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Protein synthesis is one of the most fundamental biological processes, whichconsumes a significant amount of cellular resources. Despite existence ofmultiple mathematical models of translation, varying in the level ofmechanistical details, surprisingly, there is no basic and simple chemicalkinetic model of this process, derived directly from the detailed kineticmodel. One of the reasons for this is that the translation process ischaracterized by indefinite number of states, thanks to existence of polysomes.We bypass this difficulty by applying a trick consisting in lumping multiplestates of translated mRNA into few dynamical variables and by introducing avariable describing the pool of translating ribosomes. The simplest model canbe solved analytically under some assumptions. The basic and simple model canbe extended, if necessary, to take into account various phenomena such as theinteraction between translating ribosomes, limited amount of ribosomal units orregulation of translation by microRNA. The model can be used as a buildingblock (translation module) for more complex models of cellular processes. Wedemonstrate the utility of the model in two examples. First, we determine thecritical parameters of the single protein synthesis for the case when theribosomal units are abundant. Second, we demonstrate intrinsic bi-stability inthe dynamics of the ribosomal protein turnover and predict that a minimalnumber of ribosomes should pre-exists in a living cell to sustain its proteinsynthesis machinery, even in the absence of proliferation.

Basic, simple and extendable kinetic model of protein synthesis