A passive physical model for DnaK chaperoning.

Almost all living organisms use protein chaperones with a view to preventing proteins from misfolding or aggregation either spontaneously or during cellular stress. This work uses a reaction-diffusion stochastic model to describe the dynamic localization of the Hsp70 chaperone DnaK in Escherichia coli cells during transient proteotoxic collapse characterized by the accumulation of insoluble proteins. In the model, misfolded ('abnormal') proteins are produced during alcoholic stress and have the propensity to aggregate with a polymerization-like kinetics. When aggregates diffuse more slowly they grow larger. According to Michaelis-Menten-type kinetics, DnaK has the propensity to bind with misfolded proteins or aggregates in order to catalyse refolding. To match experimental fluorescence microscopy data showing clusters of DnaK-GFP localized in multiple foci, the model includes spatial zones with local reduced diffusion rates to generate spontaneous assemblies of DnaK called 'foci'. Numerical simulations of our model succeed in reproducing the kinetics of DnaK localization experimentally observed. DnaK starts from foci, moves to large aggregates during acute stress, resolves those aggregates during recovery and finally returns to its initial punctate localization pattern. Finally, we compare real biological events with hypothetical repartitions of the protein aggregates or DnaK. We then notice that DnaK action is more efficient on protein aggregates than on protein homogeneously distributed.