2.1. Phase Relationships

While the mechanistic picture given above is necessary for explaining rhythmicity, it is not sufficient. Several subsequent investigations have shown that it is not only that the mechanism operates according to the schema above that is important, but also that key quantities in the mechanism bear particular temporal relationships to each other. Looking for these relationships involved measuring and conceptualizing data in certain ways not entailed just by knowing the mechanistic organization.

One such important relationship was discovered by Ueda et al. (Reference Ueda, Hayashi, Chen, Sano, Machida, Shigeyoshi, Iino and Hashimoto2005), who decided to look at the temporal relationships between the activations of gene promoter types as such—meaning, regardless of the particular genes that they regulated. Since each type of promoter occurs on multiple distinct genes, analysis of promoters had generally taken a back seat to the study of the genes themselves. However, Ueda et al. showed that the particular patterns of activity for each promoter type are important for explaining how an entire cell can oscillate in the quantities of its gene products. They first noticed that all of the different activators of a particular promoter type tended to hit their peak expression at similar times, and the same for its repressors. Moreover, for each promoter type—E-boxes, D-boxes, and RREs—there is a distinct phase relationship between their activators and inhibitors. This suggested two ideas to the researchers: (i) that each promoter of a given type is activated in phase with other promoters of the same type, even if they regulate different genes, and (ii) that each type of promoter should have a particular phase of peak activation. This is indeed what they found—E-boxes are most active in the morning, D-boxes during the day, and RREs in the evening.

Ueda et al. claimed a functional import for these relationships—they produce “an integrated network of regulatory loops” (Reference Ueda, Hayashi, Chen, Sano, Machida, Shigeyoshi, Iino and Hashimoto2005, 187) within which many distinct regulatory components can operate on a coherent schedule. For current purposes, however, the explanatory import of the patterns is most clear in a subsequent study by Ukai-Tadenuma et al. (Reference Ukai-Tadenuma, Yamada, Xu, Ripperger, Liu and Ueda2011). They noted that Cry1 expression, known to be mediated by the E-box, is delayed relative to other E-box-mediated genes; moreover, without this delay, the cell will not produce coherent rhythms. This prompted biochemical investigation that discovered D-box and RRE elements on the Cry1 gene. These regulatory elements both perform the same operation—delaying Cry1 expression relative to other E-box-mediated genes. But they exert their peak influence at different times, as per the story given by Ueda et al., and their combined influence produces a specific delay in Cry1 expression. By manipulating these elements on the gene, Ukai-Tadenuma et al. showed that a precise temporal delay of Cry1 expression is necessary for cellular rhythmicity: too little delay and no rhythm occurs; too much delay and the rhythm has a period distinct from wild type. So, Cry1 phase delay is important for rhythmicity, and that delay is the product of the combined relative phases of the promoter regions on the Cry1 gene.

Importantly, the goal in Ukai-Tadenuma et al.’s study was not primarily to manipulate parts or operations but to manipulate phase delay. They showed that not only must the particular parts, operations, and causal organization of the mechanism be in place for it to work, but it must also have these elements coordinated according to the appropriate temporal patterns. Put simply, if the mechanism did not exhibit this particular set of temporal relations between its promoters, it would not oscillate as normal, and learning this fact was an important addition to the explanation, beyond the standard mechanism schema given in the clock model.

What, then, is the explanatory role being played by the pattern? I suggest that it is adverbial (Burnston Reference Burnston2016). A mechanistic description shows what the operations are and shows the causal organization of their interactions. The representation of patterns shows how these interactions are coordinated in their levels and timing to produce quantitative phenomena like rhythmicity. The next example will further illustrate this role.

2.2. Proportionality and Compensation

Baggs et al. (Reference Baggs, Price, DiTacchio, Panda, Fitzgerald and Hogenesch2009) sought to study an important phenomenon related to molecular clocks, namely, that of compensation. In noisy molecular networks, shifts above and below normal quantities of key components are common, but they can also be problematic—as shown above, for instance, the clock requires precise temporal coordination of gene product levels in the mechanism, which can be interrupted by fluctuations in gene product levels. Baggs et al. showed that compensation in clock mechanisms relies both on their particular mechanistic organization and on the particular patterns of change in quantities of particular gene products as the quantities of other products vary. Their manipulations consisted in insertion of small interfering RNA (siRNA) into cells in vitro, targeted to specific mRNAs. SiRNA knocks down its targeted mRNAs in a dose-dependent fashion, thus allowing for the comparison of responses in varying levels of knockdown. Baggs et al. represented their results in a variety of bar graphs, taken to show the types of responses that were important in implementing compensation. Two are shown in figure 2.

Figure 2.

Proportionality patterns in knockdown conditions. From Baggs et al. (Reference Baggs, Price, DiTacchio, Panda, Fitzgerald and Hogenesch2009).

The left panel of figure 2 shows that, with increasing levels of knockdown for Cry1 mRNA, Cry2 mRNA increases. But not only does it increase, it does so proportionally—the greater the knockdown of mCry1, the greater the increase of mCry2. Since Cry2 is the paralog of Cry1, its products perform similar operations at similar targets. So, as mCry1 is depleted, the rising mCry2 level results in the overall level of Cry influence at its targets remaining the same, thus allowing for the cell’s overall pattern of rhythmic gene interactions to continue. Proportional responses are also important in nonparalogous compensation. The right panel of figure 2 shows the effect of mPer1 knockdown on mRev-erbß and mBmal1. Rev-erbß is activated by PER proteins, and the proteins it codes for inhibit Bmal1. When mPer1 levels go down, mRev-erbß levels go up proportionally. This in turn produces a proportional decrease in mBmal1. The fact that knockdown of mPer1 should cause mRev-erb levels to go up, and that increasing mRev-erb levels should subsequently cause Bmal1 transcription to decrease, makes sense given the known operations performed by each part: PER inhibits Rev-erb, whose products in turn inhibit Bmal1. However, the discovery that each relationship is proportional is presented by Baggs et al. as an important further fact in explaining compensation.

It is important for compensation for the following reason: the clock relies on precise interacting levels of inhibition and excitation between the positive and negative loops. Having the levels of one abnormally higher than the levels of the other would wreak havoc on the necessary interplay of inhibition and excitation. As is evident in the right panel of figure 2, the combined proportional interactions result in a balance between the levels of mBmal1 (positive loop) and mPer1 (negative loop), hence keeping the interaction between loops functioning as normal. Knockdowns of other components are compensated for according to similar principles, inducing no loss of rhythmicity elsewhere in the clock.

Proportional relationships, as revealed in the bar graphs, are inherently patterns of quantitative responses across knockdown conditions. And, as with the case above, one must represent these patterns in addition to the mechanistic organization to understand how compensation comes about. As Baggs et al. summarize: “the clock network combines these activator and repressor modules with various forms of proportionality to construct relays that generate complex gene expression responses to single gene perturbations” (Reference Baggs, Price, DiTacchio, Panda, Fitzgerald and Hogenesch2009, 570). So, it is not only the operations performed by entities (“activator and repressor modules”) but also the particular quantitative patterns in which they interact (“forms of proportionality”) that explain compensation. This in turn helps explain how functioning rhythms at the cellular level can be maintained despite noisy conditions.

3.1. Patterns Are Distinct from Operations

A category is explanatory when representing it shows, perhaps in part, how the phenomenon of interest comes about. In previous work (Burnston Reference Burnston2016), I argued in detail that the explanatory role played by representations of patterns is dissociable from that played by representations of operations (e.g., in a mechanism diagram). I will only summarize these arguments here, before moving on to discuss the relationship between patterns and generalizations. The key point to note is that in each of Ueda et al. and Baggs et al. studies above, the parts, operations, and causal organization of the mechanism were already known—neither study extends, revises, or modifies the known mechanistic organization. In each case, however, the researchers discovered and represented a set of relationships between quantities in the system at specific times or across specific conditions. As such, knowing the relevant facts about parts and operations constrains, but does not determine, all of the relevant facts about the patterns. For instance, in discussing the Baggs et al. case I only focused on linear proportional patterns of responses, but these are not the only possible ones. Baggs et al. also explore several other types, including proportional relationships with fractional coefficients and nonlinear responses, which play roles in compensation for other knockdowns. The point is this: these distinct patterns of relationships are all (epistemically) possible even given the known operations performed by each part and the targets they perform them on. So, specifying the parts and operations does not give us all of the information we need to explain. We must also represent quantitative patterns.

3.2. Patterns Are Distinct from Generalizations

Those who are inspired to consider generalizations as fundamental in explanation often note that mechanisms comprise causal relations of a certain sort, namely, ones that are “stable” or “robust” (Leuridan Reference Leuridan2010; Woodward Reference Woodward2010). A mechanism, the intuition runs, is one that exhibits a stable organization that can produce “regular changes” (Machamer, Darden, and Craver Reference Machamer, Darden and Craver2000) in its environment. Hence, mechanisms depend on generalizations instantiated among their parts. Those who consider operations fundamental often point to the shortcomings of generalizations for explaining causal relationships between particulars. It is the activities of particulars, the intuition goes, that have effects on other particulars, not whether they instantiate some generalization. These relationships can hold even in statistically unlikely or rare cases—in extreme cases, we could want to explain singular events, which only happen once. Bogen (Reference Bogen2005) and Craver and Kaiser (Reference Craver and Kaiser2013) take this argument to show that explanations do not depend on relationships with a significant domain of invariance or scope and, thus, that generalizations only play subsidiary epistemic roles, which help us to access the operations that actually explain.

Patterns of the type I have described, however, are explanatorily distinct from generalizations. The argument for this involves two claims, one against the generalizationists and one against the operationists. Against the operationists: representing patterns is necessary for explanation even in cases of minimal scope or domain of invariance. Against the generalizationists: it is the specific pattern in the relationship, not any specific facts about its domain of invariance or scope, that is important for explanation. Presumably, if it were really the case that the explanatory role of a pattern depended on its status as a generalization, then that role would be closely related to how wide a scope the pattern has or how broad its domain of invariance is. The following two simple thought experiments show this not to be the case. The first assesses domain of invariance, and the second assesses scope.