An Allosteric Coagonist Model for Propofol Effects on α1β2γ2L γ-Aminobutyric Acid Type A Receptors

• Propofol acts via γ-aminobutyric acid type A (GABA^A) receptors. Low concentrations of propofol enhance agonist-stimulated GABA^Areceptor activity, and high concentrations directly activate receptors.

• Whether these two effects are mediated by different types of propofol sites is unknown.

• Quantitative GABA^AR electrophysiology indicates that the propofol-binding sites causing GABA enhancement are the same as those mediating direct activation.

• Allosteric coagonist models fitted to the data suggest that there may be three such propofol sites per receptor.

PROPOFOL and other potent intravenous sedative-hypnotic drugs such as alphaxalone and etomidate act via γ-aminobutyric acid type A (GABA^A) receptors, a major class of inhibitory ligand-gated ion channels in mammalian brain.1,2In both neuronal synaptic receptors and heterologously expressed GABA^Areceptors with subunit composition 2α:2β:1γ, clinical concentrations of these anesthetics potentiate ion channel activation by GABA, shifting concentration-responses leftward.3,–,7These drugs also slow the deactivation of GABA^Areceptor-mediated currents, prolonging decay of GABA-stimulated inhibitory postsynaptic currents.8,–,11At higher concentrations, the potent intravenous anesthetics also directly activate GABA^Areceptor channels (i.e ., in the absence of GABA).6,7,10,12,–,14 

Two contrasting mechanistic models for anesthetic effects in GABA^Areceptors have been proposed to account for these observations. One type of model postulates that modulation of GABA responses is mediated by high-affinity anesthetic sites, whereas direct receptor agonism is mediated by distinct low-affinity anesthetics sites. This type of model with two classes of anesthetic sites has been used to interpret the actions of neuroactive steroids, which include alphaxalone.14A second type of model supposes that a single class of drug-binding sites mediate both GABA modulation and direct receptor activation. Quantitative electrophysiological analysis of etomidate effects on α1β2γ2L GABA^Areceptors were modeled using a two-state (inactive and active) Monod-Wyman-Changeux (MWC) allosteric coagonist mechanism.6This MWC model fits functional data best with two equivalent etomidate sites per receptor, a stoichiometry that is supported by [³H]-azi-etomidate photolabeling of purified bovine GABA^Areceptors.15 

Despite the strong similarities between propofol actions and those of neuroactive steroids and etomidate, it remains uncertain whether propofol modulation and direct activation are mediated by the same versus  distinct GABA^Areceptor sites. Our first aim was to test the hypothesis that propofol actions, like those of etomidate, behave in accordance with MWC coagonist models. Because the same drug-binding sites mediate both direct-channel activation and modulation of GABA responses in these models, the quantitative relationship between these two drug effects is predicted to be independent of both the specific drug and the number of binding sites. Thus, our hypothesis implies that etomidate and propofol concentrations that elicit equal direct-receptor activation will also produce equal shifts in apparent agonist sensitivity (GABA EC⁵⁰). To test this idea, we used electrophysiology in Xenopus  oocytes and identified a pair of equiefficacious direct activating solutions of etomidate and propofol in α1β2γ2L GABA^Areceptors. We then compared how these two drug solutions alter GABA modulation of receptors by quantifying shifts in GABA EC⁵⁰. Our second goal, contingent on the outcome of the first aim, was to develop a quantitative two-state coagonist model for propofol, including an estimate of the number of propofol sites per GABA^Areceptor. We performed quantitative electrophysiological studies of both propofol direct activation and propofol-dependent enhancement of currents elicited with low GABA. Data from all the above experiments were combined and globally fitted to MWC models with a variable number of propofol sites.

Xenopus laevis  maintenance and oocyte harvest procedures were performed in accordance with National Institutes of Health guidelines and approved by the local committees for animal care of Marburg University Hospital (Marburg, Germany) or Massachusetts General Hospital (Boston, Massachusetts).

Plasmids containing DNA encoding wild-type bovine α1and human β2 and γ2L GABA^Areceptor subunits were provided by Paul Whiting (Merck Sharp & Dohme Research Labs, Essex, United Kingdom). DNAs were linearized and used as templates for messenger RNA synthesis with the mMessage mMachine High Yield Capped RNA Transcription Kit (Ambion Inc., Austin, TX).

Oocytes were collected from human chorionic gonadotropin-injected adult female Xenopus laevis  anesthetized with 0.2% tricaine and hypothermia. Stage V and VI oocytes were injected with 10–17 ng (30–50 nl) of a messenger RNA mixture encoding α1, β2, and γ2L GABA^Areceptor subunits. At least three-fold excess γ2L RNA was used to ensure uniform incorporation into receptors. Oocytes were cultured at 18°C in ND96 solution (96 MM NaCl, 2 MM KCl, 10 MM HEPES, 1.8 MM CaCl², 1.0 MM MgCl², pH 7.5) supplemented with 2.5 MM pyruvate and 20 μg/ml gentamicin.

Ethyl 3-aminobenzoate methanesulfonate salt (tricaine), collagenase IA, dimethyl sulfoxide, propylene glycol, GABA, 2,6-di-isopropylphenol (propofol), and all salts and buffers were obtained from Sigma-Aldrich (St Louis, MO). R-etomidate was from Bedford Laboratories (Bedford, OH) or Janssen-Cilag GmbH (Neuss, Germany) as the commercially available solution for clinical use containing 2 mg/ml (8.2 MM) drug in 35% propylene glycol.

Etomidate was diluted in ND96 recording solution (without antibiotics) to make a 1 MM stock solution containing 4.3% propylene glycol. This etomidate stock was kept refrigerated and diluted to a final concentration of 10 μM etomidate on each experimental day. Propylene glycol at 0.5% (more than 10-fold higher than the concentration in 10 μM etomidate solutions) did not have any effect on resting leak currents or on GABA-activated currents. Propofol was dissolved in dimethyl sulfoxide to make a 100 MM stock solution, which was diluted into recording solution to the desired propofol concentration. Dimethyl sulfoxide at 1% (about 50-fold higher than the concentration in experiments) did not have any effect on resting leak currents or on GABA-activated currents.

Two-microelectrode voltage clamp experiments were performed at room temperature (21°C) 2–7 days after the injection of the messenger RNA mix into oocytes. The electrophysiology equipment and techniques have been previously described.6,16 

Currents elicited by propofol were compared to currents evoked by 10 μM etomidate using the following procedure. Etomidate at 10 μM was applied to an oocyte expressing GABA^Areceptors until the peak current reached a plateau (I^etoprepropofol). After a 10 min period of oocyte wash in recording solution, the oocyte was exposed to propofol (at 10 μM initially) until the peak current reached a plateau (I^pro). Following another 10 min wash period, the oocyte was again exposed to 10 μM etomidate until the peak current reached a plateau (I^etopostpropofol). The propofol-induced current was compared with the average of the two etomidate-induced currents. Depending on the ratio of I^pro/I^etoaveraged from three oocytes, the propofol concentration was increased or decreased in steps of 1–3 μM for the next set of three cells. When the equiefficacious propofol concentration (19 μM) was identified (I^pro/I^etorange 0.95–1.05), the equivalence of direct-activating efficacies of the two drug solutions were confirmed in another seven cells.

GABA solutions ranging from 0.03 μM to 10 mM were prepared in recording solution or recording solution supplemented with either 10 μM etomidate or 19 μM propofol. Oocyte exposure time to GABA (15–60 s) depended on GABA concentration and the time to plateau current. Every test sweep (GABA, GABA + 10 μM etomidate, GABA + 19 μM propofol) was preceded and followed by a sweep elicited by a maximally activating concentration of GABA (10 mM) for normalization. To ensure complete washout of agonist and anesthetic as well as return of the receptors to the resting state, cells were washed with recording buffer for 5 min following every 10 mM GABA control exposure, for 3–5 min following every GABA test exposure, and for 10–15 min after every exposure to GABA + anesthetic.

In one set of experiments (two-drug protocol), we compared the GABA-enhancing effects of 10 μM etomidate and 19 μM propofol in the same cell at one GABA concentration. Because propofol displayed slower washout than etomidate, we exposed oocytes to etomidate before propofol. Current from an oocyte was initially activated by a chosen GABA concentration (I^GABA). After wash, the oocyte was exposed to 10 μM etomidate until the elicited-inward current reached a plateau. At this point, a solution with GABA at the same test dose, plus 10 μM etomidate, was applied (I^GABA+ETO). After wash, the same oocyte was then exposed to 19 μM propofol until the elicited-inward current reached a plateau, then to GABA at the same test dose, plus 19 μM propofol (I^GABA+PRO). For each concentration of GABA, a minimum of 5 cells was studied.

To control for possible interactions between etomidate and propofol, we also measured GABA enhancement with 10 μM etomidate and 19 μM propofol in separate sets of cells (single-drug protocol). For each concentration of GABA, a minimum of 5 cells was studied.

Concentration-dependent direct activation by propofol was measured over a range of concentrations (5 μM–1 mM) in oocytes. Each cell was first activated with 10 MM GABA as a control, followed by 5 min wash before activation with propofol. After activation with propofol, oocytes were washed for 10–15 min and the 10 MM GABA response was repeated. If the postpropofol control differed from the prepropofol control by more than 15%, the data were not included for analysis. Propofol responses were normalized to the average of pre- and postpropofol GABA controls. Three to five oocytes were tested at each propofol concentration.

The GABA concentration eliciting 2–3% of maximal response (EC2.5) was established in each oocyte by testing various solutions against 10 mM GABA, with 3–5 min washes between. GABA EC2.5 ranged from 3 to 8 μM (mean ± SD = 5 ± 1.5 μM). After the EC2.5 response was stable for two sequential sweeps, the same oocytes was exposed to the test propofol concentration for 1 min, followed by propofol plus GABA at EC2.5. Oocytes were then washed for 10–15 min and retested against GABA at EC2.5 alone. Each propofol concentration was tested in three to five oocytes.

Unless otherwise indicated, results are reported as mean ± SD. The criterion for statistical significance was P < 0.05 unless otherwise stated.

At each GABA concentration studied, normalized leak corrected peak currents elicited by GABA, GABA + 10 μM etomidate, and GABA + 19 μM propofol were compared using two-way ANOVA with Bonferroni correction posttest in GraphPad Prism 5.02 (GraphPad Software, San Diego, CA).

Leak-corrected and normalized agonist concentration response curves, both in the absence and presence of anesthetic drugs, were constructed with the data obtained using the single drug protocol and fitted by nonlinear least squares to the logistic (Hill) equation:

where I is the current evoked by agonist; I^maxand I^minare the maximal and minimal currents, respectively; EC⁵⁰is the agonist concentration that evokes a current halfway between I^maxand I^min; agonist is either GABA or propofol; and nH is the Hill coefficient. When direct activation by etomidate or propofol was present during a GABA concentration-response study, I^minreflects this basal activity. Nonlinear least-squares method fits to Equation 1 were performed using GraphPad Prism 5.02. Results of these fits are reported as best fit (95% CI). Statistical comparison of fitted parameters for multiple data sets was performed in GraphPad Prism using the “compare” function in the nonlinear least-squares method fitting module. The EC⁵⁰shifts for each anesthetic were calculated from the fitted EC⁵⁰s in the presence versus  absence of drug. The logEC⁵⁰difference (anesthetic − control) errors were calculated from the fitting errors and used to determine 95% CIs for EC⁵⁰shifts.

Average peak current data from GABA concentration-responses in the presence and absence of propofol, propofol direct activation responses, and GABA EC2.5 enhancement were pooled and renormalized to provide estimated P^openvalues:(P^estopen) This was achieved by assuming that maximum peak current elicited by high GABA concentrations in the presence of etomidate (125% of maximal GABA response) represented 100% channel activation. Nonlinear least-squares regression was use to fit the pooled data to the following equation:

This equation describes a two-state equilibrium allosteric mechanism with two classes of agonist sites (one for GABA and one for propofol). The model assumes two equivalent GABA sites, while the number of propofol sites is variable (n). L⁰is a dimensionless basal equilibrium gating variable, inversely related to the open probability of unliganded receptors. Based on previous estimates in our lab6,17and others,18we used a L⁰value of 50,000 in fitting Equation 2 to data. K^Gand K^Pare equilibrium dissociation constants for GABA and propofol binding to inactive states, and c and d are dimensionless parameters representing the respective ratios of binding constants in active versus  inactive states. The agonist efficacies of GABA and propofol are inversely related to c and d, respectively. Nonlinear least-squares method fits to Equation 2 were performed using Origin 6.1 software (OriginLab, Northampton, MA). Fitted parameters for MWC models are reported as best fit ± SE.

Our first set of experiments was aimed at identifying a pair of etomidate and propofol concentrations that were equiefficacious for directly activating currents mediated by α1β2γ2L GABA^Areceptors. We chose 10 μM etomidate as our benchmark, because previous studies have shown that 10 μM etomidate predictably activates GABA^Areceptors, producing approximately 3–5% of maximal GABA-activated current.6In addition, GABA^Areceptor currents elicited with 10 μM etomidate do not display desensitization, and this low concentration of etomidate washes out of oocytes within several minutes. Sets of oocytes expressing α1β2γ2L receptors were activated with 10 μM etomidate and varying propofol concentrations, starting with 10 μM. For each set of oocytes, the average ratio I^pro/I^10etowas calculated, and in subsequent sets of oocytes, propofol was adjusted upward or downward in steps of 1–3 μM until the average ratio of I^pro/I^10etowas 0.95 to 1.05. This process identified 19 μM propofol as equiefficacious with 10 μM etomidate (fig. 1). This match was confirmed in a total of 10 oocytes. The ratio of I^19pro/I^10etofrom these oocytes was 0.97 ± 0.11 (mean ± SD). We also observed that current activation by propofol was significantly slower in onset than that by etomidate (fig. 1).

We next compared the effects of 10 μM etomidate versus  19 μM propofol on electrophysiological responses to GABA. Oocytes (n ≥ 5) were tested for responses to a single concentration of GABA alone (1 μM, 3 μM, 10 μM, 30 μM, 100 μM, 300 μM, or 1 MM), and then sequentially to GABA supplemented with each anesthetic. Results are summarized in figure 2. Both anesthetics significantly enhanced responses at all seven GABA concentrations tested (two-way ANOVA; P < 0.001 at all concentrations), including concentrations eliciting maximal current responses (1 MM GABA; P < 0.001 for both etomidate and propofol). In contrast, pairwise comparison of current responses in the presence of 10 μM etomidate versus  19 μM propofol showed no significant differences at any GABA concentration (P > 0.05). Thus, two different anesthetic solutions with identical direct activating effects on GABA^Areceptors also produce the same degree of enhancement in GABA-elicited channel activity.

Because the sequential application of etomidate and propofol may have influenced the above results, we also assessed changes in GABA concentration-responses in additional sets of oocytes (n ≥ 5), where each oocyte was exposed to only one anesthetic. This resulted in two sets of control GABA concentration-responses, one for comparison with GABA plus 10 μM etomidate and another for GABA plus 19 μM propofol. These results, displayed in figure 3, show that the two control GABA concentration responses do not significantly differ [F(4,172) = 1.39; P = 0.24]. Moreover, comparison of logistic fits to normalized GABA concentration responses in the presence of 10 μM etomidate versus  19 μM propofol also identified no significant difference [F(4,129) = 0.30; P = 0.88]. The logEC⁵⁰shifts produced by 10 μM etomidate and 19 μM propofol were respectively −1.388 ± 0.035 and −1.367 ± 0.039. These correspond to EC⁵⁰ratios (95% C.I.) of 0.041 (0.035–0.0480) for 10 μM etomidate and 0.043 (0.036–0.051) for 19 μM propofol. Given the large overlap in 95% CIs, the EC⁵⁰shifts produced by these two drug solutions are also indistinguishable.

In our allosteric model analysis of etomidate actions,6experiments that most determined the fitted number of anesthetic sites were etomidate-dependent reduction of GABA EC⁵⁰and enhancement of GABA EC5 responses. To provide a data set sufficient to constrain MWC coagonist model parameters for propofol and GABA actions on GABA^Areceptors, we quantified propofol-dependent direct activation and propofol-dependent enhancement of GABA EC2.5 (5 ± 1.5 μM). The results of these experiments, normalized to maximal GABA responses, are shown in figure 4.

Data from figures 3B (GABA concentration responses with and without 19 μM propofol) and 4B (propofol concentration-responses with and without EC2.5 GABA) were pooled and renormalized based on the assumption that 1 MM GABA + 19 μM propofol activates all channels. In the nonlinear least-squares method fit to Equation 2, we constrained L⁰to 50,000, a value based on earlier studies of wild-type α1β2γ2L GABA^Areceptors.6,17,18The resulting fitted parameters were K^G= 209 + 43 μM, c = 0.0017 ± 0.00018, K^P= 97 ± 56 μM, d = 0.020 ± 0.023, and n = 2.8 ± 0.79. The model is shown overlaid on the data in figure 5.

Given the large uncertainty in the parameters for propofol efficacy and number of sites, we investigated the sensitivity of these fitted values in two ways. First, we examined the chi-square for the global fit while constraining the number of propofol sites (n) to different values. The chi-square test analysis showed that models with multiple propofol sites were clearly better than a one-site model, but there was a very shallow minimum near n = 3, with only 20% change in the chi-square tes as n varied between 2 and 5. We also investigated how the fitted parameters for the number of propofol sites changed as we varied the constrained L⁰value two-fold up or down. When L⁰was 25,000, the fitted value for n was 2.3 ± 0.50, while L⁰constrained to 100,000 resulted in n = 2.7 ± 0.67.

The major finding of our experiments is that the linkage between propofol direct activation of GABA^Areceptors and its modulation of GABA-induced activation (left shift) is identical to that observed with etomidate. This result is consistent with the hypothesis that both propofol actions are mediated by the same binding sites, rather than different sites separately mediating agonism and GABA modulation. In addition, we found that MWC coagonism can quantitatively account for both propofol actions. The fitted propofol dissociation constant (K^P= 97 μM) is higher than values we have fitted for etomidate (K^E= 35–79 μM), and the fitted efficacy value for propofol (d = 0.02) is larger than those for etomidate (d = 0.0077–0.0096),6,19,20suggesting that propofol affinity for open receptors (dK^P= 1.9 μM) is weaker than that for etomidate (dK^E= 0.27–0.76 μM).

It is conceivable that independent GABA^Areceptor sites mediate propofol-induced agonism and modulating effects, but it is extremely unlikely that the relative effects of propofol at separate agonist and GABA-modulating sites happen by chance to exactly match those we observed with our selected etomidate solution. Furthermore, the allosteric coagonist model accounts for both direct activation and GABA modulation over a wide range of propofol concentrations (fig. 5), not just at the one concentration we studied in detail.

The idea that a single class of sites mediates both propofol modulation and direct activation of GABA^Areceptors is consistent with many prior studies. For example, a strong correlation between GABA modulation and direct-activation potencies is apparent for a large series of propofol analogs, including 13 compounds that display neither activity.21Furthermore, mutations at both β2N26513,22and β2M28613in α1β2γ2L GABA^Areceptors reduce or eliminate both direct propofol activation and GABA modulation. However, in GABA^Areceptors with different subunit composition, a βM286W mutation reduces GABA modulation by propofol without abolishing direct activation.3,13,22We have reported similar results for etomidate actions in α1β2γ2L receptors containing the α1M236W mutation.20,23These observations remain consistent with allosteric coagonist models, because αM236W and βM286W mutations also produce spontaneous receptor gating,20which sensitizes receptors to direct activation by both agonists and allosteric coagonists.6,17,20 

Other prior studies also reinforce strong parallels between the actions of propofol and etomidate on GABA^Areceptors. Both drugs enhance the agonist efficacy of piperidine-4-sulfonic acid, a partial GABA^Areceptor agonist.6,24Single amino acid mutations on GABA^Areceptor β subunits, at positions 265 and 286, similarly alter molecular sensitivity to both propofol and etomidate.13,22,25,26Knock-in mice containing β3N265M mutations display dramatically reduced sensitivity to both propofol- and etomidate-induced loss-of-righting reflexes and suppression of nociceptive reflexes.27These observations, combined with the results of this study, indicate that propofol and etomidate affect GABA^Areceptors through similar molecular mechanisms, and perhaps at nearby sites. Nonetheless, a high concentration of propofol only partially inhibits GABA^Areceptor photolabeling by azi-etomidate, indicating that the sites where these drugs bind do not fully overlap.28 

Our results are in good accord with other studies of propofol effects at human GABA^Areceptors expressed in oocytes.26The majority of other electrophysiological studies have examined propofol effects on rodent GABA^Areceptors.13,21,29We also observed that both onset of GABA^Areceptor activation by propofol and its washout from oocytes weres slower than with etomidate. In addition, onset and offset of agonism by both these drugs is slower in oocytes than with GABA, despite their use at similar concentrations. The most likely explanation for these observations is that propofol binds more avidly than etomidate to lipids and proteins inside the oocyte, and these binding sites act to buffer the intramembrane concentration of drug when the extracellular solution changes. Similar buffering effects have been described to explain the slow onset and offset of neuroactive steroid actions in cultured cells.30,–,32GABA, as a charged molecule that acts at the extracellular structures of the receptor, equilibrates more rapidly when its concentration is changed.

The presence of multiple allosteric propofol sites per receptor is supported by our data. The Hill slope for propofol direct activation is 2.5 (fig. 4), and the best fit for the number of equivalent propofol sites in the global MWC model is 2.8 (fig. 5). These values lead us to conclude that there are at least two propofol sites per receptor, and perhaps more. Our modeling is most consistent with the presence of three equivalent propofol sites, but does not strongly favor this value relative to models with two, four, or five sites. In comparison, our modeling of etomidate actions clearly showed a best fit with two sites per receptor.6One factor contributing to the uncertainty in the propofol model is that propofol at high concentrations inhibits GABA^Areceptors, which may result in underestimating propofol efficacy and overestimating its affinity (etomidate also inhibits GABA^Areceptors, but less potently than propofol). While our model assumes noninteracting equivalent sites, distinct propofol sites may interact with each other allosterically and may not contribute equally to receptor gating. Moreover, MWC models with higher numbers of sites are intrinsically more difficult to distinguish, as the contributions of each site to receptor gating becomes smaller.

This uncertainty may be short-lived. A propofol-based anesthetic photolabel has recently been synthesized33and another is being developed (written personal communication from Keith W. Miller, Ph.D., Professor of Anesthesia, Department of Anesthesia, Critical Care and Pain Medicine, Massachusetts General Hospital, Boston, Massachusetts, in February 2011). In parallel, cultured cell-lines have been developed that produce high levels of homogeneous purified GABA^Areceptors suitable for photolabeling experiments.34The combination of these new technologies may reveal, in the near future, both the number of propofol sites on GABA^Areceptors and their locations.

The MWC coagonist model provides a formal framework for future experiments aimed at understanding how and where propofol produces its beneficial actions via  GABA^Areceptors, which may help guide development of improved clinical anesthetics. Reframing anesthetics as coagonists also provides insights into how anesthetics affect neuronal circuits through different types of GABA^Areceptors. Specifically, important behavioral effects of anesthetics may be mediated by extrasynaptic GABA^Areceptors formed from α, β, and δ subunits, that display tonic low-level gating activity (extrasynaptic GABA is approximately 0.5–1 μM), and that may be spontaneously active.35Assuming that their propofol sites are similar to those on synaptic receptors, allosteric coagonism predicts that extrasynaptic receptors will be directly activated and/or significantly modulated by low, clinically relevant propofol concentrations, resulting in significantly reduced neuronal excitability. In contrast, clinical propofol concentrations only modestly increase the peak activity of synaptic GABA^Areceptors in response to presynaptic release of brief high (more than 1 MM) GABA concentrations. Instead, propofol prolongs activation of synaptic receptors, likely influencing the frequency response of neuronal circuits. Moreover, with a predicted K^Pnear 100 μM and clinical concentrations in the low micromolar range, another implication of our model is that propofol may occupy only a small fraction of its GABA^Areceptor sites when producing its central nervous system effects.

In conclusion, quantitative comparisons of direct GABA^Areceptor agonism and GABA-induced receptor activation in the presence of both propofol and etomidate show that the relationship between these measurements is the same for both drugs. This finding strongly favors the hypothesis that propofol-binding sites on these receptors mediate both effects, rather than separate sites independently mediating each effect. Furthermore, quantitative analysis of propofol effects using a MWC coagonist model indicates the presence of multiple propofol-binding sites per GABA^Areceptor, with three sites being the value most consistent with this class of model.

The authors thank Anika Schuster, B.S., and Ralf Poeschke, B.S. (Technicians, Department of Anesthesia and Intensive Care, University Hospital Giessen-Marburg, Marburg, Germany), for assistance with experiments, as well as Horst Schneider, Ph.D. (Research Fellow, Department of Physiology, University of Marburg, Marburg, Germany), and Konstantin Strauch, Ph.D. (Institute of Medical Biometry and Epidemiology Medical Faculty, Philipps University Marburg, Germany), for helpful discussions.