  Photosynthetic starch reserves that accumulate in Arabidopsis leaves during
the day decrease approximately linearly with time at night to support
metabolism and growth. We find that the rate of decrease is adjusted to
accommodate variation in the time of onset of darkness and starch content, such
that reserves last almost precisely until dawn. Generation of these dynamics
therefore requires an arithmetic division computation between the starch
content and expected time to dawn. We introduce two novel chemical kinetic
models capable of implementing analog arithmetic division. Predictions from the
models are successfully tested in plants perturbed by a night-time light period
or by mutations in starch degradation pathways. Our experiments indicate which
components of the starch degradation apparatus may be important for appropriate
arithmetic division. Our results are potentially relevant for any biological
system dependent on a food reserve for survival over a predictable time period.
