A Detailed Modular Analysis of Heat-Shock Protein Dynamics under Acute and Chronic Stress and Its Implication in Anxiety Disorders

Physiological and psychological stresses cause anxiety disorders such as depression and post-traumatic stress disorder (PTSD) and induce drastic changes at a molecular level in the brain. To counteract this stress, the heat-shock protein (HSP) network plays a vital role in restoring the homeostasis of the system. To study the stress-induced dynamics of heat-shock network, we analyzed three modules of the HSP90 network—namely trimerization reactions, phosphorylation–dephosphorylation reactions, and the conversion of HSP90 from an open to a closed conformation—and constructed a corresponding nonlinear differential equation model based on mass action kinetics laws. The kinetic parameters of the model were obtained through global optimization, and sensitivity analyses revealed that the most sensitive parameters are the kinase and phosphatase that drive the phosphorylation–dephosphorylation reactions. Bifurcation analysis carried out with the estimated kinetic parameters of the model with stress as bifurcation parameter revealed the occurrence of “mushroom”, a type of complex dynamics in which S-shaped and Z-shaped hysteretic bistable forms are present together. We mapped the molecular events responsible for generating the mushroom dynamics under stress and interpreted the occurrence of the S-shaped hysteresis to a normal level of stress, and the Z-shaped hysteresis to the HSP90 variations under acute and chronic stress in the fear conditioned system, and further, we hypothesized that this can be extended to stress-related disorders such as depression and PTSD in humans. Finally, we studied the effect of parameter variations on the mushroom dynamics to get insight about the role of phosphorylation–dephosphorylation parameters in HSP90 network in bringing about complex dynamics such as isolas, where the stable steady states in a bistable system are isolated and separated from each other and not connected by an unstable steady state.