{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T12:11:41Z","timestamp":1789560701920,"version":"build-2803163510"},"reference-count":190,"publisher":"Oxford University Press (OUP)","license":[{"start":{"date-parts":[[2026,8,17]],"date-time":"2026-08-17T00:00:00Z","timestamp":1786924800000},"content-version":"am","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001659","name":"German Research Foundation","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001659","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>Advances in computational power and structured representation of biochemical knowledge have fostered the development and use of models of plant metabolic pathways of increasing complexity. These advances have pointed out knowledge gaps for parameters inherent to these models and the need for large-scale data sets to conduct effective model calibrations. This bottleneck hampers wider application of plant metabolic models in plant biotechnology and crop breeding. Here, we argue that the recent advances in artificial intelligence offer the means for efficient model parameterization while strategically guiding the use of resources for data generation to increase precision of parameter values. We focus on surrogate models that have been applied with both stoichiometric and kinetic metabolic models as well as recent machine learning approaches for model parameterization using different data inputs. The review not only showcases applications with plant metabolic pathways, but also points out recent examples from non-plant and chemical systems that can be readily adopted in the study of plant metabolism. Finally, we point out limitations and future directions that may deepen the synergies between machine\/deep learning and mechanistic metabolic models to enable predictions of and mitigating actions for plant responses adapted to future climate scenarios.<\/jats:p>","DOI":"10.1093\/jxb\/erag400","type":"journal-article","created":{"date-parts":[[2026,8,12]],"date-time":"2026-08-12T11:44:18Z","timestamp":1786535058000},"source":"Crossref","is-referenced-by-count":0,"title":["Machine learning for mechanistic modeling of plant metabolic pathways"],"prefix":"10.1093","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-0155-6217","authenticated-orcid":false,"given":"Philipp","family":"Wendering","sequence":"first","affiliation":[{"name":"Bioinformatics Department, Institute of Biochemistry and Biology, University of Potsdam , Potsdam 14476 ,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2671-6763","authenticated-orcid":false,"given":"Zoran","family":"Nikoloski","sequence":"additional","affiliation":[{"name":"Bioinformatics Department, Institute of Biochemistry and Biology, University of Potsdam , Potsdam 14476 ,","place":["Germany"]},{"name":"Systems Biology and Mathematical Modeling, Max Planck Institute of Molecular Plant Physiology , Potsdam 14476 ,","place":["Germany"]}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"286","published-online":{"date-parts":[[2026,8,17]]},"reference":[{"key":"2026091607563551100_erag400-B1","doi-asserted-by":"crossref","first-page":"1118","DOI":"10.3389\/fpls.2017.01118","article-title":"CERES\u2013maize model for determining the optimum planting dates of early maturing maize varieties in northern Nigeria","volume":"8","author":"Adnan","year":"2017","journal-title":"Frontiers in Plant Science"},{"key":"2026091607563551100_erag400-B2","doi-asserted-by":"crossref","first-page":"384","DOI":"10.1016\/j.compag.2016.03.015","article-title":"Calibration and validation of APSIM-wheat and CERES-wheat for spring wheat under rainfed conditions: models evaluation and application","volume":"123","author":"Ahmed","year":"2016","journal-title":"Computers and Electronics in Agriculture"},{"key":"2026091607563551100_erag400-B3","doi-asserted-by":"crossref","first-page":"11437","DOI":"10.1038\/s41598-021-90835-x","article-title":"A time-dependent parameter estimation framework for crop modeling","volume":"11","author":"Akhavizadegan","year":"2021","journal-title":"Scientific Reports"},{"key":"2026091607563551100_erag400-B4","doi-asserted-by":"crossref","first-page":"158","DOI":"10.1016\/j.ymben.2015.10.002","article-title":"ISCHRUNK\u2014in silico approach to characterization and reduction of uncertainty in the kinetic models of genome-scale metabolic networks","volume":"33","author":"Andreozzi","year":"2016","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B5","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.cherd.2022.01.041","article-title":"Physics-informed neural networks for hybrid modeling of lab-scale batch fermentation for \u03b2-carotene production using Saccharomyces cerevisiae","volume":"179","author":"Bangi","year":"2022","journal-title":"Chemical Engineering Research & Design"},{"key":"2026091607563551100_erag400-B6","doi-asserted-by":"crossref","first-page":"27","DOI":"10.1016\/bs.agron.2015.11.004","article-title":"A comprehensive review of the CERES-wheat, -maize and -rice models\u2019 performances","volume":"136","author":"Basso","year":"2016","journal-title":"Advances in Agronomy"},{"key":"2026091607563551100_erag400-B7","first-page":"1","article-title":"Automatic differentiation in machine learning: a survey","volume":"18","author":"Baydin","year":"2018","journal-title":"Journal of Machine Learning Research"},{"key":"2026091607563551100_erag400-B8","doi-asserted-by":"crossref","first-page":"12663","DOI":"10.1073\/pnas.0609845104","article-title":"Intracellular crowding defines the mode and sequence of substrate uptake by Escherichia coli and constrains its metabolic activity","volume":"104","author":"Beg","year":"2007","journal-title":"Proceedings of the National Academy of Sciences, USA"},{"key":"2026091607563551100_erag400-B9","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1186\/s12859-019-3329-9","article-title":"Automatic construction of metabolic models with enzyme constraints","volume":"21","author":"Bekiaris","year":"2020","journal-title":"BMC Bioinformatics"},{"key":"2026091607563551100_erag400-B10","doi-asserted-by":"crossref","first-page":"1180","DOI":"10.1111\/pce.12560","article-title":"An Excel tool for deriving key photosynthetic parameters from combined gas exchange and chlorophyll fluorescence: theory and practice","volume":"39","author":"Bellasio","year":"2016","journal-title":"Plant, Cell & Environment"},{"key":"2026091607563551100_erag400-B11","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1007\/s11120-018-0601-1","article-title":"A generalised dynamic model of leaf-level C3 photosynthesis combining light and dark reactions with stomatal behaviour","volume":"141","author":"Bellasio","year":"2019","journal-title":"Photosynthesis Research"},{"key":"2026091607563551100_erag400-B12","doi-asserted-by":"crossref","DOI":"10.1002\/9783527806461","volume-title":"Enzyme kinetics: principles and methods","author":"Bisswanger","year":"2017"},{"key":"2026091607563551100_erag400-B13","doi-asserted-by":"crossref","first-page":"2072","DOI":"10.1038\/s41467-025-57215-9","article-title":"CatPred: a comprehensive framework for deep learning in vitro enzyme kinetic parameters","volume":"16","author":"Boorla","year":"2025","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B14","first-page":"3043","volume-title":"Computer Aided Chemical Engineering","author":"Borisyak","year":"2024"},{"key":"2026091607563551100_erag400-B15","doi-asserted-by":"crossref","first-page":"16330","DOI":"10.1021\/acs.iecr.1c00552","article-title":"Two-stage approach to parameter estimation of differential equations using neural ODEs","volume":"60","author":"Bradley","year":"2021","journal-title":"Industrial & Engineering Chemistry Research"},{"key":"2026091607563551100_erag400-B16","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1007\/s40139-020-00216-8","article-title":"Acceleration of PDE-based biological simulation through the development of neural network metamodels","volume":"8","author":"Burzawa","year":"2020","journal-title":"Current Pathobiology Reports"},{"key":"2026091607563551100_erag400-B17","doi-asserted-by":"crossref","first-page":"3344","DOI":"10.1111\/pce.14815","article-title":"A guide to photosynthetic gas exchange measurements: fundamental principles, best practice and potential pitfalls","volume":"47","author":"Busch","year":"2024","journal-title":"Plant, Cell & Environment"},{"key":"2026091607563551100_erag400-B18","doi-asserted-by":"crossref","first-page":"e0170523","DOI":"10.1128\/spectrum.01705-23","article-title":"Simultaneous application of enzyme and thermodynamic constraints to metabolic models using an updated Python implementation of GECKO","volume":"11","author":"Carrasco Muriel","year":"2023","journal-title":"Microbiology Spectrum"},{"key":"2026091607563551100_erag400-B19","doi-asserted-by":"crossref","first-page":"D633","DOI":"10.1093\/nar\/gkx935","article-title":"The MetaCyc database of metabolic pathways and enzymes","volume":"46","author":"Caspi","year":"2018","journal-title":"Nucleic Acids Research"},{"key":"2026091607563551100_erag400-B20","doi-asserted-by":"crossref","first-page":"D498","DOI":"10.1093\/nar\/gkaa1025","article-title":"BRENDA, the ELIXIR core data resource in 2021: new developments and updates","volume":"49","author":"Chang","year":"2021","journal-title":"Nucleic Acids Research"},{"key":"2026091607563551100_erag400-B21","first-page":"31","article-title":"Neural ordinary differential equations","volume":"109","author":"Chen","year":"2018","journal-title":"News in Physiological Sciences"},{"key":"2026091607563551100_erag400-B22","doi-asserted-by":"crossref","first-page":"629","DOI":"10.1038\/s41596-023-00931-7","article-title":"Reconstruction, simulation and analysis of enzyme-constrained metabolic models using GECKO Toolbox 3.0","volume":"19","author":"Chen","year":"2024","journal-title":"Nature Protocols"},{"key":"2026091607563551100_erag400-B23","first-page":"100","article-title":"A neural ordinary differential equation model for predicting the growth of Chinese Hamster Ovary cell in a bioreactor system","volume":"30","author":"Chiu","year":"2024","journal-title":"Biotechnology and Bioprocess Engineering"},{"key":"2026091607563551100_erag400-B24","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.coisb.2019.02.009","article-title":"Reconstruction of context-specific genome-scale metabolic models using multiomics data to study metabolic rewiring","volume":"15","author":"Cho","year":"2019","journal-title":"Current Opinion in Systems Biology"},{"key":"2026091607563551100_erag400-B25","doi-asserted-by":"crossref","first-page":"710","DOI":"10.1038\/s42256-022-00519-y","article-title":"Reconstructing kinetic models for dynamical studies of metabolism using generative adversarial networks","volume":"4","author":"Choudhury","year":"2022","journal-title":"Nature Machine Intelligence"},{"key":"2026091607563551100_erag400-B26","doi-asserted-by":"crossref","first-page":"1086","DOI":"10.1038\/s41929-024-01220-6","article-title":"Generative machine learning produces kinetic models that accurately characterize intracellular metabolic states","volume":"7","author":"Choudhury","year":"2024","journal-title":"Nature Catalysis"},{"key":"2026091607563551100_erag400-B27","doi-asserted-by":"crossref","first-page":"303","DOI":"10.1146\/annurev-arplant-050718-100221","article-title":"Modeling plant metabolism: from network reconstruction to mechanistic models","volume":"71","author":"Clark","year":"2020","journal-title":"Annual Review of Plant Biology"},{"key":"2026091607563551100_erag400-B28","doi-asserted-by":"crossref","first-page":"519","DOI":"10.1071\/PP9920519","article-title":"Coupled photosynthesis-stomatal conductance model for leaves of C4 plants","volume":"19","author":"Collatz","year":"1992","journal-title":"Functional Plant Biology"},{"key":"2026091607563551100_erag400-B29","doi-asserted-by":"crossref","first-page":"4897","DOI":"10.1038\/s41467-023-40644-9","article-title":"Identification of gene function based on models capturing natural variability of Arabidopsis thaliana lipid metabolism","volume":"14","author":"C\u00f3rdoba","year":"2023","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B30","doi-asserted-by":"crossref","first-page":"30055","DOI":"10.1073\/pnas.1912789117","article-title":"The frontier of simulation-based inference","volume":"117","author":"Cranmer","year":"2020","journal-title":"Proceedings of the National Academy of Sciences, USA"},{"key":"2026091607563551100_erag400-B31","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1007\/s10915-022-01939-z","article-title":"Scientific machine learning through physics-informed neural networks: where we are and what\u2019s next","volume":"92","author":"Cuomo","year":"2022","journal-title":"Journal of Scientific Computing"},{"key":"2026091607563551100_erag400-B32","doi-asserted-by":"crossref","first-page":"1130","DOI":"10.1111\/nph.13815","article-title":"A test of the \u2018one-point method\u2019 for estimating maximum carboxylation capacity from field-measured, light-saturated photosynthesis","volume":"210","author":"De Kauwe","year":"2016","journal-title":"New Phytologist"},{"key":"2026091607563551100_erag400-B33","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1016\/j.agsy.2016.05.013","article-title":"Winners and losers from climate change in agriculture: insights from a case study in the Mediterranean basin","volume":"147","author":"Dono","year":"2016","journal-title":"Agricultural Systems"},{"key":"2026091607563551100_erag400-B34","doi-asserted-by":"crossref","first-page":"1146","DOI":"10.1038\/s41467-026-68727-3","article-title":"Trustworthy prediction of enzyme commission numbers using a hierarchical interpretable transformer","volume":"17","author":"Dumontet","year":"2026","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B35","doi-asserted-by":"crossref","first-page":"e0143346","DOI":"10.1371\/journal.pone.0143346","article-title":"Plantecophys\u2014an R package for analysing and modelling leaf gas exchange data","volume":"10","author":"Duursma","year":"2015","journal-title":"PLoS One"},{"key":"2026091607563551100_erag400-B36","doi-asserted-by":"publisher","author":"El Alaoui","year":"2025","DOI":"10.1101\/2025.06.10.658179"},{"key":"2026091607563551100_erag400-B37","doi-asserted-by":"crossref","first-page":"6685","DOI":"10.1021\/acs.iecr.4c00001","article-title":"Hybrid physics-informed metabolic cybergenetics: process rates augmented with machine-learning surrogates informed by flux balance analysis","volume":"63","author":"Espinel-R\u00edos","year":"2024","journal-title":"Industrial & Engineering Chemistry Research"},{"key":"2026091607563551100_erag400-B38","doi-asserted-by":"crossref","first-page":"78","DOI":"10.1007\/BF00386231","article-title":"A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species","volume":"149","author":"Farquhar","year":"1980","journal-title":"Planta"},{"key":"2026091607563551100_erag400-B39","doi-asserted-by":"crossref","first-page":"4669","DOI":"10.1038\/s41467-023-40380-0","article-title":"A neural-mechanistic hybrid approach improving the predictive power of genome-scale metabolic models","volume":"14","author":"Faure","year":"2023","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B40","doi-asserted-by":"crossref","first-page":"146869","DOI":"10.1016\/j.cej.2023.146869","article-title":"Kinetics-constrained neural ordinary differential equations: artificial neural network models tailored for small data to boost kinetic model development","volume":"477","author":"Fedorov","year":"2023","journal-title":"Chemical Engineering Journal"},{"key":"2026091607563551100_erag400-B41","author":"Fedorov","year":"2024"},{"key":"2026091607563551100_erag400-B42","doi-asserted-by":"crossref","first-page":"1132","DOI":"10.1111\/nph.12454","article-title":"Scale dependence in the effects of leaf ecophysiological traits on photosynthesis: Bayesian parameterization of photosynthesis models","volume":"200","author":"Feng","year":"2013","journal-title":"New Phytologist"},{"key":"2026091607563551100_erag400-B43","first-page":"3135","article-title":"How to train your neural ODE: the world of Jacobian and kinetic regularization","volume":"119","author":"Finlay","year":"2020","journal-title":"Proceedings of Machine Learning Research"},{"key":"2026091607563551100_erag400-B44","doi-asserted-by":"crossref","first-page":"86","DOI":"10.1016\/j.ymben.2024.03.009","article-title":"Resource allocation modeling for autonomous prediction of plant cell phenotypes","volume":"83","author":"Goelzer","year":"2024","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B45","doi-asserted-by":"crossref","first-page":"4960","DOI":"10.1016\/j.csbj.2023.10.002","article-title":"Predicting metabolic fluxes from omics data via machine learning: moving from knowledge-driven towards data-driven approaches","volume":"21","author":"Gon\u00e7alves","year":"2023","journal-title":"Computational and Structural Biotechnology Journal"},{"key":"2026091607563551100_erag400-B46","doi-asserted-by":"crossref","first-page":"197","DOI":"10.1016\/j.ymben.2020.03.001","article-title":"K-FIT: an accelerated kinetic parameterization algorithm using steady-state fluxomic data","volume":"61","author":"Gopalakrishnan","year":"2020","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B47","doi-asserted-by":"crossref","first-page":"637","DOI":"10.1104\/pp.113.224006","article-title":"Multiscale metabolic modeling: dynamic flux balance analysis on a whole-plant scale","volume":"163","author":"Grafahrend-Belau","year":"2013","journal-title":"Plant Physiology"},{"key":"2026091607563551100_erag400-B48","doi-asserted-by":"crossref","first-page":"1205","DOI":"10.1021\/acssynbio.3c00662","article-title":"Bayesian regression facilitates quantitative modeling of cell metabolism","volume":"13","author":"Groves","year":"2024","journal-title":"ACS Synthetic Biology"},{"key":"2026091607563551100_erag400-B49","doi-asserted-by":"crossref","first-page":"1852","DOI":"10.1111\/j.1365-3040.2010.02192.x","article-title":"Reliable estimation of biochemical parameters from C3 leaf photosynthesis\u2013intercellular carbon dioxide response curves","volume":"33","author":"Gu","year":"2010","journal-title":"Plant, Cell & Environment"},{"key":"2026091607563551100_erag400-B50","doi-asserted-by":"publisher","author":"Guo","year":"2017","DOI":"10.48550\/arXiv.1705.03094"},{"key":"2026091607563551100_erag400-B51","doi-asserted-by":"crossref","first-page":"e1008208","DOI":"10.1371\/journal.pcbi.1008208","article-title":"MASSpy: Building, simulating, and visualizing dynamic biological models in Python using mass action kinetics","volume":"17","author":"Haiman","year":"2021","journal-title":"PLOS Computational Biology"},{"key":"2026091607563551100_erag400-B52","doi-asserted-by":"crossref","first-page":"diae009","DOI":"10.1093\/insilicoplants\/diae009","article-title":"Connecting detailed photosynthetic kinetics to crop growth and yield: a coupled modelling framework","volume":"6","author":"He","year":"2024","journal-title":"In Silico Plants"},{"key":"2026091607563551100_erag400-B53","doi-asserted-by":"crossref","first-page":"1792","DOI":"10.1529\/biophysj.106.093138","article-title":"Thermodynamics-based metabolic flux analysis","volume":"92","author":"Henry","year":"2007","journal-title":"Biophysical Journal"},{"key":"2026091607563551100_erag400-B54","doi-asserted-by":"crossref","first-page":"1735","DOI":"10.1162\/neco.1997.9.8.1735","article-title":"Long short-term memory","volume":"9","author":"Hochreiter","year":"1997","journal-title":"Neural Computation"},{"key":"2026091607563551100_erag400-B55","doi-asserted-by":"crossref","first-page":"744","DOI":"10.1111\/nph.19203","article-title":"A genome-scale metabolic reconstruction of soybean and Bradyrhizobium diazoefficiens reveals the cost\u2013benefit of nitrogen fixation","volume":"240","author":"Holland","year":"2023","journal-title":"New Phytologist"},{"key":"2026091607563551100_erag400-B56","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.ymben.2023.01.001","article-title":"Comparative study of two Saccharomyces cerevisiae strains with kinetic models at genome-scale","volume":"76","author":"Hu","year":"2023","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B57","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1016\/j.ymben.2024.02.002","article-title":"KETCHUP: parameterizing of large-scale kinetic models using multiple datasets with different reference states","volume":"82","author":"Hu","year":"2024","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B58","doi-asserted-by":"crossref","first-page":"2076","DOI":"10.1111\/pbi.70470","article-title":"NeuralFlux: estimation of reaction fluxes at a genome-scale level from time-resolved isotope labelling patterns using deep learning","volume":"24","author":"Hu\u00df","year":"2026","journal-title":"Plant Biotechnology Journal"},{"key":"2026091607563551100_erag400-B59","doi-asserted-by":"crossref","first-page":"638","DOI":"10.1093\/jxb\/erac368","article-title":"Predicting plant Rubisco kinetics from RbcL sequence data using machine learning","volume":"74","author":"Iqbal","year":"2023","journal-title":"Journal of Experimental Botany"},{"key":"2026091607563551100_erag400-B60","doi-asserted-by":"crossref","first-page":"D672","DOI":"10.1093\/nar\/gkae909","article-title":"KEGG: biological systems database as a model of the real world","volume":"53","author":"Kanehisa","year":"2025","journal-title":"Nucleic Acids Research"},{"key":"2026091607563551100_erag400-B61","doi-asserted-by":"crossref","first-page":"diz008","DOI":"10.1093\/insilicoplants\/diz008","article-title":"Combining gene network, metabolic and leaf-level models shows means to future-proof soybean photosynthesis under rising CO2","volume":"1","author":"Kannan","year":"2019","journal-title":"In Silico Plants"},{"key":"2026091607563551100_erag400-B62","doi-asserted-by":"crossref","first-page":"13806","DOI":"10.1038\/ncomms13806","article-title":"A genome-scale Escherichia coli kinetic metabolic model k-ecoli457 satisfying flux data for multiple mutant strains","volume":"7","author":"Khodayari","year":"2016","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B63","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1007\/s004250050225","article-title":"Modelling photosynthesis in fluctuating light with inclusion of stomatal conductance, biochemical activation and pools of key photosynthetic intermediates","volume":"204","author":"Kirschbaum","year":"1997","journal-title":"Planta"},{"key":"2026091607563551100_erag400-B64","doi-asserted-by":"crossref","first-page":"4139","DOI":"10.1038\/s41467-023-39840-4","article-title":"Turnover number predictions for kinetically uncharacterized enzymes using machine and deep learning","volume":"14","author":"Kroll","year":"2023","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B65","doi-asserted-by":"crossref","first-page":"e1008462","DOI":"10.1371\/journal.pcbi.1008462","article-title":"Biologically-informed neural networks guide mechanistic modeling from sparse experimental data","volume":"16","author":"Lagergren","year":"2020","journal-title":"PLoS Computational Biology"},{"key":"2026091607563551100_erag400-B66","doi-asserted-by":"crossref","first-page":"389","DOI":"10.1098\/rspb.1989.0057","article-title":"A mathematical model of the carbon metabolism in photosynthesis. Difficulties in explaining oscillations by fructose 2,6-bisphosphate regulation","volume":"237","author":"Laisk","year":"1989","journal-title":"Proceedings of the Royal Society of London B Biological Sciences"},{"key":"2026091607563551100_erag400-B67","doi-asserted-by":"crossref","first-page":"417","DOI":"10.1098\/rspb.1989.0058","article-title":"A mathematical model of electron transport. Thermodynamic necessity for photosystem II regulation: \u2018light stomata\u2019","volume":"237","author":"Laisk","year":"1989","journal-title":"Proceedings of the Royal Society of London B Biological Sciences"},{"key":"2026091607563551100_erag400-B68","doi-asserted-by":"crossref","first-page":"199","DOI":"10.1023\/A:1010695402963","article-title":"A mathematical model of C4 photosynthesis: the mechanism of concentrating CO2 in NADP-malic enzyme type species","volume":"66","author":"Laisk","year":"2000","journal-title":"Photosynthesis Research"},{"key":"2026091607563551100_erag400-B69","doi-asserted-by":"crossref","first-page":"45","DOI":"10.1007\/s11120-006-9109-1","article-title":"C3 photosynthesis in silico","volume":"90","author":"Laisk","year":"2006","journal-title":"Photosynthesis Research"},{"key":"2026091607563551100_erag400-B70","doi-asserted-by":"crossref","first-page":"461","DOI":"10.1002\/kin.550260408","article-title":"The CSP method for simplifying kinetics","volume":"26","author":"Lam","year":"1994","journal-title":"International Journal of Chemical Kinetics"},{"key":"2026091607563551100_erag400-B71","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/S0005-2728(99)00047-X","article-title":"Chlorophyll a fluorescence induction","volume":"1412","author":"Laz\u00e1r","year":"1999","journal-title":"Biochimica et Biophysica Acta"},{"key":"2026091607563551100_erag400-B72","doi-asserted-by":"crossref","first-page":"708944","DOI":"10.3389\/fphys.2021.708944","article-title":"Neural network differential equations for ion channel modelling","volume":"12","author":"Lei","year":"2021","journal-title":"Frontiers in Physiology"},{"key":"2026091607563551100_erag400-B73","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11120-025-01136-7","article-title":"PhoTorch: a robust and generalized biochemical photosynthesis model fitting package based on PyTorch","volume":"163","author":"Lei","year":"2025","journal-title":"Photosynthesis Research"},{"key":"2026091607563551100_erag400-B74","doi-asserted-by":"crossref","first-page":"390","DOI":"10.1038\/msb.2010.47","article-title":"Omic data from evolved E. coli are consistent with computed optimal growth from genome-scale models","volume":"6","author":"Lewis","year":"2010","journal-title":"Molecular Systems Biology"},{"key":"2026091607563551100_erag400-B75","doi-asserted-by":"crossref","first-page":"662","DOI":"10.1038\/s41929-022-00798-z","article-title":"Deep learning-based kcat prediction enables improved enzyme-constrained model reconstruction","volume":"5","author":"Li","year":"2022","journal-title":"Nature Catalysis"},{"key":"2026091607563551100_erag400-B76","doi-asserted-by":"crossref","first-page":"749","DOI":"10.3390\/metabo11110749","article-title":"Model balancing: A search for in-vivo kinetic constants and consistent metabolic states","volume":"11","author":"Liebermeister","year":"2021","journal-title":"Metabolites"},{"key":"2026091607563551100_erag400-B77","volume-title":"Gathering strength, gathering storms: the one hundred year study on artificial intelligence (AI100) 2021 Study Panel Report","author":"Littman","year":"2021"},{"key":"2026091607563551100_erag400-B78","doi-asserted-by":"crossref","first-page":"diac003","DOI":"10.1093\/insilicoplants\/diac003","article-title":"BioCro II: a software package for modular crop growth simulations","volume":"4","author":"Lochocki","year":"2022","journal-title":"In Silico Plants"},{"key":"2026091607563551100_erag400-B79","doi-asserted-by":"crossref","first-page":"744755","DOI":"10.3389\/frai.2022.744755","article-title":"Non-linearity of metabolic pathways critically influences the choice of machine learning model","volume":"5","author":"Lo-Thong-Viramoutou","year":"2022","journal-title":"Frontiers in Artificial Intelligence"},{"key":"2026091607563551100_erag400-B80","doi-asserted-by":"crossref","first-page":"11","DOI":"10.1016\/j.jtbi.2016.10.017","article-title":"Modeling the light-induced electric potential difference (\u0394\u03a8), the pH difference (\u0394pH) and the proton motive force across the thylakoid membrane in C3 leaves","volume":"413","author":"Lyu","year":"2017","journal-title":"Journal of Theoretical Biology"},{"key":"2026091607563551100_erag400-B81","doi-asserted-by":"crossref","first-page":"239","DOI":"10.1016\/0010-2180(92)90034-M","article-title":"Simplifying chemical kinetics: intrinsic low-dimensional manifolds in composition space","volume":"88","author":"Maas","year":"1992","journal-title":"Combustion and Flame"},{"key":"2026091607563551100_erag400-B82","doi-asserted-by":"crossref","first-page":"154584","DOI":"10.1016\/j.jplph.2025.154584","article-title":"Metabolic modelling: insights into the machine room of plant metabolism","volume":"314","author":"Machado","year":"2025","journal-title":"Journal of Plant Physiology"},{"key":"2026091607563551100_erag400-B83","doi-asserted-by":"crossref","first-page":"455","DOI":"10.1186\/s12859-022-05009-x","article-title":"MLAGO: machine learning-aided global optimization for Michaelis constant estimation of kinetic modeling","volume":"23","author":"Maeda","year":"2022","journal-title":"BMC Bioinformatics"},{"key":"2026091607563551100_erag400-B84","doi-asserted-by":"crossref","first-page":"1331","DOI":"10.1016\/S0006-3495(02)73903-9","article-title":"Dynamic flux balance analysis of diauxic growth in Escherichia coli","volume":"83","author":"Mahadevan","year":"2002","journal-title":"Biophysical Journal"},{"key":"2026091607563551100_erag400-B85","doi-asserted-by":"crossref","first-page":"42","DOI":"10.1021\/acs.jcim.5c02428","article-title":"Advances in machine learning models for predicting enzyme kinetic parameters","volume":"66","author":"Malli","year":"2026","journal-title":"Journal of Chemical Information and Modeling"},{"key":"2026091607563551100_erag400-B86","doi-asserted-by":"crossref","first-page":"65","DOI":"10.3390\/biom12010065","article-title":"ECMpy, a simplified workflow for constructing enzymatic constrained metabolic network model","volume":"12","author":"Mao","year":"2022","journal-title":"Biomolecules"},{"key":"2026091607563551100_erag400-B87","author":"Massaroli","year":"2021"},{"key":"2026091607563551100_erag400-B88","doi-asserted-by":"crossref","first-page":"vbac066","DOI":"10.1093\/bioadv\/vbac066","article-title":"GRASP: a computational platform for building kinetic models of cellular metabolism","volume":"2","author":"Matos","year":"2022","journal-title":"Bioinformatics Advances"},{"key":"2026091607563551100_erag400-B89","doi-asserted-by":"crossref","first-page":"diab032","DOI":"10.1093\/insilicoplants\/diab032","article-title":"Soybean-BioCro: a semi-mechanistic model of soybean growth","volume":"4","author":"Matthews","year":"2022","journal-title":"In Silico Plants"},{"key":"2026091607563551100_erag400-B90","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/0308-521X(94)00055-V","article-title":"APSIM: a novel software system for model development, model testing and simulation in agricultural systems research","volume":"50","author":"McCown","year":"1996","journal-title":"Agricultural Systems"},{"key":"2026091607563551100_erag400-B91","doi-asserted-by":"crossref","first-page":"480","DOI":"10.1016\/j.ymben.2025.05.008","article-title":"Modeling host-pathway dynamics at the genome scale with machine learning","volume":"91","author":"Merzbacher","year":"2025","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B92","doi-asserted-by":"crossref","first-page":"282","DOI":"10.1111\/j.1757-1707.2009.01019.x","article-title":"A semimechanistic model predicting the growth and production of the bioenergy crop Miscanthus \u00d7 giganteus: description, parameterization and validation","volume":"1","author":"Miguez","year":"2009","journal-title":"Global Change Biology: Bioenergy"},{"key":"2026091607563551100_erag400-B93","doi-asserted-by":"crossref","first-page":"391","DOI":"10.1016\/j.tibtech.2010.05.003","article-title":"Production of biofuels and biochemicals: in need of an ORACLE","volume":"28","author":"Miskovic","year":"2010","journal-title":"Trends in Biotechnology"},{"key":"2026091607563551100_erag400-B94","doi-asserted-by":"crossref","first-page":"44","DOI":"10.1016\/j.fcr.2019.05.012","article-title":"Advancing crop modelling capabilities through cultivar-specific parameters sets for the Italian rice germplasm","volume":"240","author":"Mongiano","year":"2019","journal-title":"Field Crops Research"},{"key":"2026091607563551100_erag400-B95","doi-asserted-by":"crossref","first-page":"589","DOI":"10.1111\/pce.13119","article-title":"Dynamic modelling of limitations on improving leaf CO2 assimilation under fluctuating irradiance","volume":"41","author":"Morales","year":"2018","journal-title":"Plant, Cell & Environment"},{"key":"2026091607563551100_erag400-B96","doi-asserted-by":"crossref","first-page":"1247","DOI":"10.1104\/pp.17.00779","article-title":"In silico analysis of the regulation of the photosynthetic electron transport chain in C3 plants","volume":"176","author":"Morales","year":"2018","journal-title":"Plant Physiology"},{"key":"2026091607563551100_erag400-B97","doi-asserted-by":"crossref","first-page":"D617","DOI":"10.1093\/nar\/gkaf1286","article-title":"MetaNetX: a bridge between metabolic resources for enhanced curation and multi-omics data harmonization","volume":"54","author":"Moretti","year":"2026","journal-title":"Nucleic Acids Research"},{"key":"2026091607563551100_erag400-B98","doi-asserted-by":"crossref","first-page":"130","DOI":"10.1016\/j.ymben.2025.03.010","article-title":"NEXT-FBA: a hybrid stoichiometric\/data-driven approach to improve intracellular flux predictions","volume":"91","author":"Morrissey","year":"2025","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B99","doi-asserted-by":"crossref","first-page":"184","DOI":"10.1016\/j.ymben.2023.09.014","article-title":"Accurate prediction of in vivo protein abundances by coupling constraint-based modelling and machine learning","volume":"80","author":"Moura Ferreira","year":"2023","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B100","doi-asserted-by":"crossref","first-page":"2339","DOI":"10.1093\/jxb\/erz175","article-title":"Plant and crop simulation models: powerful tools to link physiology, genetics, and phenomics","volume":"70","author":"Muller","year":"2019","journal-title":"Journal of Experimental Botany"},{"key":"2026091607563551100_erag400-B101","doi-asserted-by":"crossref","first-page":"1304","DOI":"10.3390\/catal11111304","article-title":"Solution and parameter identification of a fixed-bed reactor model for catalytic CO2 methanation using physics-informed neural networks","volume":"11","author":"Ngo","year":"2021","journal-title":"Catalysts"},{"key":"2026091607563551100_erag400-B102","doi-asserted-by":"crossref","first-page":"diae001","DOI":"10.1093\/insilicoplants\/diae001","article-title":"A mathematical model of photoinhibition: exploring the impact of quenching processes","volume":"6","author":"Nies","year":"2024","journal-title":"In Silico Plants"},{"key":"2026091607563551100_erag400-B103","first-page":"1443","article-title":"Inference and prediction of metabolic network fluxes","volume":"169","author":"Nikoloski","year":"2015","journal-title":"Plant Physiology"},{"key":"2026091607563551100_erag400-B104","author":"Oh","year":"2025"},{"key":"2026091607563551100_erag400-B105","doi-asserted-by":"crossref","first-page":"245","DOI":"10.1038\/nbt.1614","article-title":"What is flux balance analysis?","volume":"28","author":"Orth","year":"2010","journal-title":"Nature Biotechnology"},{"key":"2026091607563551100_erag400-B106","doi-asserted-by":"publisher","author":"Pandey","year":"2019","DOI":"10.1101\/536235"},{"key":"2026091607563551100_erag400-B107","doi-asserted-by":"crossref","first-page":"e1007036","DOI":"10.1371\/journal.pcbi.1007036","article-title":"Enhanced flux prediction by integrating relative expression and relative metabolite abundance into thermodynamically consistent metabolic models","volume":"15","author":"Pandey","year":"2019","journal-title":"PLoS Computational Biology"},{"key":"2026091607563551100_erag400-B108","doi-asserted-by":"crossref","first-page":"e2503406122","DOI":"10.1073\/pnas.2503406122","article-title":"Unveiling organ-specific metabolism of Citrus clementina","volume":"122","author":"Passi","year":"2025","journal-title":"Proceedings of the National Academy of Sciences, USA"},{"key":"2026091607563551100_erag400-B109","author":"Peng","year":"2025"},{"key":"2026091607563551100_erag400-B110","doi-asserted-by":"crossref","first-page":"661","DOI":"10.1111\/j.1432-1033.1988.tb14242.x","article-title":"A mathematical model of the Calvin photosynthesis cycle","volume":"175","author":"Pettersson","year":"1988","journal-title":"European Journal of Biochemistry"},{"key":"2026091607563551100_erag400-B111","doi-asserted-by":"crossref","first-page":"448","DOI":"10.3389\/fpls.2018.00448","article-title":"Phenotypic trait identification using a multimodel Bayesian method: a case study using photosynthesis in Brassica rapa genotypes","volume":"9","author":"Pleban","year":"2018","journal-title":"Frontiers in Plant Science"},{"key":"2026091607563551100_erag400-B112","volume-title":"The mathematical theory of optimal processes","author":"Pontryagin","year":"1962"},{"key":"2026091607563551100_erag400-B113","doi-asserted-by":"crossref","first-page":"2665","DOI":"10.1038\/s41596-025-01288-9","article-title":"Xomicstomodel: omics data integration and generation of thermodynamically consistent metabolic models","volume":"21","author":"Preciat","year":"2026","journal-title":"Nature Protocols"},{"key":"2026091607563551100_erag400-B114","doi-asserted-by":"crossref","first-page":"106690","DOI":"10.1016\/j.engappai.2023.106690","article-title":"Benchmarking chemical neural ordinary differential equations to obtain reaction network-constrained kinetic models from spectroscopic data","volume":"125","author":"Puliyanda","year":"2023","journal-title":"Engineering Applications of Artificial Intelligence"},{"key":"2026091607563551100_erag400-B115","doi-asserted-by":"crossref","first-page":"bbad506","DOI":"10.1093\/bib\/bbad506","article-title":"DLTKcat: deep learning-based prediction of temperature-dependent enzyme turnover rates","volume":"25","author":"Qiu","year":"2024","journal-title":"Briefings in Bioinformatics"},{"key":"2026091607563551100_erag400-B116","doi-asserted-by":"publisher","author":"Rackauckas","year":"2021","DOI":"10.48550\/arXiv.2001.04385"},{"key":"2026091607563551100_erag400-B117","doi-asserted-by":"crossref","first-page":"686","DOI":"10.1016\/j.jcp.2018.10.045","article-title":"Physics-informed neural networks: a deep learning framework for solving forward and inverse problems involving nonlinear partial differential equations","volume":"378","author":"Raissi","year":"2019","journal-title":"Journal of Computational Physics"},{"key":"2026091607563551100_erag400-B118","doi-asserted-by":"crossref","first-page":"1026","DOI":"10.1126\/science.aaw4741","article-title":"Hidden fluid mechanics: learning velocity and pressure fields from flow visualizations","volume":"367","author":"Raissi","year":"2020","journal-title":"Science"},{"key":"2026091607563551100_erag400-B119","doi-asserted-by":"crossref","first-page":"e1012576","DOI":"10.1371\/journal.pcbi.1012576","article-title":"Harnessing the optimization of enzyme catalytic rates in engineering of metabolic phenotypes","volume":"20","author":"Razaghi-Moghadam","year":"2024","journal-title":"PLoS Computational Biology"},{"key":"2026091607563551100_erag400-B120","doi-asserted-by":"crossref","first-page":"109","DOI":"10.1016\/j.cobme.2019.09.012","article-title":"Global sensitivity analysis of biological multiscale models","volume":"11","author":"Renardy","year":"2019","journal-title":"Current Opinion in Biomedical Engineering"},{"key":"2026091607563551100_erag400-B121","doi-asserted-by":"crossref","first-page":"e1005568","DOI":"10.1371\/journal.pcbi.1005568","article-title":"On the effects of alternative optima in context-specific metabolic model predictions","volume":"13","author":"Robaina-Est\u00e9vez","year":"2017","journal-title":"PLoS Computational Biology"},{"key":"2026091607563551100_erag400-B122","doi-asserted-by":"crossref","first-page":"429","DOI":"10.1071\/AR01106","article-title":"Simulation of growth and development of diverse legume species in APSIM","volume":"53","author":"Robertson","year":"2002","journal-title":"Australian Journal of Agricultural Research"},{"key":"2026091607563551100_erag400-B123","doi-asserted-by":"crossref","first-page":"2275","DOI":"10.1093\/jxb\/ers080","article-title":"Kinetic modelling of plant metabolic pathways","volume":"63","author":"Rohwer","year":"2012","journal-title":"Journal of Experimental Botany"},{"key":"2026091607563551100_erag400-B124","doi-asserted-by":"crossref","first-page":"318","DOI":"10.7551\/mitpress\/5236.001.0001","volume-title":"Parallel distributed processing: explorations in the microstructure of cognition, vol. 1: foundations","author":"Rumelhart","year":"1986"},{"key":"2026091607563551100_erag400-B125","doi-asserted-by":"crossref","first-page":"e1004195","DOI":"10.1371\/journal.pcbi.1004195","article-title":"A general framework for thermodynamically consistent parameterization and efficient sampling of enzymatic reactions","volume":"11","author":"Saa","year":"2015","journal-title":"PLOS Computational Biology"},{"key":"2026091607563551100_erag400-B126","doi-asserted-by":"crossref","first-page":"29635","DOI":"10.1038\/srep29635","article-title":"Construction of feasible and accurate kinetic models of metabolism: A Bayesian approach","volume":"6","author":"Saa","year":"2016","journal-title":"Scientific Reports"},{"key":"2026091607563551100_erag400-B127","doi-asserted-by":"crossref","first-page":"981","DOI":"10.1016\/j.biotechadv.2017.09.005","article-title":"Formulation, construction and analysis of kinetic models of metabolism: a review of modelling frameworks","volume":"35","author":"Saa","year":"2017","journal-title":"Biotechnology Advances"},{"key":"2026091607563551100_erag400-B128","doi-asserted-by":"publisher","author":"Salimans","year":"2017","DOI":"10.48550\/arXiv.1703.03864"},{"key":"2026091607563551100_erag400-B129","doi-asserted-by":"crossref","first-page":"167","DOI":"10.1093\/bioinformatics\/bty499","article-title":"pyTFA and matTFA: a python package and a Matlab toolbox for thermodynamics-based flux analysis","volume":"35","author":"Salvy","year":"2019","journal-title":"Bioinformatics"},{"key":"2026091607563551100_erag400-B130","doi-asserted-by":"crossref","first-page":"30","DOI":"10.1038\/s41467-019-13818-7","article-title":"The ETFL formulation allows multi-omics integration in thermodynamics-compliant metabolism and expression models","volume":"11","author":"Salvy","year":"2020","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B131","doi-asserted-by":"crossref","first-page":"935","DOI":"10.15252\/msb.20167411","article-title":"Improving the phenotype predictions of a yeast genome-scale metabolic model by incorporating enzymatic constraints","volume":"13","author":"S\u00e1nchez","year":"2017","journal-title":"Molecular Systems Biology"},{"key":"2026091607563551100_erag400-B132","doi-asserted-by":"crossref","first-page":"btad711","DOI":"10.1093\/bioinformatics\/btad711","article-title":"pyPESTO: a modular and scalable tool for parameter estimation for dynamic models","volume":"39","author":"Sch\u00e4lte","year":"2023","journal-title":"Bioinformatics"},{"key":"2026091607563551100_erag400-B133","doi-asserted-by":"crossref","first-page":"9241","DOI":"10.1038\/s41598-020-65457-4","article-title":"Introducing an optimization- and explicit Runge-Kutta-based approach to perform dynamic flux balance analysis","volume":"10","author":"Schroeder","year":"2020","journal-title":"Scientific Reports"},{"key":"2026091607563551100_erag400-B134","doi-asserted-by":"crossref","first-page":"126","DOI":"10.1016\/j.tplants.2023.09.006","article-title":"AI to enable plant cell metabolic engineering","volume":"29","author":"Sears","year":"2024","journal-title":"Trends in Plant Science"},{"key":"2026091607563551100_erag400-B135","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1111\/tpj.15551","article-title":"A hybrid kinetic and constraint-based model of leaf metabolism allows predictions of metabolic fluxes in different environments","volume":"109","author":"Shameer","year":"2022","journal-title":"The Plant Journal"},{"key":"2026091607563551100_erag400-B136","doi-asserted-by":"crossref","first-page":"1035","DOI":"10.1111\/j.1365-3040.2007.01710.x","article-title":"Fitting photosynthetic carbon dioxide response curves for C3 leaves","volume":"30","author":"Sharkey","year":"2007","journal-title":"Plant, Cell & Environment"},{"key":"2026091607563551100_erag400-B137","doi-asserted-by":"crossref","first-page":"884","DOI":"10.3389\/fpls.2018.00884","article-title":"A dynamic multi-tissue flux balance model captures carbon and nitrogen metabolism and optimal resource partitioning during Arabidopsis growth","volume":"9","author":"Shaw","year":"2018","journal-title":"Frontiers in Plant Science"},{"key":"2026091607563551100_erag400-B138","doi-asserted-by":"crossref","first-page":"diab020","DOI":"10.1093\/insilicoplants\/diab020","article-title":"Integration of crop growth model and constraint-based metabolic model predicts metabolic changes over rice plant development under water-limited stress","volume":"3","author":"Shaw","year":"2021","journal-title":"In Silico Plants"},{"key":"2026091607563551100_erag400-B139","doi-asserted-by":"crossref","first-page":"10166","DOI":"10.1038\/s41598-023-36799-6","article-title":"Physics-informed neural ODE (PINODE): embedding physics into models using collocation points","volume":"13","author":"Sholokhov","year":"2023","journal-title":"Scientific Reports"},{"key":"2026091607563551100_erag400-B140","doi-asserted-by":"crossref","first-page":"1572","DOI":"10.1111\/nph.70528","article-title":"Constraint-based metabolic modeling reveals metabolic properties underpinning the unprecedented growth of Chlorella ohadii","volume":"248","author":"Soleymani","year":"2025","journal-title":"New Phytologist"},{"key":"2026091607563551100_erag400-B141","doi-asserted-by":"crossref","first-page":"6042","DOI":"10.1038\/s41598-025-89997-9","article-title":"Coupling flux balance analysis with reactive transport modeling through machine learning for rapid and stable simulation of microbial metabolic switching","volume":"15","author":"Song","year":"2025","journal-title":"Scientific Reports"},{"key":"2026091607563551100_erag400-B142","doi-asserted-by":"crossref","first-page":"705","DOI":"10.1093\/bioinformatics\/btx676","article-title":"PESTO: Parameter EStimation TOolbox","volume":"34","author":"Stapor","year":"2018","journal-title":"Bioinformatics"},{"key":"2026091607563551100_erag400-B143","doi-asserted-by":"crossref","first-page":"plab059","DOI":"10.1093\/aobpla\/plab059","article-title":"Principles of resilient coding for plant ecophysiologists","volume":"13","author":"Stinziano","year":"2021","journal-title":"AoB Plants"},{"key":"2026091607563551100_erag400-B144","doi-asserted-by":"crossref","first-page":"131","DOI":"10.1006\/jtbi.1998.0692","article-title":"Chlorophyll a fluorescence induction in higher plants: modelling and numerical simulation","volume":"193","author":"Stirbet","year":"1998","journal-title":"Journal of Theoretical Biology"},{"key":"2026091607563551100_erag400-B145","doi-asserted-by":"crossref","first-page":"112732","DOI":"10.1016\/j.combustflame.2023.112732","article-title":"Kinetics parameter optimization of hydrocarbon fuels via neural ordinary differential equations","volume":"251","author":"Su","year":"2023","journal-title":"Combustion and Flame"},{"key":"2026091607563551100_erag400-B146","doi-asserted-by":"crossref","first-page":"464346","DOI":"10.1016\/j.chroma.2023.464346","article-title":"Physics-informed neural networks to solve lumped kinetic model for chromatography process","volume":"1708","author":"Tang","year":"2023","journal-title":"Journal of Chromatography A"},{"key":"2026091607563551100_erag400-B147","doi-asserted-by":"crossref","DOI":"10.1137\/1.9780898717921","volume-title":"Inverse problem theory and methods for model parameter estimation","author":"Tarantola","year":"2005"},{"key":"2026091607563551100_erag400-B148","doi-asserted-by":"crossref","first-page":"3609","DOI":"10.1016\/j.csbj.2025.08.004","article-title":"MINN: a metabolic-informed neural network for integrating omics data into genome-scale metabolic modeling","volume":"27","author":"Tazza","year":"2025","journal-title":"Computational and Structural Biotechnology Journal"},{"key":"2026091607563551100_erag400-B149","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1186\/s13068-020-1665-7","article-title":"Large-scale kinetic metabolic models of Pseudomonas putida KT2440 for consistent design of metabolic engineering strategies","volume":"13","author":"Tokic","year":"2020","journal-title":"Biotechnology for Biofuels"},{"key":"2026091607563551100_erag400-B150","doi-asserted-by":"crossref","first-page":"5123","DOI":"10.1007\/s00018-021-03844-4","article-title":"Characterization of effects of genetic variants via genome-scale metabolic modelling","volume":"78","author":"Tong","year":"2021","journal-title":"Cellular and Molecular Life Sciences"},{"key":"2026091607563551100_erag400-B151","doi-asserted-by":"crossref","first-page":"2906","DOI":"10.1021\/acssynbio.4c00868","article-title":"The dawn of high-throughput and genome-scale kinetic modeling: recent advances and future directions","volume":"14","author":"Toumpe","year":"2025","journal-title":"ACS Synthetic Biology"},{"key":"2026091607563551100_erag400-B152","doi-asserted-by":"crossref","first-page":"5606","DOI":"10.1529\/biophysj.108.135442","article-title":"Ensemble modeling of metabolic networks","volume":"95","author":"Tran","year":"2008","journal-title":"Biophysical Journal"},{"key":"2026091607563551100_erag400-B153","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1186\/s12859-021-04122-7","article-title":"Constructing and analysing dynamic models with modelbase v1.2.3: a software update","volume":"22","author":"van Aalst","year":"2021","journal-title":"BMC Bioinformatics"},{"key":"2026091607563551100_erag400-B154","doi-asserted-by":"crossref","first-page":"16","DOI":"10.1111\/j.1475-2743.1989.tb00755.x","article-title":"WOFOST: a simulation model of crop production","volume":"5","author":"van Diepen","year":"1989","journal-title":"Soil Use and Management"},{"key":"2026091607563551100_erag400-B155","volume-title":"SUCROS97: simulation of crop growth for potential and water-limited production situations","author":"van Laar","year":"1997"},{"key":"2026091607563551100_erag400-B156","doi-asserted-by":"crossref","first-page":"e1012733","DOI":"10.1371\/journal.pcbi.1012733","article-title":"Jaxkineticmodel: neural ordinary differential equations inspired parameterization of kinetic models","volume":"21","author":"van Lent","year":"2025","journal-title":"PLoS Computational Biology"},{"key":"2026091607563551100_erag400-B157","doi-asserted-by":"crossref","DOI":"10.1071\/9780643103405","volume-title":"Biochemical models of leaf photosynthesis","author":"von Caemmerer","year":"2000"},{"key":"2026091607563551100_erag400-B158","doi-asserted-by":"crossref","first-page":"110750","DOI":"10.1016\/j.compag.2025.110750","article-title":"Global sensitivity analyses prior to parameter calibration significantly improves prediction quality","volume":"238","author":"Wang","year":"2025","journal-title":"Computers and Electronics in Agriculture"},{"key":"2026091607563551100_erag400-B159","doi-asserted-by":"crossref","first-page":"bbae387","DOI":"10.1093\/bib\/bbae387","article-title":"MPEK: a multitask deep learning framework based on pretrained language models for enzymatic reaction kinetic parameters prediction","volume":"25","author":"Wang","year":"2024","journal-title":"Briefings in Bioinformatics"},{"key":"2026091607563551100_erag400-B160","doi-asserted-by":"crossref","first-page":"4354","DOI":"10.1038\/s41467-019-12342-y","article-title":"Massive computational acceleration by using neural networks to emulate mechanism-based biological models","volume":"10","author":"Wang","year":"2019","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B161","doi-asserted-by":"crossref","first-page":"2231","DOI":"10.1104\/pp.113.230284","article-title":"Elements required for an efficient NADP-malic enzyme type C4 photosynthesis","volume":"164","author":"Wang","year":"2014","journal-title":"Plant Physiology"},{"key":"2026091607563551100_erag400-B162","doi-asserted-by":"crossref","first-page":"343","DOI":"10.1111\/tpj.15365","article-title":"Towards a dynamic photosynthesis model to guide yield improvement in C4 crops","volume":"107","author":"Wang","year":"2021","journal-title":"The Plant Journal"},{"key":"2026091607563551100_erag400-B163","doi-asserted-by":"crossref","first-page":"btac787","DOI":"10.1093\/bioinformatics\/btac787","article-title":"Symbolic kinetic models in python (SKiMpy): intuitive modeling of large-scale biological kinetic models","volume":"39","author":"Weilandt","year":"2023","journal-title":"Bioinformatics"},{"key":"2026091607563551100_erag400-B164","doi-asserted-by":"crossref","first-page":"178","DOI":"10.1111\/nph.20420","article-title":"Metabolic modeling identifies determinants of thermal growth responses in Arabidopsis thaliana","volume":"247","author":"Wendering","year":"2025","journal-title":"New Phytologist"},{"key":"2026091607563551100_erag400-B165","doi-asserted-by":"crossref","first-page":"1578","DOI":"10.1111\/nph.71280","article-title":"Kinetic parameter prediction using neural networks identifies limitations to C4 photosynthesis","volume":"251","author":"Wendering","year":"2026","journal-title":"New Phytologist"},{"key":"2026091607563551100_erag400-B166","doi-asserted-by":"crossref","first-page":"60","DOI":"10.1016\/j.coisb.2021.03.005","article-title":"On structural and practical identifiability","volume":"25","author":"Wieland","year":"2021","journal-title":"Current Opinion in Systems Biology"},{"key":"2026091607563551100_erag400-B167","author":"Williams","year":"1995"},{"key":"2026091607563551100_erag400-B168","doi-asserted-by":"crossref","first-page":"497","DOI":"10.13031\/2013.31032","article-title":"EPIC crop growth model","volume":"32","author":"Williams","year":"1989","journal-title":"Transactions of the American Society of Agricultural Engineers"},{"key":"2026091607563551100_erag400-B169","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1002\/csc2.20857","article-title":"Calibration of a crop growth model in APSIM for 15 publicly available corn hybrids in North America","volume":"63","author":"Winn","year":"2023","journal-title":"Crop Science"},{"key":"2026091607563551100_erag400-B170","doi-asserted-by":"crossref","first-page":"D656","DOI":"10.1093\/nar\/gkx1065","article-title":"SABIO-RK: an updated resource for manually curated biochemical reaction kinetics","volume":"46","author":"Wittig","year":"2018","journal-title":"Nucleic Acids Research"},{"key":"2026091607563551100_erag400-B171","doi-asserted-by":"crossref","first-page":"421","DOI":"10.1007\/BF00195743","article-title":"Modelling C3 photosynthesis: a sensitivity analysis of the photosynthetic carbon-reduction cycle","volume":"191","author":"Woodrow","year":"1993","journal-title":"Planta"},{"key":"2026091607563551100_erag400-B172","doi-asserted-by":"crossref","first-page":"380","DOI":"10.1038\/s41477-019-0398-8","article-title":"Quantifying impacts of enhancing photosynthesis on crop yield","volume":"5","author":"Wu","year":"2019","journal-title":"Nature Plants"},{"key":"2026091607563551100_erag400-B173","doi-asserted-by":"crossref","first-page":"1436","DOI":"10.1111\/pce.13995","article-title":"Estimating uncertainty: a Bayesian approach to modelling photosynthesis in C3 leaves","volume":"44","author":"Xiao","year":"2021","journal-title":"Plant, Cell & Environment"},{"key":"2026091607563551100_erag400-B174","doi-asserted-by":"crossref","first-page":"101685","DOI":"10.1016\/j.xplc.2025.101685","article-title":"KineticGP: A computational framework for genomic prediction of leaf photosynthetic traits","volume":"7","author":"Xu","year":"2025","journal-title":"Plant Communications"},{"key":"2026091607563551100_erag400-B175","doi-asserted-by":"crossref","first-page":"erag340","DOI":"10.1093\/jxb\/erag340","article-title":"Parameterization of steady-state models for C3 photosynthesis using photosynthesis response curves: which models to use and which parameter estimates to trust?","author":"Xu","year":"2026","journal-title":"Journal of Experimental Botany,"},{"key":"2026091607563551100_erag400-B176","author":"Yalavarthi","year":"2022"},{"key":"2026091607563551100_erag400-B177","doi-asserted-by":"crossref","first-page":"133","DOI":"10.1016\/j.ymben.2021.06.005","article-title":"Integrating thermodynamic and enzymatic constraints into genome-scale metabolic models","volume":"67","author":"Yang","year":"2021","journal-title":"Metabolic Engineering"},{"key":"2026091607563551100_erag400-B178","doi-asserted-by":"crossref","first-page":"e1007575","DOI":"10.1371\/journal.pcbi.1007575","article-title":"Systems biology informed deep learning for inferring parameters and hidden dynamics","volume":"16","author":"Yazdani","year":"2020","journal-title":"PLoS Computational Biology"},{"key":"2026091607563551100_erag400-B179","doi-asserted-by":"crossref","first-page":"8211","DOI":"10.1038\/s41467-023-44113-1","article-title":"UniKP: a unified framework for the prediction of enzyme kinetic parameters","volume":"14","author":"Yu","year":"2023","journal-title":"Nature Communications"},{"key":"2026091607563551100_erag400-B180","doi-asserted-by":"crossref","first-page":"1358","DOI":"10.1126\/science.adf2465","article-title":"Enzyme function prediction using contrastive learning","volume":"379","author":"Yu","year":"2023","journal-title":"Science"},{"key":"2026091607563551100_erag400-B181","author":"Zaheer","year":"2018"},{"key":"2026091607563551100_erag400-B182","doi-asserted-by":"crossref","first-page":"2","DOI":"10.1186\/s13321-024-00944-8","article-title":"CLAIRE: a contrastive learning-based predictor for EC number of chemical reactions","volume":"17","author":"Zeng","year":"2025","journal-title":"Journal of Cheminformatics"},{"key":"2026091607563551100_erag400-B183","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1615\/JMachLearnModelComput.2022045133","article-title":"Autoencoder neural network for chemically reacting systems","volume":"3","author":"Zhang","year":"2022","journal-title":"Journal of Machine Learning for Modeling and Computing"},{"key":"2026091607563551100_erag400-B184","doi-asserted-by":"crossref","first-page":"1812","DOI":"10.1093\/plphys\/kiab345","article-title":"Potential metabolic mechanisms for inhibited chloroplast nitrogen assimilation under high CO2","volume":"187","author":"Zhao","year":"2021","journal-title":"Plant Physiology"},{"key":"2026091607563551100_erag400-B185","doi-asserted-by":"crossref","first-page":"114","DOI":"10.1007\/s00425-005-0064-4","article-title":"Chlorophyll a fluorescence induction kinetics in leaves predicted from a model describing each discrete step of excitation energy and electron transfer associated with photosystem II","volume":"223","author":"Zhu","year":"2005","journal-title":"Planta"},{"key":"2026091607563551100_erag400-B186","doi-asserted-by":"crossref","first-page":"513","DOI":"10.1104\/pp.107.103713","article-title":"Optimizing the distribution of resources between enzymes of carbon metabolism can dramatically increase photosynthetic rate: a numerical simulation using an evolutionary algorithm","volume":"145","author":"Zhu","year":"2007","journal-title":"Plant Physiology"},{"key":"2026091607563551100_erag400-B187","doi-asserted-by":"crossref","first-page":"1711","DOI":"10.1111\/pce.12025","article-title":"e-photosynthesis: a comprehensive dynamic mechanistic model of C3 photosynthesis: from light capture to sucrose synthesis","volume":"36","author":"Zhu","year":"2013","journal-title":"Plant, Cell & Environment"},{"key":"2026091607563551100_erag400-B188","first-page":"62934","article-title":"Hybrid2 neural ODE causal modeling and an application to glycemic response","volume":"235","author":"Zou","year":"2024","journal-title":"Proceedings of Machine Learning Research"},{"key":"2026091607563551100_erag400-B189","doi-asserted-by":"crossref","first-page":"465077","DOI":"10.1016\/j.chroma.2024.465077","article-title":"A parameter estimation method for chromatographic separation process based on physics-informed neural network","volume":"1730","author":"Zou","year":"2024","journal-title":"Journal of Chromatography A"},{"key":"2026091607563551100_erag400-B190","doi-asserted-by":"crossref","first-page":"e2502160122","DOI":"10.1073\/pnas.2502160122","article-title":"Evaluating plant growth\u2013defense trade-offs by modeling the interaction between primary and secondary metabolism","volume":"122","author":"Zrimec","year":"2025","journal-title":"Proceedings of the National Academy of Sciences, USA"}],"container-title":["Journal of Experimental Botany"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/academic.oup.com\/jxb\/advance-article-pdf\/doi\/10.1093\/jxb\/erag400\/70663695\/erag400.pdf","content-type":"application\/pdf","content-version":"am","intended-application":"syndication"},{"URL":"https:\/\/academic.oup.com\/jxb\/advance-article-pdf\/doi\/10.1093\/jxb\/erag400\/70663695\/erag400.pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,9,16]],"date-time":"2026-09-16T11:57:42Z","timestamp":1789559862000},"score":1,"resource":{"primary":{"URL":"https:\/\/academic.oup.com\/jxb\/advance-article\/doi\/10.1093\/jxb\/erag400\/8762412"}},"subtitle":[],"editor":[{"given":"Robert","family":"Hancock","sequence":"additional","affiliation":[{"name":"The James Hutton Institute ,","place":["UK"]}],"role":[{"vocabulary":"crossref","role":"editor"}]}],"short-title":[],"issued":{"date-parts":[[2026,8,17]]},"references-count":190,"URL":"https:\/\/doi.org\/10.1093\/jxb\/erag400","relation":{},"ISSN":["0022-0957","1460-2431"],"issn-type":[{"value":"0022-0957","type":"print"},{"value":"1460-2431","type":"electronic"}],"subject":[],"published":{"date-parts":[[2026,8,17]]},"article-number":"erag400"}}