Nonautonomous Dynamics of Acute Cell Injury

Abstract

Medical conditions due to acute cell injury, such as stroke and heart attack, are of tremendous impact and have attracted huge amounts of research effort. The biomedical research that seeks cures for these conditions has been dominated by a qualitative, inductive mindset. Although the inductive approach has not been effective in developing medical treatments, it has amassed enough information to allow construction of quantitative, deductive models of acute cell injury. In this work we develop a modeling approach by extending an autonomous nonlinear dynamic theory of acute cell injury that offered new ways to conceptualize cell injury but possessed limitations that decrease its effectiveness. Here we study the global dynamics of the cell injury theory using a nonautonomous formulation. Different from the standard scenario in nonlinear dynamics that is determined by the steady state and fixed points of the model equations, in this nonautonomous model with a trivial fixed point, the system property is dominated by the transient states and the corresponding dynamic processes. The model gives rise to four qualitative types of dynamical patterns that can be mapped to the behavior of cells after clinical acute injuries. The nonautonomous theory predicts the existence of a latent stress response capacity (LSRC) possessed by injured cells. The LSRC provides a theoretical explanation of how therapies, such as hypothermia, can prevent cell death after lethal injuries. The nonautonomous theory of acute cell injury provides an improved quantitative framework for understanding cell death and recovery and lays a foundation for developing effective therapeutics for acute injury.