Title: Nonautonomous Dynamics of Acute Cell Injury,
Abstract: Clinically-relevant forms of acute cell injury, which include stroke and
myocardial infarction, have been of long-lasting challenge in terms of
successful intervention and treatments. Although laboratory studies have shown
it is possible to decrease cell death after such injuries, human clinical
trials based on laboratory therapies have generally failed. We suggested these
failures are due, at least partially, to the lack of a quantitative theoretical
framework for acute cell injury. Here we provide a systematic study on a
nonlinear dynamical model of acute cell injury and characterize the global
dynamics of a nonautonomous version of the theory. The nonautonomous model
gives rise to four qualitative types of dynamical patterns that can be mapped
to the behavior of cells after clinical acute injuries. In addition, the
concept of a maximum total intrinsic stress response, $S_{max}^*$, emerges from
the nonautonomous theory. A continuous transition across the four qualitative
patterns has been observed, which sets a natural range for initial conditions.
Under these initial conditions in the parameter space tested, the total induced
stress response can be increased to 2.5-11 folds of $S_{max}^*$. This result
indicates that cells possess a reserve stress response capacity which provides
a theoretical explanation of how therapies can prevent cell death after lethal
injuries. This nonautonomous theory of acute cell injury thus provides a
quantitative framework for understanding cell death and recovery and developing
effective therapeutics for acute injury.