Complex dynamics of chaperone-protein interactions under cellular stress.

We present a model of a generalizable but minimalistic network based on the properties of interactions between proteins, molecular chaperones (e.g., Hsp70, BiP) and ATP inside cells and subcellular components such as endoplasmic reticulum (ER). The dynamics of chaperone-dependent protein folding and misfolding in the cell can be modeled mathematically as a "predator-prey" problem, which can then be used to analyze the behavior of the system under conditions simulating stress (e.g., cardiac ischemia). We have tested this model under normal physiological and diseased conditions (e.g., ischemia as simulated by ATP depletion) and analyzed the effects of induction of chaperones (e.g., heat shock, tunicamycin) and inhibition of the degradative pathway (e.g., proteasome inhibition) on this model. Simulation gave the following results: (1) Under normal physiological conditions, as expected, the model predicts the stable production of correctly folded proteins. (2) A threshold of ATP levels exists below which the system tends toward increasing degrees of complex behavior. When ATP levels are just above this threshold, the system is highly vulnerable to sudden, brief drops in ATP levels such as may occur in the setting of acute ischemia: bursts of oscillations continue even when ATP levels revert to the threshold. However, if ATP levels are rapidly increased to levels considerably above the threshold, the system becomes stable again. (3) Up to 10-fold increases in chaperone levels, such as those that occur under conditions of prior heat shock or tunicamycin treatment, did not affect the behavior of the system under basal conditions, nor did it affect the tendency to complex behavior in the setting of ATP depletion. It did, however, shorten the recovery period of the system after chaotic-type oscillations were induced by acute ATP depletion. (4) Blocking the degradative pathway for misfolded proteins (e.g., proteasome inhibition) predisposes the system toward instability in the setting of ATP depletion by changing the ATP threshold at which bursts of oscillations occur. These results support the hypothesis that there are distinct thresholds for ATP, chaperones, and degradative activity, outside which cellular protein folding dynamics become unstable. They also suggest that an important mechanism by which chaperone induction protects cells from subsequent stress is by limiting the tendency to instability after an insult (e.g., acute myocardial ischemia or acute tubular injury to the kidney).