Feedbacks and tipping points in organismal response to oxidative stress

Abstract

Biological feedbacks play a crucial role in determining effects of toxicants, radiation, and other environmental stressors on organisms. Focusing on reactive oxygen species (ROS) that are increasingly recognized as a crucial mediator of many stressor effects, we investigate how feedback strength affects the ability of organisms to control negative effects of exposure. We do this by developing a general theoretical framework for describing effects of a wide range of stressors and species. The framework accounts for positive and negative feedbacks representing cellular processes: (i) production of ROS due to metabolism and the stressor, (ii) ROS reactions with cellular compounds that cause damage, and (iii) cellular control of both ROS and damage. We suggest functional forms that capture generic properties of cellular control mechanisms constituting the feedbacks, assess stability of equilibrium states in the resulting models, and investigate tipping points at which cellular control breaks down causing unregulated increase of ROS and damage. Depending on the chosen functional forms, the models can have zero, one, or two positive steady states; except in one singular case, the steady state with lowest values of ROS and damage is locally stable. We found two types of tipping points: those induced by changes in the parameters (including the stressor intensity), and those induced by the history of exposure, i.e. ROS and damage levels. The relatively simple models effectively describe several patterns of cellular responses to stress, such as the covariation of ROS and damage, the break-down of cellular control leading to explosion of ROS and/or damage, increase in damage even when ROS is (near)-constant, and the effects of exposure history on the ability of the cell to handle additional stress. The models quantify dynamics of cellular control, and could therefore be used to estimate the metabolic costs of stress and help integrate them into models that use energetic considerations to model organism's response to the environment. Although developed with unicellular organisms in mind, our models can be applied to all multicellular organisms that utilize similar feedbacks when dealing with stress.