial_t M_j &= \sum_{i \in C} \hat{v}_{i,j} (M, b) b_i \\ \hat{v}_i &= \arg \max B v_i \\ S.T \quad \begin{cases} S_i \hat{v}_i = 0 \\ C_M \le \hat{v}_i^s \le 0 \\ 0 \le \hat{v}_i^p \le C_{\max} \\ -C_{\max} \le \hat{v}_i^{in} \le C_{\max} \end{cases} \quad \begin{pmatrix} r_1 & r_2 & r_3 \\ -1 & 0 & 0 \\ -1 & 0 & 0 \\ 1 & -1 & 0 \\ 1 & 0 & -1 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ 0 & 0 & 0 \end{pmatrix} \end{align*} $$

### IMPLEMENTATION

1. NumPy and Pandas for data handling and structure.

2. PyGAM for spline smoothing.

3. Matplotlib for visual representations.

4. COBRApy for constraint-based modeling (dFBA).

5. OSQP for quadratic programming problems.

## RESULTS

### DATA SMOOTHING WITH SPLINE

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### INFERRING EXCHANGE FLUXES: dFBA VS CMFA

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### INFERRING INTERNAL FLUXES

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Comparison of simulated dFBA vs cMFA for Multiple Organisms

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### PERSPECTIVES

1. Benchmark on real data.

2. Expand the community model to incorporate a diverse set of more than 10 to 20 microorganisms,

3. The extension of MFA and the inclusion of metatranscriptomic data

### REFERENCES

1. Brunner et al., 2023, PLoS Comput. Biol. 19, e1011661

2. Gerken Starepravo et al., 2022, Digit. Chem. Eng. 2, 100011

3. Lecomte et al., 2023, Metab. Eng. doi.org/10.1016/j.ymben.2024.02.014

4. Mahadevan et al., 2002, Biophys. J. 83, 1331–1340

5. Pansu, 2004, Courbes b-splines

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