This paper introduces a methodology that enables the relational learning framework to incorporate quantitative data derived from experimental studies in microbial ecology. The focus of using Default Logic in microbial ecology is to enhance the comprehension of cellular physiological states and the interpretation of interactions among metabolites and signaling networks. To illustrate our approach, a logical model is proposed as model of the glycolysis and pentose phosphate pathways in E. coli . This method constructs a symbolic model based on kinetics, utilizing the Michaelis-Menten equation, by discretizing the concentration variations of specific metabolites over time based on relevant levels to be integrated into our Logic Inference framework. Additionally, we generate logical formulas for concentrations of metabolites that are difficult to measure during dynamic states through logical abduction. Given the resulting large set of conclusions/extensions, we employ an expectation maximization algorithm operating on binary decision diagrams for ranking.
King, R.D., Whelan, K.E., Jones, F.M., Reiser, P.G.K., Bryant, C.H., Muggleton, S.H., et al. (2004) Functional Genomic Hypothesis Generation and Experimentation by a Robot Scientist. Nature , 427, 247-252. https://doi.org/10.1038/nature02236
Kitano, H. (2002) Systems Biology: Toward System-Level Understanding of Biological Systems. Science , 295, 1662-1664.
Sriyudthsak, K., Shiraishi, F. and Hirai, M.Y. (2016) Mathematical Modeling and Dynamic Simulation of Metabolic Reaction Systems Using Metabolome Time Series Data. Frontiers in Molecular Biosciences , 3, Article 15. https://doi.org/10.3389/fmolb.2016.00015
Baral, C., Chancellor, K., Tran, N., Tran, N.L., Joy, A. and Berens, M. (2004) A Knowledge Based Approach for Representing and Reasoning about Signaling Networks. Bioinformatics , 20, i15-i22. https://doi.org/10.1093/bioinformatics/bth918
Moraru, I.I., Schaff, J.C., Slepchenko, B.M., Blinov, M.L., Morgan, F., Lakshminarayana, A., et al. (2008) Virtual Cell Modelling and Simulation Software Environment. IET Systems Biology , 2, 352-362. https://doi.org/10.1049/iet-syb:20080102
Schaffer, L.V. and Ideker, T. (2021) Mapping the Multiscale Structure of Biological Systems. Cell Systems , 12, 622-635. https://doi.org/10.1016/j.cels.2021.05.012
Bandara, S., Schlöder, J.P., Eils, R., Bock, H.G. and Meyer, T. (2009) Optimal Experimental Design for Parameter Estimation of a Cell Signaling Model. PLOS Computational Biology , 5, e1000558. https://doi.org/10.1371/journal.pcbi.1000558
Reisz, J.A. and D’Alessandro, A. (2017) Measurement of Metabolic Fluxes Using Stable Isotope Tracers in Whole Animals and Human Patients. Current Opinion in Clinical Nutrition & Metabolic Care , 20, 366-374. https://doi.org/10.1097/mco.0000000000000393
Geiger, D. (2021) Correction To: Plant Glucose Transporter Structure and Function. Pflügers Archiv — European Journal of Physiology , 473, 1687-1687. https://doi.org/10.1007/s00424-021-02603-5
Chassagnole, C., Rodrigues, J., Doncescu, A. and Yang, L.T. (2006) Differential Evolutionary Algorithms for in Vivo Dynamic Analysis of Glycolysis and Pentose Phosphate Pathway in Escherichia coli . A. Zomaya.
Emwas, A., Szczepski, K., Al-Younis, I., Lachowicz, J.I. and Jaremko, M. (2022) Fluxomics—New Metabolomics Approaches to Monitor Metabolic Pathways. Frontiers in Pharmacology , 13, Article 805782. https://doi.org/10.3389/fphar.2022.805782
King, R.D., Garrett, S.M. and Coghill, G.M. (2005) On the Use of Qualitative Reasoning to Simulate and Identify Metabolic Pathways. Bioinformatics , 21, 2017-2026. https://doi.org/10.1093/bioinformatics/bti255
Kanehisa, M., Araki, M., Goto, S., Hattori, M., Hirakawa, M., Itoh, M., et al. (2007) KEGG for Linking Genomes to Life and the Environment. Nucleic Acids Research , 36, D480-D484. https://doi.org/10.1093/nar/gkm882
Inoue, K., Sato, T., Ishihata, M., Kameya, Y. and Nabeshima, H. (2009) Evaluating Abductive Hypotheses Using EM Algorithm on BDDs. Proc eeding of IJCAI -09, Pasadena, 17-18 July 2009, 820-815.
Doncescu, A., Yamamoto, Y. and Inoue, K. (2007) Biological Systems Analysis Using Inductive Logic Programming. 21 st International Conference on Advanced Information Networking and Applications Workshops ( AINAW ’07), Niagara Falls, 21-23 May 2007, 690-695. https://doi.org/10.1109/ainaw.2007.112
Dworschak, S., Grell, S., Nikiforova, V.J., Schaub, T. and Selbig, J. (2008) Modeling Biological Networks by Action Languages via Answer Set Programming. Constraints , 13, 21-65. https://doi.org/10.1007/s10601-007-9031-y
Tiwari, A., Talcott, C., Knapp, M., Lincoln, P. and Laderoute, K. (2007) Analyzing Pathways Using Sat-Based Approaches. In: Anai, H., Horimoto, K. and Kutsia, T., Eds., Algebraic Biology , Springer, 155-169. https://doi.org/10.1007/978-3-540-73433-8_12
De Raedt, L. (2008) Logical and Relational Learning. Springer.
Benhamou, F. (1995) Interval Constraint Logic Programming. In: Podelski, A., Ed., Constraint Programming : Basics and Trends , Springer, 1-21. https://doi.org/10.1007/3-540-59155-9_1
Ji, S.H., Krishnapuram, B. and Carin, L. (2006) Variational Bayes for Continuous Hidden Markov Models and Its Application to Active Learning. IEEE Transactions on Pattern Analysis and Machine Intelligence , 28, 522-532. https://doi.org/10.1109/tpami.2006.85
Gauvain, J. and Lee, C.H. (1994) Maximum a Posteriori Estimation for Multivariate Gaussian Mixture Observations of Markov Chains. IEEE Transactions on Speech and Audio Processing , 2, 291-298. https://doi.org/10.1109/89.279278
Holmes, I. and Rubin, G.M. (2002) An Expectation Maximization Algorithm for Training Hidden Substitution Models. Journal of Molecular Biology , 317, 753-764. https://doi.org/10.1006/jmbi.2002.5405
Rabiner, L.R. (1989) A Tutorial on Hidden Markov Models and Selected Applications in Speech Recognition. Proceedings of the IEEE , 77, 257-286. https://doi.org/10.1109/5.18626
Peters-Wendisch, P.G., Schiel, B., Wendisch, V.F., Katsoulidis, E., Möckel, B., Sahm, H. and Eikmanns, B.J. (2001) Pyruvate Carboxylase Is a Major Bottleneck for Glutamate and Lysine Production by Corynebacterium glutamicum . Journal of Molecular Microbiology and Biotechnology , 3, 295-300.
Seo, J., Shin, J., Leijten, J., Jeon, O., Camci-Unal, G., Dikina, A.D., et al. (2018) High-Throughput Approaches for Screening and Analysis of Cell Behaviors. Biomaterials , 153, 85-101. https://doi.org/10.1016/j.biomaterials.2017.06.022
Fages, F. and Soliman, S. (2008) Model Revision from Temporal Logic Properties in Computational Systems Biology. In: De Raedt, L., Frasconi, P., Kersting, K. AND Muggleton, S., Eds., Probabilistic Inductive Logic Programming , Springer, 287-304. https://doi.org/10.1007/978-3-540-78652-8_11
Fife, S.T. and Gossner, J.D. (2024) Deductive Qualitative Analysis: Evaluating, Expanding, and Refining Theory. International Journal of Qualitative Methods , 23, 1-12. https://doi.org/10.1177/16094069241244856
Kanehisa, M. and Goto, S. (2000) KEGG: Kyoto Encyclopedia of Genes and Genomes. Nucleic Acids Research , 28, 27-30. https://doi.org/10.1093/nar/28.1.27