  The circadian clock can adapt itself to external cues, but the molecular
mechanisms and regulatory networks governing circadian oscillations' transient
adjustments are still largely unknown. Here we consider the specific case of
circadian oscillations transiently responding to a temperature change. Using a
framework motivated by Floquet theory, we model the mRNA expression level of
the fat body from Drosophila melanogaster following a step change from 25C to
18C. Using the method we infer the adaptation rates of individual genes as they
adapt to the new temperature. To deal with heteroskedastic noise and outliers
present in the expression data we employ quantile regression and wild bootstrap
for significance testing. Model selection with finite-sample corrected Akaike
Information Criterion (AICc) is performed additionally for robust inference. We
identify several genes with fast transition rates as potential sources of
temperature-mediated responses in the circadian system of fruit flies, and the
constructed network suggests that the proteasome may play important roles in
governing these responses.
