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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.

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Variations in the Pre-Transcriptional Local Gain (r1), Level of Constitutive Activation, Earliness of Saturation of Gene Activation, and Degree of Feedforward Activation Can Qualitatively Alter the Curvature of the Y versus Se (External Stress) Dose Response Curve in the Low-Dose Region(A) Relatively small r1, high constitutive activation, and large Kd tend to retain the superlinear appearance in the low-dose region.(B) Intermediate conditions lead to minimal curvature change.(C) Relatively large r1, small constitutive activation, and small Kd render a sublinear appearance in the low-dose region.(D) Introduction of feedforward activation can depress Y initially, giving rise to a J-shaped dose response.Note: solid lines are simulation results, dashed straight lines were drawn to show how linear extrapolation from the high-dose region to the basal level can mis-estimate the response at low doses. Saturation of gene activation was modeled by changing Kd for transcription factor T binding to the gene promoter.
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pcbi-0030024-g009: Variations in the Pre-Transcriptional Local Gain (r1), Level of Constitutive Activation, Earliness of Saturation of Gene Activation, and Degree of Feedforward Activation Can Qualitatively Alter the Curvature of the Y versus Se (External Stress) Dose Response Curve in the Low-Dose Region(A) Relatively small r1, high constitutive activation, and large Kd tend to retain the superlinear appearance in the low-dose region.(B) Intermediate conditions lead to minimal curvature change.(C) Relatively large r1, small constitutive activation, and small Kd render a sublinear appearance in the low-dose region.(D) Introduction of feedforward activation can depress Y initially, giving rise to a J-shaped dose response.Note: solid lines are simulation results, dashed straight lines were drawn to show how linear extrapolation from the high-dose region to the basal level can mis-estimate the response at low doses. Saturation of gene activation was modeled by changing Kd for transcription factor T binding to the gene promoter.

Mentions: A common practice in assessing the biological risk for exposure to low-dose external stressors is to extrapolate linearly from high doses, where the impact can be reliably measured, to the background risk level at basal conditions (where S = S0). The underlying assumption is that the dose response behaves consistently in a linear fashion from high- through low-dose regions. Yet in the absence of the knowledge of low-dose curvature and its relationship with high-dose responses, linear extrapolation is unlikely to accurately represent low-dose risks. As we demonstrated above, in a homeostatic cellular defense system the low-dose region is intrinsically nonlinear. Notably, the dose response curve for Y versus external stress Se in the low-dose region is composed primarily of the superlinear phases and the transitional sublinear segment linking phase 2 and 3 (note: in constructing the dose response curve for Y versus the external stress Se, the background stress level S0 needs to be subtracted from the total stress S, and this is simply done by shifting the dose response curve derived for S to the left by S0 amount, which is unity in this study). The primary curvature in the low-dose region depends on the relative influences from the superlinear phase and sublinear segment. Simulation results demonstrated that under conditions where the pre-transcriptional local gain (for instance r1) is relatively small, the effect of constitutive activation is not negligible, and gene activation does not saturate early, a superlinear appearance occupies the low-dose region (Figure 9A). In contrast, the reverse conditions render a sublinear curve to dominate the low-dose region (Figure 9C). Intermediate conditions lead to less dramatic curvature changes in either direction (Figure 9B). Furthermore, introduction of feedforward activation of anti-stress genes can depress concentration of Y initially, leading to a J-shaped nonmonotonic dose response in the low-dose region (Figure 9D, see Text S2 for details on feedforward activation).


Dose response relationship in anti-stress gene regulatory networks.

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

Variations in the Pre-Transcriptional Local Gain (r1), Level of Constitutive Activation, Earliness of Saturation of Gene Activation, and Degree of Feedforward Activation Can Qualitatively Alter the Curvature of the Y versus Se (External Stress) Dose Response Curve in the Low-Dose Region(A) Relatively small r1, high constitutive activation, and large Kd tend to retain the superlinear appearance in the low-dose region.(B) Intermediate conditions lead to minimal curvature change.(C) Relatively large r1, small constitutive activation, and small Kd render a sublinear appearance in the low-dose region.(D) Introduction of feedforward activation can depress Y initially, giving rise to a J-shaped dose response.Note: solid lines are simulation results, dashed straight lines were drawn to show how linear extrapolation from the high-dose region to the basal level can mis-estimate the response at low doses. Saturation of gene activation was modeled by changing Kd for transcription factor T binding to the gene promoter.
© Copyright Policy
Related In: Results  -  Collection

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

pcbi-0030024-g009: Variations in the Pre-Transcriptional Local Gain (r1), Level of Constitutive Activation, Earliness of Saturation of Gene Activation, and Degree of Feedforward Activation Can Qualitatively Alter the Curvature of the Y versus Se (External Stress) Dose Response Curve in the Low-Dose Region(A) Relatively small r1, high constitutive activation, and large Kd tend to retain the superlinear appearance in the low-dose region.(B) Intermediate conditions lead to minimal curvature change.(C) Relatively large r1, small constitutive activation, and small Kd render a sublinear appearance in the low-dose region.(D) Introduction of feedforward activation can depress Y initially, giving rise to a J-shaped dose response.Note: solid lines are simulation results, dashed straight lines were drawn to show how linear extrapolation from the high-dose region to the basal level can mis-estimate the response at low doses. Saturation of gene activation was modeled by changing Kd for transcription factor T binding to the gene promoter.
Mentions: A common practice in assessing the biological risk for exposure to low-dose external stressors is to extrapolate linearly from high doses, where the impact can be reliably measured, to the background risk level at basal conditions (where S = S0). The underlying assumption is that the dose response behaves consistently in a linear fashion from high- through low-dose regions. Yet in the absence of the knowledge of low-dose curvature and its relationship with high-dose responses, linear extrapolation is unlikely to accurately represent low-dose risks. As we demonstrated above, in a homeostatic cellular defense system the low-dose region is intrinsically nonlinear. Notably, the dose response curve for Y versus external stress Se in the low-dose region is composed primarily of the superlinear phases and the transitional sublinear segment linking phase 2 and 3 (note: in constructing the dose response curve for Y versus the external stress Se, the background stress level S0 needs to be subtracted from the total stress S, and this is simply done by shifting the dose response curve derived for S to the left by S0 amount, which is unity in this study). The primary curvature in the low-dose region depends on the relative influences from the superlinear phase and sublinear segment. Simulation results demonstrated that under conditions where the pre-transcriptional local gain (for instance r1) is relatively small, the effect of constitutive activation is not negligible, and gene activation does not saturate early, a superlinear appearance occupies the low-dose region (Figure 9A). In contrast, the reverse conditions render a sublinear curve to dominate the low-dose region (Figure 9C). Intermediate conditions lead to less dramatic curvature changes in either direction (Figure 9B). Furthermore, introduction of feedforward activation of anti-stress genes can depress concentration of Y initially, leading to a J-shaped nonmonotonic dose response in the low-dose region (Figure 9D, see Text S2 for details on feedforward activation).

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