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Non-monotonic dose–response relationship in steroid
hormone receptor-mediated gene expression
Li Li1,2, Melvin E And...
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      Table 1 Conditions in which U- or inverted U-sh...
Non-monotonic dose–response relationship in steroid hormone ...
Non-monotonic dose–response relationship in steroid hormone ...
Non-monotonic dose–response relationship in steroid hormone ...
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Non-monotonic dose–response relationship in steroid hormone ...

  1. 1. 569 Non-monotonic dose–response relationship in steroid hormone receptor-mediated gene expression Li Li1,2, Melvin E Andersen2, Steffen Heber1 and Qiang Zhang2 1 Bioinformatics Research Center, North Carolina State University, Raleigh, North Carolina 27695-7566, USA 2 The Hamner Institutes for Health Sciences, CIIT Centers for Health Research, Division of Computational Biology, 6 Davis Drive, PO Box 12137, Research Triangle Park, North Carolina 27709-2137, USA (Requests for offprints should be addressed to Q Zhang; Email: qzhang@thehamner.org) Abstract Steroid hormone receptors are the targets of many environmental endocrine active chemicals (EACs) and synthetic drugs used in hormone therapy. While most of these chemical compounds have a unidirectional and monotonic effect, certain EACs can display non-monotonic dose–response behaviors and some synthetic drugs are selective endocrine modulators. Mechanisms underlying these complex endocrine behaviors have not been fully understood. By formulating an ordinary differential equation-based computational model, we investigated in this study the steady-state dose– response behavior of exogenous steroid ligands in an endogenous hormonal background under various parameter conditions. Our simulation revealed that non-monotonic dose–responses in gene expression can arise within the classical genomic framework of steroid signaling. Specifically, when the exogenous ligand is an agonist, a U-shaped dose–response appears as a result of the inherently nonlinear process of receptor homodimerization. This U-shaped dose–response curve can be further modulated by mixed-ligand heterodimers formed between endogenous ligand- bound and exogenous ligand-bound receptor monomers. When the heterodimer is transcriptionally inactive or repressive, the magnitude of U-shape increases; conversely, when the heterodimer is transcriptionally active, the magnitude of U-shape decreases. Additionally, we found that an inverted U-shaped dose–response can arise when the heterodimer is a strong transcription activator regardless of whether the exogenous ligand is an agonist or antagonist. Our work provides a novel mechanism for non-monotonic, particularly U-shaped, dose–response behaviors observed with certain steroid mimics, and may help not only understand how selective steroid receptor modulators work but also improve risk assessment for EACs. Journal of Molecular Endocrinology (2007) 38, 569–585 Introduction and enhance their ligand-binding affinity (Fang et al. 1996, Pratt & Toft 1997). During ligand binding, SHRs Steroid hormone receptors (SHRs) comprise a super- first dissociate from the chaperone complexes, followed family of transcription factors that are activated by by nuclear translocation of those SHRs initially located steroid hormones to regulate specific gene expression. in the cytoplasm (Htun et al. 1996, Georget et al. 1997, They play critical roles in a variety of physiological Tyagi et al. 2000). Liganded receptor monomers then processes including homeostasis, metabolism, repro- homodimerize with each other to form receptor dimers duction, and behaviors. Widely studied SHRs include (Kumar & Chambon 1988, Wrange et al. 1989, Wang androgen receptor (AR), estrogen receptor (ER), et al. 1995). Depending on the type of SHRs, receptor progesterone receptor (PR), and glucocorticoid dimers recognize and bind specifically to the DNA of receptor (GR). The overall structure of these SHRs is target hormone response elements (HREs), with each highly conserved and contains four major functional monomer recognizing one half-site of the HRE domains: a conserved DNA-binding domain (DBD), a (Nordeen et al. 1990, Langley et al. 1995, Klinge et al. C-terminal ligand-binding domain (LBD), an 1997). The receptor dimer–DNA complex then recruits N-terminal transactivational domain (NTD), and a a battery of nuclear coregulators to alter the local hinge region connecting DBD and LBD (Ruff et al. chromatin structures (Heinlein & Chang 2002, Smith & 2000, Gelmann 2002, Bledsoe et al. 2004, Rogerson et al. O’Malley 2004). With a relaxed chromatin structure, 2004). In its most general form, the classical genomic polymerase II gains access to the promoter to initiate action of steroid hormones involves the following gene transcription. Ligands that allow recruitment of intracellular processes. In the absence of natural ligand, corepressors (CoR) can induce condensation of the SHRs in the cytoplasm or nucleus are associated with chromatin, thus turning off gene transcription chaperone complexes, which function to stabilize SHRs (Fernandes & White 2003). Journal of Molecular Endocrinology (2007) 38, 569–585 DOI: 10.1677/JME-07-0003 0952–5041/07/038–569 q 2007 Society for Endocrinology Printed in Great Britain Online version via http://www.endocrinology-journals.org
  2. 2. 570 L LI and others . Non-monotonic dose–response relationship SHRs that are normally activated by endogenous of kinases such as mitogen-activated protein kinase, may ligands can also respond to exogenous substances, modulate the genomic actions of the same ligands in including synthetic drugs and environmental opposite directions via receptor or coregulator phos- chemicals. Acting on an endogenous hormonal back- phorylation, resulting in non-monotonic responses in ground, these chemical compounds can potentially gene expression (Acconcia & Marino 2003, Rochette-Egly modulate endocrine events, resulting in altered SHR- 2003). mediated biological functions. Many therapeutic drugs The present study focused on the steady-state dose– are designed to interact directly with SHRs as agonists response for gene expression mediated through SHRs. or antagonists to alter gene transcriptional activities in Using a computational modeling approach, we demon- target tissues. The effects exerted by many of these strated that non-monotonic dose–responses can readily drugs may vary from tissue to tissue (Dutertre & Smith arise within the classical framework of steroid signaling. 2000, Giannoukos et al. 2001, Berrevoets et al. 2002). For Our results indicated that the inherently nonlinear example, while both tamoxifen and raloxifene reduce process of receptor homodimerization in SHR signaling the risk of invasive breast cancers by acting as ER plays an important role in rendering U-shaped dose– antagonists in mammary tissues, they have a strong response curves, which can be further modulated by agonistic activity in bones that helps maintain bone mixed-ligand heterodimers. density in women (Dutertre & Smith 2000, Francucci et al. 2005). Because of the opposing effects, these drugs are more appropriately termed as selective receptor Methods modulators (SRMs). Besides synthetic drugs, a large set of chemicals that can interfere with endocrine func- Model structure tions are environmental pollutants termed as endo- Definitions for a pure agonist, antagonist, and partial crine active chemicals (EACs). EACs may interfere agonist in particular, in the endocrine literature have with the synthesis and metabolism of endogenous been largely observational rather than mechanistic. For hormones, or in many cases, interact with SHRs directly modeling purposes, we need to be more explicit, and so (Amaral Mendes 2002, Markey et al. 2002). An these terms are defined as follows. A pure agonist is a important aspect of health risk assessment for EACs is ligand that is able to recruit CoA exclusively to activate understanding dose–response curves at low doses that gene transcription. If a ligand is able to recruit CoR are relevant to human exposure in the environment. A exclusively to deactivate gene transcription, it is termed large body of evidence indicates that SHR-mediated as an active antagonist, whereas if a ligand can recruit adverse effects of EACs are sometimes nonlinear or neither CoR nor CoA after binding to a steroid receptor, even non-monotonic (i.e. U-shaped or inverted it is termed as a passive antagonist. A partial agonist is a U-shaped) in dose ranges exerting no overt cytotoxicity ligand that is able to recruit both CoA and CoR, albeit (Kemppainen & Wilson 1996, vom Saal et al. 1997, not simultaneously. In this way, when a partial agonist Maness et al. 1998, Putz et al. 2001a,b, Almstrup et al. acts alone in our model, it always activates gene 2002, Terouanne et al. 2003, Kohlerova & Skarda 2004). transcription but with a reduced maximal response The molecular basis for the bidirectional actions of when compared with a pure agonist. It is generally SRMs and non-monotonic or hormetic effects of EACs is believed that whether a receptor is able to recruit CoA or not completely understood. A variety of mechanisms have CoR depends on its conformational changes after ligand been proposed to explain these observations. For instance, binding, particularly in the LBD domain (Brzozowski the ratio of coactivators (CoA) to corepressors in a cell may et al. 1997, Shiau et al. 1998), and the phosphorylation determine whether an exogenous ligand behaves status of the receptor also modulates this recruiting primarily as an agonist or antagonist (Smith et al. 1997, process (Atanaskova et al. 2002, Rochette-Egly 2003). Szapary et al. 1999, Smith & O’Malley 2004). Alternatively, Since there are always background levels of the opposing effect of SRMs in different tissues may endogenous hormones in a physiological state, we result from the involvement of different SHR subtypes simulated gene expression driven by exogenous (McInerney et al. 1998, Zhou & Cidlowski 2005). Kohn and ligand X in the presence of endogenous ligand L Melnick found that an inverted U-shaped dose–response (Fig. 1). In the absence of X, endogenous ligand can arise from conditions where there are unoccupied L first binds to a receptor SHR to form a liganded receptors by endogenous hormones and recruitment of receptor complex LR. Two LRs then associate with CoA by xenobiotic ligands is relatively weak (Kohn & each other to form a receptor homodimer LRRL. Melnick 2002). Conolly and Lutz hypothesized that a LRRL in turn binds to the HRE in the promoter of U-shaped dose–response curve can result from transcrip- target genes. While bound to HRE, LRRL is able to tionally inactive mixed-ligand receptor dimers (Conolly & recruit CoA to the local promoter site and together Lutz 2004). Possibilities also exist that the non-genomic these molecules produce an activational complex effect of steroid ligands, which often leads to the activation CoALRRLH. Since L mimics an endogenous Journal of Molecular Endocrinology (2007) 38, 569–585 www.endocrinology-journals.org
  3. 3. Non-monotonic dose–response relationship . L LI and others 571 Figure 1 Structure of the ODE-based model for SHR-mediated gene expression. For a detailed description of the signaling pathway, see Methods. For ODEs, parameter values, and supporting references, see Tables S1 and S2 in the Supplementary Material. kf01, kf11, kf21, kf31, kf02, kf12, kf22, kf32, kf42, kf13, kf23, kf33, and kf43 are the association rate constants; kb01, kb11, kb21, kb31, kb02, kb12, kb22, kb32, kb42, kb13, kb23, kb33, and kb43 are the dissociation rate constants. hormone here, we assumed that L acts only as a The control of gene activation at the promoter pure agonist, thus by our definition, recruiting no was modeled based on the current understanding of CoR to the local promoter. Exogenous ligand X gene induction in eukaryotic cells (Zhang et al. follows a similar signaling process as the endogen- 2006). At any given time, a gene could be in one of ous ligand L. However, X may function as either a two discrete transcriptional states, inactive (GENEi) pure agonist by recruiting CoA, a partial agonist by or active (GENEa), corresponding to compact and recruiting both CoA and CoR, or a passive or active relaxed chromatin structures respectively. Once in antagonist. When both endogenous ligand L and the active state, gene transcription proceeds at a exogenous ligand X are present, it is also possible relatively constant rate, whereas in the inactive state, that L-bound receptor LR may interact with no transcription occurs. Transitions between the X-bound receptor XR to form mixed-ligand hetero- inactive and active states are controlled by rate dimers (LRRX). Similar to XRRX, LRRX may constant kf5 and kb5 as indicated below: regulate gene transcription differentially, depending kf5 on whether CoA, CoR, or both are recruited. GENEi % GENEa Although Fig. 1 indicates that recruitment of CoA kb5 or CoR occurs after a receptor dimer binds to HRE, where the dimer may also interact with CoA or CoR directly prior to occupying HRE (Thenot et al. 1999, kf5 Z kf51 ½CoALRRLHŠ C kf52 ½CoAXRRXHŠ Margeat et al. 2001). We found that the inclusion of (1) C kf53 ½CoALRRXHŠ; these DNA-independent interactions between receptor dimers and coregulators did not quali- kb5Zkb51Ckb52 ½CoRXRRXHŠCkb53 ½CoRLRRXHŠ: (2) tatively change the simulation results obtained in the absence of these interactions, except for the Notably, the transition from the inactive to active state is circumstance of receptor overexpression, in which regulated by coactivator-bound receptor–DNA excessive receptors may serve to scavenge the free complexes CoALRRLH, CoAXRRXH, and CoALRRXH coregulators resulting in repression of gene (Eq. (1)). These complexes would work to relax local expression at high doses of X. This auto-inhibitory chromatin structures by acting as or recruiting histone effect of receptor overexpression has been observed acetyltransferase, a process not explicitly modeled. in vitro with ERs (Bocquel et al. 1989, Webb et al. Conversely, transition from the active to inactive state is 1992). Therefore, the present study presents only regulated by corepressor-bound receptor–DNA the results considering DNA-dependent recruitment. complexes CoRXRRXH and CoRLRRXH (Eq. (2)), www.endocrinology-journals.org Journal of Molecular Endocrinology (2007) 38, 569–585
  4. 4. 572 L LI and others . Non-monotonic dose–response relationship which presumably convert relaxed chromatin into a Exogenous ligand X as a pure agonist compact structure by acting as or recruiting histone deacetylase. The term kb51 serves as a constitutive In the absence of mixed-ligand heterodimer LRRX repressor activity, which turns off gene transcription in Contrary to the intuition that an agonistic exogenous the absence of ligand-induced corepressor recruitment. ligand X would add to the basal gene expression Once in the active state, the gene transcribes primary sustained by endogenous ligand L, simulations surpris- transcripts (PTs). PTs are processed to become mature ingly revealed that X, acting on top of L, exhibits non- mRNAs, followed by protein translation. By modeling the monotonic U-shaped dose–response curves (Fig. 2, left process of gene regulation with these steps, we were able panels). X at relatively low doses first depresses the to incorporate both positive and negative transcriptional basal gene expression, and after reaching a minimum controls in a mechanistically more accurate manner, expression, the steady-state protein level reverses the rather than relying on empirical equations. downtrend as the dose of X continues to increase and finally reaches a saturated phase. This U-shaped profile was preserved in most of the conditions where Model parameters parameter values associated with the signaling events Ordinary differential equations (ODEs) and par- were varied (see details below). To quantify the ameter values are listed in the Supplementary U-shape, we regard the magnitude of U-shape as the Material (Tables S1 and S2), including references difference between the expression level at the nadir and and rationale for the choice of parameter values. For the lesser of the basal and saturated expression levels. direct comparison, the default parameter values for Conversely, the magnitude of inverted U-shape is the exogenous ligand X-initiated processes and mixed- difference between the expression level at the peak and ligand heterodimer-initiated processes were set the the greater of the basal and saturated expression levels. same as for endogenous ligand L. But these For continuity, the difference in positive values denotes parameters were varied systemically in the present a U-shaped response and negative values an inverted study to investigate their effects on dose–response U-shaped response. curves. Since we are interested only in the steady- Since the physiological level of an endogenous state dose–response behavior, only the forward steroid hormone (represented by L), such as association rate constants of reversible reactions testosterone and estrogen, varies between individuals were varied to investigate the effects of these or fluctuates through various physiological states, we processes. investigated the dose–response curve for exogenous ligand X in the presence of different L levels. As indicated in Fig. 2A, with higher L levels, the nadir of the U-shaped dose–response curve shifts pro- Modeling tools gressively to the right, indicating increasing difficulty The computational model was first constructed and for X to initially repress gene expression activated by parameterized in PathwayLab (InNetics Inc., L. However, with higher L levels, the magnitude of Linkoping, Sweden) and then exported into MatLab ¨ U-shape becomes more prominent, although it (The Mathworks, Inc., Natick, MA, USA). Dose– eventually levels off (Fig. 2A, right panel). Exogenous response curves were obtained by running the ligands often differ in their binding affinity towards model to steady state in MatLab. The model in target SHRs. By varying kf02, the association rate the Systems Biology Markup Language (SBML) and constant between X and SHR, our simulation MatLab format is provided as additional supple- demonstrated that an increase in the binding affinity mentary materials. merely results in a parallel, leftward shift of the dose–response curve without affecting the magnitude of U-shape (Fig. 2B). Another important variable is the intracellular concentration of SHRs, which may Results be at different levels among different cell types and tissues (Kuiper et al. 1997) or at different develop- Since exogenous ligand X can be either a pure agonist, mental and physiological stages, thus affecting an antagonist, or a partial agonist, we explored the cellular responses to endogenous hormones and steady-state dose–response relationship between gene exogenous ligands. By increasing the initial abun- expression and X for each of the three possibilities in dance of SHR in the model, we found that the dose– this order. Moreover, with each possibility, we also response curve generally shifts upward, with the dose considered situations in which mixed-ligand hetero- of X associated with the expression nadir remaining dimers either do not form at all, act as an activator, or as largely unchanged (Fig. 2C). Increasing the abun- a repressor. dance of SHR initially enhances the magnitude of Journal of Molecular Endocrinology (2007) 38, 569–585 www.endocrinology-journals.org
  5. 5. Non-monotonic dose–response relationship . L LI and others 573 A Protein Expression Level 500 180 150 Magnitude of U-shape 400 120 300 90 200 60 L= 0 100 L= 1e-9* L= 5e-9 30 L= 1e-7 L= 1e-6 0 0 10-12 10-10 10-8 10-6 10-4 10-10 10-9 10-8 10-7 10-6 [L] (M) B [X] (M) 500 60 Protein Expression Level Magnitude of U-shape 50 400 40 300 30 200 kf02=1.66e-7 20 kf02=1.66e-6 100 kf02=1.66e-5* 10 kf02=1.66e-4 kf02=1.66e-3 0 0 10-12 10-10 10-8 10-6 10-4 10-8 10-6 10-4 10-2 [X] (M) kf02 (1/S) C 150 Protein Expression Level 3000 Magnitude of U-shape 100 2000 SHR= 1.0e-9 SHR= 2.0e-9* SHR= 8.0e-9 50 1000 SHR= 1.6e-8 SHR= 3.2e-8 0 0 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [SHR] (M) D 80 1200 kf12=3e-8 kf12=8e-8 Protein Expression Level Magnitude of U-shape kf12=3e-7* 900 kf12=8e-7 60 kf12=3e-6 600 40 300 20 0 0 10-12 10-10 10-8 10-6 10-4 10-10 10-8 10-6 10-4 [X] (M) kf12 (1/S) Figure 2 U-shaped steady-state dose–response in gene expression and magnitude of U-shape when exogenous ligand X is a pure agonist and the heterodimer LRRX is absent. (A) Effect of the level of endogenous ligand L. (B) Effect of the binding affinity between X and SHR (implemented by varying the association rate constant kf02). (C) Effect of SHR concentrations. (D) Effect of the binding affinity between XRs to form homodimer XRRX (implemented by varying the association rate constant kf12). Note: parameter values marked by asterisk are default settings (same denotation for other figures). www.endocrinology-journals.org Journal of Molecular Endocrinology (2007) 38, 569–585
  6. 6. 574 L LI and others . Non-monotonic dose–response relationship U-shape, which then diminishes as SHR increases higher dose of X, more XRRX will be formed, which further. Next, we examined how the ability of is eventually high enough to compensate for all the receptor monomer XR to form homodimer XRRX losses of LRRL, thus reversing the downtrend in affects the dose–response curve. With a low associ- gene expression. ation rate constant (kf12) for homodimerization, exogenous ligand X behaves almost as a pure antagonist (Fig. 2D). In contrast, with a high kf12 In the presence of mixed-ligand heterodimer LRRX value, X produces a complete agonistic effect. With In this case, we considered situations in which LRRX intermediate kf12 values, however, the dose–response acts as either a transcriptional activator by recruiting curve remains U-shaped. Similar to the effect of CoA, an active repressor by recruiting CoR, an passive varying SHR abundance, the magnitude of U-shape repressor by not binding to HRE or recruiting any also has a biphasic appearance (Fig. 2D, right panel). coregulators, or a partial activator by recruiting both Lastly, we investigated how the ability of receptor CoA and CoR, though not simultaneously. dimer XRRX to bind HRE (kf22), XRRXH to recruit CoA (kf32), and CoAXRRXH to activate GENEi- to-GENEa transition (kf52), affects the shape of the LRRX as an activator. Compared with the situation dose–response curve. Variations in these parameters devoid of heterodimer formation (i.e. kf13Z0), emer- give rise to similar curvature changes as varying kf12 gence of LRRX as a transcriptional activator attenuates (results not shown). the magnitude of U-shape. As kf13, the association rate With the above analyses, it appears that the constant between LR and XR, increases, more LRRX U-shaped profile of dose–response persists in most heterodimers are formed to activate gene expression, of the situations explored. Varying parameter values pushing the nadir of the U-shaped dose–response curve at different stages of the signaling pathway seems to upward and thereby reducing the magnitude of affect, in most cases, only the magnitude and/or U-shape (Fig. 4A, top panel). When kf13 reaches a position of the U-shape, rather than completely value comparable to the equivalent parameters in the eradicate it. To identify the origin of the U-shaped homodimerization processes (i.e. kf11 and kf12), the dose–response, we then focused on the step of U-shape essentially disappears and the response only homodimerization between receptor monomers. increases monotonically. The dose–response curve This is an inherently nonlinear process, with a remains monotonic within a range of kf13, as indicated quadratic term describing the forward association by the extended horizontal line at zero in Fig. 4A rate, as indicated in Eqs (3) and (4), (middle panel). As kf13 increases further, the dose– response curve leaves the monotonic bounds and fflux11 Z kf11 ½LRŠ2 ; (3) appears non-monotonic again. Instead of a U-shape, an inverted U-shape emerges in this case, and its fflux12 Z kf12 ½XRŠ2 : (4) magnitude, as represented by negative values, increases sharply with small increments of kf13. Notably, the Linearizing the dimerization processes by converting overall shape of the dose–response curve is the sum of Eqs (3) and (4) into (5) and (6) respectively contributions from both homodimers LRRL and 0 XRRX, and the heterodimer LRRX (Fig. 4A bottom fflux11 Z kf11 ½LRŠ; (5) panel). At a high kf13 value, an inverted U-shaped dose– 0 response curve results because LRRX, which itself is fflux12 Z kf12 ½XRŠ (6) inverted U-shaped in appearance, has a dominant 0 0 influence. Varying the association rate constant for (where and kf11 were set to maintain the same kf12 basal gene expression level), we found that the LRRXH to recruit CoA (kf33) has a modulatory effect U-shape was completely eliminated, and under no similar to kf13 on the steady-state dose–response circumstances did it recur by varying parameter (Fig. 4B). However, when kf33 is too low, the magnitude values in any of the signaling steps (Fig. 3). These of the U-shape has a tendency to increase as LRRX results indicated that the U-shaped response must essentially degenerates to a passive repressor. Variations originate from receptor homodimerization, and it in the association rate constant for LRRX to bind HRE may be understood as follows. When X is competing (kf23) and for CoALRRXH to activate GENEi-to-GENEa against L for SHR at a low dose, the loss of transition (kf53) have an effect similar to varying kf33 homodimer LRRL from this competition cannot be (results not shown). Overall, the inverted U-shaped fully compensated by newly formed XRRX due to the curve originates from the formation of LRRX, which nonlinearity inherent in homodimerization. This play a dominant role in gene expression when they are inability to replenish lost LRRL with XRRX results in high abundance or are highly transcriptionally in an initial depression in gene expression. At a active. Journal of Molecular Endocrinology (2007) 38, 569–585 www.endocrinology-journals.org
  7. 7. Non-monotonic dose–response relationship . L LI and others 575 A B 300 300 Protein Expression Level Protein Expression Level 200 250 100 200 kf02=1.66e-7 L=0 kf02=1.66e-6 L = 1e-9* kf02=1.66e-5* L = 5e-9 kf02=1.66e-4 L = 1e-7 L = 1e-6 kf02=1.66e-3 0 150 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) C D 2500 800 SHR=1.0e-9 kf12=3e-8 SHR=2.0e-9* kf12=8e-8 SHR=8.0e-9 Protein Expression Level Protein Expression Level kf12=3e-7* 2000 SHR=1.6e-8 SHR=3.2e-8 600 kf12=8e-7 kf12=1e-6 1500 400 1000 200 500 0 0 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) Figure 3 Linearization of the homodimerization process eliminates the U-shaped dose–response when exogenous ligand X is a pure agonist and the heterodimer LRRX is absent. Refer to Eqs (5) and (6) for method of linearization. (A) Effect of the level of endogenous ligand L. (B) Effect of the binding affinity between X and SHR (implemented by varying the association rate constant kf02). (C) Effect of SHR concentrations. (D) Effect of the binding affinity between XRs to form homodimer XRRX (implemented by varying the association rate constant kf12). LRRX as a repressor. If the mixed-ligand heterodimer the magnitude of the U-shape, with the nadir of the LRRX does not recruit CoA, it functions as a U-shape eventually dropping to zero expression level transcriptional repressor, either active or passive, (Fig. 5A). Similarly, mimicking LRRX as a passive depending on whether CoR can be recruited. If repressor that can bind to HRE but unable to recruit LRRX does not bind to the response element HRE or, CoR (i.e. kf43Z0) also produces a U-shape-deepening after binding, does not recruit CoR, then LRRX would effect (results not shown). When LRRX acts as an active behave as a passive repressor by making LR and XR repressor, increasing kf43 (which represents the ability less available for formation of homodimers, or by of LRRXH to recruit CoR) augments the magnitude of making HRE less available for homodimers which the U-shape, as well (Fig. 5B). activate gene expression. If LRRX recruits CoR after binding to HRE, then LRRX acts as an active repressor by promoting transition from GENEa to GENEi. LRRX as a partial activator. When LRRX is able to recruit Simulations revealed that regardless of being passive both CoA and CoR, thus acting as a partial activator by or active, the existence of LRRX as a repressor further itself, its effect on regulating the direction of gene deepens the U-shaped dose–response curve observed in expression in the presence of endogenous ligand L the absence of LRRX formation (Fig. 5). When LRRX is depends on the relative strength of activation and mimicked as a passive repressor, which cannot bind to repression. If LRRX recruits CoA more strongly than HRE (i.e. kf23Z0), increasing kf13, the association rate CoR, the shape of dose–response curves will range from constant between LR and XR, progressively enhances blunted U-shape to inverted U-shape (results not www.endocrinology-journals.org Journal of Molecular Endocrinology (2007) 38, 569–585
  8. 8. 576 L LI and others . Non-monotonic dose–response relationship A B 800 800 kf13=3e-8 kf33=2.32e-6 kf13=3e-7* kf33=2.32e-5* kf13=9e-7 kf33=4.64e-5 Protein Expression Level Protein Expression Level 600 kf13=3e-6 600 kf33=9.32e-5 kf13=6e-6 kf33=1.66e-4 400 400 200 200 0 0 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) 40 50 Magnitude of U-shape Magnitude of U-shape 20 25 0 0 -20 -25 -40 -50 10-9 10-8 10-7 10-6 10-5 10-7 10-6 10-5 10-4 10-3 kf13 (1/S) kf33 (1/S) x10-3 [CoALRRLH], [CoAXRRXH], [CoALRRXH] 30 20 LRRL CoALRRLH XRRX CoAXRRXH LRRX CoALRRXH [LRRL], [XRRX], [LRRX] Sum Total 15 20 10 10 5 0 0 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) Figure 4 Mixed-ligand heterodimer LRRX acting as an activator reduces and inverts the U-shaped dose–response when exogenous ligand X is a pure agonist. (A) Effect of the binding affinity between LR and XR to form heterodimer LRRX (implemented by varying the association rate constant kf13). Results in the bottom panel were obtained with kf13 set at 3!10K6. (B) Effect of the ability of LRRX to recruit CoA (implemented by varying the association rate constant kf33). Results in the bottom panel were obtained with kf33 set at 2.32!10K4. Journal of Molecular Endocrinology (2007) 38, 569–585 www.endocrinology-journals.org
  9. 9. Non-monotonic dose–response relationship . L LI and others 577 A 500 200 kf13=3e-8 kf13=3e-7* kf13=3e-6 Protein Expression Level 400 kf13=6e-6 160 Magnitude of U-shape kf13=3e-5 300 120 200 80 100 40 0 0 10-12 10-10 10-8 10-6 10-4 10-8 10-6 10-4 10-2 [X] (M) kf13 (1/S) B 500 200 kf43=2.32e-6 kf43=2.32e-5* kf43=7.32e-5 Protein Expression Level 400 kf43=2.32e-4 160 Magnitude of U-shape kf43=7.32e-4 300 120 200 80 100 40 0 0 10-12 10-10 10-8 10-6 10-4 10-6 10-5 10-4 10-3 10-2 10-1 [X] (M) kf43 (1/S) Figure 5 Mixed-ligand heterodimer LRRX acting as a repressor deepens the U-shaped dose–response when exogenous ligand X is a pure agonist. (A) Effect of the binding affinity between LR and XR to form heterodimer LRRX (implemented by varying the association rate constant kf13). In this case, LRRX was simulated as a passive repressor by setting kf23 to zero. (B) Effect of the ability of LRRX to recruit CoR (implemented by varying the association rate constant kf43). shown), similar to the effect of LRRX acting as a pure shifts the dose–response curve to the left in parallel activator. Conversely, if LRRX recruits CoR more (Fig. 6A). In comparison, increasing the association strongly than CoA, a deepened U-shaped dose– rate constants in downstream steps (i.e. kf12, kf22, kf42) response curve arises (results not shown), similar to not only shifts the dose–response curve to the left, but the effect of LRRX acting as a repressor. also steepens the monotonically decreasing slope (Fig. 6B–D). In no circumstances was a non-monotonic dose–response curve, either U- or inverted U-shaped, Exogenous ligand X as an antagonist observed. In the absence of mixed-ligand heterodimer LRRX In the presence of mixed-ligand heterodimer LRRX As an antagonist, X may repress gene expression either passively or actively. With passive repression, X LRRX as an activator. By acting as an activator, LRRX competes against L for receptors or response elements; alleviates the antagonistic action of X (Fig. 7). with active repression, X recruits CoR to promote Increasing kf13, the association rate constant between deactivation of actively transcribing genes. Simulations LR and XR, initially shifts the monotonically decreasing revealed that as an antagonist, regardless of being dose–response curve to the right without changing its passive or active, X produces monotonically decreasing monotonic nature (Fig. 7A). As kf13 increases further, responses in gene expression (Fig. 6). Increasing the the activity of LRRX starts to dominate the shape of the binding affinity between X and SHR by adjusting kf02 dose–response curve, resulting in an inverted U-shape, www.endocrinology-journals.org Journal of Molecular Endocrinology (2007) 38, 569–585
  10. 10. 578 L LI and others . Non-monotonic dose–response relationship A B 200 200 kf02=1.66e-7 kf12=3e-8 kf02=1.66e-6 kf12=3e-7* kf02=1.66e-5* kf12=3e-6 Protein Expression Level Protein Expression Level 150 kf02=1.66e-4 150 kf12=3e-5 kf02=1.66e-3 kf12=3e-4 100 100 50 50 0 0 10-14 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) C D 200 200 kf22=2.32e-6 kf42=2.32e-6 kf22=2.32e-5* kf42=2.32e-5* kf22=2.32e-4 kf42=1.16e-4 Protein Expression Level Protein Expression level 150 kf22=2.32e-3 150 kf42=2.32e-4 kf22=7.32e-3 kf42=6.96e-4 100 100 50 50 0 0 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) Figure 6 Monotonically decreasing dose–response in gene expression when exogenous ligand X is a pure antagonist and the heterodimer LRRX is absent. (A) Effect of the binding affinity between X and SHR (implemented by varying the association rate constant kf02). In this case, X was simulated as a passive antagonist by setting kf12 to zero. (B) Effect of the binding affinity between XRs to form homodimer XRRX (implemented by varying the association rate constant kf12). In this case, X was simulated as a passive antagonist by setting kf22 to zero. (C) Effect of the binding affinity between XRRX and HRE (implemented by varying the association rate constant kf22). In this case, X was simulated as a passive antagonist by setting kf42 to zero. (D) Effect of the ability of XRRX to recruit CoR (implemented by varying the association rate constant kf42). the magnitude of which (in negative values) increases antagonistic action of X (Fig. 8). Increasing kf13, kf23 sharply for small increment of kf13. Similar to the effect (results not shown), kf43, and kb53 (results not of varying kf13, emergence of the inverted U-shape was shown), which enhances LRRX as a repressor at also obtained by varying the following constants: kf23, different signaling stages, results in leftward shifting the association rate constant between LRRX and HRE of the monotonically decreasing dose–response (results not shown); kf33, the association rate constant curve. But unlike the case where X functions as for LRRXH to recruit CoA (Fig. 7B); and kf53, the an antagonist in the absence of heterodimer LRRX, constant for CoALRRXH to activate GENEi-to-GENEa the slope of the dose–response curves tends to transition (results not shown). In all the cases, high decrease in steepness as they shift to the left (Fig. 8 doses of X eventually repress the gene expression versus Fig. 6). completely after an expression peak. This behavior is in contrast to the situation when X is a pure agonist, which LRRX as a partial activator. When LRRX is able to recruit induces high expression at high doses instead of both CoA and CoR, thus acting as a partial activator by depressing it to zero (Fig. 7 versus Fig. 4). itself, its effect on regulating the direction of gene expression depends on the relative strength of acti- LRRX as a repressor. By acting as a repressor, either vation and repression. If LRRX recruits CoA more passive or active, LRRX further strengthens the strongly than CoR, the shape of dose–response curves Journal of Molecular Endocrinology (2007) 38, 569–585 www.endocrinology-journals.org
  11. 11. Non-monotonic dose–response relationship . L LI and others 579 A 300 20 kf13=7.5e-8 kf13=1.5e-7 kf13=3.0e-7* Protein Expression Level Magnitude of U-shape kf13=6.0e-7 0 kf13=1.2e-6 200 -20 100 -40 0 -60 10-12 10-10 10-8 10-6 10-4 10-8 10-7 10-6 [X] (M) kf13 (1/S) B 300 20 kf33=5.80e-6 kf33=1.16e-5 kf33=2.32e-5* Protein Expression Level Magnitude of U-shape kf33=4.64e-5 0 kf33=6.96e-5 200 -20 100 -40 0 -60 10-12 10-10 10-8 10-6 10-4 10-6 10-5 10-4 [X] (M) kf33 (1/S) Figure 7 Mixed-ligand heterodimer LRRX acting as an activator shifts rightward and converts the monotonically decreasing dose– response to inverted U-shape, when exogenous ligand X is a pure antagonist. (A) Effect of the binding affinity between LR and XR to form heterodimer LRRX (implemented by varying the association rate constant kf13). (B) Effect of the ability of LRRX to recruit CoA (implemented by varying the association rate constant kf33). will range from monotonically decreasing to inverted activator, both U-shaped and inverted U-shaped U-shaped (results not shown), similar to the effect of responses can be observed, depending on its abun- LRRX acting as a pure activator. Conversely, if LRRX dance and strength of activity (Fig. 9C and D). The ratio recruits CoR more strongly than CoA, only a mono- between intracellular CoR and CoA has been proposed tonically decreasing dose–response curve can be to explain the differential effects in different target observed (results not shown), similar to the effect of tissues of many exogenous steroid mimics acting LRRX acting as a repressor. through SHRs (Smith et al. 1997, Smith & O’Malley 2004). Our simulation indicated that the CoR/CoA ratio does indeed affect the dose–response behavior in Exogenous ligand X as a partial agonist a very sensitive manner (Fig. 9). An increase in CoR/ CoA ratio tends to render the action of X completely If exogenous ligand X is a partial agonist, then by antagonistic, whereas a decrease in the ratio makes X our definition both CoA and CoR can be recruited, behave more like an agonist. Therefore, the relative albeit not simultaneously, by XRRX occupying the abundance of CoR and CoA is a key modulator of SHR- response element HRE. A series of simulations revealed mediated gene expression. that when heterodimer LRRX is absent or acts as a In summary, we have simulated the steady-state repressor, U-shaped dose–response curves can arise gene expression in an endogenous hormonal back- (Fig. 9A and B). When LRRX acts as a pure or partial ground with varying assumptions about the exogenous www.endocrinology-journals.org Journal of Molecular Endocrinology (2007) 38, 569–585
  12. 12. 580 L LI and others . Non-monotonic dose–response relationship A Discussion 200 kf13=3e-8 kf13=3e-7* The biological responses invoked by an exogenous kf13=3e-6 chemical may be non-monotonic (Calabrese & Baldwin Protein Expression Level 150 kf13=6e-6 2001b, 2003). With respect to SHR-mediated action, a kf13=3e-5 variety of mechanisms have been proposed to explain the non-monotonic effects of certain EACs and the 100 bidirectional effects of SRMs in different target tissues (Smith et al. 1997, McInerney et al. 1998, Kohn & Melnick 2002, Conolly & Lutz 2004, Smith & O’Malley 50 2004). Using numerical simulation of a relatively standard model of steroid hormone action, the present study demonstrated that non-monotonic steady-state 0 response may be a property intrinsic to SHR-mediated 10-14 10-11 10-8 10-5 gene expression under a variety of conditions. [X] (M) An essential step in the genomic action of steroid B hormones is the dimerization of liganded receptor 200 monomers (Kumar & Chambon 1988, Wrange et al. kf43=2.32e-6 1989). The requirement for SHRs to function as a kf43=2.32e-5* kf43=7.32e-5 dimer lies at least in the fact that a steroid HRE Protein Expression Level 150 kf43=2.32e-4 invariably comprises two half-sites of either direct or kf43=7.32e-4 inverted repeats, and each monomer can only recog- nize one half-site weakly (Nordeen et al. 1990, Langley 100 et al. 1995, Kuntz & Shapiro 1997). Therefore, SHRs need to function as a dimer, with each monomer binding to one half-site to gain enough overall affinity for the promoter (Kuntz & Shapiro 1997). Homo- 50 dimerization of liganded receptors is a nonlinear process because of the quadratic term defining the association between receptor monomers (Eqs (3) and 0 10-14 10-11 10-8 10-5 (4)). In the absence of mixed-ligand heterodimer [X] (M) formation and at low doses of exogenous ligand X, newly formed XRRX cannot completely compensate for the loss of LRRL from receptor competition. As a result, Figure 8 Mixed-ligand heterodimer LRRX acting as a repressor shifts leftward the monotonically decreasing dose–response when even if X is a pure or partial agonist with enough exogenous ligand X is a pure antagonist. (A) Effect of the binding activity, X would initially reduce gene expression from affinity between LR and XR to form heterodimer LRRX the basal level instead of adding to it. At higher doses, (implemented by varying the association rate constant kf13). In this the amount/activity of XRRX formed is able to case, LRRX was simulated as a passive repressor by setting kf23 to zero. (B) Effect of the ability of LRRX to recruit CoR completely replace and surpass lost LRRL, thereby (implemented by varying the association rate constant kf43). reversing the downtrend in gene expression and producing a U-shaped dose–response curve. The essentiality of homodimerization to the occurrence of steroid ligand. The shape of dose–response curves can U-shape was demonstrated by linearization of this vary from monotonically increasing or decreasing to process, which produced monotonic dose–responses non-monotonically U-shaped or inverted U-shaped, in all circumstances. Although in our model receptor depending on the transcriptional nature of the monomers form dimers prior to binding to HRE, a exogenous ligand and the intermediate complexes similar nonlinear response would also be expected if formed with the endogenous ligand. Conditions monomers were able to bind HRE sequentially and in a under which non-monotonic dose–responses could positively cooperative manner, forming the homodimer occur are summarized in Table 1. U-shaped dose– on the promoter. response curves may arise when exogenous ligand X is As illustrated in Fig. 2A, the magnitude of the U-shape either a pure or partial agonist, regardless of the is positively correlated with endogenous hormone levels. presence of mixed-ligand heterodimer LRRX; while The U-shape becomes less pronounced or would be too inverted U-shape arises only when LRRX functions as a subtle to be identified if the endogenous hormone is at pure or partial activator, regardless of whether X by levels below its Kd for the receptors (Kd is 1 nM in the itself is an agonist or antagonist. model). Given that endogenous hormones are usually Journal of Molecular Endocrinology (2007) 38, 569–585 www.endocrinology-journals.org
  13. 13. Non-monotonic dose–response relationship . L LI and others 581 A B x102 x102 5 5 CoR/CoA =0.25 CoR/CoA =0.25 CoR/CoA =0.5 CoR/CoA =0.5 CoR/CoA =1* CoR/CoA =1* Protein Expression Level Protein Expression Level 4 CoR/CoA =2 4 CoR/CoA =2 CoR/CoA =5 CoR/CoA =5 3 3 2 2 1 1 0 0 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) C x102 x102 5 5 CoR/CoA =0.25 CoR/CoA =0.25 CoR/CoA =0.5 CoR/CoA =0.5 CoR/CoA =1* CoR/CoA =1* Protein Expression Level Protein Expression Level 4 CoR/CoA =2 4 CoR/CoA =2 CoR/CoA =5 CoR/CoA =5 3 3 2 2 1 1 0 0 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) D x102 x102 5 5 CoR/CoA =0.25 CoR/CoA =0.25 CoR/CoA =0.5 CoR/CoA =0.5 CoR/CoA =1* CoR/CoA =1* Protein Expression Level Protein Expression Level 4 CoR/CoA =2 4 CoR/CoA =2 CoR/CoA =5 CoR/CoA =5 3 3 2 2 1 1 0 0 10-12 10-10 10-8 10-6 10-4 10-12 10-10 10-8 10-6 10-4 [X] (M) [X] (M) Figure 9 Effect of the CoR/CoA ratio on dose–responses when exogenous ligand X is a partial agonist. To achieve different CoR/CoA ratios while keeping the basal expression level sustained by L unchanged, only the initial concentration of CoR was varied. (A) In the absence of heterodimer LRRX. (B) LRRX acting as an active repressor. (C) LRRX acting as a pure activator. In this case, kf13 was set to 50% of the default value in the left panel, and twofold in the right panel. (D) LRRX acting as a partial activator. In this case, kf13 was set to 50% of the default value in the left panel and fourfold in the right panel. www.endocrinology-journals.org Journal of Molecular Endocrinology (2007) 38, 569–585
  14. 14. 582 L LI and others . Non-monotonic dose–response relationship Table 1 Conditions in which U- or inverted U-shaped dose– model, which deepens the U-shape (Fig. 5A). With response curves may appear respect to inverted U-shape, Kohn & Melnick (2002) suggested that one condition for this to occur is when LRRX there are excessive unoccupied receptors and recruit- Pure/ ment of CoA by xenobiotic ligands is weaker than by partial Absent activator Repressor endogenous ligands. However, in their model, receptor dimerization was not considered. In comparison, occur- rence of inverted U-shaped curves in our model relies on Pure/partial U U U agonist Inverted U the formation of LRRX functioning as activators. X Additionally, as noted in the Method, an inverted Antagonist None Inverted U None U-shape can also arise if SHRs exist in such a high abundance that the excessive receptors may titrate away free CoA, provided DNA-independent association at relatively low physiological levels, this may explain, at between these two species is allowed. This auto-inhibitory least in part, why SHR-mediated dose–responses are phenomenon due to self-squelching has been demon- observed more often as monotonic rather than as strated in vitro (Bocquel et al. 1989, Webb et al. 1992). U-shaped. Importantly, our results further showed that SRMs represent a group of compounds whose activity, formation of mixed-ligand heterodimer LRRX can i.e. agonistic or antagonistic, varies in a cellular and tissue modulate the magnitude of U-shape observed with context-dependent manner. For example, tamoxifen and agonistic X. As the activity of LRRX becomes more raloxifene are selective ER modulators, which are influential, the overall shape of the dose–response curve antiestrogenic in the breast but estrogenic in the bone for gene expression is increasingly amenable to the (Dutertre & Smith 2000, Francucci et al. 2005). Asoprisnil, profile of LRRX, which itself is inverted U-shaped (Fig. 4, a selective PR modulator, has an antiproliferative effect on bottom panels). If it is an activator, LRRX would first primate endometrium, but cannot induce labor in animal lessen the original U-shape of the dose–response curve, models of pregnancy and parturition (Chwalisz et al. and then push it upward into an inverted U-shape; 2005). Current understanding of the molecular conversely, if LRRX is a repressor, it would further deepen mechanism for tissue-selective action of SRMs hinges on the original U-shape. In comparison, when the exogen- the notion that SRMs can induce different confor- ous ligand X is an antagonist, no U-shape is observed, and mational changes to their cognate SHRs, particularly in only an inverted U-shape can be obtained when LRRX the C-terminal LBD, which in turn determine whether functions as a strong activator. Despite their significant CoA or CoR will be recruited (Brzozowski et al. 1997, role discussed here, it remains to be investigated whether LRRX indeed exist in cells in vitro and in vivo. But Shiau et al. 1998). Conformational changes and differ- apparently, if they cannot be formed at all, cells would ential coregulator recruitment also appear to be have a tendency to exhibit U-shaped responses when the regulated by the phosphorylation status of SHRs and exogenous ligand is an agonist. coregulators (Atanaskova et al. 2002, Michalides et al. Non-monotonic dose–responses in steroid or nuclear 2004). For SRMs that are capable of recruiting, to some receptor signaling have been previously investigated degree, both CoA and CoR, the relative abundance through numerical simulations (Kohn & Portier 1993, between these two types of opposing coregulators is a key Kohn & Melnick 2002, Conolly & Lutz 2004). Kohn and to the direction of their genomic actions (Smith et al. Portier had proposed that positive cooperative binding 1997, Smith & O’Malley 2004, Wang et al. 2004). In between liganded receptor and DNA may result in a keeping with this concept, our simulation demonstrated U-shaped dose–response curve (Kohn & Portier 1993). that with a high CoR/CoA ratio, the activity of exogenous The origin of U-shape from the nonlinear dimerization ligand X is primarily antagonistic, whereas with a low process, as we noted in the present study, has a similar CoR/CoA ratio, the activity is primarily agonistic (Fig. 9). mathematical basis to their findings. Generation of Moreover, the present study revealed that the differential U-shaped dose–responses with the latter mechanism effect of SRMs could result from factors other than the relies, however, on the existence of more than one copy CoR/CoA ratio. For instance, an exogenous ligand may of the HRE in the promoter, which may not always be the have different affinities for the same type of receptor in case. With respect to the role of LRRX in U-shaped different cell types or tissues. This affinity difference may responses, Conolly and Lutz have relied on regarding cause, in a certain dose range, antagonistic activity in cells them as transcriptionally inactive (Conolly & Lutz 2004) with lower affinity (resulting from the U-shape) and to explain the U-shaped response observed with AR agonistic activity in cells with higher affinity (Fig. 2B). In agonist hydroxyflutamide (Maness et al. 1998). This the presence of a mixed-ligand heterodimer, the ability of transcriptionally inactive heterodimer is equivalent to LXXR to recruit CoA or CoR, which may depend on the the case of LRRX acting as a passive repressor in our phosphorylation status of the receptor and coactivator Journal of Molecular Endocrinology (2007) 38, 569–585 www.endocrinology-journals.org

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