Limits...
Dose response relationship in anti-stress gene regulatory networks.

Zhang Q, Andersen ME - PLoS Comput. Biol. (2006)

Bottom Line: Multimerization of anti-stress enzymes and transcription factors into homodimers, homotrimers, or even higher-order multimers, play a significant role in maintaining robust homeostasis.Each phase relies on specific gain-changing events that come into play as stressor level increases.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.

View Article: PubMed Central - PubMed

Affiliation: Division of Computational Biology, CIIT Centers for Health Research, Research Triangle Park, North Carolina, United States of America. qzhang@ciit.org

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 O2, 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 (controlled variables, transcription factors, and gene products) in these gene regulatory networks. Our work indicated that the shape of dose response curves (linear, superlinear, or sublinear) depends on changes in the specific values of local response coefficients (gains) 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.

Show MeSH

Related in: MedlinePlus

Effect of Saturation of Gene Activation on Systems-Level Gains and Dose Response CurvesSaturation of gene activation was modeled by implementing saturable T binding to the gene promoter.(A) In the presence of saturation of gene activation, the lnY versus lnS curve transitions from a linear function lnY =lnS + lny1 to lnY = lnS + lny2.(B) Systems-level gain(dash-dotted line) increases fromto asymptotically approach unity. The Y versus S curve (solid line) transitions from a superlinear function, through a sublinear segment, to a linear function Y = y2S.(C) Systems-level gain(dash-dotted line) decreases from the maximumto asymptotically approach zero. The G versus S curve (solid line) transitions from a functionto a horizontal line G = g2.
© Copyright Policy
Related In: Results  -  Collection

License
getmorefigures.php?uid=PMC1808489&req=5

pcbi-0030024-g005: Effect of Saturation of Gene Activation on Systems-Level Gains and Dose Response CurvesSaturation of gene activation was modeled by implementing saturable T binding to the gene promoter.(A) In the presence of saturation of gene activation, the lnY versus lnS curve transitions from a linear function lnY =lnS + lny1 to lnY = lnS + lny2.(B) Systems-level gain(dash-dotted line) increases fromto asymptotically approach unity. The Y versus S curve (solid line) transitions from a superlinear function, through a sublinear segment, to a linear function Y = y2S.(C) Systems-level gain(dash-dotted line) decreases from the maximumto asymptotically approach zero. The G versus S curve (solid line) transitions from a functionto a horizontal line G = g2.

Mentions: After recovering from gain repression by constitutive activation or in its absence, each local step operates at its characteristic gain value. However, it is unlikely that local gains would remain at these values for very high input of S. The saturable nature of biochemical interactions sets an upper limit for the degree of activation. For instance, if the transcription factor is activated by phosphorylation, then the abundance of the phosphorylated form cannot be greater than the total amount of that transcription factor. With respect to promoter binding, once the concentration of the specific transcription factor becomes much greater than the dissociation constant (Kd), the percentage binding will increase little even if the transcription factor continues to rise in concentration. In the process of approaching saturation of activation, local gains fall from their characteristic values toward zero. Accordingly, the loop gain Rloop decreases from an initial value to zero, as well. For the controlled variable Y, the systems-level gain would increase, according to Equation 8, from an initial value to unity (Figure 5A and dash-dotted line in Figure 5B). The resulting Y versus S dose response (Figure 5B, solid line) is characterized by a curve transitioning from an initial superlinear function for small S to a linear function Y = y2S for large S, interposed with a transitional sublinear segment. In the process of approaching saturation, the systems-level gain for G (Figure 5C, dash-dotted line) decreases from a fixed value to zero. Accordingly, the G versus S dose response starts with a function of , then plateaus as approaches zero (Figure 5C, solid line). In a sense, once gene activation is saturated, the control scheme degenerates to an open-loop system.


Dose response relationship in anti-stress gene regulatory networks.

Zhang Q, Andersen ME - PLoS Comput. Biol. (2006)

Effect of Saturation of Gene Activation on Systems-Level Gains and Dose Response CurvesSaturation of gene activation was modeled by implementing saturable T binding to the gene promoter.(A) In the presence of saturation of gene activation, the lnY versus lnS curve transitions from a linear function lnY =lnS + lny1 to lnY = lnS + lny2.(B) Systems-level gain(dash-dotted line) increases fromto asymptotically approach unity. The Y versus S curve (solid line) transitions from a superlinear function, through a sublinear segment, to a linear function Y = y2S.(C) Systems-level gain(dash-dotted line) decreases from the maximumto asymptotically approach zero. The G versus S curve (solid line) transitions from a functionto a horizontal line G = g2.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC1808489&req=5

pcbi-0030024-g005: Effect of Saturation of Gene Activation on Systems-Level Gains and Dose Response CurvesSaturation of gene activation was modeled by implementing saturable T binding to the gene promoter.(A) In the presence of saturation of gene activation, the lnY versus lnS curve transitions from a linear function lnY =lnS + lny1 to lnY = lnS + lny2.(B) Systems-level gain(dash-dotted line) increases fromto asymptotically approach unity. The Y versus S curve (solid line) transitions from a superlinear function, through a sublinear segment, to a linear function Y = y2S.(C) Systems-level gain(dash-dotted line) decreases from the maximumto asymptotically approach zero. The G versus S curve (solid line) transitions from a functionto a horizontal line G = g2.
Mentions: After recovering from gain repression by constitutive activation or in its absence, each local step operates at its characteristic gain value. However, it is unlikely that local gains would remain at these values for very high input of S. The saturable nature of biochemical interactions sets an upper limit for the degree of activation. For instance, if the transcription factor is activated by phosphorylation, then the abundance of the phosphorylated form cannot be greater than the total amount of that transcription factor. With respect to promoter binding, once the concentration of the specific transcription factor becomes much greater than the dissociation constant (Kd), the percentage binding will increase little even if the transcription factor continues to rise in concentration. In the process of approaching saturation of activation, local gains fall from their characteristic values toward zero. Accordingly, the loop gain Rloop decreases from an initial value to zero, as well. For the controlled variable Y, the systems-level gain would increase, according to Equation 8, from an initial value to unity (Figure 5A and dash-dotted line in Figure 5B). The resulting Y versus S dose response (Figure 5B, solid line) is characterized by a curve transitioning from an initial superlinear function for small S to a linear function Y = y2S for large S, interposed with a transitional sublinear segment. In the process of approaching saturation, the systems-level gain for G (Figure 5C, dash-dotted line) decreases from a fixed value to zero. Accordingly, the G versus S dose response starts with a function of , then plateaus as approaches zero (Figure 5C, solid line). In a sense, once gene activation is saturated, the control scheme degenerates to an open-loop system.

Bottom Line: Multimerization of anti-stress enzymes and transcription factors into homodimers, homotrimers, or even higher-order multimers, play a significant role in maintaining robust homeostasis.Each phase relies on specific gain-changing events that come into play as stressor level increases.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.

View Article: PubMed Central - PubMed

Affiliation: Division of Computational Biology, CIIT Centers for Health Research, Research Triangle Park, North Carolina, United States of America. qzhang@ciit.org

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 O2, 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 (controlled variables, transcription factors, and gene products) in these gene regulatory networks. Our work indicated that the shape of dose response curves (linear, superlinear, or sublinear) depends on changes in the specific values of local response coefficients (gains) 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.

Show MeSH
Related in: MedlinePlus