Measurement for a Nonlinear Dynamical Theory of Acute Cell Injury

Abstract

Many clinically important acute injuries have been intractable to treatment, including stroke and cardiac arrest brain damage. We have attributed this failure to inadequate theoretical understanding of acute cell injury in biological systems. We developed a nonlinear dynamical theory of acute cell injury describing a competition between total injury-induced damage, D and total injury-induced stress responses, S. The attractor states (D∗, S∗) determine the outcome of the model. We tested the theory using a rodent model of global cerebral ischemia and hypothesized that changes in polysome-bound mRNAs and denatured protein aggregates in injured neurons would estimate S and D, respectively. After 10 min ischemia and reperfusion from 8 to 72 hours, hippocampal CA1 and CA3 were dissected. Regions were homogenized, polysomes isolated by sucrose pad, RNA extracted, then analyzed on Affymetrix Rat Gene 2.0 ST microarrays that detect ∼26,000 rat genes. Transcript changes were treated as positions in a multidimensional space, and distance between each time point and controls was plotted verses time. Detergent-insoluble protein aggregates were isolated, quantified by anti-ubiquitin Western blot and density plotted vs time. Data was fit to the theory using the Nelder-Mead method. The parameters obtained from data fitting allowed a self-consistency check by calculating the injury magnitude at the tipping point between recovery and death. This value is well-known to be 10 minutes of ischemia for CA1. Our calculations yielded 9.5 minutes for CA1, and 14.7 min for CA3 neurons. The agreement with the known tipping point of CA1 indicates our markers were reasonable estimates of S and D. This validation of the model is the first step towards applying it to develop effective therapies against clinically-important forms of acute cell injury.