### abstract ###
To maintain a stable intracellular environment, cells utilize complex and specialized defense systems against a variety of external perturbations, such as electrophilic stress, heat shock, and hypoxia, etc. Irrespective of the type of stress, many adaptive mechanisms contributing to cellular homeostasis appear to operate through gene regulatory networks that are organized into negative feedback loops.
In general, the degree of deviation of the controlled variables, such as electrophiles, misfolded proteins, and O 2, is first detected by specialized sensor molecules, then the signal is transduced to specific transcription factors.
Transcription factors can regulate the expression of a suite of anti-stress genes, many of which encode enzymes functioning to counteract the perturbed variables.
The objective of this study was to explore, using control theory and computational approaches, the theoretical basis that underlies the steady-state dose response relationship between cellular stressors and intracellular biochemical species in these gene regulatory networks.
Our work indicated that the shape of dose response curves depends on changes in the specific values of local response coefficients distributed in the feedback loop.
Multimerization of anti-stress enzymes and transcription factors into homodimers, homotrimers, or even higher-order multimers, play a significant role in maintaining robust homeostasis.
Moreover, our simulation noted that dose response curves for the controlled variables can transition sequentially through four distinct phases as stressor level increases: initial superlinear with lesser control, superlinear more highly controlled, linear uncontrolled, and sublinear catastrophic.
Each phase relies on specific gain-changing events that come into play as stressor level increases.
The low-dose region is intrinsically nonlinear, and depending on the level of local gains, presence of gain-changing events, and degree of feedforward gene activation, this region can appear as superlinear, sublinear, or even J-shaped.
The general dose response transition proposed here was further examined in a complex anti-electrophilic stress pathway, which involves multiple genes, enzymes, and metabolic reactions.
This work would help biologists and especially toxicologists to better assess and predict the cellular impact brought about by biological stressors.
### introduction ###
Cells in vivo must maintain a relatively stable intracellular milieu in an extracellular environment that is constantly changing and is potentially unpredictable.
Notably, many intracellular biomolecules need to be held within closely regulated ranges of concentrations for normal cell functions.
Examples of these biochemical species, which could be detrimental and/or beneficial to cellular health, are electrophiles, reactive oxygen species, DNA adducts, misfolded proteins, O 2, and glucose.
When external stressors cause these molecules to deviate from their basal operating concentrations for an extended period of time, normal cell functions become disrupted, and cell cycle arrest and apoptosis may ensue CITATION.
Homeostatic regulation of vital intracellular biochemical species appears to operate primarily via gene regulatory networks that respond specifically to particular types of physical/chemical insults, such as electrophilic chemicals, heat shock, hypoxia, and hyperosmolarity CITATION CITATION.
As with many manmade control devices, such as thermostats and automobile cruise controls, these homeostatic gene regulatory networks are usually organized into negative feedback circuits that can be generalized into a common control scheme.
The output of the system, referred to as controlled variable, is the biochemical species that is perturbed by external stressors and therefore needs to be tightly controlled.
The system contains specific transcription factors that serve as transducers to either directly or indirectly sense the level of the controlled variable.
In this fashion, alterations in the concentration of the controlled variable affect the activity or abundance of the transcription factor.
Activated transcription factors then upregulate expression of individual or suites of anti-stress genes, many of which encode enzymes that participate in an array of interconnected biochemical reactions to counteract the perturbation of the controlled variable.
Control and dynamic system theory has benefited applied fields such as electronic and mechanical engineering for many decades, and in recent years increasing efforts have been made to apply similar concepts to biological systems including adaptive responses CITATION CITATION.
Our goal is to understand nature's design principle for anti-stress cellular homeostasis and to improve prediction of the disrupting effects of biological stressors.
Of practical importance for risk assessment at the cellular level is the steady-state dose response relationship between stressor levels and various measurable biochemical endpoints including the controlled variables, transcription factors, and gene expression.
Cell responses in the low-dose region are particularly relevant to human health risk assessment, and it is traditionally difficult to explain and predict dose response behaviors in this region due to uncertainty and subtlety of the curvature.
To accurately describe and fully understand complex dose response behaviors, the underlying biochemical networks will have to be examined through quantitative models.
With respect to the mathematical approaches involved, theoretical development in quantitative analysis of controls in biochemical networks, including metabolic control analysis and biochemical systems theory, has proven to be of great value CITATION CITATION.
Using numerical simulation and concepts from MCA, BST, and classical control theory, the present study focused on understanding the quantitative basis for the steady-state dose response in an anti-stress gene regulatory network.
While some of the conclusions presented in this paper may seem implicitly familiar, or even obvious, to engineers, they nonetheless provide an important framework by which biologists and especially toxicologists can improve the accuracy with which they evaluate the influence of biological stressors on intracellular control processes under different exposure conditions.
