Spatiotemporal modeling of microbial metabolism
Open accessAbstract
BACKGROUND: Microbial systems in which the extracellular environment varies both spatially and temporally are very common in nature and in engineering applications. While the use of genome-scale metabolic reconstructions for steady-state flux balance analysis (FBA) and extensions for dynamic FBA are common, the development of spatiotemporal metabolic models has received little attention. RESULTS: We present a general methodology for spatiotemporal metabolic modeling based on combining genome-scale reconstructions with fundamental transport equations that govern the relevant convective and/or diffusional processes in time and spatially varying environments. Our solution procedure involves spatial discretization of the partial differential equation model followed by numerical integration of the resulting system of ordinary differential equations with embedded linear programs using DFBAlab, a MATLAB code that performs reliable and efficient dynamic FBA simulations. We demonstrate our methodology by solving spatiotemporal metabolic models for two systems of considerable practical interest: (1) a bubble column reactor with the syngas fermenting bacterium Clostridium ljungdahlii; and (2) a chronic wound biofilm with the human pathogen Pseudomonas aeruginosa. Despite the complexity of the discretized models which consist of 900 ODEs/600 LPs and 250 ODEs/250 LPs, respectively, we show that the proposed computational framework allows efficient and robust model solution. CONCLUSIONS: Our study establishes a new paradigm for formulating and solving genome-scale metabolic models with both time and spatial variations and has wide applicability to natural and engineered microbial systems.
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Based on the C. ljungdahlii genome-scale model, spatiotemporal modeling of gas fermentation in a bubble column was performed recently.
“Based on the C. ljungdahlii GEM, spatiotemporal modeling of gas fermentation in a bubble column was performed recently (Chen et al., 2015, 2016).”
From Gas Fermentation—A Flexible Platform for Commercial Scale Production of Low-Carbon-Fuels and Chemicals from Waste and Renewable Feedstocks (2016) · cites this paper as Chen et al., 2016
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Cites
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“The limitations of steady-state metabolic models have been addressed through dynamic extensions of stoichiometric models and classical FBA [4 – 7].”
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ResultA reliable simulator for dynamic flux balance analysis
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MethodTranscriptomic Analysis of the Sulfate Starvation Response of Pseudomonas aeruginosa
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“the metabolic byproducts, especially succinate, which could potentially serve as a carbon source for aerobic growth in glucose depleted regimes at the top of the biofilm [43].”
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“Our predictions were in qualitative agreement with published experimental studies [27, 29, 30] showing that enhanced gas–liquid mass transfer increases gas consumption, the ethanol titer and the ethanol/acetate split.”
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ResultMetabolic modeling of synthesis gas fermentation in bubble column reactors
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“Genome-scale spatiotemporal models have been solved using table lookups of precomputed FBA solutions [11 – 13], lattice based descriptions of nutrient diffusion [14, 15] and agent-based simulations [16].”
MethodChronic Wound Colonization, Infection, and Biofilms
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MethodMeasurement of local effective diffusivity in heterogeneous biofilms
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Method
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BackgroundAdvances in flux balance analysis by integrating machine learning and mechanism-based models
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“As described in our previous publications [53, 54], we pursued a spatial discretization approach based on converting the PDEs into a large set of ordinary differential equations (ODEs) in time with embedded LPs (Fig.”
MethodNature’s recyclers: anaerobic microbial communities drive crude biomass deconstruction
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A structured evaluation of genome-scale constraint-based modeling tools for microbial consortia
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In silico metabolic engineering of Clostridium ljungdahlii for synthesis gas fermentation
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Genome-scale metabolic networks in time and space
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Microbially mediated climate feedbacks from wetland ecosystems
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“Biofilm models connect microbial activity (kinetic or stoichiometric) with diffusive transport to understand how diffusion gradients shape process outcomes at biofilm and soil aggregate scales (Batstone et al., 2006; Chen et al., 2016).”
BackgroundByproduct Cross Feeding and Community Stability in an In Silico Biofilm Model of the Gut Microbiome
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MethodGenome-scale modelling of microbial metabolism with temporal and spatial resolution
Henson, M. A. (2015) · Biochemical Society Transactions · doi:10.1042/bst20150146 · Cited by 30 · see citing works
“…with integration of the PDEs on a coarse spatial grid [61, 63, 65]; (M2) real-time FBA solution combined with lattice-based descriptions of metabolite transport [62, 64]; and (M3) spatial discretization of the PDEs followed by time integration of the resulting ODE/LP system (Figure 4) [60, 66].”
InfluentialTack, I. L. M. M., Nimmegeers, P., Akkermans, S., Hashem, I., & van Impe, J. F. M. (2017) · Frontiers in Microbiology · doi:10.3389/fmicb.2017.02509 · Cited by 29 · see citing works
“Over the last years, several models have been developed for the description of single species biofilm structures using information of genome-scale metabolic models (Biggs and Papin, 2013; Chen et al., 2016; Bauer et al., 2017).”
BackgroundIncorporating hydrodynamics into spatiotemporal metabolic models of bubble column gas fermentation
Li, X., Griffin, D. W., Li, X., & Henson, M. A. (2018) · Biotechnology and Bioengineering · doi:10.1002/bit.26848 · Cited by 28 · see citing works
“Our previous bubble column models (Chen et al., 2015, 2016) required the solution of ODE‐LP systems, while the current models required the solution of DAE‐LP systems due to the introduction of two‐phase hydrodynamics.”
MethodInfluentialLi, X., & Henson, M. A. (2019) · Biochemical Engineering Journal · doi:10.1016/j.bej.2019.107338 · Cited by 22 · see citing works
Ngu, V., Morchain, J., & Cockx, A. (2022) · Chemical Engineering Science · doi:10.1016/j.ces.2022.117478 · Cited by 21 · see citing works
Zieringer, J., & Takors, R. (2018) · Computational and Structural Biotechnology Journal · doi:10.1016/j.csbj.2018.06.002 · Cited by 20 · see citing works
Dynamic Flux Balance Analysis Using DFBAlab
Gomez, J. A., & Barton, P. I. (2017) · Methods in molecular biology · doi:10.1007/978-1-4939-7528-0_16 · Cited by 18 · see citing works
Song, H., Ahamed, F., Lee, J., Henry, C. S., Edirisinghe, J. N., Nelson, W. C., Chen, X., Moulton, D., & Scheibe, T. (2025) · Scientific Reports · doi:10.1038/s41598-025-89997-9 · Cited by 17 · see citing works
“While this numerical issue with the original dFBA may be relieved by using specially designed numerical solvers 10,25 , no special treatment was necessary for the ANN-based dFBA model.”
Siebler, F., Lapin, A., & Takors, R. (2020) · Engineering in Life Sciences · doi:10.1002/elsc.201900132 · Cited by 15 · see citing works
“Accordingly, simplifications are often made either by assuming ideal mixing, 1-D gas gradients [14] or dissembling the large bioreactor into numerous volumes [15–19].”
BackgroundInfluentialPeterson, J. R., Cole, J. A., & Luthey-Schulten, Z. A. (2017) · PLoS ONE · doi:10.1371/journal.pone.0182570 · Cited by 15 · see citing works
Kudva, A., Tang, W.-T., & Paulson, J. A. (2023) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2023.108515 · Cited by 14 · see citing works
Cadavid, J. L., Li, N. T., & McGuigan, A. P. (2024) · Biophysics Reviews · doi:10.1063/5.0179125 · Cited by 11 · see citing works
Metabolic Modeling of Clostridium difficile Associated Dysbiosis of the Gut Microbiota
Phalak, P., & Henson, M. A. (2019) · Processes · doi:10.3390/pr7020097 · Cited by 12 · see citing works
A Genome‐Scale Modeling Approach to Quantify Biofilm Component Growth of Salmonella Typhimurium
Ribaudo, N., Li, X., Brett, D., Wood, T. K., & Huang, Z. J. (2016) · Journal of Food Science · doi:10.1111/1750-3841.13565 · Cited by 11 · see citing works
Generalized Derivatives of Lexicographic Linear Programs
Gomez, J. A., Höffner, K., Khan, K. A., & Barton, P. I. (2018) · Journal of Optimization Theory and Applications · doi:10.1007/s10957-018-1309-2 · Cited by 10 · see citing works
Biophysical metabolic modeling of complex bacterial colony morphology
Dukovski, I., Golden, L., Zhang, J., Osborne, M. L., Segrè, D., & Korolev, K. S. (2024) · Cell Systems · doi:10.1016/j.cels.2025.101352 · Cited by 9 · see citing works
Patel, A., Carlson, R. P., & Henson, M. A. (2019) · Biotechnology Journal · doi:10.1002/biot.201800511 · Cited by 8 · see citing works
Dynamic Matrix Control of a Bubble‐Column Reactor for Microbial Synthesis Gas Fermentation
Fu, Y., Chang, L., Henson, M. A., & Liu, X. G. (2017) · Chemical Engineering & Technology · doi:10.1002/ceat.201600520 · Cited by 6 · see citing works
Nasershariat, M., Pishvaie, M. R., Boozarjomehry, R. B., & Waldherr, S. (2024) · Bioprocess and Biosystems Engineering · doi:10.1007/s00449-024-02966-w · Cited by 5 · see citing works
“In recent years, genome-scale models of intracellular reactions have also been used in combination with process models of bioreactors [17–19].”
Rees-Zimmerman, C. R., & Chaffin, S. T. (2021) · Biochemical Engineering Journal · doi:10.1016/j.bej.2021.108195 · Cited by 5 · see citing works
Multiscale Flux-Based Modeling of Biofilm Communities
Zhang, T., Parker, A. E., Carlson, R. P., Stewart, P. S., & Klapper, I. (2020) · Multiscale Modeling and Simulation · doi:10.1137/18m1234096 · Cited by 5 · see citing works
Pearl, J. E., Das, M., & Cooper, A. M. (2018) · Cellular and Molecular Immunology · doi:10.1038/cmi.2017.145 · Cited by 4 · see citing works
Discretised Flux Balance Analysis for Reaction–Diffusion Simulation of Single-Cell Metabolism
Chew, Y. H., & Spill, F. (2024) · Bulletin of Mathematical Biology · doi:10.1007/s11538-024-01264-6 · Cited by 3 · see citing works
“In this manner, our work differs from existing FBA methods that also extend to implement diffusion, because they coupled FBA with PDE or other methods to represent diffusion outside of the linear programming framework (Henson 2015; Chen et al. 2016; Borer et al. 2019; Dukovski et al. 2021).”
Interaction Steady State Transportation Network and Planning Optimization Model
Chen, B., Fu, D., & Yang, Y. (2019) · Advances in intelligent systems and computing · doi:10.1007/978-3-030-15235-2_105 · Cited by 3 · see citing works
Li, X., & Henson, M. A. (2021) · Journal of Applied Microbiology · doi:10.1111/jam.15155 · Cited by 3 · see citing works
“autoethanogenum, which synthesize acetate and ethanol as their primarily secreted byproducts (Phillips et al. 1993; Younesi et al. 2005; Köpke et al. 2010; Chen et al. 2015; Chen and Henson 2016; Chen et al. 2016; Valgepea et al. 2017b; Wan et al. 2017; Chen et al. 2018).”
BackgroundPhalak, P., Chen, J., Carlson, R. P., & Henson, M. A. (2016) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2016.12.099 · Cited by 3 · see citing works
Methods in Computational Biology
Carlson, R. P., & Sauro, H. M. (2019) · MDPI eBooks · doi:10.3390/books978-3-03921-164-7 · Cited by 2 · see citing works
Patel, A., Carlson, R. P., & Henson, M. A. (2021) · Biochemical Engineering Journal · doi:10.1016/j.bej.2021.108032 · Cited by 2 · see citing works
Klapper, I., Szyld, D. B., Yu, X., Zengler, K., Zhang, T., & Zúñiga, C. (2024) · SIAM Journal on Applied Mathematics · doi:10.1137/22m1511023 · Cited by 1 · see citing works
“There is some history of coupling FBA and related metabolic modeling methods with environmental models, sometimes termed dynamic flux balance analysis [25], see for example [7, 15, 18, 30, 41], though the connection to GNEPs has not been considered.”
MethodHenson, M. A., & Phalak, P. (2016) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2016.12.118 · Cited by 1 · see citing works
Construction of Calculation Model for Critical Safe Distance of Shared Lanes
Chen, B., Fu, D., & Yang, Y. (2019) · Advances in intelligent systems and computing · doi:10.1007/978-3-030-15740-1_93 · Cited by 1 · see citing works
Observability of Bacterial Growth Models in Bubble Column Bioreactors
Lecca, P., & Re, A. (2020) · Lecture notes in computer science · doi:10.1007/978-3-030-63061-4_27 · Cited by 1 · see citing works
Phalak, P., Bernstein, H. C., Lindemann, S. R., Renslow, R. S., Thomas, D., Henson, M. A., & Song, H. (2022) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2022.07.430 · Cited by 1 · see citing works
Towards the construction of GSMN-based community model for an oral biofilm
Winter, K. D., Ghesquière, J., Teughels, W., Waldherr, S., & Bernaerts, K. (2019) · IFAC-PapersOnLine · doi:10.1016/j.ifacol.2019.12.257 · Cited by 1 · see citing works
Flux-Balance Based Modeling of Biofilm CommunitiesPreprint
Zhang, T., Parker, A. E., Carlson, R. P., Stewart, P. S., & Klapper, I. (2018) · bioRxiv (Cold Spring Harbor Laboratory) · doi:10.1101/441311 · Cited by 1 · see citing works
“diffusion, and given fluxes of chemicals into cells, and a cellular level model which updates metabolic fluxes based on new influx bounds arising from updated chemical concentrations [10, 14, 21, 22, 24, 33, 36, 42, 47, 51].”
BackgroundCooperative metabolic resource allocation in spatially-structured systems
Tourigny, D. S. (2021) · Journal of Mathematical Biology · doi:10.1007/s00285-021-01558-6
Model-driven design of synthetic microbial communities for the upcycling of One-Carbon feedstocks
Benito-Vaquerizo, S. (2023) · doi:10.18174/630256
Nasershariat, M., Pishvaie, M. R., Boozarjomehry, R. B., & Waldherr, S. (2025) · ACS Sustainable Chemistry & Engineering · doi:10.1021/acssuschemeng.5c01815
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“…approach that integrates efficient steady-state simulations of metabolism with dynamic simulations of the propagation of biomass and metabolites (Dukovski et al., 2021; Harcombe et al., 2014; Bauer et al., 2017; Biggs and Papin, 2013; Cole et al., 2015; Chen et al., 2016; Borer et al., 2019).”
A 1D model for scale-up of CO2 fermentation to acetic acid in industrial scale bubble columns
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- Authors
- Chen, J., Gomez, J. A., Höffner, K., Phalak, P., Barton, P. I., & Henson, M. A.
- Affiliations
- University of Massachusetts Amherst (US)
- Massachusetts Institute of Technology (US)
- Corresponding author
- Henson, Michael A.
- Venue
- BMC Systems Biology
- Published
- 2016-03-01
- Volume
- 10
- Issue
- 1
- Pages
- 21-21
- ISSN
- 1752-0509 (ISSN-L)
- PMC
- PMC4774267
- OpenAlex
- W2290703973
- Cited by
- 69
- References
- 47
- Citations by year
- 2026: 3 · 2025: 4 · 2024: 5 · 2023: 4 · 2022: 2 · 2021: 10 · 2020: 6 · 2019: 8 · 2018: 7 · 2017: 11 · 2016: 8 · 2015: 1
- FWCI
- 5.89
- Type
- journal article
- Language
- en
- Open access
- gold
- doi.org
- Locations
- BMC Systems Biology (publishedVersion, cc-by)
- Europe PMC (PubMed Central) (publishedVersion, cc-by)
- PubMed Central (publishedVersion, cc-by)
- PubMed (publishedVersion)
- Funders
- National Science Foundation (1511346)
- National Institutes of Health (U01EB019416)
- Topics
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Microbial Metabolic Engineering and Bioproduction
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Bioinformatics and Genomic Networks
- Keywords
- dynamic flux balance analysis, genome-scale metabolic reconstruction, transport equation, partial differential equation model, bubble column, Clostridium ljungdahlii, syngas fermentation, Pseudomonas aeruginosa
- MeSH terms
- Biological Transport, Clostridium, Diffusion, Extracellular Space, Fermentation, Humans, Models, Biological, Pseudomonas aeruginosa, Biofilms, Genomics, Intracellular Space, Spatio-Temporal Analysis
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