Stem cells and systems models: clashing views of explanation


This paper examines a case of failed interdisciplinary collaboration, between experimental stem cell research and theoretical systems biology. Recently, two groups of theoretical biologists have proposed dynamical systems models as a basis for understanding stem cells and their distinctive capacities. Experimental stem cell biologists, whose work focuses on manipulation of concrete cells, tissues and organisms, have largely ignored these proposals. I argue that ‘failure to communicate’ in this case is rooted in divergent views of explanation: the theoretically-inclined modelers are committed to a version of the covering-law view, while experimental stem cell biologists aim at mechanistic explanations. I propose a way to reconcile these two explanatory approaches to cell development, and discuss the significance of this result for interdisciplinary collaboration in systems biology and beyond.

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  1. 1.

    See Fagan (2013a, especially Chaps. 3 and 6–7) for more on stem cell experiments.

  2. 2.

    In addition to the works cited above, see: Furusawa and Kaneko (1998, 2001, 2009), Huang (2009a, b, 2011a), Huang et al. (2007, 2009), Kaneko (2011), Kaneko and Yomo (1999), Kaneko et al. (2008), Kauffman (1969, 1971, 1973, 1993), Nagajima and Kaneko (2008) ,Wang et al. (2010), Zhou and Huang (2010).

  3. 3.

    Citations to Furusawa and Kaneko (2012) as of 7/1/2014: Web of Science (23) and GoogleScholar (38). Programs of the International Society for Stem Cell Research annual meeting assessed: 2011–2014. Meetings on the Systems Biology of Stem Cells (UC Irvine) show a sharp decline in participation from experimental stem cell biologists between 2010 and 2011.

  4. 4.

    These critical assessments are examined in Sect. 5.

  5. 5.

    This is not of course the only obstacle to integrating experimental and modeling approaches. Different views about data and evidence, as well as long-term scientific aims, are likely to play a role as well. However, the clash of explanatory standards is the most serious at present, inhibiting even early stages of collaboration between stem cell experimentalists and DST modelers. Thanks to Miles MacLeod for raising this point on an earlier draft.

  6. 6.

    See Sects. 2 and 5.

  7. 7.

    A brief discussion of this case appears in Green et al. (2015). However, the conclusions of that paper concern another field—evolutionary systems biology; the stem cell case played the role of a negative example. This paper considers the example more in depth, and proposes a different positive solution than that of Green et al.

  8. 8.

    By a ‘view of explanation’ I mean the methodological commitments and assumptions held by a scientific community, which approximate philosophical accounts of scientific explanation.

  9. 9.

    See Fagan (2012a, 2013a, b) for more detailed discussion.

  10. 10.

    State space is also referred to as phase space; the DST modelers discussed here use these terms interchangeably.

  11. 11.

    Linear stability analysis involves using the Taylor expansion and combining equations representing changes for different variables into the product of a vector and matrix (see Newman 2010, pp. 679–686; Strogatz 2000, pp. 24–26, 150–155).

  12. 12.

    Other special cases involve complex values of matrix vectors, such that the steady-state is not a fixed point, but an oscillation or spiral. A scientifically significant example is stable oscillation or limit cycle, such as that of Lotka–Volterra predator–prey equations.

  13. 13.

    Interestingly, Waddington’s own representation of changing parameters is not cited by recent treatments.

  14. 14.

    Note that these DST models are not the only mathematical approach to stem cells (Sect. 1).

  15. 15.

    Though DST theorists term them ‘genes,’ nodes in GRNs do not represent DNA sequences (Fagan 2013a, Chap. 9). Kaneko and Yomo (1999) explicitly state that nodes of “autocatalytic reaction networks” may be interpreted as genes or proteins (p. 247).

  16. 16.

    Kauffman’s (1993) framework is another version of this idea: that the basic principles of living things are selection and self-organization, the latter taking priority.

  17. 17.

    In a further extension, robustness and plasticity are taken to be “essential features of all biological systems” (Kaneko 2011, pp. 403–404).

  18. 18.

    ODEs are the most commonly used formal framework for cellular systems models, both in systems biology generally, and for stem cell phenomena in particular. Alternative frameworks include directed graphs, Bayesian and Boolean networks (see Fagan 2013a, Chap. 9 for more detail).

  19. 19.

    These GRNs share a few key features: positive feedback loops, oscillating behavior, and an intermediate number of connecting paths between nodes (3–6, for small networks).

  20. 20.

    The smaller basins reflect a smaller number of nodes with values of the state variable \({>}\)0; fewer molecular species are present in networks at these states.

  21. 21.

    The “quasi-” qualifier is included to indicate that ‘elevation’ is not a true potential energy calculated by integrating the system of equations. Rather, relative ‘height’ and ‘depth’ of hills and valleys on the global landscape are computed as the probability of finding a cell at a given point in state space (Huang 2009a, p. 555).

  22. 22.

    E.g., Kaneko (2011, p. 408), see also Huang (2009b, p. 3859), Furusawa and Kaneko (2012, p. 215).

  23. 23.

    E.g., DST models can help us “understand the characteristics that distinguish stem cells from other cell types and allow them to conduct stable proliferation [aka self-renewal] and differentiation” (Furusawa and Kaneko 2012, p. 215).

  24. 24.

    Pluripotency is the capacity to develop into all cell types that make up an adult body (see Sect. 2).

  25. 25.

    For more on abstraction in biological explanations, see Levy and Bechtel (2013) on connectionist networks in neuroscience, Green et al. (2015) on principled design explanations in developmental biology.

  26. 26.

    For example: “[experimental data] are consistent with this picture. In other words, development is the distribution of cells into a set of (“low energy”) attractors and their balanced occupation by cell populations” (Huang et al. 2009, p. 873; italics mine).

  27. 27.

    Had the DST models predicted reprogramming in advance of Yamanaka’s experiments, this would have been a very surprising result—and might well have caught experimenters’ attention.

  28. 28.

    Though it is not clear why the model predicts that reprogramming requires “few genes” rather than many.

  29. 29.

    This is why DST models’ support of counterfactual reasoning regarding elements of the state space does not obviate this concern: the terms in which such counterfactuals can be articulated do not make contact with the molecular details that experimentalists seek to explain. Thanks to an anonymous reviewer for Synthese for raising this point.

  30. 30.

    In the model, every point in the state space represents a gene expression pattern that “approximately represents” a cell phenotype. Movement on the landscape represents change in the gene expression profile of a GRN, “and, hence, of the cell phenotype” (Huang 2009b, p. 3859; italics mine). Relatedly, interactions are “hard-wired” such that there is only one GRN per genome (Huang 2009b, p. 550).

  31. 31.

    Elsewhere, Kauffman (1993) is more circumspect, treating the thesis that cell types are attractors as a reasonable hypothesis with some experimental support (p. 469).

  32. 32.

    Thanks to an anonymous reviewer for Synthese for pushing me to clarify this point.

  33. 33.

    This is not to say that all DST models of biological phenomena are committed to the covering law view. The analysis of this section, like other critical sections of this paper, is focused on the narrowly-defined community of theoretical DST modelers proposing an alternative explanation of stem cell capacities.

  34. 34.

    Kaneko et al. (2008, p. 501) suggest that V may represent the extent of methylation on chromosomal DNA; however, it is difficult to see how this feature could be attributed to entire cell states without loss of information needed to derive general features of cell development.

  35. 35.

    The two features are: few inputs per node, and canalyzing Boolean functions (see Kauffman 1993 for details).

  36. 36.

    But see Fagan (2012b), for a dissenting view.

  37. 37.

    Thanks to an anonymous reviewer for Synthese for raising this point.

  38. 38.

    Kauffman’s (1993) methodology is a response to a biological research community pre-dating stem cell biology today. His ‘order for free’ account is designed as an alternative to detailed, part-by-part reductionistic analysis based on experimental methods. The latter cannot satisfy Kauffman’s explanatory aims, which are not just to analyze GRN structure and behavior, but explain why they exhibit the structure and behavior they do, and how these features might evolve. Although experimental details about specific cascades and network reactions are useful, these cannot reveal the overall architecture of GRN systems, to “deduce these statistical features [of GRNs] from some deeper theory,” not “merely list them” (p. 25).

  39. 39.

    Machamer et al.’s (2000) definition of ‘mechanism’ does suggest a linear causal view of mechanisms (see above). However, more recent accounts of mechanisms in biology are more consonant with the ‘network’ view (e.g., Bechtel 2011).

  40. 40.

    The reverse accommodation, prioritizing the covering law view while relating mechanistic explanation to it, is illustrated by “constraint-based explanations” that articulate principles used to narrow down the ranges of possible mechanisms underlying phenomena of interest (Green et al. 2015).

  41. 41.

    For more detail, and a specific example, see Fagan (2012a, 2013a).

  42. 42.

    Because the same molecular components may interact differently in different contexts, we cannot extrapolate rate laws from one cellular context to another. This makes cellular systems models highly localized. The same molecular components operate differently in developing than in mature cells, across species, and across mature cell types. So molecular networks operating in developing cells require data from the cells in question, to formulate the equations.

  43. 43.

    Zednik (2008, 2011) argues, similarly, that dynamical models and methods can contribute to mechanistic as well as covering-law explanations.

  44. 44.

    See Green et al. (2015) for another example: evolutionary systems biology.

  45. 45.

    Paralleling foundationalist theories of epistemic justification, explanatory power is localized to the terminus of the explanatory chain.

  46. 46.

    See also Zednik (2008, note 1).


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This paper has benefited from comments by William Bechtel, Sara Green, Matt Haber, Oleg Igoshin, Johannes Jaeger, Lucie Laplane, Miles MacLeod, Elijah Millgram, Miriam Thalos, and two anonymous reviewers for Synthese. Funding was provided by a Faculty Innovation Fellowship from the Rice University Division of Humanities, and a Scholar’s Award from the National Science Foundation (Award No. 1354515).

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Correspondence to Melinda Bonnie Fagan.

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Earlier versions of this paper were presented at the 2013 ISHPSSB Biennial meeting (Montpellier, France), the 29th Altenberg Workshop in Theoretical Biology (Konrad Lorenz Institute, September 2013), and discussed among participants in Jim Bogen and Peter Machamer’s seminar on ‘Mechanisms, Explanation, and Reduction’ at University of Pittsburgh (Fall 2013).

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Fagan, M.B. Stem cells and systems models: clashing views of explanation. Synthese 193, 873–907 (2016).

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  • Explanation
  • Mechanisms
  • Covering law
  • Stem cells
  • Systems biology
  • Interdisciplinarity