The proteasome is the major protease for intracellular degradation of proteins. The proteasome plays an key role in the cellular metabolism and in the function of the immune system. In order to develop the proteasome model that will allow to explain, predict and control its function, I would like to discuss two modeling approaches. The first approach deals with transport features of the proteasome, whereas second approach describes kinetics of the proteasome degradation. Following first approach we propose a simple model for the transport of peptides inside the proteasome and suggest a transport mechanism based on fluctuation influence and on a spatially asymmetric interaction potential. We compute the peptide-size-dependent transport rates for peptide translocation. For certain value of temperature the peptide of optimal length will be transported with the highest probability. Using these transport rates and assuming a constant cleavage rate we simulate the cleavage of the protein chain. The simulations are based on precomputed translocation rates and are performed using the Gillespie algorithm. These simulations demonstrate that a maximum observed experimentally in proteasome product size distribution may be explained by the fact that peptide of some optimal length will be translocated with the highest probability. This model also explain three peak distribution observed in the experiment. Following second approach I discuss the model, that describes kinetics of protein degradation by the proteasome. The model includes equations for the substrate concentrations of different length and also able to explain experimental length distributions. The possibility to extend this model and include the sequence specific cleavage is discussed.
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