I consider three explanatory strategies from recent systems biology that are driven by mathematics as much as mechanistic detail. Analysis of differential equations drives the first strategy; topological analysis of network motifs drives the second; mathematical theorems from control engineering drive the third. I also distinguish three abstraction types: aggregations, which simplify by condensing information; generalizations, which simplify by generalizing information; and structurations, which simplify by contextualizing information. Using a common explanandum as reference point—namely, the robust perfect adaptation of chemotaxis (...) in Escherichia coli—I argue that each strategy invokes a different combination of abstraction types and that each targets its abstractions to different mechanistic details. (shrink)

In the 1950s and 1960s, an interfield interaction between molecular biologists and biochemists integrated important discoveries about the mechanism of protein synthesis. This extended discovery episode reveals two general reasoning strategies for eliminating gaps in descriptions of the productive continuity of mechanisms: schema instantiation and forward chaining/backtracking. Schema instantiation involves filling roles in an overall framework for the mechanism. Forward chaining and backtracking eliminate gaps using knowledge about types of entities and their activities. Attention to mechanisms highlights salient features of (...) this historical episode while providing general reasoning strategies for mechanism discovery. (shrink)