  Many proteins that undergo sequential enzymatic modification in the Golgi
cisternae are displayed at the plasma membrane as cell identity markers. The
modified proteins, called glycans, represent a molecular code. The fidelity of
this glycan code is measured by how accurately the glycan synthesis machinery
realises the desired target glycan distribution for a particular cell type and
niche. In this paper, we quantitatively analyse the tradeoffs between the
number of cisternae and the number and specificity of enzymes, in order to
synthesize a prescribed target glycan distribution of a certain complexity. We
find that to synthesize complex distributions, such as those observed in real
cells, one needs to have multiple cisternae and precise enzyme partitioning in
the Golgi. Additionally, for fixed number of enzymes and cisternae, there is an
optimal level of specificity of enzymes that achieves the target distribution
with high fidelity. Our results show how the complexity of the target glycan
distribution places functional constraints on the Golgi cisternal number and
enzyme specificity.
