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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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Effect of Constitutive Activation on Systems-Level Gains and Dose Response CurvesConstitutive activation was modeled by implementing a basal-level expression of G in addition to T-driven expression.(A) The lnY versus lnS curve transitions from a linear function lnY = lnS + lny0 to lnY =lnS + lny1 in the presence of constitutive activation.(B) In the presence of constitutive activation, systems-level gain(dash-dotted line) decreases from unity to asymptotically approach; in the absence of constitutive activation,remains at(unpublished data). Y responds to S in a more sensitive or less controlled manner in the presence of constitutive activation (solid line) than in its absence (dotted line).(C) In the presence of constitutive activation, systems-level gain(dash-dotted line) increases from zero to asymptotically approach a maximum; in the absence of constitutive activation,remains at(unpublished data). G responds to S in a more sluggish manner in the presence of constitutive activation (solid line) than in its absence (dotted line).
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pcbi-0030024-g004: Effect of Constitutive Activation on Systems-Level Gains and Dose Response CurvesConstitutive activation was modeled by implementing a basal-level expression of G in addition to T-driven expression.(A) The lnY versus lnS curve transitions from a linear function lnY = lnS + lny0 to lnY =lnS + lny1 in the presence of constitutive activation.(B) In the presence of constitutive activation, systems-level gain(dash-dotted line) decreases from unity to asymptotically approach; in the absence of constitutive activation,remains at(unpublished data). Y responds to S in a more sensitive or less controlled manner in the presence of constitutive activation (solid line) than in its absence (dotted line).(C) In the presence of constitutive activation, systems-level gain(dash-dotted line) increases from zero to asymptotically approach a maximum; in the absence of constitutive activation,remains at(unpublished data). G responds to S in a more sluggish manner in the presence of constitutive activation (solid line) than in its absence (dotted line).

Mentions: In a feedback control scheme such as in Figure 2A, in addition to being activated by its upstream species with a characteristic response coefficient, each downstream species in the feedback loop may have an independent basal constitutive activity. For instance, gene G may be constitutively expressed at a certain level even in the absence of transcription factor T. With T controlling G on top of this basal level, the actual value of local gain r2 varies as T drives the expression of G to higher levels. With small S and therefore small T, constitutive expression of G dominates, rendering the overall expression of G insensitive to changes in T, hence a small r2. As S and T increases, T-induced expression of G will gradually surpass the constitutive expression and become dominant. In this process, r2 steadily recovers to approach a maximal level (i.e., the characteristic local response coefficient of G controlled by T in the absence of constitutive expression). Local gains in other steps in the feedback loop may undergo a similar recovery from repression owing to constitutive activities. Such slow increases in local gains in approaching their respective characteristic values lead to a similar sluggish increase in the loop gain Rloop. As a result, the systems-level gain for Y (Figure 4A and dash-dotted line in Figure 4B) begins with unity, then decreases to asymptotically approach a fixed value . The corresponding Y versus S dose response (Figure 4B, solid line) is characterized by a curve transitioning from an initial linear function of Y = y0S for very small S to a superlinear function of for very large S. And compared with the situation devoid of constitutive activation (Figure 4B, dotted line), the dose response in its presence, though superlinear in appearance, does not bend downward as much, indicating a less controlled stage of stress response. For G, the systems-level gain (Figure 4C, dash-dotted line) increases from zero, asymptotically approaching a fixed value . The G versus S dose response (Figure 4C, solid line) is characterized by a curve transitioning from a horizontal line G = g0, through a transient sublinear stage, to function . And compared with the situation devoid of constitutive activation (Figure 4C, dotted line), gene expression in its presence is sluggish.


Dose response relationship in anti-stress gene regulatory networks.

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

Effect of Constitutive Activation on Systems-Level Gains and Dose Response CurvesConstitutive activation was modeled by implementing a basal-level expression of G in addition to T-driven expression.(A) The lnY versus lnS curve transitions from a linear function lnY = lnS + lny0 to lnY =lnS + lny1 in the presence of constitutive activation.(B) In the presence of constitutive activation, systems-level gain(dash-dotted line) decreases from unity to asymptotically approach; in the absence of constitutive activation,remains at(unpublished data). Y responds to S in a more sensitive or less controlled manner in the presence of constitutive activation (solid line) than in its absence (dotted line).(C) In the presence of constitutive activation, systems-level gain(dash-dotted line) increases from zero to asymptotically approach a maximum; in the absence of constitutive activation,remains at(unpublished data). G responds to S in a more sluggish manner in the presence of constitutive activation (solid line) than in its absence (dotted line).
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Related In: Results  -  Collection

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pcbi-0030024-g004: Effect of Constitutive Activation on Systems-Level Gains and Dose Response CurvesConstitutive activation was modeled by implementing a basal-level expression of G in addition to T-driven expression.(A) The lnY versus lnS curve transitions from a linear function lnY = lnS + lny0 to lnY =lnS + lny1 in the presence of constitutive activation.(B) In the presence of constitutive activation, systems-level gain(dash-dotted line) decreases from unity to asymptotically approach; in the absence of constitutive activation,remains at(unpublished data). Y responds to S in a more sensitive or less controlled manner in the presence of constitutive activation (solid line) than in its absence (dotted line).(C) In the presence of constitutive activation, systems-level gain(dash-dotted line) increases from zero to asymptotically approach a maximum; in the absence of constitutive activation,remains at(unpublished data). G responds to S in a more sluggish manner in the presence of constitutive activation (solid line) than in its absence (dotted line).
Mentions: In a feedback control scheme such as in Figure 2A, in addition to being activated by its upstream species with a characteristic response coefficient, each downstream species in the feedback loop may have an independent basal constitutive activity. For instance, gene G may be constitutively expressed at a certain level even in the absence of transcription factor T. With T controlling G on top of this basal level, the actual value of local gain r2 varies as T drives the expression of G to higher levels. With small S and therefore small T, constitutive expression of G dominates, rendering the overall expression of G insensitive to changes in T, hence a small r2. As S and T increases, T-induced expression of G will gradually surpass the constitutive expression and become dominant. In this process, r2 steadily recovers to approach a maximal level (i.e., the characteristic local response coefficient of G controlled by T in the absence of constitutive expression). Local gains in other steps in the feedback loop may undergo a similar recovery from repression owing to constitutive activities. Such slow increases in local gains in approaching their respective characteristic values lead to a similar sluggish increase in the loop gain Rloop. As a result, the systems-level gain for Y (Figure 4A and dash-dotted line in Figure 4B) begins with unity, then decreases to asymptotically approach a fixed value . The corresponding Y versus S dose response (Figure 4B, solid line) is characterized by a curve transitioning from an initial linear function of Y = y0S for very small S to a superlinear function of for very large S. And compared with the situation devoid of constitutive activation (Figure 4B, dotted line), the dose response in its presence, though superlinear in appearance, does not bend downward as much, indicating a less controlled stage of stress response. For G, the systems-level gain (Figure 4C, dash-dotted line) increases from zero, asymptotically approaching a fixed value . The G versus S dose response (Figure 4C, solid line) is characterized by a curve transitioning from a horizontal line G = g0, through a transient sublinear stage, to function . And compared with the situation devoid of constitutive activation (Figure 4C, dotted line), gene expression in its presence is sluggish.

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