Abstract

Desulfovibrio desulfuricans is a Gram-negative, anaerobic sulfate-reducing bacterium with applications in bioremediation and is likely to involve metabolic engineering and synthetic biology. Metabolic engineering and synthetic biology approaches are often guided by mathematical models. To date, no whole-cell kinetic model has been reported for this organism. In this study, we present an Ab initio whole-cell kinetic model of D. desulfuricans L4, ddsAAR26, comprising of 701 metabolites, 275 enzymes with associated transcription and translation processes and 573 enzymatic reactions, formulated as a system of ordinary differential equations. Enzymatic reactions are represented using Michaelis-Menten kinetics with median kinetic values. This establishes computational framework for future model refinement and extension.

Keywords: Whole-Cell Model; Kinetic Model; Differential Equations; AdvanceSyn Toolkit

Introduction

Sulfur is a highly dynamic element that cycles continuously between soil, water, microorganisms and living organisms. In oxygen-limited environments; such as wetlands, sediments and rice paddies; much of this cycling is driven by anaerobic microorganisms that use sulfate as a terminal electron acceptor and release hydrogen sulfide as a metabolic by-product [1]. Sulfate-Reducing Bacteria (SRB), including members of the genus Desulfovibrio are abundant in these environments and play a major role in shaping sulfur availability and redox conditions; thereby, linking environmental sulfur cycling to human exposure through soil, water and sulfur-rich foods [2,3]. Desulfovibrio desulfuricans is a Gram-negative, anaerobic, sulfate-reducing bacterium [4]. The anaerobic and nutrient-rich conditions of the human gastrointestinal tract closely resemble sedimentary environments, making it a suitable habitat for SRB. In the gut, Desulfovibrio species can reduce sulfate to hydrogen sulfide which may disrupt epithelial barrier integrity; thus, making sulfur metabolism a key determinant of gut homeostasis [2,5,6]. Hydrogen sulfide may influence the gut-brain axis through modulation of vagal signalling, mitochondrial function and neuroinflammatory pathways [3]. Elevated levels of Desulfovibrio species have been reported in neurodegenerative disorders such as Parkinson’s disease [7]. Besides human health, SRB including D. desulfuricans are also used in the industry, including wastewater treatment systems and bioremediation of sulfate-rich effluents and these efforts is likely to involve metabolic engineering and synthetic biology in the foreseeable future [8-19].

Metabolic engineering frequently relies on mathematical modelling to evaluate potential genetic interventions [20,21]. Good Statistical Monitorings (GSMs) and Knowledge Graphs (KGs) are the prevailing modelling styles in the field [22,23]. GSMs are useful for rate-based analyses but are not ideal for predicting yields or handling complex gene knock-ins [24]. KMs address these gaps: they can forecast yields and rates and make simulated knock-ins much easier to conduct [25]. This combination of capabilities positions KMs as a strong candidate for pre-experimental evaluation of engineering concepts. Consequently, there has been an increasing call in recent years to accelerate the development of new kinetic models [26,27].

However, there is no whole cell KM of D. desulfuricans to-date. As such, this study aims to construct a KM of D. desulfuricans L4 using Ab initio approach by identifying enzymes from its annotated genome and identifying the corresponding reaction from KEGG [28]. The result is a whole cell KM of D. desulfuricans L4, named as ddsAAR26 using the nomenclature proposed by Cho and Ling which consists of 701 metabolites, 275 enzymes with corresponding transcriptions and translations and 573 enzymatic reactions [29].

Materials and Methods

Identification of Reactome

The genome of Desulfovibrio desulfuricans L4 (NCBI RefSeq assembly GCF_017815575.1; NCBI GenBank Accession NZ_CP072608.1) was used as source to identify enzymatic genes using the process previously described [24,30,31]. Briefly, each enzymatic gene was identified as a presence of complete Enzyme Commission (EC) number in the GenBank record and mapped into reaction IDs via KEGG Ligand Database for Enzyme Nomenclature [28]. For example, EC 1.1.1.23 (https://www.genome.jp/entry/1.1.1.23) catalyses reactions R01158, R01163 and R03012; where the substrates and products of each rection can be identified.

Model Development

The model was developed using the Ordinary Differential Equation (ODE) formats described in Sim, et al. [32]. Estimating transcriptional activity in E. coli can be done directly using BioNumbers. The cell contains roughly 3000 RNA polymerases (BioNumbers 106199) and only about 25% are actively polymerizing (BioNumbers 111676) at 22 nt/s (BioNumbers 104109) [33-35]. With each nucleotide weighing 339.5 Da, the total output is ~5600 kDa/s (9.3×10⁻¹⁸ g/s). When this synthesis is expressed relative to a 7×10⁻¹⁶ L cell volume and 4225 genes (BioNumbers 105443), it yields 2.92 micromolar per gene per second [36]. Coupling this with an average transcript stability of 107.56 seconds (BioNumbers 107666) (0.93% decay per second), the resulting ODE is d[mRNA]/dt = 0.00292 – 0.0093[mRNA] [36-38]. Protein synthesis occurs at ~0.278 peptides/mRNA/s (BioNumbers 106382) while degradation is slow (2.78×10⁻⁶/s) (BioNumbers 109924) [39,40]. Thus, d[peptide]/dt = 0.278[mRNA]-0.00000278[peptide]. The whole biochemical network was encoded as ODEs using typical enzyme constants (kcat = 13.7 s⁻¹; Km = 1 mM) and aligned with the AdvanceSyn modelling framework [30,41-43].

Model Simulation

The constructed model was tested for simulatability using AdvanceSyn Toolkit [43]. Initial concentrations of all mRNA and enzymes were set to 0 mM. Initial concentrations of all metabolites were set to 1 mM except the following which were set to 1000 mM: (I) C00001 (Water), (II) C00002 (ATP), (III) C00003 (NAD+), (IV) C00004 (NADH), (V) C00005 (NADPH), (VI) C00006 (NADP+), (VII) C00007 (Oxygen), (VIII) C00011 (Carbon Dioxide), (IX) C00016 (FAD), (X) C00024 (Acetyl-CoA), (XI) C00025 (L-Glutamate), (XII) C00026 (2-Oxoglutarate), (XIII) C00029 (UDP-glucose), (XIV) C00033 (Acetate), (XV) C00039 (DNA), (XVI) C00043 (UDP-N-Acetyl-Alpha-D-Glucosamine), (XVII) C00045 (Amino Acid), (XVIII) C00048 (Glyoxylate), (XIX) C00051 (Glutathione), (XX) C00063 (CTP), (XXI) C00065 (L-Serine), (XXII) C00066 (tRNA), (XXIII) C00074 (Phosphoenolpyruvate), (XXIV) C00079 (L-Phenylalanine), (XXV) C00080 (H+), (XXVI) C00084 (Acetaldehyde), (XXVII) C00093 (sn-Glycerol 3-Phosphate), (XXVIII) C00125 (Ferricytochrome c), (XXIX) C00149 ((S)-Malate), (XXX) C00188 (L-Threonine). The model was simulated using the fourth-order Runge-Kutta method from time zero to 3600 seconds with timestep of 0.1 second and the concentrations of metabolites were bounded between 0 millimolar and 1000 millimolar. The simulation results were sampled every 2 seconds [44,45].

Results and Discussion

As of 29 April 2024, the annotated genome of D. desulfuricans L4 consists of 3030 genes, including 2943 protein coding sequences. 275 unique EC numbers consisting of 573 enzymatic reactions involving 701 metabolites were identified and developed into a model based on AdvanceSyn Model Specification [43]. In addition, 550 ODEs acting as placeholder for enzyme transcriptions and translations were added.

Using the AdvanceSyn Toolkit [43], we executed the ddsAAR26 system and verified successful simulation through the trajectories displayed in Fig. 1. This validation confirms that the model is syntactically clean and structurally coherent as argued by previous studies constructions [24,31,46-48], which is a necessary foundation for future biological refinement. Although the relative concentrations of Adenosine Diphosphate (ADP) and coenzyme A appears elevated, this may reflect the imposed uniformity of median kinetic constants, which were chosen to allow structural validation before detailed parameterization [42]. Therefore, such results should therefore not be viewed as physiologically meaningful outputs. Instead, this model establishes a working whole-cell kinetic framework for D. desulfuricans L4 that is ready for enrichment with additional pathways, regulatory circuits or organism-specific kinetic datasets to support more realistic simulations [49-51].

Figure 1. Selection of simulation results.

Conclusion

In this study, we present an Ab initio whole cell kinetic model of Desulfovibrio desulfuricans L4, ddsAAR26; comprising of 701 metabolites, 275 enzymes with corresponding transcriptions and translations and 573 enzymatic reactions.

Conflict of Interest

The authors declared no potential conflicts of interest with respect to the research, authorship and/or publication of this article.

Funding details

None.

Ethical Approval

The project did not meet the definition of human subject research under the purview of the IRB according to federal regulations and therefore, was exempt.

Acknowledgment

The authors wish to thank the institute, Management Development Institute of Singapore, for its support towards this work. The cost of publication fees was borne by the authors.

Supplementary Materials

Reaction descriptions and model can be download from https://bit.ly/ddsAAR26.

References

1. Pester M, Knorr KH, Friedrich MW, Wagner M, Loy A. Sulfate-reducing microorganisms in wetlands-fameless actors in carbon cycling and climate change. Front Microbiol. 2012;3:72.
2. Singh SB, Carroll-Portillo A, Lin HC. Desulfovibrio in the gut: the enemy within? Microorganisms. 2023;11(7):1772.
3. Birg A, Lin HC. The role of bacteria-derived hydrogen sulfide in multiple axes of disease. Int J Mol Sci. 2025;26(7):3340.
4. Warren YA, Citron DM, Merriam CV, Goldstein EJC. Biochemical differentiation and comparison of Desulfovibrio species and other phenotypically similar genera. J Clin Microbiol. 2005;43(8):4041-5.
5. Buret AG, Allain T, Motta JP, Wallace JL. Effects of hydrogen sulfide on the microbiome: from toxicity to therapy. Antioxid Redox Signal. 2022;36(4-6):211-9.
6. Kushkevych I, Dordevic D, Vitezova M. Possible synergy effect of hydrogen sulfide and acetate produced by sulfate-reducing bacteria on inflammatory bowel disease development. J Adv Res. 2021;27:71-8.
7. Murros KE. Hydrogen sulfide produced by gut bacteria may induce Parkinson’s disease. Cells. 2022;11(6):978.
8. Joo JO, Choi JH, Kim IH, Kim YK, Oh BK. Effective bioremediation of cadmium(II), nickel(II) and chromium(VI) in a marine environment using Desulfovibrio Biotechnol Bioprocess Eng. 2015;20(5):937-41.
9. Zhou L, Bai N, Xiao R, Yang Z, Jiang G, Yin H, et al. Unlocking the bioremediation potential of adapted Desulfovibrio desulfuricans in acidic low-temperature uranium-contaminated groundwater. J Environ Sci. 2025;155:303-15.
10. Zhang P, Wei C, Yang F. Optimization of growth conditions of Desulfovibrio desulfuricans strain REO-01 and evaluation of its Cd(II) bioremediation potential. Microorganisms. 2025;13(7):1511.
11. Chen Q, Min Q, Wu H, Zhang L, Si Y. Biomineralization of Cd²⁺ and Pb²⁺ by sulfate-reducing bacteria Desulfovibrio desulfuricans and Desulfobulbus propionicus. Front Environ Sci. 2025;13:1591564.
12. Zhao B, Chen X, Chen H, Zhang L, Li J, Guo Y, et al. Biomineralization of uranium by Desulfovibrio desulfuricans A3-21ZLL under various hydrochemical conditions. Environ Res. 2023;237(Pt 2):116950.
13. Enning D, Garrelfs J. Corrosion of iron by sulfate-reducing bacteria: new views of an old problem. Appl Environ Microbiol. 2014;80(4):1226-36.
14. Nikel PI, De Lorenzo V. Metabolic engineering for large-scale environmental bioremediation. In: Nielsen J, Stephanopoulos G, Lee SY, editors. Metabolic Engineering. 1^st Wiley. 2021:859-90.
15. Sharma B, Shukla P. Futuristic avenues of metabolic engineering techniques in bioremediation. Biotechnol Appl Biochem. 2022;69(1):51-60.
16. Jiang T, Montgomery VA, Jetty K, Ganesan V, Incha MR, Gladden JM, et al. Metabolic engineering and synthetic biology for the environment. Biotechnol Environ. 2025;2(1):14.
17. Ruan Z, Chen K, Cao W, Meng L, Yang B, Xu M, et al. Engineering natural microbiomes toward enhanced bioremediation by microbiome modeling. Nat Commun. 2024;15(1):4694.
18. Rylott EL, Bruce NC. How synthetic biology can help bioremediation. Curr Opin Chem Biol. 2020;58:86-95.
19. Lea-Smith DJ, Hassard F, Coulon F, Partridge N, Horsfall L, Parker KDJ, et al. Engineering biology applications for environmental solutions: potential and challenges. Nat Commun. 2025;16(1):3538.
20. Khanijou JK, Kulyk H, Berges C, Khoo LW, Ng P, Yeo HC, et al. Metabolomics and modelling approaches for systems metabolic engineering. Metab Eng Commun. 2022;15:e00209.
21. Gudmundsson S, Nogales J. Recent advances in model-assisted metabolic engineering. Curr Opin Syst Biol. 2021;28:100392.
22. Richelle A, David B, Demaegd D, Dewerchin M, Kinet R, Morreale A, et al. Towards widespread adoption of metabolic modeling tools in the biopharmaceutical industry. NPJ Syst Biol Appl. 2020;6(1):6.
23. Lee YQ, Choi YM, Park SY, Kim SK, Lee M, Kim D, et al. Genome-scale metabolic model-guided framework for designing customized live biotherapeutic products. NPJ Syst Biol Appl. 2025;11(1):73.
24. Yeo KY, Arivazhagan M, Senthilkumar A, Saisudhanbabu T, Le MA, Wong B, et al. Ab initio whole-cell kinetic model of Yarrowia lipolytica CLIB122. Medicon Med Sci. 2025;8(4):1-6.
25. Prabhu S, Kosir N, Kothare MV, Rangarajan S. Derivative-free domain-informed data-driven discovery of sparse kinetic models. Ind Eng Chem Res. 2025;64(5):2601-15.
26. Foster CJ, Wang L, Dinh HV, Suthers PF, Maranas CD. Building kinetic models for metabolic engineering. Curr Opin Biotechnol. 2021;67:35-41.
27. Lazaro J, Wongprommoon A, Julvez J, Oliver SG. Enhancing genome-scale metabolic models with kinetic data. Bioinform Adv. 2025;5(1):vbaf166.
28. Okuda S, Yamada T, Hamajima M, Itoh M, Katayama T, Bork P, et al. KEGG Atlas mapping for global analysis of metabolic pathways. Nucleic Acids Res. 2008;36(Web Server issue):W423-6.
29. Cho JL, Ling MH. Adaptation of whole-cell kinetic model template UniKin1 to Escherichia coli. EC Microbiol. 2021;17(2):254-60.
30. Kwan ZJ, Teo W, Lum AK, Ng SM, Ling MH. Ab initio whole-cell kinetic model of Stutzerimonas balearica DSM 6083. Acta Sci Microbiol. 2024;7(2):28-31.
31. Maiyappan S, Sim SS, Ramesh G, Low L, Matarage ML, Ling MH. Four Ab initio whole-cell kinetic models of Bacillus subtilis strains. J Clin Immunol Microbiol. 2025;6(2):1-6.
32. Sim BJH, Tan NTF, Ling MHT. Multilevel metabolic modelling using ordinary differential equations. In: Ranganathan S, Cannataro M, Khan AM, editors. Encyclopedia of Bioinformatics and Computational Biology. 2^nd Elsevier. 2025;491-8.
33. Muller-Hill B. The lac operon: a short history of a genetic paradigm. Berlin: Springer. 1996.
34. Churchward G, Bremer H, Young R. Transcription in bacteria at different DNA concentrations. J Bacteriol. 1982;150(2):572-81.
35. Gray WJ, Midgley JE. Control of RNA synthesis in bacteria. Biochem J. 1971;122(2):161-9.
36. Kubitschek HE. Cell volume increase in Escherichia coli after shifts to richer media. J Bacteriol. 1990;172(1):94-101.
37. Hu P, Janga SC, Babu M, Diaz-Mejia JJ, Butland G, Yang W, et al. Global functional atlas of Escherichia coli. PLoS Biol. 2009;7(4):e96.
38. So LH, Ghosh A, Zong C, Sepulveda LA, Segev R, Golding I. General properties of transcriptional time series in Escherichia coli. Nat Genet. 2011;43(6):554-60.
39. Schwanhausser B, Busse D, Li N, Dittmar G, Schuchhardt J, Wolf J, et al. Global quantification of mammalian gene expression control. Nature. 2013;495(7439):126-7.
40. Maurizi MR. Proteases and protein degradation in Escherichia coli. Experientia. 1992;48(2):178-201.
41. Murthy MV, Balan D, Kamarudin NJ, Wang VC, Tan XT, Ramesh A, et al. UniKin1: A universal whole-cell kinetic model. Acta Sci Microbiol. 2020;3(10):4-8.
42. Bar-Even A, Noor E, Savir Y, Liebermeister W, Davidi D, Tawfik DS, et al. The moderately efficient enzyme. Biochemistry. 2011;50(21):4402-10.
43. Ling MH. AdvanceSyn toolkit: An open-source suite for model development. MOJ Proteomics Bioinform. 2020;9(4):83-6.
44. Yong B. Comparison of fourth-order Runge-Kutta and homotopy analysis methods. J Phys Conf Ser. 2019;1317:012020.
45. Ling MH. COPADS IV: Fixed time-step ODE solvers implemented in Python. Adv Comput Sci Int J. 2016;5(3):5-11.
46. Senthilkumar A, Madhunisha A, Yeo KY, Saisudhanbabu T, Le MA, Wong TB, et al. Ab initio whole-cell kinetic model of Lactobacillus acidophilus NCFM. J Clin Immunol Microbiol. 2025;6(1):1-5.
47. Wong TB, Le MA, Arivazhagan M, Senthilkumar A, Yeo KY, Saisudhanbabu T, et al. Ab initio whole-cell kinetic models of Escherichia coli Scholastic Med Sci. 2025;3(2):1-4.
48. Ambel WB, Tan LP, Toh D, Thirunavukarasu D, Natarajan K, Ling MH. UniKin2: A universal pan-reactome kinetic model. Int J Res Med Clin Sci. 2025;3(2):77-80.
49. Ahn-Horst TA, Mille LS, Sun G, Morrison JH, Covert MW. Expanded whole-cell model of E. coli. NPJ Syst Biol Appl. 2022;8(1):30.
50. Chagas MS, Trindade Dos Santos M, Argollo de Menezes M, da Silva FAB. Boolean model of gene regulatory network of Pseudomonas aeruginosa. Front Microbiol. 2023;14:1274740.
51. Hao T, Song Z, Zhang M, Zhang L, Yang J, Li J, et al. Reconstruction of metabolic-protein interaction network of Eriocheir sinensis. Genes. 2024;15(4):410.