  In many models of the Calvin cycle of photosynthesis it is observed that
there are solutions where concentrations of key substances belonging to the
cycle tend to zero at late times, a phenomenon known as overload breakdown. In
this paper we prove theorems about the existence and non-existence of solutions
of this type and obtain information on which concentrations tend to zero when
overload breakdown occurs. As a starting point we take a model of Pettersson
and Ryde-Pettersson which seems to be prone to overload breakdown and a
modification of it due to Poolman which was intended to avoid this effect.
