A dynamic coculture model based on mechanistic coupling of genome scale metabolic models

To understand, predict and ultimately control the behavior of the synthetic microbial consortium, we designed a mechanistic, dynamic model of the microbial consortium. The balance of concentration of extracellular substrates and/or products of our microbial consortium are described by a system of ordinary differential equations (ODEs), and intracellular processes are modeled using genome scale metabolic models (GSMs) that contain all metabolic capabilities of each organism. The final model integra tes 2000 metabolites and 2442 reactions representing a broad range of processes (growth of each microorganism, metabolite production and utilization, transport between compartments, diffusion, etc). This model can be written by SBML and utilized by cobra in python. Our model are based on the model developed by Toulouse INSA-UPS.

Representation of the model

Figure 1. Representation of the dynamic coculture model.

Construction of the system of ODEs

Growth

The growth of each of the microorganisms is modeled using their growth rate $ \scriptsize{\mu ~(in~h^{-1})} $ $$ \scriptsize{\frac{dX_{cyano}}{dt}=X_{cyano}\cdot\mu_{cyano}} $$ $$ \scriptsize{\frac{dX_{yeast}}{dt}=X_{yeast}\cdot\mu_{yeast}} $$

Where $ \scriptsize{X_{cyano}} $ and $ \scriptsize{X_{yeast}} $ denote the biomass concentration for cyanobacteria and yeasts, respectively.

$\scriptsize{CO_2}$ gas transfer

The $\scriptsize{CO_2}$ balance can be represented by considering three processes: the input of $\scriptsize{CO_2}$ in the reactor provided by the bubbling of $\scriptsize{CO_2}$-enriched air ($\scriptsize{I_{CO_2}}$), the transfer of $\scriptsize{CO_2}$ from the gas to the liquid phase ($\scriptsize{T_{CO_2}}$) and finally the output of gas $\scriptsize{CO_2}$ outside of the reactors ($\scriptsize{O_{CO_2}}$) (Figure 1). $$ \scriptsize{\frac{d_{CO_2,g}}{dt}=I_{CO_2}-T_{CO_2}-O_{CO_2}} $$ $$ \scriptsize{I_{CO_2}=Q_{gas}\cdot CO_{2,input}} $$ $$ \scriptsize{T_{CO_2}=\kappa_l\alpha(\beta\cdot CO_{2,g}-CO_{2,l})} $$ $$ \scriptsize{O_{CO_2}=Q_{gas}\cdot CO_{2,g}} $$

Where $\scriptsize{CO_{2,g}}$and $\scriptsize{CO_{2,l}}$ are the $ \scriptsize{CO_2}$ concentrations in the gas and liquid phase respectively (in mM), $\scriptsize{Q_{gas}}$ is the flow of air bubbled in the reactor (in L.h-1), κlα is the global mass transfer coefficient of $ \scriptsize{CO_2}$ (in h-1) and β is Henry's law constant which models the gas-liquid equilibrium.

Carbon source uptake

In our co-culture system, cyano utilize $\scriptsize{CO_2}$ as carbon source while yeast utilize sucrose as carbon source. $$ \scriptsize{q_{CO_2,cyano}=q_{CO_2,cyano}^{max}\cdot(\frac{CO_{2,l}}{K_{CO_2}+CO_{2,l}})} $$ $$ \scriptsize{q_{sucrose,yeast}=q_{sucrose,yeast}^{max}\cdot(\frac{Sucrose}{K_{Sucrose}+Sucrose})} $$ $$ \scriptsize{\frac{d_{CO_2}}{dt}=T_{CO_2}-q_{CO_2,cyano}\cdot X_{cyano}+q_{CO_2,yeast}\cdot X_{yeast}} $$ $$ \scriptsize{\frac{d_{Sucrose}}{dt}=q_{sucrose,cyano}\cdot X_{cyano}-q_{sucrose,yeast}\cdot X_{yeast}} $$

Light

Light is an important aspect of our model. First, we converted the experimentally measured light intensity $\scriptsize{I_{light}}$ ($\scriptsize{\mu mol_{photon}\cdot m^{-2}\cdot s^{-1}}$) into a specific flux $\scriptsize{q_{photon}}$($\scriptsize{mmol_{photon}\cdot g_{DCW}^{-1}\cdot h^{-1}}$) using the reaction rate proposed by Clark et al.[1]: $$\scriptsize{q_{photon}=I_{light}\cdot \frac{3600\cdot Surface}{1000\cdot X_{cyano}\cdot Volume_{reactor}}}$$

Caffeic acid cycle

Each step of the caffeic cycle can be regarded as a first order reaction: $$ \scriptsize{\frac{d[caffeic~acid]}{dt}=q_{caffeic ~acdi}\cdot X_{yeast}-K_1\cdot [caffeic ~acid]+K_5\cdot [Caffeylpyruvic~acid]} $$ $$ \scriptsize{\frac{d[caffeoyl~CoA]}{dt}=K_1\cdot [caffeic~acid]} $$ $$ \scriptsize{\frac{d[hispidin]}{dt}=K_2\cdot [caffeoyl~CoA]} $$ $$ \scriptsize{\frac{d[3-Hydroxy-hispidin]}{dt}=K_3\cdot [hispidin]} $$ $$ \scriptsize{\frac{d[Caffeyl-pyruvic~acid]}{dt}=K_4\cdot [3-Hydroxy-hispidin]} $$

where $\scriptsize{q_{caffeic~acid}(mmol\cdot g_{DW}^{-1}\cdot h^{-1})}$​ represents the production rate of caffeic acid of interest.

Genome Scale Models

Flux Balance Analysis (FBA), a key method for simulating metabolic fluxes in silico, represents intracellular dynamics in our model using genome scale metabolic models (GSMs) [2]. FBA employs the GSM, which encompasses the metabolic network reconstruction, to forecast phenotypic responses under environmental constraints. In the equations mentioned, various fluxes, including growth rates and specific fluxes of odorant molecule production, are described, impacting the entire production process.

Our model of S.cerevisiae is based on the GSM iMM904 developed by Monica L Mo et al. in 2009 [3]. iMM904 is a basic model in yeast, containing 1226 metabolites and 1577 reactions. And for the S.elongatus, we chose model iJB785 developed by Jared T Broddrick et al. in 2016 [4]. This model contains 768 metabolites and 849 reactions. We further added 6 metabolites and 16 reactions to complete the system.

Figure 2. Escher map of model iMM904 from BIGG

AlphaFold2 Structure Prediction

Introduction

AlphaFold2 is an artificial intelligence software developed by DeepMind to predict the 3D structure of proteins. AlphaFold2 predicts with high enough accuracy to approximate experimental measurements. This power depends on a large enough database and a well-developed deep learning model. Specifically, it analyzes amino acid interactions and predicts how proteins are likely to fold through a technique called graph neural networks. By extracting and pairing feature information from protein-level structures, a deep learning model called “Transformer” is used to understand and interpret patterns in amino acid sequences and translate these structures into the 3D structure of the protein. Finally, optimization is performed to match the predicted pairs and distances [5].

Figure 3. Homepage of AlphaFold.

Design

In our experiments, we used AlphaFold2 colab to design a fusion protein we needed. According to our previous research, we need to fuse protein TUP1(Figure 4) and protein FHY1(Figure 5) together. What's more these two proteins should function themselves respectively. Protein TUP1 needs its N-terminal sequences to function normally [6]. When we simply put the sequences together, we found that TUP1 positioned through FHY1. And that wasn't what we need as we proposed that mixing structure of two proteins will cause functional loss. So we decided to choose a proper linker to link two proteins as well as separate them into two clear part in space.

Figure 4. 3D structure of TUP1.

Figure 5. 3D structure of FHY1.

Reference

[1] R.L. Clark, L.L. McGinley, H.M. Purdy, T.C. Korosh, J.L. Reed, T.W. Root, B.F. Pfleger, Light-optimized growth of cyanobacterial cultures: growth phases and productivity of biomass and secreted molecules in light-limited batch growth, Metabolic engineering, 47 (2018) 230-242.
[2] H.S. Choi, S.Y. Lee, T.Y. Kim, H.M. Woo, In silico identification of gene amplification targets for improvement of lycopene production, Applied and environmental microbiology, 76 (2010) 3097-3105.
[3] M.L. Mo, B.Ø. Palsson, M.J. Herrgård, Connecting extracellular metabolomic measurements to intracellular flux states in yeast, BMC systems biology, 3 (2009) 1-17.
[4] J.T. Broddrick, B.E. Rubin, D.G. Welkie, N. Du, N. Mih, S. Diamond, J.J. Lee, S.S. Golden, B.O. Palsson, Unique attributes of cyanobacterial metabolism revealed by improved genome-scale metabolic modeling and essential gene analysis, Proceedings of the National Academy of Sciences, 113 (2016) E8344-E8353.
[5] J. Jumper, R. Evans, A. Pritzel, T. Green, M. Figurnov, O. Ronneberger, K. Tunyasuvunakool, R. Bates, A. Žídek, A. Potapenko, Highly accurate protein structure prediction with AlphaFold, Nature, 596 (2021) 583-589.
[6] D. Tzamarias, K. Struhl, Functional dissection of the yeast Cyc8-Tupl transcriptional co-repressor complex, Nature, 369 (1994) 758-761.