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Design principles and mechanistic explanation

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Abstract

In this essay I propose that what design principles in systems biology and systems neuroscience do is to present abstract characterizations of mechanisms, and thereby facilitate mechanistic explanation. To show this, one design principle in systems neuroscience, i.e., the multilayer perceptron, is examined. However, Braillard (2010) contends that design principles provide a sort of non-mechanistic explanation due to two related reasons: they are very general and describe non-causal dependence relationships. In response to this, I argue that, on the one hand, all mechanisms are more or less general (or abstract), and on the other, many (if not all) design principles are causal systems.

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Notes

  1. Notice that different authors of the mechanistic camp employ slightly different terminology, e.g., Machamer et al., (2000) use activities rather than operations. However, these differences in terminology do not concern my article.

  2. At one extreme, it might appear that some design principles are so abstract that they are no longer mechanisms, e.g., integral feedback control discussed by Braillard (2010). However, as Matthiessen (2017, p. 1) argues, it remains unclear if this principle is biological at all, for it is a principle originally developed in the engineering context and later borrowed to biology. More importantly, once this abstract mathematical framework is applied to the biological context where mechanistic information is added and mechanistic interpretations of the key terms in the framework are made, it inevitably becomes a biological mechanism.

  3. Wouters (2007) also employs the term “design explanation”, but in a different sense. For Wouters, a “design explanation” explains why an actual design of some organisms is better than some contrasting design, e.g., why fishes respire with gills rather than lungs. So, his “design explanation” differs from design principles in systems biology.

  4. Systems biology and systems neuroscience are different disciplines. However, since both study signal transduction in neuronal networks, in what follows I treat them as interchangeably—unless otherwise noted.

  5. Although the terms design principles and network motifs are used interchangeably throughout the essay, they are not exactly the same thing. Network motifs are almost always associated with a network with a number of nodes connected in a certain way, while design principles are more general and are not restricted to network representations. We may say network motifs are a type of design principles but not vice versa.

  6. It is worth mentioning that Abrahamsen and Bechtel (1991) is perhaps the earliest philosophical discussion of perceptrons, where they examined in detail both single-layer and multilayer perceptrons. I thank one anonymous reviewer for letting me know this.

  7. Perceptrons were first introduced to characterize how neurons might work to perceive patterns (hence the name). Later, the limitations of single-layer perceptrons were noticed by scientists, who also recognized that multilayer systems could overcome the limitations. However, they dismissed these multilayer systems (because there was no learning rule for them) until considerably later with the introduction of backpropagation. I thank one anonymous reviewer for letting me notice this history.

  8. Phosphorylation is the chemical reaction in which a charged PO4 group is added to a specific site on the target protein, whereas dephosphorylation is the removal of the PO4 group. Both reactions are catalyzed by specific enzymes, e.g., kinases and phosphatases.

  9. Receptors are proteins that detect input signals to signal transduction networks, and ligands are specific molecules, a kind of input signal, that can be detected by receptors.

  10. I thank one anonymous reviewer for letting me emphasize this point.

  11. Note that adding new layers to the perceptron will not necessarily increase the computational power of the perception, for we can always construct a simple perceptron without extra layers that will compute the same function. So, what really matters here is non-linearity. For this reason, here we assume that the relevant activation function involved is non-linear.

  12. It is worth mentioning that design principles can perform many other complicated functions not discussed in this essay, e.g., discrimination (being able to tell apart a set of very similar stimuli patterns), generalization (being able to “fill in the gaps” in partial stimuli patterns), graceful degradation (deteriorating rather than crashing down upon damage to parts or connections of the perceptron), etc. For details of these functions, see Hertz et al. (1991).

  13. Those early characterizations primarily refer to Machamer et al., (2000), Glennan (2002) and Bechtel & Abrahamsen (2005).

  14. Bechtel and Richardson anticipated this extension in their early book Discovering Complexity, where they not only noticed the simplicity of some accounts of mechanisms but also concerned how to overcome the simplicity (see Bechtel & Richardson (1993)). I thank one anonymous reviewer for letting me notice this early discussion.

  15. Fang (2021) recently has taken a further step, i.e., a dynamic causal approach, to extend the mechanistic framework, which highlights the dynamic and causal dimensions of a mechanism, and stresses the relevance of computational and causal modeling to establishing a mechanistic explanation.

  16. Notice that Bechtel & Abrahamsen (2010) employ a different example, i.e., circadian rhythm, to illustrate their dynamic mechanistic explanation. However, their purpose and mine are the same, i.e., showing how a computational part must be incorporated into a mechanistic explanation so as to explain phenomena arising from complex dynamic systems.

  17. Mechanistic information here means the information about the properties of a system’s components, the kinds of interactions amongst the components, and the components and their interactions’ spatiotemporal organization. Dynamic information means the information encoded in the mathematical or dynamic tools, e.g., differential equations.

  18. Kaplan & Craver (2011) hold that the mechanistic part of a mechanism and the mathematical tools (used to represent the dynamic parts of the mechanism) stand in a one-to-one mapping relationship. However, my position remains neutral with this view.

  19. Andersen (2014a, 2014b) argues that the different characterizations might suit to different projects of interest to philosophers and that the minimal conception might only suit to some more permissive sense of that term, e.g., ontological or causal structure sense.

  20. Craver and Tabery (2019) also think that a mechanism typically has these four basic elements.

  21. By referring to Carl Craver, one anonymous reviewer suggests that we view design principles as providing how-possibly explanations. However, whether design principles can correspond to Craver’s how-possibly explanations remains an open question. Since, according to Craver, how-possibly explanations are usually not adequate explanations because they are “only loosely constrained conjectures about the sort of mechanism that might suffice to produce the explanandum phenomenon” (2007b, p. 112). In Craver’s framework, at the other extreme are how-actually explanations, explanations that invoke real components, interactions and organizational features that actually bring about the phenomenon of interest. How-plausibly explanations reside in the middle of these extremes, which are “more or less consistent with the known constraints on the components, their activities, and their organization” (Ibid., p. 112–113). For the limitations of space, I will leave this problem for another occasion.

  22. One anonymous reviewer points out that in constructing design principles one is not carrying out research to figure out a mechanism but is building upon it, because she has already had knowledge about the mechanism—what she now needs to do is to abstract away from the details of this particular mechanism and obtain an overall design. I agree with this view, but with a slightly different interpretation of what is really going on here, for I think when developing a design principle, researchers are indeed engaged in figuring out a yet-to-be-discovered meta-mechanism, i.e., an abstract characterization of mechanisms, though not a particular mechanism. This meta-mechanism, though built upon existing mechanistic knowledge about specific systems, is obtained by abstracting a whole load of details away from any specific systems. So, in a sense, this meta-mechanism has not been already present because of our prior mechanistic knowledge, but only starts to emerge when we strive for a level of abstraction that goes beyond any particular mechanism. Hence, the reviewer is right to point out that in constructing design principles one is not carrying out research to figure out a mechanism, because one is carrying out research to figure out a meta-mechanism; and the reviewer is also right to point out that this carrying out research to figure out a meta-mechanism is built upon existing mechanistic knowledge about specific mechanisms. Interpreted in this way, I think my view in the article is consistent with the reviewer’s view.

  23. In fact, the multilayer perceptron is also studied in artificial intelligence and artificial neural networks. See Bray (1995), Gardner & Dorling (1998), Ramchoun et al., (2016).

  24. One thing about the relationship between generality and abstraction must be noted. Undoubtedly, generality and abstraction are closely related concepts, but they are not equivalent, for an abstract model may only apply to a limited set of physical systems, while a detailed, not-so-abstract model may apply very generally. However, by omitting details and thus making the model more abstract, we usually obtain a more general model. Levy & Bechtel (2013) also discuss the relationship between realism and generality in network motifs and connectivity models (and they also highlight the generality of network motifs), though their terminology is slightly different: abstraction versus generality. For them, abstraction denotes the degree to which specific details about parts and connections are left out, which corresponds to what I mean “realism” in this essay. So, in what follows, unless otherwise noted, I will use these two terms interchangeably.

  25. One anonymous reviewer points out that how general a design principle is depends on what one takes to be the design principle. For instance, a perceptron can be very general prior to training but very specific/realistic after training (due to the acquired weights). This contrast is not unlike the distinction between uninstantiated models (parameter values not assigned) and instantiated models (parameter values assigned), and it is not difficult to see that an uninstantiated model is not the same as an instantiated model (for many instantiated models can be derived from a single uninstantiated model). For the same reason, I do not think a perceptron before training is the same perceptron as the one after training.

  26. In fact, many authors view mechanistic explanations through the lens of mechanistic models, e.g., Craver (2007b) distinguishes how-possibly, how-plausibly and how-actually (mechanistic) models, Weiskopf (2011) directly takes mechanistic explanations to be mechanistic models, etc. Notice that Craver (2007b) holds an ontic-conception of explanation, according to which models are derivative of the real explanations, which for Craver (like Salmon (1984)) are the mechanisms in the world. For a discussion of the ontic conception, see Wright and Van Eck (2018).

  27. Notice that these authors (Machamer et al., 2000; Darden, 2006; Craver, 2007) often assume that the more concrete (or specific) a mechanistic explanation is, the better it is. So, mechanism sketch and schemata are not really explanatory for they are just way stations on the road to genuine mechanistic explanations. Craver expresses this very explicitly: “progress in building mechanistic explanations involves movement along […] the sketch-schema-mechanism axis” (2007b, p. 114). However, following Brigandt (2013) and Levy & Bechtel (2013), I do not think this is true, for a very abstract mechanistic explanation, e.g., the protein kinase cascade, can also be a good mechanistic explanation, and abstraction is even an indispensable part of a good mechanistic explanation.

  28. Note that the degree of generality of a model is largely driven by the target phenomenon to be explained and the intended goal of modeling, for an explanatory model is built for the purpose of providing explanation for the target phenomenon in the first place. Therefore, if the phenomenon to be explained is quite general in the sense that it is exhibited in a wide range of actual instances, then the corresponding model for this phenomenon is also relatively general. By contrast, if the phenomenon to be explained includes many specifics of a given case, then the corresponding model for the phenomenon can be less general. I thank one anonymous reviewer for letting me notice this point.

  29. One anonymous reviewer points out that Braillard’s conception of generality differs from what we usually associate with the term, for his conception is about constraint-based generality. Roughly speaking, constraint-based generality stems from the fact that different systems share the same organizational pattern because they are all under the same set of constraints. In our current situation regarding design principles, this refers to the fact that the dependence relation between a structure (or a design) and a function (or a phenomenon/behavior) arises from “constraints on the possible stable states, the possible functional relations, or the possible evolutionary trajectories of a class of systems” (Green, 2015, p. 632). The very existence of these constraints means that a given function can only be produced by a particular structure (or a limited set of structures). On the other hand, the underlying structure (as well as the manifested function) can still be found in a whole range of different systems, so here comes generality. I admit that this is an interesting sense of generality, but do not think that this sense of generality cannot be accommodated within the orthodoxic framework of generality. For one thing, although constraint-based generality concerns the way generality arises (due to constraints), it is ultimately still linked to how many actual (or potential) systems it can be applied to. Essentially, we say a design principle is general because we see it is instantiated in many different systems. So, I see no difference between constraint-based generality and our usual sense of generality. For another, and more importantly, constraint-based generality does not only applies to design principles but also to typical-sense mechanisms. Constraints exist at all levels of biology, and, due to physical (e.g., thermodynamic) and biological reasons (e.g., evolutionary processes and historical contingencies), it is also the case that in reality a given function can only be realized by one (or a limited set of) mechanisms. Perhaps there is a difference in degree with respect to constraints, but this sort of difference should not justify the claim that design principles’ constraint-based generality deserves an entirely distinct category.

  30. For a discussion of when it is both sufficient and advisable to leave out causal details while still capturing causal relations, see Levy (2013).

  31. It remains an open question whether there are any non-causal explanations provided by design principles. Although I am noncommittal about the answer(s) to this question, I’d like to briefly discuss one example that advocates of design explanation usually treat as providing an exemplar of non-causal explanation (Braillard, 2010; Green, 2015): integral feedback control (IFC). IFC is an abstract mathematical principle that shows the property of robust adaption exhibited by diverse living and nonliving systems across multiple scales, e.g., thermostats, bacterial chemotaxis (Yi et al., 2000), calcium homeostasis (El-Samad et al., 2002), resilience of insect societies (Schmickl & Karsai, 2018), etc. However, as Matthiessen has argued, in the context of bacterial chemotaxis, discovering IFC only marks the beginning of constructing a mechanistic explanation and “we can understand the mathematical modelling techniques of systems biologists as part of a broader practice of constructing and evaluating mechanism schemas” (2017, p. 1). This is simply because—as Matthiessen argues—IFC itself is merely an abstractum with some abstract properties; it starts to explain a phenomenon only when it is embedded into a particular (or a particular type of) system. So, when embedded into a biological system, mechanistic details are incorporated so as to explain a biological phenomenon of interest. I am fully aware that this discussion ultimately leads to the question of whether mathematical explanation can explain physical phenomena (Colyvan, 2001; Baker, 2005; Lyon, 2012; Lange, 2013; Pincock, 2015). Nevertheless, addressing this issue is surely beyond this essay’s scope and the success (or failure) of this essay does not rely on whether this issue is addressed or not.

  32. The FFLs actually consist of a whole set of design principles depending on how one component interacts with the others (e.g., whether it is activation or repression). For simplicity, what I show in this article is only one type of them, i.e., the type-1 incoherent FFL.

  33. For a comprehensive explanation of how these design principles’ dynamics help them fulfil the speeding function, see Alon (2007a, pp. 27–70).

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Acknowledgements

This work was presented to the Theory and Method in Biosciences research group at the University of Sydney, where I received helpful feedback from a number of colleagues including Pierrick Bourrat, Carl Brusse, Joshua Christie, Stefan Gawronski, Paul Griffiths, Kate Lynch and Peter Takacs. Also thanks to the National Social Science Fund provided by the National Office for Philosophy and Social Sciences, China (grant number: 20BZX038).

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This study was funded by the National Social Science Fund, provided by the National Office for Philosophy and Social Sciences, China (grant number: 20BZX038).

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Fang, W. Design principles and mechanistic explanation. HPLS 44, 55 (2022). https://doi.org/10.1007/s40656-022-00535-6

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