  Protein synthesis is one of the most fundamental biological processes, which
consumes a significant amount of cellular resources. Despite existence of
multiple mathematical models of translation, varying in the level of
mechanistical details, surprisingly, there is no basic and simple chemical
kinetic model of this process, derived directly from the detailed kinetic
model. One of the reasons for this is that the translation process is
characterized by indefinite number of states, thanks to existence of polysomes.
We bypass this difficulty by applying a trick consisting in lumping multiple
states of translated mRNA into few dynamical variables and by introducing a
variable describing the pool of translating ribosomes. The simplest model can
be solved analytically under some assumptions. The basic and simple model can
be extended, if necessary, to take into account various phenomena such as the
interaction between translating ribosomes, limited amount of ribosomal units or
regulation of translation by microRNA. The model can be used as a building
block (translation module) for more complex models of cellular processes. We
demonstrate the utility of the model in two examples. First, we determine the
critical parameters of the single protein synthesis for the case when the
ribosomal units are abundant. Second, we demonstrate intrinsic bi-stability in
the dynamics of the ribosomal protein turnover and predict that a minimal
number of ribosomes should pre-exists in a living cell to sustain its protein
synthesis machinery, even in the absence of proliferation.
