From Mechanisms to Mathematical Models and Back to Mechanisms: Quantitative Mechanistic Explanations

  • Tudor M. Baetu
Part of the History, Philosophy and Theory of the Life Sciences book series (HPTL, volume 11)


Despite the philosophical clash between deductive-nomological and mechanistic accounts of explanation, in scientific practice, both approaches are required in order to achieve more complete explanations and guide the discovery process. I defend this thesis by discussing the case of mathematical models in systems biology. Not only such models complement the mechanistic explanations of molecular biology by accounting for poorly understood aspects of biological phenomena, they can also reveal unsuspected ‘black boxes’ in mechanistic explanations, thus prompting their revision while providing new insights about the causal-mechanistic structure of the world.


Scientific explanation Quantitative-dynamic explanation Mechanism Mathematical model Systems biology 



This work was supported by a generous fellowship from the KLI Institute. I would also like to thank the editors of the volume, Christophe Malaterre and Pierre-Alain Braillard, for their thoughtful comments on previous drafts of the paper.


  1. Baetu, T. M. (2011a). A defense of syntax-based gene concepts in postgenomics: ‘Genes as modular subroutines in the master genomic program’. Philosophy of Science, 78(5), 712–723.CrossRefGoogle Scholar
  2. Baetu, T. M. (2011b). Mechanism schemas and the relationship between biological theories. In P. McKay, J. Williamson, & F. Russo (Eds.), Causality in the sciences. Oxford: Oxford University Press.Google Scholar
  3. Baetu, T. M. (2012a). Filling in the mechanistic details: Two-variable experiments as tests for constitutive relevance. European Journal for Philosophy of Science, 2(3), 337–353.CrossRefGoogle Scholar
  4. Baetu, T. M. (2012b). Genomic programs as mechanism schemas: A non-reductionist interpretation. British Journal for the Philosophy of Science, 63(3), 649–671.CrossRefGoogle Scholar
  5. Baetu, T. M. (2014). Models and the mosaic of scientific knowledge. The case of immunology. Studies in History and Philosophy of Biological and Biomedical Sciences, 45, 49–56.CrossRefGoogle Scholar
  6. Baetu, T. M. (2015). When is a mechanistic explanation satisfactory? Reductionism and antireductionism in the context of mechanistic explanations. In G. Sandu, I. Parvu, & I. Toader (Eds.), Romanian studies in the history and philosophy of science. Dordrecht: Springer.Google Scholar
  7. Baetu, T. M., & Hiscott, J. (2002). On the TRAIL to apoptosis. Cytokine & Growth Factors Reviews, 13, 199–207.CrossRefGoogle Scholar
  8. Baker, M., Wolanin, P., & Stock, J. (2006). Systems biology of bacterial chemotaxis. Current Opinion in Microbiology, 9, 187–192.CrossRefGoogle Scholar
  9. Bechtel, W. (2006). Discovering cell mechanisms: The creation of modern cell biology. Cambridge: Cambridge University Press.Google Scholar
  10. Bechtel, W. (2015). Generalizing mechanistic explanations using graph-theoretic representations. In P.-A. Braillard & C. Malaterre (Eds.), Explanation in biology. An enquiry into the diversity of explanatory patterns in the life sciences (pp. 199–225). Dordrecht: Springer.Google Scholar
  11. Bechtel, W., & Abrahamsen, A. (2005). Explanation: A mechanist alternative. Studies in History and Philosophy of Biological and Biomedical Sciences, 36, 421–441.CrossRefGoogle Scholar
  12. Bechtel, W., & Abrahamsen, A. (2010). Dynamic mechanistic explanation: Computational modeling of circadian rhythms as an exemplar for cognitive science. Studies in History and Philosophy of Science Part A, 41, 321–333.CrossRefGoogle Scholar
  13. Bechtel, W., & Abrahamsen, A. (2011). Complex biological mechanisms: Cyclic, oscillatory, and autonomous. In C. A. Hooker (Ed.), Philosophy of complex systems (pp. 257–285). New York: Elsevier.CrossRefGoogle Scholar
  14. Braillard, P.-A. (2010). Systems biology and the mechanistic framework. History and Philosophy of Life Sciences, 32, 43–62.Google Scholar
  15. Braillard, P.-A. (2015). Prospect and limits of explaining biological systems in engineering terms. In P.-A. Braillard & C. Malaterre (Eds.), Explanation in biology. An enquiry into the diversity of explanatory patterns in the life sciences (pp. 319–344). Dordrecht: Springer.Google Scholar
  16. Breidenmoser, T., & Wolkenhauer, O. (2015). Explanation and organizing principles in systems biology. In P. A. Braillard & C. Malaterre (Eds.), Explanation in biology. An enquiry into the diversity of explanatory patterns in the life sciences (pp. 249–264). Dordrecht: Springer.Google Scholar
  17. Brigandt, I. (2015). Evolutionary developmental biology and the limits of philosophical accounts of mechanistic explanation. In P.-A. Braillard & C. Malaterre (Eds.), Explanation in biology. An enquiry into the diversity of explanatory patterns in the life sciences (pp. 135–173). Dordrecht: Springer.Google Scholar
  18. Craver, C. (2006). When mechanistic models explain. Synthese, 153, 355–376.CrossRefGoogle Scholar
  19. Craver, C. (2007). Explaining the brain: Mechanisms and the mosaic unity of neuroscience. Oxford: Clarendon Press.CrossRefGoogle Scholar
  20. Darden, L. (2006). Reasoning in biological discoveries: Essays on mechanisms, interfield relations, and anomaly resolution. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  21. Davidson, E., & Levine, M. (2005). Gene regulatory networks. Proceedings of the National Academy of Science, 102(14), 4935.CrossRefGoogle Scholar
  22. Elowitz, M., & Leibler, S. (2000). Synthetic gene oscillatory network of transcriptional regulators. Nature, 403, 335–338.CrossRefGoogle Scholar
  23. Glennan, S. (2002). Rethinking mechanistic explanation. Philosophy of Science, 69, S342–S353.CrossRefGoogle Scholar
  24. Glennan, S. (2010). Ephemeral mechanisms and historical explanation. Erkenntnis, 72, 251–266.CrossRefGoogle Scholar
  25. Goodwin, B. (1963). Temporal organization in cells: A dynamic theory of cellular control processes. London: Academic.Google Scholar
  26. Gross, F. (2015). The relevance of irrelevance: Explanation in systems biology. In P.-A. Braillard & C. Malaterre (Eds.), Explanation in biology. An enquiry into the diversity of explanatory patterns in the life sciences (pp. 175–198). Dordrecht: Springer.Google Scholar
  27. Hodgkin, A. L., & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology, 117, 500–544.CrossRefGoogle Scholar
  28. Hoffmann, A., Levchenko, A., Scott, M., & Baltimore, D. (2002). The I κB–NF-κB signaling module: Temporal control and selective gene activation. Science, 298, 1241–1245.CrossRefGoogle Scholar
  29. Horne-Badovinac, S., & Munro, E. (2011). Tubular transformations. Science, 333, 294–295.CrossRefGoogle Scholar
  30. Huang, S. (1999). Gene expression profiling, genetic networks, and cellular states: An integrating concept for tumorigenesis and drug discovery. Journal of Molecular Medicine, 77(6), 469–480.CrossRefGoogle Scholar
  31. Huxford, T., Huang, D.-B., Malek, S., & Ghosh, G. (1998). The crystal structure of the I κB/NF-κ B complex reveals mechanisms of NF- κB inactivation. Cell, 95, 759–770.CrossRefGoogle Scholar
  32. Issad, T., & Malaterre, C. (2015). Are dynamic mechanistic explanations still mechanistic? In P.-A. Braillard & C. Malaterre (Eds.), Explanation in biology. An enquiry into the diversity of explanatory patterns in the life sciences (pp. 265–292). Dordrecht: Springer.Google Scholar
  33. Kauffman, S. (1993). The origins of order: Self-organization and selection in evolution. New York: Oxford University Press.Google Scholar
  34. Kauffman, S. (2004). A proposal for using the ensemble approach to understand genetic regulatory networks. Journal of Theoretical Biology, 230(4), 581–590.CrossRefGoogle Scholar
  35. Kritikou, E., Pulverer, B., & Heinrichs, A. (2006). All systems go! Nature Reviews Molecular Cell Biology, 7, 801.CrossRefGoogle Scholar
  36. Lakatos, I. (1978). Philosophical papers Vol I: The methodology of scientific research programmes. Cambridge: Cambridge University Press.CrossRefGoogle Scholar
  37. Machamer, P., Darden, L., & Craver, C. (2000). Thinking about mechanisms. Philosophy of Science, 67, 1–25.CrossRefGoogle Scholar
  38. McKay, P., & Williamson, J. (2011). What is a mechanism? Thinking about mechanisms across the sciences. European Journal for Philosophy of Science, 2, 119–135.Google Scholar
  39. Morange, M. (2009). Synthetic biology: A bridge between functional and evolutionary biology. Biological Theory, 4(4), 368–377.CrossRefGoogle Scholar
  40. Pahl, H. L. (1999). Activators and target genes of Rel/NF-κB transcription factors. Oncogene, 18, 6853–6866.CrossRefGoogle Scholar
  41. Shmulevich, I., & Aitchison, J. (2009). Deterministic and stochastic models of genetic regulatory networks. Methods in Enzymology, 467, 335–356.CrossRefGoogle Scholar
  42. Smart, J. J. C. (1963). Philosophy and scientific realism. New York: Humanities Press.Google Scholar
  43. Sun, S.-C., Ganchi, P. A., Ballard, D. W., & Greene, W. C. (1993). NF-κB controls expression of inhibitor I κB α: Evidence for an inducible autoregulatory pathway. Science, 259, 1912–1915.CrossRefGoogle Scholar
  44. Tang, N., Marshall, W., McMahon, M., Metzger, R., & Martin, G. (2011). Control of mitotic spindle angle by the RAS-regulated ERK1/2 pathway determines lung tube shape. Science, 333, 342–345.CrossRefGoogle Scholar
  45. Taniguchi, K., Maeda, R., Ando, T., Okumura, T., Nakazawa, N., Hatori, R., Nakamura, M., Hozumi, S., Fujiwara, H., & Matsuno, K. (2011). Chirality in planar cell shape contributes to left-right asymmetric epithelial morphogenesis. Science, 333, 339–341.CrossRefGoogle Scholar
  46. Théry, F. (2015). Explaining in contemporary molecular biology: Beyond mechanisms. In P.-A. Braillard & C. Malaterre (Eds.), Explanation in biology. An enquiry into the diversity of explanatory patterns in the life sciences (pp. 113–133). Dordrecht: Springer.Google Scholar
  47. von Bertalanffy, K. (1976). General system theory: Foundations, development, applications. New York: George Braziller.Google Scholar
  48. Weber, M. (2005). Philosophy of experimental biology. Cambridge: Cambridge University Press.Google Scholar
  49. Weber, M. (2008). Causes without mechanisms: Experimental regularities, physical laws, and neuroscientific explanation. Philosophy of Science, 75(5), 995–1007.CrossRefGoogle Scholar
  50. Wimsatt, W. C. (1972). Complexity and organization. In K. F. Schaffner & R. S. Cohen (Eds.), PSA 1972, Proceedings of the philosophy of science association (pp. 67–86). Dordrecht: Reidel.Google Scholar
  51. Woodward, J. (2003). Making things happen: A theory of causal explanation. Oxford: Oxford University Press.Google Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2015

Authors and Affiliations

  1. 1.Programa de FilosofiaUniversidade do Vale do Rio dos SinosSão LeopoldoBrasil

Personalised recommendations