  HIF (Hypoxia Inducible Factor) is an oxygen-regulated transcription factor
that mediates the intracellular response to hypoxia in human cells. There is
increasing evidence that cell signaling pathways encode temporal information,
and thus cell fate may be determined by the dynamics of protein levels. We have
developed a mathematical model to describe the transient dynamics of the
HIF-1{\alpha} protein measured in single cells subjected to hypoxic shock. The
essential characteristics of these data are modeled with a system of
differential equations describing the feedback inhibition between HIF-1{\alpha}
and Prolyl Hydroxylases (PHD) oxygen sensors. Heterogeneity in the single-cell
data is accounted for through parameter variation in the model. We previously
identified the PHD2 isoform as the main PHD responsible for controlling the
HIF-1{\alpha} transient response, and make here testable predictions regarding
HIF-1{\alpha} dynamics subject to repetitive hypoxic pulses. The model is
further developed to describe the dynamics of HIF-1{\alpha} in cells cultured
as 3D spheroids, with oxygen dynamics parameterized using experimental
measurements of oxygen within spheroids. We show that the dynamics of
HIF-1{\alpha} and transcriptional targets of HIF-1{\alpha} display a
non-monotone response to the oxygen dynamics. Specifically we demonstrate that
the dynamic transient behavior of HIF-1{\alpha} results in differential
dynamics in transcriptional targets.
