Abstract
Chemical space exploration is an important part of chemistry and biology, enabling the discovery and optimization of metabolic pathways, advancing synthetic metabolic functions, and understanding biochemical network evolution. We use a graph-based computational approach implemented in the cheminformatics software MØD, integrated with Integer Linear Programming (ILP) optimization, to systematically search chemical spaces. This approach allows for flexible and targeted queries, including identification of autocatalytic cycles, thermodynamic considerations, and discovery of novel enzymatic cascades. Specifically, we explore the chemical space of natural and artificial carbon fixation pathways defined from relevant enzyme reactions. By applying different optimization criteria, we identify new varieties and recombinations of natural autocatalytic pathways, and compare the properties of the pathways. This work highlights the versatility of graph-based cheminformatics for the purpose of chemical space exploration and artificial pathway design. Potential applications of this framework extend to carbon capture technologies, improved agricultural yields, and value-added chemical production, advancing efforts to address global sustainability challenges.
Similar content being viewed by others
Data availability
The datasets generated and analyzed during the current study, as well as the underlying code are available in the GitHub repository https://github.com/anne-susann/C_fixation_pathway_design.
References
Burkart, M. D., Hazari, N., Tway, C. L. & Zeitler, E. L. Opportunities and Challenges for Catalysis in Carbon Dioxide Utilization. ACS Catal. 9, 7937–7956 (2019).
Yusuf, N., Almomani, F. & Qiblawey, H. Catalytic CO2 conversion to C1 value-added products: Review on latest catalytic and process developments. Fuel 345, 128178 (2023).
Bar-Even, A., Flamholz, A., Noor, E. & Milo, R. Thermodynamic constraints shape the structure of carbon fixation pathways. Biochimica et. Biophysica Acta (BBA) - Bioenerg. 1817, 1646–1659 (2012).
Bar-Even, A., Noor, E. & Milo, R. A survey of carbon fixation pathways through a quantitative lens. J. Exp. Bot. 63, 2325–2342 (2012).
Evans, M. C., Buchanan, B. B. & Arnon, D. I. A new ferredoxin-dependent carbon reduction cycle in a photosynthetic bacterium. Proc. Natl. Acad. Sci. 55, 928–934 (1966).
Benson, A. A. et al. The path of carbon in photosynthesis: XV. Ribulose and sedoheptulose.J. Biol. Chem. 196, 703–716 (1952).
Ragsdale, S. W. The Eastern and Western branches of the Wood/Ljungdahl pathway: how the East and West were won. BioFactors 6, 3–11 (1997).
Berg, I. A., Kockelkorn, D., Buckel, W. & Fuchs, G. A 3-hydroxypropionate/4-hydroxybutyrate autotrophic carbon dioxide assimilation pathway in Archaea. Sci. (N. Y., N.Y.) 318, 1782–1786 (2007).
Huber, H. et al. A dicarboxylate/4-hydroxybutyrate autotrophic carbon assimilation cycle in the hyperthermophilic Archaeum Ignicoccus hospitalis. Proc. Natl. Acad. Sci. 105, 7851–7856 (2008).
Zarzycki, J., Brecht, V., Müller, M. & Fuchs, G. Identifying the missing steps of the autotrophic 3-hydroxypropionate CO2 fixation cycle in Chloroflexus aurantiacus. Proc. Natl. Acad. Sci. 106, 21317–21322 (2009).
Figueroa, I. A. et al. Metagenomics-guided analysis of microbial chemolithoautotrophic phosphite oxidation yields evidence of a seventh natural CO2 fixation pathway. Proc. Natl. Acad. Sci. 115, E92–E101 (2018).
Zhao, T., Li, Y. & Zhang, Y. Biological carbon fixation: a thermodynamic perspective. Green. Chem. 23, 7852–7864 (2021).
Santos Correa, S., Schultz, J., Lauersen, K. J. & Soares Rosado, A. Natural carbon fixation and advances in synthetic engineering for redesigning and creating new fixation pathways. J. Adv. Res. 47, 75–92 (2023).
Barenholz, U. et al. Design principles of autocatalytic cycles constrain enzyme kinetics and force low substrate saturation at flux branch points. eLife 6, e20667 (2017).
Luo, S. et al. A cell-free self-replenishing CO2-fixing system. Nat. Catal. 5, 154–162 (2022).
Schwander, T., Schada von Borzyskowski, L., Burgener, S., Cortina, N. S. & Erb, T. J. A synthetic pathway for the fixation of carbon dioxide in vitro. Science 354, 900–904 (2016).
McLean, R. et al. Exploring alternative pathways for the in vitro establishment of the HOPAC cycle for synthetic CO2 fixation. Sci. Adv. 9, eadh4299 (2023).
Löwe, H. & Kremling, A. In-Depth Computational Analysis of Natural and Artificial Carbon Fixation Pathways. BioDesign Res. 2021, 9898316 (2021).
Andersen, J. L., Flamm, C., Merkle, D. & Stadler, P. F. A Software Package for Chemically Inspired Graph Transformation. In Echahed, R. & Minas, M. (eds.) Graph Transformation, 73–88 (Springer International Publishing, Cham, 2016).
Andersen, J. L., Flamm, C., Merkle, D. & Stadler, P. F. Chemical Transformation Motifs–Modelling Pathways as Integer Hyperflows. IEEE/ACM Trans. Computational Biol. Bioinforma. 16, 510–523 (2019).
Ni, Z., Stine, A. E., Tyo, K. E. & Broadbelt, L. J. Curating a comprehensive set of enzymatic reaction rules for efficient novel biosynthetic pathway design. Metab. Eng. 65, 79–87 (2021).
Machado, D. et al. Modeling formalisms in Systems Biology. AMB Express 1, 45 (2011).
Flamholz, A., Noor, E., Bar-Even, A. & Milo, R. eQuilibrator–the biochemical thermodynamics calculator. Nucleic Acids Res. 40, D770–D775 (2012).
Beber, M. E. et al. eQuilibrator 3.0: a database solution for thermodynamic constant estimation. Nucleic Acids Res. 50, D603–D609 (2022).
Xiao, L. et al. A Minimized Synthetic Carbon Fixation Cycle. ACS Catal. 12, 799–808 (2022).
Bar-Even, A., Noor, E., Lewis, N. E. & Milo, R. Design and analysis of synthetic carbon fixation pathways. Proc. Natl. Acad. Sci. 107, 8889–8894 (2010).
Kanehisa, M. et al. KEGG for linking genomes to life and the environment. Nucleic Acids Res. 36, D480–D484 (2008).
Shen, C. R. et al. Driving Forces Enable High-Titer Anaerobic 1-Butanol Synthesis in Escherichia coli. Appl. Environ. Microbiol. 77, 2905–2915 (2011).
Sperl, J. M. & Sieber, V. Multienzyme Cascade Reactions–Status and Recent Advances. ACS Catal. 8, 2385–2396 (2018).
Cutlan, R., De Rose, S., Isupov, M. N., Littlechild, J. A. & Harmer, N. J. Using enzyme cascades in biocatalysis: Highlight on transaminases and carboxylic acid reductases. Biochimica et. Biophysica Acta (BBA) - Proteins Proteom. 1868, 140322 (2020).
Benítez-Mateos, A. I., Roura Padrosa, D. & Paradisi, F. Multistep enzyme cascades as a route towards green and sustainable pharmaceutical syntheses. Nat. Chem. 14, 489–499 (2022).
Hellgren, J., Godina, A., Nielsen, J. & Siewers, V. Promiscuous phosphoketolase and metabolic rewiring enables novel non-oxidative glycolysis in yeast for high-yield production of acetyl-CoA derived products. Metab. Eng. 62, 150–160 (2020).
Müller, S., Flamm, C. & Stadler, P. F. What makes a reaction network “chemical”? J. Cheminformatics 14, 63 (2022).
Andersen, J. L., Flamm, C., Merkle, D. & Stadler, P. F. Generic Strategies for Chemical Space Exploration http://arxiv.org/abs/1302.4006 ArXiv:1302.4006 [cs, q-bio] (2014).
Andersen, J. L. & Merkle, D. A Generic Framework for Engineering Graph Canonization Algorithms. In 2018 Proceedings of the Meeting on Algorithm Engineering and Experiments (ALENEX), Proceedings, 139–153 (Society for Industrial and Applied Mathematics, 2018).
Himsolt, M. GML: A portable graph file format. Tech. Rep., Technical report, Universitat Passau (1997).
Andersen, J. L., Flamm, C., Merkle, D. & Stadler, P. F. Defining Autocatalysis in Chemical Reaction Networks. J. Syst. Chem. 8, 121–133 (2020).
Muller, P. Glossary of terms used in physical organic chemistry (IUPAC Recommendations 1994). Pure Appl. Chem. 66, 1077–1184 (1994).
Orth, J. D., Thiele, I. & Palsson, B. What is flux balance analysis? Nat. Biotechnol. 28, 245–248 (2010).
Gurobi Optimization, LLC. Gurobi Optimizer Reference Manual https://www.gurobi.com (2024).
Forst, C. V., Flamm, C., Hofacker, I. L. & Stadler, P. F. Algebraic comparison of metabolic networks, phylogenetic inference, and metabolic innovation. BMC Bioinforma. 7, 67 (2006).
Noor, E., Haraldsdóttir, H. S., Milo, R. & Fleming, R. M. T. Consistent Estimation of Gibbs Energy Using Component Contributions. PLOS Computational Biol. 9, e1003098 (2013).
Jankowski, M. D., Henry, C. S., Broadbelt, L. J. & Hatzimanikatis, V. Group Contribution Method for Thermodynamic Analysis of Complex Metabolic Networks. Biophysical J. 95, 1487–1499 (2008).
Acknowledgements
We thank Prof. Annette Taylor (University of South Hampton) for scientific discussions and her input on the manuscript. This project was funded by the European Unions Horizon Europe Doctoral Network program under the Marie-Skłodowska-Curie grant agreement No 101072930 (TACsy - Training Alliance for Computational systems chemistry). The funder played no role in study design, analysis, and interpretation of the data.
Author information
Authors and Affiliations
Contributions
C.F., R.F., J.L.A., D.M. conceptualized and supervised the study. J.L.A., N.L., and C.F. provided the computational framework, and with A-S.A. they designed the set-up and experiments. A-S.A. implemented and performed the computational experiments, the data analysis, and the writing and editing of the paper. C.F., R.F., J.L.A., and D.M. revised and with N.L. edited the manuscript.
Corresponding authors
Ethics declarations
Competing interests
The authors declare no competing interests.
Additional information
Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary information
Rights and permissions
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
About this article
Cite this article
Abel, AS., Lauber, N., Andersen, J.L. et al. Computational approaches in chemical space exploration for carbon fixation pathways. npj Syst Biol Appl (2026). https://doi.org/10.1038/s41540-025-00641-8
Received:
Accepted:
Published:
DOI: https://doi.org/10.1038/s41540-025-00641-8


