Generalizing Mechanistic Explanations Using Graph-Theoretic Representations
Mechanistic explanations appeal to the parts, operations, and organizations of mechanisms to explain the phenomena for which they are responsible. Scientists have developed accounts of myriads of mechanisms thought to be operative in biology, each involving distinctive parts and operations organized in idiosyncratic ways. The focus on specific mechanisms (e.g., those found in a particular cell type in a given model organism) appears opposed to the idea that explanations ought to be generalizable to new instances. Some generalizability can arise from the fact that many biological mechanisms inherit their parts and operations from mechanisms found in ancestral species and one can often identify commonalities in these parts and the operations they perform. But organization seems to be idiosyncratic to specific mechanisms, thwarting attempts to develop generalizations about how mechanisms organized in a specific way will behave. For example, as a result of different genes being expressed, the organizational pattern of interactions between proteins varies in different tissues or in the same tissue in different strains of a species. This poses an even greater problem when it is recognized that many biological mechanisms exhibit non-sequential organization of non-linear operations, making it difficult to use mental simulation to determine the behavior of the mechanism. Instead researchers resort to computational models, resulting in dynamic mechanistic explanations that integrate mathematical modeling with empirically ascertained details of parts and operations. These models, though, appear to be even more idiosyncratic, revealing only the behavior of the specific organization employed in a specific mechanism.
In recent years, however powerful tools have been developed for abstracting from the details of individual networks, providing a basis for informative generalizations about how networks employing the same abstract design will behave. These involve developing graph-theoretic representations of mechanisms and analyzing the properties of classes of graphs. Watts and Strogatz, Barabási, and Sporns have shown that large networks (e.g., neural circuits or gene networks) often exhibit a scale-free, small-world organization capable of efficient, flexible coordination of operations and appeal to these properties to explain behaviors of specific mechanisms. Alon and Tyson, focusing on sub-networks with just two to four nodes, have identified different motifs (distinctive micro-architectures such as feedforward loops and double negative feedback loops) that are specialized for particular types of processing. These tools offer abstract organizational principles to which researchers appeal in their efforts to explain the behaviors generated by the mechanisms in which they are implemented. In this paper I show how these projects provide a basis for developing generalizable accounts of complex mechanisms and their dynamical behavior.
KeywordsDynamic mechanistic explanations Generalizing explanations Graph-theory formalizations Motifs Scale-free small worlds
Initial research on this project began when I was a Fellow at the Institute for Advanced Studies at Hebrew University. I thank the members of the group for productive discussions and especially Arnon Levy for introducing me to the work of Uri Alon and facilitating a meeting with him. Subsequently I have benefited from many further discussions with Arnon and with Sara Green. I presented much of the material here at colloquia at the University of California, Irvine and the University of Cincinnati, at workshop at the University of Wollongong, and to the reunion conference of the research group at the Institute for Advanced Studies. I thank the audiences at these various forums for very helpful comments. I also thank members of the WORGODS research group (Adele Abrahamsen, Daniel Burnston, and Benjamin Sheredos) at the University of California, San Diego for valuable discussion of the diagrammatic representations of circadian clock mechanisms. Thanks as well to Marta Halina and to the editors of this volume, Pierre-Alain Braillard and Christophe Malaterre, for valuable comments and suggestions.
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