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. CJC MA2024 - Congrès des Jeunes Chercheur.e.s en Mathématiques Appliquées, Oct 2024, Lyon, France. . hal-04874275

HAL Id: hal-04874275

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Submitted on 8 Jan 2025

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Distributed under a Creative Commons Attribution 4.0 International License
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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<figure><img src="image_5.png" /><figcaption>Population count data</figcaption></figure>

<caption>Metabolomics data</caption>

<figure><img src="image_6.png" /><figcaption>Microbial Community</figcaption></figure>

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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 $\bar{N}_b$ micro-organisms the flux vector

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

such that

$$ \hat{v}(t) := \arg \min \sum_{m \in \mathcal{M}} \left\| R_{m,t} - \sum_{b \in \mathcal{B}_m} \chi_t^{(b)} \nu_{m,t}^{(b)} \right\|_2^2 + \lambda \mathcal{R}(\nu) $$

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

Regression problem is:

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* High-dimensional ($N_r \sim 4000$)

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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

$$ (\text{where } C_{\min}^{(b)} = C_{\max}^{(b)} = 0) $$

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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 with co-consumption

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### 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.

$$ \begin{aligned} \partial_t b_i &= B \hat{v}_i (M, b) b_i \\ \partial_t M_j &= \sum_{i \in C} \hat{v}_{i,j} (M, b) b_i \end{aligned} $$

$$ \hat{v}_i = \arg \max B \nu_i \qquad S = \begin{pmatrix} m_1 & r_1 & 0 & 0 \\ m_2 & -1 & 0 & 0 \\ m_3 & -1 & 0 & 0 \\ 1 & 0 & -1 & 0 \\ 0 & 1 & 0 & 0 \\ 0 & 0 & 1 & 0 \\ 0 & 0 & 0 & 0 \end{pmatrix} $$

### IMPLEMENTATION

1. NumPy and Pandas for data handling and structure.

2. SciPy for time integration tasks, PyGAM for spline smoothing.

3. Scikit-learn for cross-validation.

4. Matplotlib for visual representations.

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

6. OSQP for quadratic programming problems.

## RESULTS

### DATA SMOOTHING WITH SPLINE

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### INFERRING EXCHANGE FLUXES: SPLINE VS CMFA
& DFBA VS CMFA

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### INFERRING INTERNAL FLUXES

Comparison of simulated dFBA vs cMFA for Multiple Organisms

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### PERSPECTIVES

1. Benchmark on different Co-culture.

2. Benchmark on real data.

3. Develop a machine learning approach to predict MFA results from the state variables, in order to be able to simulate the community dynamics.

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

### REFERENCES

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

2. Chesson, 1990, Theor. Popul. Biol. 37, 26-38

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

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

5. Mahadevan et al., 2002, Biophys. J. 83, 1331-1340

6. Pansu, 2004, Courbes b-splines, URL: https://www.math.u-psud.fr/pansu/web_maitrise/bsplines.pdf