  We study the impact of light on the mammalian circadian system using the
theory of phase response curves. Using a recently developed ansatz we derive a
low-dimensional macroscopic model for the core circadian clock in mammals.
Significantly, the variables and parameters in our model have physiological
interpretations and may be compared with experimental results. We focus on the
effect of four key factors which help shape the mammalian phase response to
light: heterogeneity in the population of oscillators, the structure of the
typical light phase response curve, the fraction of oscillators which receive
direct light input and changes in the coupling strengths associated with
seasonal day-lengths. We find these factors can explain several experimental
results and provide insight into the processing of light information in the
mammalian circadian system. In particular, we find that the sensitivity of the
circadian system to light may be modulated by changes in the relative coupling
forces between the light sensing and non-sensing populations. Finally, we show
how seasonal day-length, after-effects to light entrainment and seasonal
variations in light sensitivity in the mammalian circadian clock are
interrelated.
