Abstract
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.
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Notes
- 1.
Machamer, Darden, and Craver define mechanisms as “entities and activities organized such that they are productive of regular changes from start or set-up to finish or termination conditions” (2000, 3). Alternatively, a mechanism is “a complex system that produces that behavior by the interaction of a number of parts, where the interactions among parts can be characterized by direct, invariant, change relating generalization” (Glennan 2002), or “a structure performing a function in virtue of its component parts, component operations, and their organization […] responsible for one or more phenomena” (Bechtel and Abrahamsen 2005). McKay and Williamson (2011) propose a more generally applicable characterization, according to which a “mechanism for a phenomenon consists of entities and activities organized in such a way that they are responsible for the phenomenon.”
- 2.
- 3.
“Intelligibility […] is provided by descriptions of mechanisms, that is, through the elaboration of constituent entities and activities that, by an extension of sensory experience with ways of working, provide an understanding of how some phenomenon is produced” (Machamer et al. 2000, 22).
- 4.
Both views admit gradations in explanatory value. Models incorporating fundamental laws provide deeper explanations than models relying on more superficial regularities describing the behavior of a certain type of systems. Likewise, under a mechanistic approach, a model incorporating a more complete description of a mechanism is better than a model relying on a sketchier description. For an account of the completeness of mechanistic explanations, see (Baetu 2015)
- 5.
For a more technical description, consult Shmulevich and Aitchison (2009). Additional assumptions are required in order to construct a model of a network. One has to choose between a synchronic and an asynchronous updating scheme, between a binary, multi-value, or stochastic logic, between different kinetic laws, between ordinary and partial differential equations, etc. Without these assumptions, it is impossible to model the dynamic behavior of the network.
- 6.
These states amount to long-term behaviors of networks and can be experimentally measured, thus allowing for precise quantitative predictions, as well as an assessment of the empirical adequacy of the model.
- 7.
Robustness is insensitivity to the precise values of biochemical parameters (changes in reaction rates, concentrations of substrates), thus allowing a system to function in a wide range of conditions and resist certain perturbations. Sensitivity denotes the contrary, namely a situation where a mechanism is operational only if the values of its parameters are fine-tuned to specific values. Robustness and sensitivity allow for optimization analysis, which is especially useful for identifying which mechanistic components should be targeted in order to achieve a desired result with maximal efficiency and minimal side effects.
- 8.
Ability to adapt to ‘background noise’: the smallest change in stimulus intensity that can be sensed (ΔS) increases with the background stimulus intensity (S), such that ΔS/S remains constant (Weber-Fechner law).
- 9.
A network may display more than one ‘stable state’, and it is possible that a change in the system’s state caused by a transient stimulus (e.g., external input, temporary change in gene expression) is not followed by a return to the initial state when the stimulus is withdrawn. It has been hypothesized that such states may underlie developmentally differentiated cell types (Kauffman 2004) or physiological cell states [e.g., proliferating vs. apoptotic cells; (Huang 1999)].
- 10.
The ‘laws’ to which they refer have a variable degree of generality, ranging from common features of networks displaying specific properties, such as robustness or adaptability, to more general properties of generic networks. Examples of the latter are found in Kauffman’s (1993) seminal work on Random Boolean Networks (networks in which the connections between nodes are wired randomly). By investigating the behavior of such networks, some general principles emerged; for instance, networks become chaotic as the number of connections per node increases.
- 11.
Weber (2005) argues for an ‘explanatory heteronomy’ of biology on physics and chemistry, and spells out the sense in which the former reduces to the latter: biology relies on the laws of physics and chemistry in order to generate explanations, and, in this respect, can be viewed as applied physics and chemistry.
- 12.
For instance, current discrete modeling strategies assume that a network is either updated synchronously (the values of all its nodes are updated at the same time) or asynchronously (no two nodes are updated at the same time). Set aside the difficulty of finding out which of the two assumptions holds true of the particular system under investigation – a situation that makes it such that investigators simply test several models until they find one that simulates well characterized features of the system –, it is also possible that no real biological system will perfectly fall into one or the other of these two categories.
- 13.
“A mechanism schema is a truncated abstract description of a mechanism that can be easily instantiated by filling it with more specific descriptions of component entities and activities” (Darden 2006, 111–12).
- 14.
GRNs are “hardwired genomic regulatory codes, the role of which is to specify the sets of genes that must be expressed in specific spatial and temporal patterns. […] these control systems consist of many thousands of modular DNA sequences. Each such module receives and integrates multiple inputs, in the form of regulatory proteins (activators and repressors) that recognize specific sequences within them. The end result is the precise transcriptional control of the associated genes” (Davidson and Levine 2005, 4935).
- 15.
For example, in order to physically inhibit the activity of a repressor, detailed knowledge of its structure, such as a mapping of the amino acids responsible for DNA binding, is required; the repressor activity is tempered with by mutating specifically these DNA-binding amino acids.
- 16.
In resting cells, NF-κB is held in the cytoplasm by IκB (Huxford et al. 1998). When cells are stimulated (Fig. 15.1, middle panel, A), a chain of protein-protein interactions leads to the degradation of IκB (B); NF-κB is freed (C), translocates to the nucleus (D) where it binds κB sequences in the promoter regions of target genes drastically enhancing their transcription (Pahl 1999). NF-κB also binds the promoter of the IκB gene (E), and the newly synthesized IκB binds NF-κB, trapping it back in the cytoplasm (Sun et al. 1993).
- 17.
By analogy with Lakatos’ (1978, 33) notion of ‘progressive research programme’ in which “each new theory […] predicts some novel, hitherto unexpected fact.”
- 18.
In mice, IκBα−/− is associated with exacerbated inflammation and embryonic lethality, while IκBβ/ε−/− females have a shorter fertility span. Nevertheless, other experiments suggest that the three forms are partially redundant. For a review of the original scientific literature, consult Hoffmann (2002, 1241–42).
- 19.
Furthermore, there are cases when significantly distinct mechanisms responsible for distinct phenomena nevertheless share mechanistic components. Thus, in addition to a modular mode of organization whereby systems of mechanisms are organized serially or in parallel, the output of a mechanism serving as input for one or more other mechanisms (Bechtel 2006; Craver 2007; Darden 2006), significantly distinct mechanisms may also be firmly interlocked in the same manner as the partially overlapping mechanisms described above. The lessons learned form the NF-κB regulatory mechanism raise the possibility that non-modular sharing of mechanistic components plays a physiologically relevant role in adjusting quantitative-dynamic aspects of the phenomena produced by these mechanisms. If this turns out to be the case, then molecular mechanisms are unlike any man-made mechanisms, first because they are heterogeneous populations rather than individual objects, and second because they operate both in a modular and a non-modular fashion. In other words, there is a sense in which a cell or organism cannot be decomposed into a set of mechanism-modules, but is one integrated mechanism consisting of heterogeneous populations of mechanisms overlapping to various degrees.
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Acknowledgments
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.
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Baetu, T.M. (2015). From Mechanisms to Mathematical Models and Back to Mechanisms: Quantitative Mechanistic Explanations. In: Explanation in Biology. History, Philosophy and Theory of the Life Sciences, vol 11. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9822-8_15
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