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First published online August 9, 2006
doi: 10.1242/10.1242/jcs.03087
Research Article |
Department of Biomedical Engineering, School of Medicine, Johns Hopkins University, 613 Traylor Bldg, 720 Rutland Avenue, Baltimore, MD 21205, USA
* Author for correspondence (e-mail: aqutub{at}jhu.edu)
Accepted 6 June 2006
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Summary |
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hydroxylation. Results provide crucial insight into the effects of iron and prolyl hydroxylase on oxygen sensing. The model advances quantitative molecular level understanding of HIF1 pathways - an endeavor that will help elucidate the diverse responses to hypoxia found in cancer, ischemia and exercise.
Key words: Computational modeling, Mathematical modeling, Oxygen sensing, Hypoxic response
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; Wang et al., 1995). Angiogenesis, the formation of blood vessels from preexisting vessels, is regulated in part by local tissue O2 levels. This regulatory pathway links cell and tissue metabolic demand with vascular oxygen supply. The pathway is intricately governed by HIF1 regulation and HIF1 transcriptional activation of angiogenic factors.
HIF1 is a heterodimer, comprised of subunits HIF1 and HIF1ß. The beta subunit is constitutively expressed in cells. Expression of the alpha subunit may be induced by a number of pathways, and its degradation is highly sensitive to O2 levels. Called a `master switch for hypoxic gene expression' (Powell, 2003; Semenza, 2004), intracellular HIF1 in normoxia is experimentally undetectable; during hypoxia, it rapidly accumulates in the cell nucleus, and triggers gene expression. Molecular players involved in this process have come to light over the past six years. In normoxia, enzymes called prolyl hydroxylase domains (PHDs) react with HIF1 (Fig. 1). PHDs hydroxylate HIF1 at Pro402 and Pro564 in the oxygen-dependant degradation domain. The activity of PHDs depends on the amount of oxygen available. Three isoforms of HIF PHDs exist: PHD1, PHD2 and PHD3. Each isoform performs a separate function, with different kinetic properties and primary cellular locations (Appelhoff et al., 2004). PHD2 is the most abundant prolyl hydroxylase isoform in the cell cytoplasm during normoxia, and it has been credited as a controller of steady-state HIF1 concentrations under these conditions in a range of cell types (Berra et al., 2003). Conversely, in normoxia, intracellular PHD1 and PHD3 levels are low, if experimentally detectable (Appelhoff et al., 2004).
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is free to bind to a von Hippel Lindau (VHL) ubiquitin ligase complex, which tags HIF1 for proteasomal destruction. Like PHD2, VHL is found primarily in the cell cytosol in many cell types (Los et al., 1996), though VHL trafficking between nucleus and cytoplasm may be necessary in HIF1 degradation during reoxygenation from hypoxia (Groulx and Lee, 2002). VHL forms a stable complex with proteins including Elongin B, Elongin C, Cul2 and Rbx1 (Kamura et al., 1999). This VHL ligase complex binds to hydroxylated HIF1 and tags the protein with a polyubiquitin tail (Ivan et al., 2001; Kamura et al., 2000). A multi-protein complex, called the proteasome, recognizes this tail and destroys HIF1.
In hypoxia, HIF1 escapes hydroxylation, accumulates and enters the cell nucleus, where it binds to HIF1ß (known also as ARNT) (Fig. 1). The dimer transcriptionally activates a host of genes, including those encoding the angiogenic protein vascular endothelial growth factor (VEGF) and its receptor, Flk-1 or VEGFR2 (Milkiewicz et al., 2003); platelet-derived growth factor (Bos et al., 2005); and erythropoetin (Marti, 2004). By activating these genes, HIF1 contributes to angiogenesis, which provides nutrients to facilitate tumor growth or to extend muscle contraction, for example. As prominent players in the cell response to hypoxia and the onset of angiogenesis, HIF1 and its related pathways are attractive therapeutic targets in cancer and ischemia (Hewitson and Schofield, 2004).
In vitro studies have shown how the hypoxic response varies in tumors, based on their vascular microenvironment (Blouw et al., 2003). A balance of HIF1 levels and HIF1 activity seems necessary to achieve health (Josko and Mazurek, 2004; Koshiji and Huang, 2004). The underlying molecular mechanisms of how this balance is achieved and how the system responds to its microenvironment are not fully understood. One hypothesis is that HIF1 acts literally as a `switch' - an on/off mechanism for the onset of hypoxia-induced angiogenesis when a critical O2 level is reached (Kohn et al., 2004). Fundamental issues include understanding how HIF1 acting as a generic switch would be correlated to the varied hypoxic responses found in tumor cells. Alternatively, if HIF1 and its pathways do not act as a switch, the observed sensitivity to oxygen and the rapid induction of hypoxic genes would need to be otherwise explained. We address these questions, by developing a detailed model of HIF1 degradation, which allows molecular mechanisms to be tested quantitatively. The one known existing computer simulation related to HIF1, a network representation of cell hypoxic response, has included a subset of core HIF1 pathways and tested the hypothetical dependency of gene expression on HIF1 synthesis and degradation rates (Kohn et al., 2004). This model led to the above HIF1 switch hypothesis, which to our knowledge, has not been tested further. No computational model has explored the biochemical kinetics of the HIF1 pathways in detail or in a quantitative relationship to experimental data. The current model is the first molecular level, mechanistic model of HIF1 hydroxylation and degradation. We used the model to study the effects of different intracellular molecular compositions on hypoxic response, where the cellular microenvironment is currently inaccessible in vivo, and is only measurable in isolated instances in vitro.
From the model, we predict several key characteristics of the mechanisms involved in the HIF1 pathway. We show that HIF1-activated cellular responses can be divided into two categories depending on the molecular environment: a switch-like response to O2 levels, and a gradual one. We found conditions where iron and PHD2 are individual sensors of oxygen and determinants of the hypoxic response; and we showed the combined effects of three highly oxygen-sensitive compounds. From these studies, we compare two proposed therapeutic strategies targeting the HIF1 pathway, iron supplementation and PHD2 targeting, and predict under what microenvironments either would most efficiently increase HIF1 hydroxylation. These observations contribute to a better understanding of the hypoxic response at the molecular level and should stimulate further computational and experimental exploration, with particular applications to therapies that target cofactors in HIF1 hydroxylation.
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were consistent with experimental results from the collagen PHDs (Myllyla et al., 1977); this confirmed that the model represents the uncompetitive binding of Fe2+, O2 and 2-oxoglutarate (2-OG) to PHD2 (Fig. 2A shows the example of iron binding). The reaction can proceed without ascorbate (Fig. 2B,C), however, high ascorbate concentrations (>100 µM) significantly increase the reaction rate (Fig. 2B).
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hydroxylation by PHD2 (Fig. 3). One form of validation was the amount of VHL captured at different O2 levels. Tuckerman et al. measured the activity of endogenous HIF-PHDs (from MDA-MB-435 cell extracts) by a pVHL capture assay (Tuckerman et al., 2004). Oxygen concentrations in the simulations, all 
200 µM, are below the Km values of PHD2 for O2 of 250 µM (Table 2). This is reflected in Fig. 3A, where the model is compared with published data (Tuckerman et al., 2004). The 21% oxygen values show a near-linear increase in the fraction of the maximal pVHL capture with time; it is reasonable to conclude (Tuckerman et al., 2004), that all of the experiments were conducted below the threshold for oxygen saturation.
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half-life in normoxia fall within the range of experimental data (Fig. 3B). Experimental half-life of HIF1 was estimated as 5-8 minutes from reoxygenated (1-2% O2 to 20% O2) CCL39 and NHE-1 cell lysates (Berra et al., 2001). [Using oxygen solubility in water at 37°C = 1.30 µmol/l/mmHg (Tuckerman et al., 2004), exposure to 1% oxygen corresponds to an O2 level of 9.9 µM; 21% to an O2 level of 207 µM.] This complements independent finding in lysates from Hep3B cells exposed to 21% oxygen after hypoxia (1% oxygen) where the half-life of HIF1 was found to be <5 minutes (Huang et al., 1998); and from HeLaS3 cells reoxygenated at 20% from hypoxia (0.5% oxygen), where the half-life of HIF1 was 8 minutes (Jewell et al., 2001).
A third form of validation was the comparison of the predicted relative HIF1 accumulation of the model at different oxygen levels, with data from HeLa cell nuclear extracts (Jiang et al., 1996) (Fig. 3C). Studies have shown that HIF1 expression is maximal at low oxygen concentrations in vivo [e.g. at 0 or 1% O2, in normal ferret lung ventilated for 4 hours (Yu et al., 1998)], and in vitro assays indicated the most pronounced changes in HIF1 expression occur at O2 levels considered physiologically relevant (0-5%) (Jiang et al., 1996). To compare the computational model with these experiments, a constant [HIF1]0 was assumed, and [HIF1] that was not hydroxylated was taken as a relative measure of HIF1 nuclear accumulation.
Fourth, the effects of ascorbate and iron in the model are qualitatively comparable to HIF1 expression observed in human prostate adenocarcinoma (PC3) cells (Knowles et al., 2003). Fig. 3E shows the model results of supplementing the system with 2000 µM ascorbate. Relative HIF1 values are a fraction of the maximum HIF1 expression during hypoxia, without supplementation. For different cell types, including PC3 cells, the PHD2:HIF1 concentration ratio has not been quantified. Fig. 3E provides an example of how the ratio affects the accumulation of HIF1, during the first 3 hours of exposure to different O2 levels. A PHD2:HIF1 ratio of 0.004 is an estimate from measurements in breast carcinoma cells (Tuckerman et al., 2004). In normoxia, ascorbate and iron supplementation have similar effects on suppressing HIF1 expression (Fig. 3F). Comparable experimental results in PC3 cells show decreased expression of HIF1 over time with ascorbate supplemented at 2000 µM, and no appreciable expression of HIF1 in normoxia after 4 hours of supplementation with 25 µM ascorbate or >40 µM FeCl2 (40 µM FeCl2 added to medium containing 
26 µM Fe2+), see figure 2C,D in Knowles et al. (Knowles et al., 2003).
Sensitivity analysis
Sensitivity analysis was performed to confirm estimates for the unknown kinetic rate constants. The parameter of interest was varied over a minimum range of 1000-fold, while the remaining parameters were held constant. Calculated HIF1 half-life values were compared with experimental data, and this was used to narrow the range of reasonable parameter values. Details of the analysis are in provided in the Materials and Methods. Estimated values for five kinetic binding rates were determined: kcat,H=0.098-0.164 minute-1; koff,Fe2=36 minute-1; koff,DG=10.8 minute-1; koff,O2=10.8 minute-1; koff,AS=3.6 minute-1; koff,H=0.7 minute-1. Binding of Fe2+, 2-OG and O2 to PHD2 are the more reversible steps in the hydroxylation reaction, with significant off-rates relative to on-rate binding. The final step in the hydroxylation, binding to HIF1 is largely irreversible, as indicated by a low koff,H value and a significant kcat,H.
A recent study reported the apparent Km for Fe2+ of 0.03 µM (Hirsila et al., 2005). Using this estimate, as opposed to the Km of 2 µM, estimated from binding of factor-inhibiting HIF (FIH) with Fe2+ in the hydroxylation of HIF1 (Koivunen et al., 2004), the model predicts a higher specific activity for PHD2 than found in vitro (Hirsila et al., 2005) (see supplementary material Fig. S1). This discrepancy may reflect different concentrations of PHD2 and HIF1 relative to other compounds in the hydroxylation reaction; the model used initial conditions where quantitative concentrations of PHD2 were reported (Tuckerman et al., 2004).
Sensitivity analysis for all kinetic parameters found from experiments, was also performed using the protocol described for the estimated parameters (see Materials and Methods). Over a wide range of feasible Km,Fe2, Km,DG, Km,O2, Km,Asc and Km,H values (supplementary material Figs S2, S3), the changes in oxygen sensitivity were consistent, and the model features described below can be considered robust over these values.
Oxygen sensing
In many in vitro cell extract experiments monitoring HIF1 reactions, there is an excess concentration of initial 2-OG, iron, ascorbate and PHD2. When any of these compounds was limiting, the sensitivity to oxygen in the model was uniform at all O2 levels from 0-200 µM. Fig. 4 shows how initial reactant concentrations affect HIF1 hydroxylation at different O2 concentrations. When [PHD2]0 is in excess, the response to decreasing O2 results in a steep change in hydroxylation upon reaching hypoxia - whereas 21 and 10% O2 levels result in similar amounts of HIF1hydroxylated; at hypoxic levels of 1%, the amount hydroxylated at 20 minutes is half of that at normoxia (Fig. 4A). However, when [PHD2]0 is low, the response to a 20% drop in O2 levels is far less sensitive (Fig. 4D). Sensitivity to oxygen is measured by the slope of the [HIF1hydroxylated] vs [O2] curve. A constant slope represents a uniform sensitivity across O2 levels. Iron has a similar effect on HIF1 at different O2 concentrations. When iron is available in excess, the response curve is steep. At initial iron concentrations of 0.05 µM, or one-thousandth of the default value, the amount of HIF1 hydroxylated is linearly related to the O2 level (Fig. 4C). Changes in the concentration of ascorbate did not have such a significant effect on hydroxylation (Fig. 4F). The steepness of the response decreased when two or more compounds were limiting factors in the HIF1 hydroxylation (Fig. 5). Table 2 shows the theoretical range of initial conditions where steep, switch-like changes in hydroxylation occur.
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and PHD2 synthesis half-life range of 5-8 minutes in normoxia is consistent with at least three experiments (Berra et al., 2001; Huang et al., 1998; Jewell et al., 2001). However, the half-life of HIF1 upon reoxygenation depends on conditions such as duration of hypoxic exposure. For example, exposure to low oxygen levels beyond 6 hours, appears to decrease HIF1 half-life (G. Semenza, Johns Hopkins University, Baltimore, MD, personal communication). For short-term hypoxic exposure, the model assumes a maximum half-life of 5-8 minutes. The cited HIF1 half-life studies exposed cells to hypoxia for 1 hour (Jewell et al., 2001), 4 hours (Berra et al., 2001), and 4-6 hours (Huang et al., 1998) before reoxygenation. Beyond 4-6 hours of hypoxia, synthesis of HIF1 and PHD2 proteins occur. Fig. 6 shows the variability of HIF1 hydroxylation under conditions of chronic hypoxia, where a synthesis production term was added to the mass balance equations for HIF1 and PHD2 in the model. The simulated curves represent both the synthesis of HIF1 and its hydroxylation by increasing amounts of PHD2. In vivo, systems can adapt to chronic conditions, decreasing HIF1 expression within days of hypoxic exposure. A balance of HIF1 and PHD2 synthesis is a possible contributing mechanism.
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hydroxylation Increased HIF1 nuclear expression has been associated with poor prognosis in several cancers (Nomura et al., 2004; Zagzag et al., 2000), and decreased susceptibility to radiotherapy (Vordermark and Brown, 2003; Vordermark et al., 2004). By enhancing HIF1 hydroxylation, the proteasome degradation rate of HIF1 can be increased, leading to a drop in nuclear accumulation of the dimer and associated hypoxia-dependent transcriptional activation. Targeting cofactors in the PHD reactions is one viable approach to increasing the hydroxylation rate. As our computational model predicted different oxygen sensitivity based on intracellular concentrations of key cofactors in the HIF1 reactions, we hypothesized that the microenvironment would also dictate the effectiveness of therapeutic strategies, and computationally, we would be able to predict the relative efficacy of each strategy at the molecular level.
Using the model, we tested two proposed approaches to increasing HIF1 hydroxylation: (1) increasing intracellular iron concentration (McCarty, 2003; Siddiq et al., 2005; Wartenberg et al., 2003) while simultaneously increasing intracellular ascorbate (Jones et al., 2006; Knowles et al., 2006; Knowles et al., 2003) and (2) increasing the expression of the main cytosolic prolyl hydroxylase, PHD2, directly (Fig. 7). Results show that increasing ascorbate is a proportionately more effective way to increase hydroxylation (Fig. 7A,B), when all other compounds are not limiting factors. At low levels of iron, doubling the amount of ascorbate from the standard in vitro level of 1000 µM, increases hydroxylation by as much as 60% at 50 µM O2; when iron is above 2 µM, the effect of additional ascorbate diminishes to a constant 3% increase in hydroxylated HIF1 (Fig. 7C,D).
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expression in response to a decrease in O2 levels to a critical level was tested (Kohn et al., 2004). The model demonstrated that based on the molecular environment and characteristics of the cell type, the response to hypoxia varies considerably.
There are several ways that cells are hypothesized to sense and respond to oxygen. The sensor of O2 levels has been independently attributed to iron (Postovit et al., 2005), HIF1 and HIF1 PHDs experimentally, but how their responses differ and when, has yet to be understood. The model shows two classes of HIF1 oxygen responses: a steep drop and a gradual drop in HIF1 hydroxylation in response to decreasing O2 levels. When all hydroxylation reactants are in excess, a steep drop in hydroxylation occurs during hypoxia. When 2-OG, Fe2+ or PHD2 are limiting, model results show the gradual response - a near-linear relationship between HIF1 hydroxylation and O2 level, i.e. a constant sensitivity to O2; this reflects the saturation kinetics used to represent the binding of HIF1 to these compounds (Fig. 4C-E). HIF1 hydroxylation is reduced when two or more required compounds are limiting (Fig. 5); what is notable is not only a significant reduction in the net amount of HIF1 hydroxylated, but a significant decrease in the relative sensitivity to O2 levels, defined by the steepness of the slope of the [HIF1hydroxylated] vs [O2] curve.
Characterizing the role of ascorbate in the hydroxylation is complicated by its reaction with oxidized iron. At low levels of ascorbate (i.e. 1 µM, one-thousandth of the default initial value), HIF1 hydroxylation follows the curve shown in Fig. 4F. The decline in HIF1 hydroxylation at low O2 levels is less steep than the case where all compounds are in excess, however, it is not approaching linearity. This reflects the dual role of ascorbate: reactivating PHD2, by reducing the accumulating Fe3+; and, binding independently to the saturable enzyme complex formed by the binding of PHD2 with Fe2+, 2-OG and O2 (Majamaa et al., 1986). The decarboxylation of 2-OG without subsequent hydroxylation (termed uncoupled decarboxylation), which is catalyzed by PHDs and requires ascorbate, is not yet considered in the model. From the above observations, HIF1-activated cellular responses can largely be divided into two categories depending on the molecular environment: a steep, switch-like response to O2 levels, and a gradual one. The model shows that independently Fe2+ and PHD2 can act as the determinant of which response occurs. The high sensitivity of HIF1 hydroxylation to these compounds, notably at low (<5 µM) levels of oxygen, suggests that both iron and PHD2 play the role of hypoxic sensor.
Cellular in vivo concentrations of these compounds are difficult, if not yet possible, to measure. The concentration of HIF1 in vivo is thought to be in the sub-nanomolar range (Tuckerman et al., 2004). Based on the relative concentrations of other reactants in the HIF1 system, the response to O2 could be anticipated by the model. Although the quantitative values are largely unknown in vivo, it is known that iron and PHD2 concentrations are variable and affected by conditions such as hypoxia and anemia (Berra et al., 2003; Wardrop and Richardson, 1999). From the model, it would be predicted that this variability confers an advantage. With the HIF system being highly sensitive to the effects of multiple O2-dependent compounds, the response to O2 levels could be finely tuned, as well as robust.
Furthermore, the computational prediction that increasing ascorbate has significantly more effect at iron levels below 2 µM compared with higher iron levels, might later be extrapolated to characterizing tumor responsiveness to therapy based on in vivo microenvironments.
Using oxygen solubility in water, 37°C STP, 1.30 µmol/l/mmHg, [O2] of 21% corresponds to an O2 concentration of 200 µM for in vitro experiments using cell lysates (Tuckerman et al., 2004). This is below the Km of oxygen reacting with PHD2, which was reported as 250 µM (Hirsila et al., 2003). Typical in vivo tissue concentrations are significantly lower, in the range of 6-25 µM, corresponding to 5-20 mmHg tissue pO2. The high Km indicates that the HIF1 reaction response remains highly sensitive to tissue O2 levels all the way from 0% oxygen to normoxia, under certain conditions. The model supports research on HIF1 nuclear expression changes being greatest at oxygen levels below 5% (Jiang et al., 1996), while showing how the most pronounced response by HIF1 to acute hypoxia can be achieved only with sufficient Fe2+, 2-OG and PHD2 (Fig. 4A,B). Varying the relative concentrations of the compounds involved in HIF1 hydroxylation, Fe2+ and PHD2 in particular, alters this sensitivity.
Other forms of variability and specificity could add to the flexibility of the HIF1 system in responding to oxygen. Although, as mentioned, PHD2 is the main PHD enzyme present in the cell cytoplasm during normoxia, the concentration of each PHD isoform varies by cellular microenvironment (Appelhoff et al., 2004; Berra et al., 2003). Hypoxia and estrogen change the relative concentrations of the PHD isoforms, and their relative contribution to the hydroxylation of HIF1 (Appelhoff et al., 2004).
While discussing other factors that influence HIF1 hydroxylation, it is appropriate to mention the limitations of the presented model. Five independent kinetic rates used in the model are unknown, and their values were estimated computationally. Their estimated values appear consistent with experimental results, and the key features of the hydroxylation reaction (steep and gradual responses to hypoxia) are robust over a range of all kinetic parameters. Additional experiments would be useful to validate the binding on- and off-rates. Kinetic rate constants taken from in vitro experiments may depend on slight differences in pH or other experimental variables (e.g. relative concentration of proteins) that have a limited degree of controllability within the cell. The enzyme used experimentally for the binding reactions was a minimal HIF1 peptide (residues 556-574) (Hirsila et al., 2003). Although increasing peptide length does not seem to affect the binding affinities in vitro to pVHL (Hon et al., 2002) or PHD2 (Hirsila et al., 2003) with HIF1, the possibility that it may in vivo, cannot be ruled out. Additionally, estimates for binding kinetic rates are assumed sequential - this may or may not be what is actually measured by experiments, e.g. reactions may include PHD2-Fe2+ or PHD2-Fe2+-2-OG binding to HIF1, etc., not just the completely modified PHD2 enzyme.
From the model, we predict several key characteristics about the mechanisms involved in the HIF1 pathway and apply the results to evaluate proposed therapies. Doing so, we provide a molecular representation of hypoxic response that merits further exploration experimentally and computationally. Future modeling studies include representing the independent hydroxylation of HIF1 on its Asn803 residue by factor-inhibiting HIF. To further approximate in vivo conditions, the model will need to represent the effect of pH, such as the acidic conditions found in tumors or in muscle during exercise, and its influence on VHL nucleolus sequestration. HIF2 and the different isoforms of PHD will become a part of the model, initially through modification of the binding rate constants and incorporation of spatial concentration heterogeneity. Incorporating the different sensitivity of the HIF1 degradation binding domains to iron and oxygen may yield a better mechanistic understanding of how the cell copes independently with a drop in iron or oxygen by altering PHD binding (Lee et al., 2005). Recently characterized compounds that influence the hydroxylation of HIF1 and its nuclear accumulation could be added, including OS-9, a protein that binds to HIF1 and the PHDs (Baek et al., 2005), and SUMO-1 protein, which covalently binds to HIF1 and affects its stability and transcriptional regulation (Bae et al., 2004). Although its role has yet to be fully elucidated, p53 binds to HIF1 in anoxia (0-0.2% O2) and can promote its degradation (Fels and Koumenis, 2005); representing this binding in the model may account for the in vitro observation that a maximum in HIF1 nuclear expression occurs at 0.5% O2 (Jiang et al., 1996). Research into this maximum would consider the relative concentrations of PHD isoforms, and their binding site specificity as a function of O2 level (Chan et al., 2005), as well as the effect of reactive oxygen species (Schroedl et al., 2002).
It is the authors' anticipation that the computational predictions will stimulate new experiments. An immediate proposal for an in vitro assay would be to quantitatively compare the effects of iron, ascorbate and PHD2 enzyme levels on the hydroxylation rate across a spectrum of O2 concentrations in a range of cell types. This would give an indication of whether indeed the response to O2 is of two natures, and whether concentrations of HIF1 co-factors determine if there is a steep drop in hydroxylation or a gradual decrease. Fig. 7C,D provide valuable predictions for therapeutic studies. Experiments to assess the relationship of ascorbate supplementation (e.g. 25, 1000, 2000 µM) in relationship to iron availability at different O2 levels (e.g. 0, 2, 5, 10, 20%) in cancer (e.g. MDA-MB-435) and endothelial cells (e.g. HUVEC, HBEC) would follow-up on the predictions of the model, and in vitro experiments (Jones et al., 2006; Knowles et al., 2006) to verify in which microenvironments the proposed therapies work effectively, and in what cells these microenvironments are found would be useful. Imaging techniques could be used to assess the variability present in tumor microenvironments - providing a basis for intra-tumor concentrations of compounds in the HIF1 pathway and allowing in vivo application of the computational model.
Different cell types may respond very differently to intracellular hypoxia than the model predicts, and the above experiments could help determine this. Deviations from predictions may reflect unaccounted mechanisms of the HIF1 pathway, and specifically, different reactions in the hydroxylation and degradation of HIF1. There remains a question of whether the action of ascorbate is as described in the model (reducing Fe3+ to Fe2+ and binding the PHD2-2-OG-Fe2+-O2 intermediate complex), and whether this varies by cell type and in vivo conditions. The possibility of ascorbate working as a pro-oxidant at low concentrations and an antioxidant at high concentrations intracellularly involves alternate reactions affecting Fe2+, H2O2, O2 and HIF1 hydroxylation in the model, which could be assessed using techniques to determine ascorbate and H2O2 relationships (Kramarenko et al., 2006), in combination with VHL capture assays and HIF1 quantitative assessment.
The presented computational model adds a novel perspective to understanding the molecular details of how cells sense oxygen. It demonstrates how iron and PHD2 can determine whether the response to an acute hypoxic exposure is a pronounced or gradual change in the amount of HIF1hydroxylated. This knowledge is applied to predict the response to proposed therapies targeting the HIF1 pathway. The model provides evidence as to how a changing microenvironment can significantly alter cell susceptibility to drugs that target cofactors in the HIF1 hydroxylation reactions. Even before experimental techniques allow measurements sensitive enough to detect intracellular molecular concentrations changes, a HIF1 pathway computational model can be used to gain an understanding of the molecular mechanisms underlying pre-angiogenic hypoxic response.
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Materials and Methods |
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by PHDs and the ubiquitylation of hydroxylated HIF1 by VHL (Fig. 1). In normoxia, PHD2 is the dominant PHD isoform that hydroxylates HIF1 and determines HIF1 concentrations in a range of cell types (Berra et al., 2003). We modeled the hydroxylation of HIF1 by PHD2 in the cell cytoplasm. The compounds involved in binding to PHD2 in preparation for the hydroxylation of HIF1 include iron, 2-oxoglutarate (2-OG), oxygen and ascorbate. The modified PHD2 then binds and hydroxylates HIF1. Hydroxylated HIF1 is recognized and ubiquitylated by VBC, the complex that includes VHL bound to Elongins B and C, Cul2 and Rbx1. Equations 1, 2, 3, 4 describe the overall scheme of HIF1 degradation. This includes HIF1 hydroxylation (Eqn 1), independent reactions of iron and ascorbate (Asc) (Eqns 2 and 3), and the binding of HIF1 to VHL (Eqn 4). Table 3 lists the compounds included in the model.
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Overall biochemical reaction of HIF1 hydroxylation:
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 | (2) |
; Williams and Yandell, 1982):
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. HIF1 is polyubiquitylated and subsequently degraded:
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The hydroxylation reactions follow enzyme-substrate binding kinetics. Governing equations are determined from mass balances surrounding the substrate and the intermediate enzyme-substrate complexes. Equation 5 shows an example of the kinetic reaction (Eqn 5A) and accompanying kinetic model (Eqn 5B) for initial steps in PHD2 hydroxylation of HIF1 (Eqn 5B). The full kinetic model can be found in Eqns 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26. A combination of enzyme-substrate saturation assumptions was used for the binding of iron, ascorbate, oxygen and 2-oxoglutarate to PHD2, PHD2 hydroxylation of HIF, and VHL-mediated ubiquitylation. Model inputs are initial compound concentrations, including cellular O2 levels (Table 1). Output is HIF1 levels in the cell cytoplasm.
PHD2r is the PHD2 enzyme modified following its reaction to iron.
 | (5A) |
 | (5B) |
PHD hydroxylation of HIF1
While HIF1 was discovered in 1993, and its degradation kinetics have only been characterized in the past few years, the reactions of PHDs and lysyl hydroxylases have been analyzed for their roles in collagen hydroxylation since the mid-1960s (Adams and Frank, 1980; Gunsalus et al., 1975). During hydroxylation, sequential binding of collagen prolyl hydroxylase has been observed in the order of iron, 2-oxoglutarate, oxygen and peptide (Myllyla et al., 1977). The hydroxylation reaction of PHDs with HIF1 is thought to occur in the same sequence (M. Hirsila, Characterization of the novel human prolyl 4-hydroxlyases and asparaginyl hydroxylase that modify the hypoxia-inducible factor. PhD Thesis University of Oulu, Finland, 2004; http://herkules.oulu.fi/isbn9514275756/index.html?lang=en). Reflecting this in the model, we represent the binding of PHD2 with the substrates iron (Eqns 10, 11, 12), 2-oxoglutarate (Eqns 13 and 14), and oxygen (Eqns 15 and 16) sequentially. According to experiments (Hirsila et al., 2003), the reactions of the hydroxlyase binding to its cofactors follow saturation curves consistent with Michaelis-Menten kinetics. This is reflected in our model. Each reaction of a compound with PHD2 in the computational model is defined by three kinetic parameters: kon, koff and kcat (e.g. see Eqn 12). In pseudo-steady-state conditions, where the fluxes of intermediate compounds (enzyme-substrate) are constant, the Michaelis-Menten constant, Km, relates these three parameters:
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 | (7) |
In the human type I collagen prolyl hydroxylase reactions with iron, 2-oxoglutarate, oxygen and the peptide substrate (Pro-Pro-Gly)10, the reported Km values are close to the dissociation constants, and the assumption of their equality (Eqn 7) appears valid (Hieta et al., 2003; Myllyla et al., 1977). The HIF-PHDs and the collagen PHDs share the same hydroxylation reaction sequence and binding cosubstrates. At first glance, it seems reasonable to make the same equilibrium binding assumptions for HIF-PHDs as for the collagen PHDs. However, the overall PHD2 hydroxylation of HIF1 is not at equilibrium and probably unidirectional (Chan et al., 2005; Willam et al., 2004). For the model presented here, the binding was assumed bi-directional between PHD2, iron, 2-oxoglutarate, oxygen (Epstein et al., 2001) and ascorbate, with negligible intermediates formed (Eqn 9) (Goda et al., 2003). For the intermediate complexes of PHD2 and its cofactors, this means the catalytic production terms involving kcat,Fe2, kcat,DG, kcat,O2 and kcat,AS were set to zero during model runs.
The final step of the PHD2 reaction sequence, the hydroxylation of HIF1 by the modified PHD2 enzyme complex, was first modeled using the assumption of near irreversibility, and Briggs-Haldane, where kcat>>koff. Assuming pseudo-steady-state conditions, characteristics of Briggs-Haldane kinetics hold (Briggs and Haldane, 1925; Cornish-Bowden, 2004):
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Effects of larger relative koff rates were also tested, and the current model includes a final irreversible hydroxylation step that considers all three constants, kon, koff and kcat, to be significant (Eqns 19, 20, 21).
Ascorbate and iron reactions
Ascorbate is assumed to be a co-reactant with compounds in the hydroxylation reaction, as has been shown with collagen PHDs (Majamaa et al., 1986). Hydroxylation proceeds without ascorbate when there is sufficient iron in the form of Fe2+ present (Myllyla et al., 1984; Tuderman et al., 1977). To account for the possibility of the reaction proceeding without ascorbate, the ascorbate-independent binding of HIF1 to PHD2 · Fe2+ · 2-OG · O2 and subsequent hydroxylation is part of the model (third term in Eqn 20). However, eventually without any ascorbate, Fe2+ can be oxidized to its Fe3+ (or Fe4+) form, leaving insufficient iron to bind to PHD2 and halting the hydroxylation reaction. The role of ascorbate in the model is to bind to O2 and reduce Fe3+ back to Fe2+. We represent the Fe2+ reaction with H2O2 (Eqns 2, 10 and 22) and Fe3+ reduction by ascorbate (Eqns 3, 17 and 22) in the model.
HIF1 ubiquitylation and degradation
Following hydroxylation, VHL ubiquitylation of HIF1 is likely also not at equilibrium. However VHL binding is notably reversible (kcat,HV=0, in Eqns 23, 24, 25, 26). The deubiquitylating enzyme, VDU2, interacts with pVHL, mediates the backward reaction and stabilizes HIF1 (Li et al., 2005). We make the kinetic assumption that proteosome degradation of HIF1 after ubiquitylation is approximately first order in ubiquitylated HIF1. This simplification seems a valid approximation from reoxygenation experiments (Huang et al., 1998), although it leaves to future studies the exploration of how decay rate varies with the ratio of free to bound or modified HIF1.
Model parameters
The model rate constants are given in Table 1. Ten of the constants are derived from experimental data (Buettner and Jurkiewicz, 1993; Hirsila et al., 2003; Hirsila et al., 2005; Hon et al., 2002; Kersteen et al., 2004; Lovstad, 2003; Tuckerman et al., 2004). Km was available from experimental data while individual kon and koff were calculated from the model for all but the VHL binding step, where on and off rates were known experimentally. Values for the unknown parameters were estimated as described above and shown in supplementary figures. Default values for kinetic constants and initial conditions are shown in Table 1 with corresponding references. For experiments, O2 levels are given in percentages, mmHg, or micromolar quantities. The last is reserved for cell culture experiments, where O2 concentration is calculated in solution. Where appropriate for comparison, we converted model results to the measured experimental units. For cell culture experiments characterizing conditions in cell lysates, values given as percent oxygen or mmHg were equated to micromolar quantities based on an oxygen solubility in water (Tuckerman et al., 2004).
Numerical solution
The system of nonlinear differential equations presented in Eqns 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26 was solved using Mathworks Matlab software. The ode23s solver, based on a modified Rosenbrock formula, was used to find a solution for the series of seventeen differential equations. For the time integration, the solver used adjustable time steps with default absolute error tolerance in the solution of 10-6 µM.
Governing equations
Overall reaction sequence, incorporating the assumptions of pseudo-steady-state and bidirectionality in the binding of prolyl hydroxylase with iron, deoxyglutarate, oxygen and ascorbate; assumptions of pseudo-steady-state and unidirectionality in the hydroxylation of HIF1; and reversibility in the ubiquitylation of hydroxylated HIF1 by the VHL complex where H is unhydroxylated HIF1 and Hh is hydroxylated HIF1 (the following equations use the notation defined in Table 3):
 | (9) |
Production terms qo in Eqn 12 and q in Eqn 20 are nonzero only in chronic hypoxia (>6 hours, Fig. 6). Estimates of these functions are based on experiments (Appelhoff et al., 2004; Berra et al., 2003; D'Angelo et al., 2003).
Reactions of PD2 and Fe2 and Fe2 with H2O2
 | (10) |
 | (11) |
 | (12) |
 | (13) |
 | (14) |
 | (15) |
 | (16) |
Reaction of PD2·Fe2·DG·O2 and AS
 | (17) |
 | (18) |
Reaction of PD2·Fe2·DG·O2·AS (PD2mod) and H
Note for reactions 19 and 20, these equations were modified to allow reaction with an intermediate uncoupled to AS
 | (19) |
 | (20) |
 | (21) |
Reaction of Fe3 with AS and O2
 | (22) |
Related reactions:
 |
 | (23) |
The following reactions represent degradation kinetics involving ubiquitylation and proteasome degradation of HIF1. The current model is limited to the VHL complex binding to hydroxylated HIF1, where degradation is assumed a first order reaction.
 | (24) |
 | (25) |
 | (26) |
Parameter estimation
Ten parameters (five of them independent), were unknown experimentally: kon,Fe2, koff,Fe2, kon,DG, koff,DG, kon,O2, koff,O2,, kon,AS, koff,AS, kon,H and koff,H. The following protocol was used to estimate these parameters. Initial rough estimates for kon and koff, for the reactions of iron, 2-OG and ascorbate with PHD2, were found from binding of these reactants with other substrates (collagen prolyl hydroxylase, lysyl hydroxylase). Fe2+ oxidization and reduction rate constants were estimated respectively from values for the Fenton reaction and from (Buettner and Jurkiewicz, 1996). Sensitivity analysis confirmed estimates for kinetic constants. With the assumption kcat=0 for intermediate steps, kon rates were determined by koff/Km. In the case of kon,H and koff,H, where kcat,H was a significant value estimated from experiments, the relationship Km=(kcat+koff)/kon was used.
Sensitivity analysis
For all estimated parameters, the kinetic parameter of interest was varied over a minimum range of 1000-fold, while the remaining parameters were held constant. Calculated HIF1 half-lives were compared with experimental data (Berra et al., 2001; Huang et al., 1998; Jewell et al., 2001), to narrow the range of reasonable kinetic parameter values (supplementary material Fig. S4).
The estimated range for the catalytic constant kcat,H (Eqn A12) was relatively small: 0.098-0.164 minute-1; this corresponds well with a 0.1 minute-1 approximation from experiments (Tuckerman et al., 2004). Testing ±100-fold differences in kcat showed the model's high sensitivity to this parameter (supplementary material Fig. S4i). The remaining kinetic parameters estimated from the model were koffs for the binding of iron (Eqns 10, 11, 12), 2-OG (Eqns 13,14), oxygen (Eqns 15,16) and ascorbate (Eqns 17,18) with PHD2. These were determined using the time of 5 minutes for half [HIF1]0 = 1 µM to be hydroxylated (this is based on experiments and the estimate that ubiquitylation of hydroxylated HIF1 takes 3 minutes; see Model validation section). With this assumption, the estimated minimum kFe,off is 36 minute-1; if the 5-8 minute HIF1 half-life range is considered, the range of kFe,off is 0.019-36 minute-1 (supplementary material Fig. S4ii). Kinetic off-rate ranges were also determined for the PHD2 enzyme complex binding to 2-OG (supplementary material Fig. S4iii), 2-OG (supplementary material Fig. S4iv), and ascorbate (supplementary material Fig. S4v). To test the assumption of irreversibility in the binding of modified PHD2 with HIF1, a range of koff values were explored (supplementary material Fig. S4vi). The graph shows the feasibility of a nearly irreversible reaction, with koff,H close to zero giving a half-life within the experimental range expected. However the sensitivity of the HIF1 half-life to koff,H was low, and another comparison was needed to help limit its value.
A second means to confirm estimates for kinetic constants was a comparison of PHD2 specific activity with that from Tuckerman et al. (Tuckerman et al., 2004), which estimated a lower limit of 20 mol HIF1 hydroxylated/mol PHD2/minute, as a constant rate over the first 6 minutes in hypoxic MDA-MB-435 cell extracts. Using initial concentrations consistent with those reported in the experiment, [HIF1]0=1 µM; [Ascorbate]0=1 mM; [-ketoglutarate]0=1 mM (model, [2-oxoglutarate]0=1 mM); [FeCl2]0=50 µM (model, [Fe2+]0=50 µM); [PHD2]0=4 nM; [O2]0=209 µM (ambient, 21%), and varying the kinetic parameters of interest, the model was compared with experiments to determine minimum estimates for kcat,H, koff,Fe2, koff,DG, koff,O2, koff,AS and koff,H using the best fit determined by linear regression of the computational curves and least squares analysis comparisons to the data (supplementary material Fig. S5). The model's lower estimates for the kinetic rates corresponded well to the specific activity value from experiments. An exception was seen consistently at two minutes, where lower estimates for the model's kinetic constants underestimated the reported specific activity. Using the range of kcat,H corresponding to the HIF1 half-life of 5-8 min, the higher kcat,H values increased the predicted specific activity for the same koffs.
After determining estimated kinetic constants, we investigated the sensitivity of the hydroxylation reaction to initial concentrations of reactants (supplementary material Fig. S6). Fig. S1 in supplementary material shows model estimates for PHD2 specific activity and HIF1 half-life using the newly reported Km,Fe2 value of 0.03 µM, and the corresponding best fit kon and koff rates for the other binding reactions. Alternate choices for the set of kon and koff rates, using the maximum HIF1 half-life of 8 minutes, resulted in higher estimates for PHD2 specific activity.
Sensitivity analysis was also performed for all parameters found from experiments: Km,Fe2, Km,DG, Km,O2, Km,AS, Km,H, kFe3, kASFe, kon,VL and koff,VL using the protocol described for estimated parameters (supplementary material Fig. S2 show examples of Km,Fe2 and Km,DG). Changes in kFe3 and kASFe, for the reactions of Fe2+ with H2O2 and ascorbate, had negligible effects on hydroxylation at default initial conditions; as determined by the model, constants for ubiquitylation (kon,VL and koff,VL) have no effect on hydroxylation. Sensitivity analysis shows the switch-like, steep drop in HIF1 hydroxylation at low O2 levels is a consistent feature (supplementary material Fig. S3). The range of kinetic values used for analysis was 0.2Km-4Km, where Km is the experimental value (Table 1). Comparison of PHD2 specific activity to experiments determined this was an appropriate range (supplementary material Fig. S2ii,iv). An exception was Km,Fe2, where the range was 0.025Km,Fe2-4Km,Fe2 (supplementary material Fig. S2ii). Changes in Km,Fe2 had minimal effects on the hydroxylation curve (supplementary material Fig. S3i). For Km,DG, Km,O2, Km,AS, and Km,H, increasing Km values increase the time for hydroxylation, thereby decreasing the steepness of the HIF1 response (supplementary material Fig. S3ii). Increasing Km values also make the system more sensitive to changes in oxygen at higher O2 levels.
Numerical methods
A script was written in Mathworks Matlab to run the model repeatedly and perform sensitivity analysis over the described parameter range.
Note on the definition of switch-like
The term `switch' in its mathematical use is a gate, defining two states of a system (e.g. `on' or `off'). For biological purposes, switch takes a broader definition - a distinct change in conditions that triggers a physiological state change (e.g. HIF1 or a threshold concentration of HIF1 protein as the angiogenic switch). Here we define `switch-like' as a threshold change in HIF1 protein concentration in response to a specified decrease in O2 levels; this definition is to distinguish the change from a gradual increase in protein levels. Switch-like properties can be determined by calculating the slope of the fraction of [HIF1 hydroxylated] vs [O2] curve. A constant slope indicates a uniform response to increasing hypoxia across all O2 levels. A gradual response in this article (Fig. 4C,D,E and Fig. 5), refers to a constant slope of
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expression with changing O2 levels. |
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