Evaluation of consistency for multiple experiments of a single combination in the time-dependence mixture toxicity assay.

Test-to-test consistency was evaluated for a single binary combination of organic chemicals using an assay that examined toxicity over multiple exposure times. Six experiments were conducted. The toxicities of 3-chloro-2-butanone (3C2B), methyl crotonate (MC) and the mixture of both (MX) were evaluated in each experiment at 15, 30 and 45 min of exposure using the Microtox® system. Concentration-response (x/y) curves were generated via the five-parameter logistic minus one-parameter (5PL - 1P) curve-fitting function and were used to develop predicted x/y curves for the dose-addition (DA) and independence (I) models of combined effect. A variety of toxicity (e.g. effective concentration, EC50) and time-dependent toxicity (TDT) endpoints, 5PL - 1P parameters and various combined-effects metrics (e.g. MX/DA) were calculated. Test-to-test consistency was evaluated via the coefficient of variation (CV) or, for TDT, the standard deviation of mean values. In the study, CVs obtained for single-chemical and mixture toxicity endpoints (EC25, EC50 and EC75) at each exposure time were <20, as were those for the predicted DA and I curves. For the MX/DA metric, mixture toxicity was consistent with that predicted for DA at each exposure time in each experiment with CVs <6, despite some substantial variation in TDT for MC-alone at the EC25 and for the 30-45 min time-interval. There was a lower variation in TDT for 3C2B and MX. Mean and CV values for 5PL - 1P-derived slope and asymmetry parameters were also assessed to provide bases for comparisons in future reports.

Chemometrics quality assessment of wastewater treatment plant effluents using physicochemical parameters and UV absorption measurements.

Chemometric techniques like Principal Component Analysis (PCA) and Partial Least Squares Regression (PLS) are used to explore, analyze and model relationships among different water quality parameters in wastewater treatment plants (WWTP). Different data sets generated by laboratory analysis and by an automatic multi-parametric monitoring system with a new designed optical device have been investigated for temporal variations on water quality parameters measured in the water influent and effluent of a WWTP over different time scales. The obtained results allowed the discovery of the more important relationships among the monitored parameters and of their cyclic dependence on time (daily, monthly and annual cycles) and on different plant management procedures. This study intended also the modeling and prediction of concentrations of several water components and parameters, especially relevant for water quality assessment, such as Dissolved Organic Matter (DOM), Total Organic Carbon (TOC) nitrate, detergent, and phenol concentrations. PLS models were built to correlate target concentrations of these constituents with UV spectra measured in samples collected at (1) laboratory conditions (in synthetic water mixtures); and at (2) WWTP conditions (in real water samples from the plant). Using synthetic water mixtures, specific wavelengths were selected with the aim to establish simple and reliable prediction models, which gave good relative predictions with errors of around 3-4% for nitrates, detergent and phenols concentrations and of around 15% for the DOM in external validation. In the case of nitrate and TOC concentrations modeling in real water samples from the effluent of the WWTP using the reduced spectral data set, results were also promising with low prediction errors (less than 20%).

Mixture toxicity of SN2-reactive soft electrophiles: 3. Evaluation of ethyl α-halogenated acetates with α-halogenated acetonitriles.

Mixture toxicity for each of four ethyl α-halogenated acetates with each of three α-halogenated acetonitriles (xANs) was assessed. Inhibition of bioluminescence in Vibrio fischeri was measured after 15, 30, and 45 min of exposure. Concentration-response curves were developed for each chemical at each exposure duration and used to develop predicted concentration-response curves for the dose-addition and independence models of combined effect. Concentration-response curves for each mixture and each exposure duration were then evaluated against the predicted curves using three metrics per model: (1) EC50-based additivity quotient (AQ) or independence quotient (IQ) values; (2) mean AQ (mAQ) or mean IQ (mIQ) values, which were calculated by averaging the EC25, EC50, and EC75 AQ or IQ values; and (3) deviation values from additivity (DV-A) or independence (DV-I). Mixture toxicity for ethyl iodoacetate was dose-additive with each of the xANs at all exposure durations and was also often consistent with independence. The same was true for mixture toxicity of ethyl bromoacetate with each xAN. However, for the two more slowly reactive chemicals, ethyl chloroacetate (ECAC) and ethyl fluoroacetate (EFAC), mixture toxicity with each xAN only became consistent with dose-addition on increasing exposure duration. Consistency with independence for both ECAC and EFAC with the xANs was essentially limited to the EC50-IQ metric, thereby showing the utility of calculating the mean quotient (mAQ, mIQ) and deviation value (DV-A, DV-I) metrics. On review of these findings with those from the first two studies in the series, the results suggest that instances in which mixture toxicity was not consistent with dose-addition relate (1) to differences in the capability of the chemicals to form strong H-bonds with water; and (2) to differences in relative reactivity and time-dependent toxicity levels of the chemicals.

Mixture toxicity of S(N)2-reactive soft electrophiles: 2-evaluation of mixtures containing ethyl α-halogenated acetates.

Four ethyl α-halogenated acetates were tested in (1) sham and (2) nonsham combinations and (3) with a nonreactive nonpolar narcotic. Ethyl iodoacetate (EIAC), ethyl bromoacetate (EBAC), ethyl chloroacetate (ECAC), and ethyl fluoroacetate (EFAC), each considered to be an SN2-H-polar soft electrophile, were selected for testing based on their differences in electro(nucleo)philic reactivity and time-dependent toxicity (TDT). Agent reactivity was assessed using the model nucleophile glutathione, with EIAC and EBAC showing rapid reactivity, ECAC being less reactive, and EFAC lacking reactivity at ≤250 mM. The model nonpolar narcotic, 3-methyl-2-butanone (3M2B), was not reactive. Toxicity of the agents alone and in mixture was assessed using the Microtox acute toxicity test at three exposure durations: 15, 30 and 45 min. Two of the agents alone (EIAC and EBAC) had TDT values >100%. In contrast, ECAC (74 to 99%) and EFAC (9 to 12%) had partial TDT, whereas 3M2B completely lacked TDT (<0%). In mixture testing, sham combinations of each agent showed a combined effect consistent with predicted effects for dose-addition at each time point, as judged by EC(50) dose-addition quotient values. Mixture toxicity results for nonsham ethyl acetate combinations were variable, with some mixtures being inconsistent with the predicted effects for dose-addition and/or independence. The ethyl acetate-3M2B combinations were somewhat more toxic than predicted for dose-addition, a finding differing from that observed previously for α-halogenated acetonitriles with 3M2B.

Mixture toxicity of SN2-reactive soft electrophiles: 1. Evaluation of mixtures containing α-halogenated acetonitriles.

The concept of multiple modes of toxic action denotes that an individual chemical can induce two or more toxic effects within the same series of concentrations, for example, reactive toxicity and narcosis. It appears that such toxicity confounds the ability to develop precise predictions of mixture toxicity and makes it more difficult to clearly link a dose-additive combined effect to agents in the mixture having a single common mechanism of toxic action. This initial study of a three-part series begins to examine this issue in greater detail by testing three α-halogenated acetonitriles: (1) in sham combinations, (2) in true combinations, and (3) with a nonreactive nonpolar narcotic. Iodo-, bromo-, and chloro-derivatives of acetonitrile were selected for testing based on their electro(nucleo)philic reactivity, via the S(N)2 mechanism, and their time-dependent toxicity individually. Reactivity of each agent was assessed in tests with the model nucleophile glutathione (GSH). Each acetonitrile was reactive with GSH, but the nonpolar narcotic 3-methyl-2-butanone was not. In addition, toxicity of the agents alone and in mixtures was assessed using the Microtox(®) acute toxicity test at three time points: 15, 30, and 45 min of exposure. Each of the three agents alone had time-dependent toxicity values of about 100%, making it likely that most of the toxicity of these agents, at these times, was due to reactivity. In contrast, the nonpolar narcotic agent lacked time-dependent toxicity. In mixture testing, sham combinations of each acetonitrile showed a combined effect consistent with predicted effects for dose-addition at each time point, as did the sham combination of the nonpolar narcotic. Mixture toxicity results for true acetonitrile combinations were also consistent with dose-addition, but the acetonitrile-nonpolar narcotic combinations were generally not consistent with either the dose-addition or independence models of combined effect. Based on current understanding of mixture toxicity, these results were expected and provide a foundation for the second and third studies in the series.

Time dependence in mixture toxicity with soft electrophiles: 1. Combined effects of selected SN2- and SNAr-reactive agents with a nonpolar narcotic.

Frequently the toxicity of an organic chemical mixture is close to dose-additive, even when the agents are thought to induce toxicity at different molecular sites of action. These findings appear to conflict with the hypothesis that a strictly dose-additive combined effect will be observed for agents sharing a single molecular site of toxic action within the organism. In this study, several SN2-reactive (alpha-halogen) or S(N)Ar-reactive (halogenated dinitrobenzene) soft electrophiles were tested with a model nonpolar narcotic (NPN) to determine the toxicity of the combinations. A sham combination of the model NPN (3-methyl-2-butanone) was also tested as a positive control. The study design incorporated time-dependent toxicity (TDT) determinations at 15, 30, and 45 minutes using a Microtox (Vibrio fischeri) protocol that included testing seven duplicated concentrations for each single agent and mixture per combination. Additionally, in chemico reactivity was determined for each compound using thiol in glutathione as a model nucleophile. The model NPN alone lacked reactivity and TDT. The SN2-reactive agents individually showed varying levels of both reactivity and TDT alone, while the SNAr-reactive chemicals alone were reactive and had toxicity that was fully time-dependent between 15 and 45 minutes of exposure. Data analyses indicated that the sham combination was dose additive, as expected, whereas three of four SN2:NPN combinations showed effects close to that predicted for dose addition but with some differences. The fourth SN2:NPN combination, which included an alpha-halogen with full TDT, showed a less-than-dose-additive combined effect as did both of the SNAr:NPN pairings. By incorporating TDT values, shapes of the dose-response curves, chemical reactivity data with thiol, reactive mechanisms for the soft electrophiles, and quantitative structure activity relationship information on whether the toxicity of the individual soft electrophiles did or did not exceeded that predicted for baseline narcosis, the results suggested that the alpha-halogens elicited two toxic effects at the concentrations tested (reactivity and narcotizing effects), whereas toxicity induced by the halogenated dinitrobenzenes was essentially limited to reactive effects. Collectively, these results provide experimental evidence consistent with previous explanations as to why binary mixtures of industrial organic chemicals often show combined effects that are close to dose additive, even when the chemicals are thought to induce toxicity at different molecular sites of action.

Simultaneous GC-MS analysis of meta- and para-hydroxybenzoylecgonine and norbenzoylecgonine: a secondary method to corroborate cocaine ingestion using nonhydrolytic metabolites.

Positive benzoylecgonine (BZE) urinalysis results are sometimes challenged in legal and administrative proceedings on the grounds that the presence of BZE is due to the addition of cocaine to the urine sample with subsequent in vitro hydrolysis to BZE. Consequently, counsel for the respondent or defendant may move that an ecgonine methyl ester (EME) analysis be preformed because EME is presumed to be solely an in vivo cocaine metabolite. For these reasons, a sensitive and rapid gas chromatographic-mass spectrometric procedure was developed for the simultaneous analysis of m-hydroxybenzoylecgonine (m-OHBZE), p-hydroxybenzoylecgonine (p-OHBZE), and N-desmethyl benzoyl ecgonine (norBZE), all of which are cocaine metabolites believed to arise exclusively via in vivo metabolism. Analysis of human urine specimens previously reported positive for BZE using GC-MS at the Department of Defense cutoff of 100 ng/mL demonstrated that at least one of the three metabolites was present in 79 of the 82 specimens studied (96.3%). Thus, the simultaneous analysis of r-OHBZE, p-OHBZE, and norBZE could be used to substantiate that the presence of BZE in urine specimens is the result of cocaine ingestion. Additionally, the premise that EME is a "true" in vivo cocaine metabolite was investigated by assessing the stability of cocaine in unpreserved urine samples at several pHs ranging from 5.0 to 9.0.

Metabolism of lysergic acid diethylamide (LSD) to 2-oxo-3-hydroxy LSD (O-H-LSD) in human liver microsomes and cryopreserved human hepatocytes.

The metabolism of lysergic acid diethylamide (LSD) to 2-oxo-3-hydroxy lysergic acid diethylamide (O-H-LSD) was investigated in liver microsomes and cyropreserved hepatocytes from humans. Previous studies have demonstrated that O-H-LSD is present in human urine at concentrations 16-43 times greater than LSD, the parent compound. Additionally, these studies have determined that O-H-LSD is not generated during the specimen extraction and analytical processes or due to parent compound degradation in aqueous urine samples. However, these studies have not been conclusive in demonstrating that O-H-LSD is uniquely produced during in vivo metabolism. Phase I drug metabolism was investigated by incubating human liver microsomes and cryopreserved human hepatocytes with LSD. The reaction was quenched at various time points, and the aliquots were extracted using liquid partitioning and analyzed by liquid chromatography-mass spectrometry. O-H-LSD was positively identified in all human liver microsomal and human hepatocyte fractions incubated with LSD. In addition, O-H-LSD was not detected in any microsomal or hepatocyte fraction not treated with LSD nor in LSD specimens devoid of microsomes or hepatocytes. This study provides definitive evidence that O-H-LSD is produced as a metabolic product following incubation of human liver microsomes and hepatocytes with LSD.

Analysis of the combined osteolathyritic effects of beta-aminopropionitrile and diethyldithiocarbamate on xenopus development.

In order to examine the mechanistic basis between combined effects and mechanisms of action, two osteolathyrogens, beta-aminopropionitrile (betaAPN) and diethyldithiocarbamate (DTC), were tested together on Xenopus embryos. In a separate test, DTC was also tested with copper sulfate to determine the importance of copper in DTC-induced osteolathyrism. Frog embryos (Xenopus laevis) were exposed for 96 h, with daily solution removal and replacement. Preserved tadpoles were evaluated for osteolathyritic lesions. For the betaAPN:DTC test, a 1.2-factor matrix design was used, producing two single chemical and seven mixture-response curves. The chi(2) goodness-of-fit test was used to compare the experimental mixture-response curves with theoretical effects for two combined effects models, dose-addition and independence. All seven mixture curves were consistent with expected results for dose-addition, but the correlations were generally not high. For the DTC:copper test, the three mixture-response curves generated showed that added copper increased the DTC-alone EC(50), but there was no corresponding right shift at the top of the response curves, as observed previously with betaAPN and copper. In the betaAPN:DTC and DTC:copper tests, DTC alone showed a biphasic concentration-osteolathyrism curve, and the slope of the response curve for DTC alone in each test was statistically different than the slope for the betaAPN alone response curve. Taken together, the results suggest the potential for a second osteolathyritic effect of DTC that affected the combined toxicity enough to produce a dose-addition correlation without the chemicals necessarily having the same mechanism.

Comparative evaluation of the combined osteolathyritic effects of two nitrile combinations on xenopus embryos.

Two nitrile combinations, beta-aminopropionitrile (beta APN) with aminoacetonitrile (AAN) and betaAPN with beta APN (as a sham combination), were evaluated using the frog embryo mixture toxicity assay to determine their combined osteolathyritic effects and to compare the results with theoretical effects for two combined effects models. In separate tests each nitrile was tested with copper sulfate to determine the importance of copper in osteolathyrogen-induced disruption of connective tissue cross-linking. Frog embryos (Xenopus laevis) were exposed for 96 h, with daily solution removal and replacement. Preserved tadpoles were evaluated for osteolathyritic lesions. For the nitrile:nitrile combinations, the chi(2) goodness-of-fit test was used to compare the resulting mixture-response curves to theoretical curves for dose-addition and independence. For beta APN with AAN, the combined osteolathyritic effect for five of the seven mixture curves generated was greater than expected for each of the combined effects models. For beta APN with beta APN, the combined effect for all seven mixture curves was consistent with dose-addition, the combined effect expected for chemicals inducing toxicity by the same mechanism. For the nitrile:copper combinations, the EC(50) for beta APN-induced osteolathyrism was increased two- to threefold (i.e. made less toxic) by co-administration with copper sulfate, while the EC(50) for AAN-induced osteolathyrism was unchanged. The results are consistent with the idea that beta APN and AAN induce osteolathyrism, at least in part, by different mechanisms.

The quantitation of 2-oxo-3-hydroxy lysergic acid diethylamide (O-H-LSD) in human urine specimens, a metabolite of LSD: comparative analysis using liquid chromatography-selected ion monitoring mass spectrometry and liquid chromatography-ion trap mass spectrometry.

This paper compares the potential forensic application of two sensitive and rapid procedures (liquid chromatography-mass spectrometry and liquid chromatography-ion trap mass spectrometry) for the detection and quantitation of 2-oxo-3-hydroxy lysergic acid diethylamide (O-H-LSD) a major LSD metabolite. O-H-LSD calibration curves for both procedures were linear over the concentration range 0-8,000 pg/mL with correlation coefficients (r2) greater than 0.99. The observed limit of detection (LOD) and limit of quantitation (LOQ) for O-H-LSD in both procedures was 400 pg/mL. Sixty-eight human urine specimens that had previously been found to contain LSD by gas chromatography-mass spectrometry were reanalyzed by both procedures for LSD and O-H-LSD. These specimens contained a mean concentration of O-H-LSD approximately 16 times higher than the LSD concentration. Because both LC methods produce similar results, either procedure can be readily adapted to O-H-LSD analysis for use in high-volume drug-testing laboratories. In addition, the possibility of significantly increasing the LSD detection time window by targeting this major LSD metabolite for analysis may influence other drug-free workplace programs to test for LSD.

Sigmoid model versus median-effect analysis for obtaining dose-response curves for in vitro chemosensitivity testing.

AIM: The aim of this study was to determine how the in vitro dose-response effects of chemotherapeutic agents should be analyzed and reported. METHODS: We arbitrarily evaluated the effects of mitomycin-C and 4-OH-cyclophosphamide on the human ovarian cancer cell line CAOV-3. Dose-response curves (DRCs) were calculated by non-linear (sigmoid model: SigmaPlot) and linear curve fitting (median-effect analysis: CalcuSyn). RESULTS: In theory and practice, the sigmoid model provided better curve fits and graphical presentation than the median-effect analysis. CONCLUSION: Thus, this model should preferably be used as a basis for selection of anti-cancer drugs for clinical use.

Combined osteolathyric effects of beta-aminopropionitrile and penicillamine on Xenopus embryos: statistical comparison with dose-addition and independence.

The combined osteolathyric effects of beta-aminopropionitrile (beta APN) and penicillamine (PNC) on developing Xenopus embryos were determined and compared with theoretical effects for the dose-addition and independence models. The testing protocol utilized a 1.2-factor matrix design that generated two single chemical and seven mixture concentration-response curves within 36 treatments. Testing was for 96-h with daily solution removal and replacement. The chi 2 goodness-of-fit test was used to compare experimental responses with theoretical responses. Response curve analyses indicated, in general, a combined effect between that expected for dose-addition and that for independence, which is a combined effect typical of chemicals acting dissimilarly.

Detection of metabolites of lysergic acid diethylamide (LSD) in human urine specimens: 2-oxo-3-hydroxy-LSD, a prevalent metabolite of LSD.

Seventy-four urine specimens previously found to contain lysergic acid diethylamide (LSD) by gas chromatography-mass spectrometry (GC-MS) were analyzed by a new procedure for the LSD metabolite 2-oxo-3-hydroxy-LSD (O-H-LSD) using a Finnigan LC-MS-MS system. This procedure proved to be less complex, shorter to perform and provides cleaner chromatographic characteristics than the method currently utilized by the Navy Drug Screening Laboratories for the extraction of LSD from urine by GC-MS. All of the specimens used in the study screened positive for LSD by radioimmunoassay (Roche Abuscreen). Analysis by GC-MS revealed detectable amounts of LSD in all of the specimens. In addition, isolysergic diethylamide (iso-LSD), a byproduct of LSD synthesis, was quantitated in 64 of the specimens. Utilizing the new LC-MS-MS method, low levels of N-desmethyl-LSD (nor-LSD), another identified LSD metabolite, were detected in some of the specimens. However, all 74 specimens contained O-H-LSD at significantly higher concentrations than LSD, iso-LSD, or nor-LSD alone. The O-H-LSD concentration ranged from 732 to 112 831 pg/ml (mean, 16340 pg/ml) by quantification with an internal standard. The ratio of O-H-LSD to LSD ranged from 1.1 to 778.1 (mean, 42.9). The presence of O-H-LSD at substantially higher concentrations than LSD suggests that the analysis for O-H-LSD as the target analyte by employing LC-MS-MS will provide a much longer window of detection for the use of LSD than the analysis of the parent compound, LSD.

Mitoxantrone combined with paclitaxel as salvage therapy for platinum-refractory ovarian cancer: laboratory study and clinical pilot trial.

This report describes preclinical and early clinical investigations of the mitoxantrone/paclitaxel combination (NT) for patients with platinum-refractory ovarian cancer. The preclinical activity of NT was studied ex vivo, evaluating native tumor specimens with the ATP tumor chemosensitivity assay. Of 24 tumors tested, 20 (83%) were sensitive to NT, whereas 7 (29%) responded to mitoxantrone and 8 (33%) responded to paclitaxel. In the majority of tumors assayed (19 of 24), potentiating or major independent effects between both agents were found. Subsequently, a clinical pilot trial of NT was initiated for patients with platinum-refractory ovarian cancer. Patients had failed one to four (median, two) prior chemotherapy regimens. In 11 cases, NT was administered every three weeks with 8 mg/m2 mito-xantrone and 180 mg/m2 paclitaxel (NT-I). Seven patients were treated biweekly with 6 mg/m2 mitoxantrone and weekly with 100 mg/m2 paclitaxel (NT-II). During 92 NT courses, myelosuppression with leucopenia, anemia, and thrombocytopenia was the limiting toxicity, occurring more frequently with NT-II. No patient required hospitalization due to any life-threatening complication. Five complete and nine partial remissions were observed with both NT-I and NT-II, accounting for an overall 78% response rate, with a median progression-free survival of 40 weeks. One patient showed early progression during therapy. Currently, three patients (NT-I, two; NT-II, one) have died due to progressive relapsed ovarian cancer, so that the median overall survival is not reached after a median follow-up of 40.5+ weeks. Both schedules were found to be equal in terms of response rate and overall survival. NT is highly active and practical for salvage treatment of ovarian cancer. NT-II may be preferred due to both clinical activity and patients' acceptance. However, NT-I seems to be a less myelotoxic alternative. Both schedules warrant further clinical investigation.

Apparent independent action of nimodipine and glutamate antagonists to protect cultured neurons against glutamate-induced damage.

A disturbed cellular calcium homeostasis is suggested to play a pivotal role in neuronal damage. Energy deficiency causes depolarization of the neuronal membrane and Ca2+ enters the cells through different ion channels, the voltage-sensitive L-type Ca2+ channels and the NMDA-operated channels being the main gates. In the present study we used primary cultures of rat hippocampal neurons to demonstrate that the dihydropyridine calcium antagonist nimodipine, the non-competitive NMDA antagonists dizocilpine and memantine, as well as the AMPA antagonist NBQX (2,3-dihydroxy-6-nitro -7-sulfamoyl-benzo(F)quinoxaline), attenuate the glutamate-induced neuronal damage dose-dependently. Nimodipine applied simultaneously with NMDA-antagonists and NBQX, respectively, resulted in somewhat greater neuroprotection of glutamate-treated neurons compared with the effects of these agents applied singly. The type of interaction is best described by an independent action in combination, which means that the relative effects of nimodipine were not enhanced. Therefore, it can be considered as a lack of potentiation.

Uniform characterization of potentiation in simple and complex situations when agents bind to different molecular sites.

There is general agreement about potentiation in dose-response studies, characterized by a left shift of the dose-response curve of A by a fixed dose of B when B is causing no effect by itself (simple situation). When B causes an effect similar to A (complex situation) by binding to different molecular sites, we propose an analogous analysis. This approach is based on comparison of experimental effects of A and B in combination with theoretical, independent effects, representing an effect of A that is not affected by B. We argue here that comparison of experimental effects with those of dose-additive (additive) combinations is inappropriate. Theoretical considerations and several practical examples show that the magnitude of effects due to additive combinations widely varies with the slope of dose-response curves of A. Consequently, it is also shown that one and the same theoretical effect may appear overadditive, additive, or underadditive. These situations are demonstrated by the experimental examples: inhibition of cytopathic effects in virus-infected cells, loss of righting reflex in mice, and smooth muscle relaxant effects of organic solvents.

Quantitative estimation of potentiation and antagonism by dose ratios corrected for slopes of dose-response curves deviating from one.

A shift of dose-response curves of a receptor agonist A by a receptor antagonist B to the right is frequently expressed or quantitated by calculating the dose ratio (DR) from the ED50 values obtained in the absence and presence of B. A comparison of ED50 values or a DR is also used in a more general way to express the effects of other antagonists or of potentiators. For this situation, where B is not competing with A for a binding site, slope-values may often deviate from one. Because the slope of shifted dose-response curves (deviating from one) affects the magnitude of enhancement or diminution at a given DR, we have to take it into account. For example, the same changes in effects are associated with DR = 10 at curves with slope = 1, but with DR = 2.15 in case of slope = 3. Enhancement and diminution expressed by dose ratios is more or less underestimated in case of curves with slope > 1. We therefore propose to quantitate potentiation and antagonism by a corrected DR (DRcorr), which can simply be calculated from the uncorrected DR at a given slope. Consequently, a DRcorr reflects a true measure of enhancement or diminution for curves with slope = 1, equivalent to that which would have been observed for curves with slope = 1. The practical value of this modification is exemplified and illustrated by analysis of experimental data.

Calculating slope and ED50 of additive dose-response curves, and application of these tabulated parameter values.

Comparing dose-response curves (DRCs) of a compound A in the absence and presence of a fixed dose of an antagonist B is standard in pharmacology and toxicology. When B qualitatively resembles A in its action, it is often useful to construct theoretical DRCs of additive and independent combinations. Theoretical curves are calculated from experimental values by the program ALLFIT, which uses the four parameter logistic equation. DRCs of theoretical, additive DRCs are obtained by using the respective values for slope and ED50, which were taken from tables presented here compiled on the basis of the slope of the DRC of A alone (0.6-14) and of the effect of B alone (1-75%). These tables are unnecessary for the construction of theoretical curves if A acts by an independent mechanism, giving values for slope and ED50 identical to those of the DRC of A alone. Experimental DRCs of antiviral and other effects (the latter taken from data in the literature) are compared with theoretical curves by an F-test analysis provided by ALLFIT. The method can be used successfully for the construction of theoretical curves for additive and independent DRCs and comparison with experimental curves. This comparison may help clarify the mode of interaction of A with B.