Mathematical modeling of the proteasome function

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.