Equations for estimating binary mixture toxicity: 3-methyl-2-butanone with a series of electrophiles

Mixture toxicity was determined for 32 binary combinations. One chemical was the non-reactive, non-polar narcotic 3-methyl-2-butanone (always chemical A) and the other was a potentially reactive electrophile (chemical B). Bioluminescence inhibition in Allovibrio fischeri was measured at 15-, 30-, and 45-minutes of exposure for A, B, and the mixture (MX). Concentration-response curves (CRCs) were developed for each chemical and used to develop predicted CRCs for the concentration addition (CA) and independent action (IA) mixture toxicity models. Also, MX CRCs were generated and compared with model predictions using the 45-minute data. Classification of observed mixture toxicity used three specific criteria: 1) predicted IA EC50 vs. CA EC50 values at 45-minutes, 2) consistency of 45-minute MX CRC fit to IA, CA, or otherwise at three effect levels (EC25, EC50 and EC75), and 3) the known/suspected mechanism of toxicity for chemical B. Mixture toxicity was then classified into one of seven groupings. As a result of the predicted IA EC50 being more toxic than the predicted CA EC50, IA represented the greater toxic hazard. For this reason, non-sham MXs having toxicity consistent with CA were classified as being “coincident” with CA rather than mechanistically-consistent with CA. Multiple linear regression analyses were performed to develop equations that can be used to estimate the toxicity of other 3M2B-containing binary mixtures. These equations were developed from the data for both IA and CA, at each exposure duration and effect level. Each equation had a coefficient of determination (r2) above 0.950 and a variance inflation factor <1.2. This approach can potentially reduce the need for mixture testing and is amenable to other model systems and to assays that evaluate toxicity at low effect levels.


Introduction
Chemical mixture toxicity is an active area of environmentally-relevant research [1].Studies have evaluated environmental contamination [2], organic chemicals [3], heavy metals [4], pharmaceutical presence [5], and habitat impacts [6].Such studies may focus on a few specific chemicals relevant to situations of concern or include many chemicals of interest.
When many chemicals are present in a mixture at low concentrations relative to their acute aquatic toxicities, their combined effect closely follows concentration addition or simple additivity [7].This additivity holds even when the chemicals are structurally dissimilar or exhibit different modes of action.However, as the number of chemicals decreases toward binary mixtures, increased variance in additivity is reported [7].Specifically, binary and complex mixtures of reversible membrane-perturbating chemicals (alkanes, halogenated aliphatics, alcohols, ketones, etc.) tested in bacterial assays indicated additivity in their joint action [8].In contrast, the toxicity of binary mixtures of non-polar narcotics and reactive aldehydes yielded additive to greater than additive effects in the Microtox assay [9].Another Microtox study evaluating binary mixtures of reactive toxicants, reported greater than additive effects 18% of the time among chemicals with different mechanisms of toxicity [10].The authors noted that the slope of a chemical's concentration-response curve is vital in determining the mode of joint toxic actions.
When assessing the hazard posed by chemical mixtures, several mixture toxicity models are available to provide context for the experimentally-exhibited toxicity.Two commonly used models [11] are concentration addition (CA-a.k.a.dose addition) and independent action (IA-a.k.a.independence).The former model, CA [12], describes the combined effect obtained when the chemicals in the mixture act alike, just as if their molecules were the same substance (as in a sham combination).Hence, CA suggests that the chemicals work at the same molecular site of action; however, it is not definitive but depends on the slopes of the concentrationresponse curves (CRCs) [13].Various mathematical approaches, generally derivatives of the Hill equation [14,15], can be used for calculating CA, each appearing effective for given purposes [16][17][18].The IA model [19] is used to describe the toxicity associated with chemicals that act at different molecular sites, thereby resulting in an "unaffected" action when applied with another chemical [13].Independent action has been suggested to be the appropriate model for quantitatively evaluating potentiation and antagonism [13].For any given mixture, the resulting combined effect may not be consistent with these models.
The models CA and IA were chosen to evaluate the toxicity of electrophiles in binary combinations [20].Electrophiles are electron-deficient chemicals that can react with electron-rich chemicals called nucleophiles.As Schwo ¨bel and colleagues [21] summarized, exogenous electrophilic substances are in extremes, either hard with low polarizability or soft with high polarization.When introduced into an organism, electrophiles generally follow the rule of likereacts-with-like (i.e., soft-with-soft and hard-with-hard).However, many electrophiles are not specific regarding their molecular targets -they can react with different biological nucleophilic targets (e.g., S-, N-, and O-containing moieties).Many nucleophilic target sites are found in biological molecules (e.g., proteins, lipids, DNA).Since the principle of like-reacts-with-like applies, hard biological nucleophiles include DNA and amino groups such as lysine.In contrast, soft nucleophiles include thiol groups such as cysteine.These electro(nucleo)philic interactions, via different mechanisms, result in elevated acute toxicity and cytotoxicity.
There are more than 50 specific mechanisms of reactive biomolecular binding [21,22].The particular mechanisms are traditionally grouped into "chemical modes of action" (MOA) [23], such as Michael addition, aromatic nucleophilic substitution (SNAr), bi-molecular nucleophilic substitution (SN2), and Schiff base formation.These MOA describe direct-acting reactions that covalently modify bio-nucleophiles, subsequently leading to apical toxic events [24] and allow for classifying electrophiles into appropriate mechanistic applicability domains associated with particular chemical spaces [22,23].
This study tested 3-methyl-2-butanone (3M2B) in binary combination with a series of direct-acting electrophiles.In acute aquatic toxicity profiles, 3M2B is consistently reported as a "neutral organic," "base surface narcotic," and "class 1 narcotic" [22].In the model organism Allovibrio fischeri, toxicity manifested as bioluminescence inhibition and was determined for each single chemical and mixture at 15-, 30-, and 45-min of exposure.The results of mixture tests were then compared with effects predicted by the CA and IA models.Additionally, multiple linear regression equations for estimating mixture toxicity were developed to reduce the need for mixture testing.

Chemicals, reagents and toxicity testing
Chemicals tested in this study, including abbreviations, Chemical Abstract Service Registry numbers, SMILES structures, log Kow, vapor pressure and chemical reaction mechanisms are presented (Table 1.) Test chemicals were purchased from Aldrich (Milwaukee, WI) or Sigma (St. Louis, MO) in high purity (�95%) and used without further purification.Dimethyl sulfoxide (DMSO) was used as a carrier solvent; its concentration in test vials was �0.1%.
Freeze-dried bacterial reagent, Microtox diluent, and the bacterial reconstitution solution were obtained from Modern Water (New Castle, DE).Vials of bacterial reagent were kept frozen at −20˚C before a 20-minute reconstitution period just prior to test initiation.For each given combination, separate bacterial reagent vials were used to test each chemical alone and the mixture.
The marine bacterium Allovibrio fischeri was the model organism, with bioluminescence inhibition being measured with a Microtox analyzer.The acute toxicity testing procedures were noted previously [30].For each binary combination, each chemical was tested alone, denoted as chemical A (always 3M2B) or B (an electrophile), and the A+B mixture (MX).Each test had seven duplicated concentrations and a duplicated control.Test concentrations were prepared via serial dilution in mg/L and later converted to μM.Depending primarily on B's toxicity change over time, one of three dilution factors (1.75, 1.867, or 2.0) was used in testing.The dilution factor was kept the same for all tests of a given combination.
Initial light readings for each control and treatment vial were taken before chemical exposure.Toxicity assessments were made after 15-, 30-, and 45-minutes of exposure.During testing, treatment vials were held at 15˚C ± 0.2˚C.

Procedures for curve-fitting and other calculations
Microtox software collected data and converted light readings to percent effect values.The data were input into SigmaPlot (v.15.0; Inpixon, Palo Alto, CA) and evaluated via user-developed program files.Raw data were fitted to sigmoid curves with a five-parameter logistic function from which the minimum effect parameter had been removed [17].The remaining parameters were maximum effect, EC 50 , slope, and asymmetry (s).This modified function was designated 5PL-1P to delineate it from the software's standard four and five-parameter logistic functions.
Curve fitting was performed using Eq (1): in which y = % effect, max = maximum effect, x = concentration, and s = asymmetry.The a F beta to a carbonyl group.A proven nonelectrophile, nonreactive with glutathione reactivity at 250mM, predicted cystine and lysine binding is negative-below 9%.
Initial parameters for these regressions were estimated automatically.The following constraints were used for data fitting: a) EC 50 > 0, b) 0.1 < s < 10, c) max = 100.
For all concentration-response data, the following effective concentration values: EC 25 , EC 50 , and EC 75 , as well as slope, asymmetry (s), maximum effect, and coefficient of determination (CD or r 2 ) values were calculated for A, B, and MX at each exposure duration.For the B and MX tests, chemical concentrations were converted to 3M2B-equivalents via the B factor from Eq (3) [29]: Time-dependent toxicity (TDT) values were calculated by Eq 4: to give a percentage-based value [30].These calculations were made separately for each combination of A, B, and MX.Calculation procedures for obtaining predicted CRCs for the CA and IA models have been described [31].When A and B are equally effective in CA, the CA EC 50 is left-shifted (when viewed graphically) by a dose-ratio (DR) factor of two.The CA 50 and DR were calculated using Eqs 5 and 6, respectively.

CA50 ¼ a50=DR50 ð5Þ
Herein, CA 50 is the EC 50 for CA, a 50 is the EC 50 of the more potent single chemical, and b 50 f in chemico glutathione reactivity was assessed following the protocol in [26]; experimental values were reported in [22].
g Direct peptide reactivity assay predictions followed the protocol in [27]; experimental values were reported by [28], and predictions were made from [22]. https://doi.org/10.1371/journal.pone.0306382.t001 is the EC 50 of the less potent single chemical.
Therefore, when a 50 = b 50 the DR 50 = 1 + (1) = 2, that is, the CA 50 = a50/2.This approach allows one to calculate the predicted CA EC 50 when A and B are not exactly equally effective (very common) using the calculated DR to adjust the predicted CA value.For example, suppose A has an EC 50 of 52.4 μM and B has an A-equivalent concentration EC 50 of 61.7 μM.The DR is 1 + (52.4/61.7)= 1.8493.In this example, A was the more potent agent, so the EC 50 for A was divided by this DR value to give the CA EC 50 of 28.3 μM.Calculations of the EC 25 and EC 75 values for the predicted CA curve were performed in this same manner.This approach allows the DR to be adjusted at different EC x levels (i.e., EC 25 , EC 50 , and EC 75 ) and, for example, in situations in which A is more potent than B at the EC 25 , but B is more potent than A at the EC 50 and EC 75 .Taken together, the predicted CA values for EC 25 , EC 50 , and EC 75 , as well as the CA maximum effect value (Eq 7) allow calculating the predicted CA curve using the 5PL-1P curve fitting procedure noted above.
Theoretical curves for the IA model were developed using Eq 8: with yA and yB being percent effect values for A and B, respectively.
For each combination and exposure duration, the three EC x values were calculated for A, B, MX, and for the predicted CA and IA curves.Concentration addition quotient (AQ) values were calculated via Eq 9: in which the subscript x can represent either the 25, 50 or 75% effect levels.Likewise, independent action quotient (IQ) values were calculated using Eq 10: Final mixture toxicity determinations vs. the CA and IA models were made for each combination by determining: 1) whether the predicted 45-min IA EC 50 was more toxic than that for CA, 2) whether the three 45-min AQ x or IQ x values, respectively, were from 0.90 to 1.10, and 3) by giving due consideration to the mechanisms of toxic action for A and B (as per Table 1).

Statistical analyses
Statistical tests within SigmaPlot were used to analyze the data further.In the study, 32 binary combinations were tested; for each 3M2B served as chemical A. Since one combination was a sham (i.e., 3M2B with 3M2B), there were a total of 33 tests of 3M2B alone.To determine the repeatability of the 3M2B-alone tests, the mean, standard deviation, coefficient of variation (CV), range, and Shapiro-Wilk W values were calculated for each of the following: EC 25 , EC 50 , EC 75 , slope, asymmetry (s), coefficient of determination (CD or r 2 ) and TDT.The Shapiro-Wilk test evaluated the fitting of sample quartiles to standard normal quartiles [32].
Simple linear regression analyses were performed within SigmaPlot to delineate any correlations between the 45-min MX EC 50 values and the following: 45-min EC 50 values for A-alone (3M2B), B-alone (both in 3M2B-equivalent concentrations and actual B concentrations -all in μM), AQ 50 , IQ 50 and the 15-to 45-min TDT values for B-alone.
Testing of 32 binary mixtures containing 3M2B offered an opportunity to develop equations to estimate mixture toxicity for other 3M2B-containing mixtures not tested herein.This was done by multiple linear regression (MLR) within SigmaPlot, using test data for MX EC x as the dependent variable and either the CA EC x and AQ x or the IA EC x and IQ x as independent variables at each exposure duration.For each equation, CD (r 2 ), standard error of the estimate (SEE), and variance inflation factor (VIF) values were included.The VIF assessed the likelihood of collinearity between independent variables, with values <5.0 having low concern for collinearity [33].

Results and discussion
While toxicity was determined for three exposure durations (15-, 30-, and 45-min), for space considerations detailed results are presented primarily for the latter timepoint.
The repeatability of results for Microtox testing was evaluated by examining the results from all 3M2B-alone tests (Table 2).Therein, CV values below 20 were obtained for each mean EC x value and each mean slope, CD, and TDT value.Asymmetry (s) values for 3M2B had more variable means, but CV values remained below 40, thereby being acceptable for testto-test variation [34].In addition, the W statistic from the Shapiro-Wilk test denoted the fitting of sample quartiles to standard normal quartiles.Sample values with a W score = 1 represent a perfect fit [32].For 3M2B, W values ranged from 0.771 to 0.967, with 13 of 19 endpoints above 0.900, including all nine EC x values.
For each combination, 45-min EC 50 values for MX, A, and B (the latter given as both 3M2B-equivalent and actual B concentrations), the calculated 45-min AQ 50 and IQ 50 , and the 15 to 45-min TDT values are provided (Table 3).For comparative purposes, the MX EC 50 values are listed within the table from the most toxic to the least toxic combination.Simple linear regressions conducted for the MX EC 50 values vs. those from each other data column resulted in r 2 values < 0.700, indicating no strong linear correlations between the MX data and the different variables.
When examining MX toxicity vs. the IA model at 45-min, non-sham MX toxicity was less than that predicted by IA for all combinations except for 3M2B-HPM (Table 4).When IQ x values were tabulated for individual IQ x effect levels, there were four IQ 25 values <0.90 (lowest = 0.86), twelve were IA consistent, and sixteen were >1.10 (highest = 1.87).For the IQ 50 , nine were IA consistent, the rest were >1.10 (high = 1.71).For the IQ 75 , three were IA consistent, and the rest were >1.10 (highest = 2.14).These data are available at DOI: 10.17605/OSF.IO/2NVDW.
For the CA model, before determining the combined effect of the 45-min MX data, the following points were addressed: 1) was the predicted IA EC 50 more toxic than the predicted CA EC 50 , 2) were all three AQ x values (x includes 25, 50 or 75% effect levels) from 0.90 and 1.10, and 3) were the 'B' chemicals in each combination known or suspected to have the same toxic mechanism as 3M2B.
To address the first point, the toxicities of the predicted 45-min IA EC 50 and CA EC 50 values were compared graphically for each combination.This was done by ordering the IA EC 50 data from most to least toxic on the Y-axis (Fig 1).Therein, it can be seen that the predicted IA EC 50 was more toxic than the predicted CA EC 50 for all 32 combinations.Thus, the IA model represents the greater toxic hazard for all MXs in this study.This is likely because 45-min CRC slopes for A and MX were mostly <1.6 [13].All 32 A-alone tests and 28 of 32 MX tests had slopes <1.6.Of the latter, only two had a slope >1.7.These data are available at DOI: 10.17605/OSF.IO/2NVDW.Comparatively, 17 B-alone CRCs had slopes <1.7, while 15 CRCs had slopes >1.7, with all but two of those being <2.5.Therefore, it was likely that all non-sham mixtures fitting the CA designation at 45-min (see Table 4) had toxicity that was "coincident" with CA [13].
To address the second point, nine non-sham combinations had all three AQ x values from 0.90 to 1.10.Moreover, five other combinations had at least two of the three AQ x values below 0.90 (i.e., a greater-than CA combined effect).However, none of those showed toxicity greater than that predicted by the IA model.This is additional evidence for mixture toxicity being "coincident" with CA.
The third point was addressed by noting that all B agents (except for 3M2B and EFAC) are known/suspected to have a reactive mechanism of toxicity.At the same time, 3M2B is considered a non-reactive, non-polar narcotic (see Table 1).Therefore, mechanistically it is also unlikely that each non-sham mixture having AQ x values fitting the CA designation (i.e., 0.90 � MX EC x � 1.10) were truly CA mechanistically.One should note that all chemicals exhibit a log Kow-determined, reversible, and non-covalent biomembrane fluidity change that alters cellular function (i.e., bioluminescence) [35].This reversible inhibition may be superseded by covalent reactivity with cellular proteins, especially cystine-rich functional proteins and lysine-rich structural proteins.It is deemed likely that toxic potency for reactive electrophiles may be correlated to reactive mechanism and/or reaction rates.
The results do not provide clear insights into how mixture toxicity is related to the mechanism/mode of toxic action.However, upon examining the listed order of the B-agents in Fig 1 and Table 1 (i.e., from greatest to least toxic as predicted by 45-min IA EC 50 toxicity) and in Table 3 (from greatest to least observed toxicity at the 45-min MX EC 50 ) one can see that the upper and lower chemicals in each listing are similar.As shown in Table 1, SNAr reactive chemicals (i.e., BDNB, CDNB, 26D4NP, and 2C4NP) are among the most toxic when given with 3M2B.Likewise, several chemicals (e.g., HPM, BGE, DES, DMS), that are slightly or weakly reactive with glutathione, are among the least toxic with 3M2B (Tables 1 and 3).The  most notable exception is 4VP, a well-studied directing-acting electrophile (see Table 1) that was the least toxic with 3M2B (Table 3).The toxic effect, inhibition of bioluminescence, and the short duration of the assay advocate that membrane interrelation and covalent binding to soft nucleophiles (i.e., function proteins) are the most likely MOAs.Since 3M2B is non-electrophilic and a classic baseline toxicant, its MOA is exclusively reversible membrane perturbation.The minimal changes in the mean 3M2B potency values with time (see Table 2) indicate that this MOA acts rapidly.Except for EFAC, which was unreactive experimentally, the remaining 30 chemicals demonstrated some degree of soft electrophilicity (see Table 1).However, from Table 1, neither the weight of evidence (i.e., proven, likely, probable, or suspected) nor the potency (i.e., extreme, high, moderate, slight, weak) was related to the rank order for MX toxicity (Table 3).
The 45-min combined effects for each combination as categorized, included instances in which the actual MX CRC crossed over the predicted CA and/or IA CRC.An example of one such instance is presented (Fig 2).This phenomenon suggests a difference in biological action for the chemicals in a given mixture.
Multiple linear regression equations were generated for the IA and CA models at the EC 25 , EC 50 , and EC 75 at each exposure duration (Table 5 and Fig 3).Each had an r 2 >0.950 and a VIF <1.2.These results suggest that the approach has utility in estimating mixture toxicity for 3M2B-containing binary combinations that were not tested herein.While these equations only directly apply to the model organism used in this study, conceptually, such MLR equations can be generated for other model organisms, reducing the need for actual mixture testing.Once one has the MLR equation for a given A, the established A-alone data, and the Balone data for any additional B chemical (preferably with the same dilution factor) can be used to generate predicted CA and IA EC x values.Then, the respective AQ x or IQ x values of interest can be inserted into the appropriate equation to obtain the MX EC x estimate.
Chemicals from several specific reaction mechanisms and each of the four MOA noted above were tested with 3M2B in this study, so the approach appears robust.With data and analyses already completed, future reports will demonstrate that this approach consistently produces high-quality MLR equations for other "chemical A" selections tested in an A-B series.
The MLR equations for the 15-and 30-min data are presented to allow modeling the dynamics of mixture toxicity over time.For example, the Lambert model [36] has a time component that will enable data for each exposure duration to be analyzed together and for response surface analysis.Dynamic mixture toxicity modeling may provide further insights into chemical mechanisms or modes of toxic action.
While MLR equations for estimating 45-min MX toxicity at the EC 10 were also generated, they are not presented, even though r 2 and VIF values were similar to those noted (Table 5).This choice was made because concentration selection was not designed to emphasize lowlevel effects.The general approach taken by Escher and colleagues [11] is amenable to generating MLR equations at low CRC effect levels.

aFig 1 .
Fig 1. Comparative plot of predicted independent action (IA) and concentration addition (CA) EC 50 values after 45-min exposures.Predicted IA toxicity was always greater (i.e., at a lower 3M2B-equivalent concentration) than predicted CA toxicity.The combinations are listed on the Y-axis simply as agent 'B', since 3M2B was always agent 'A'.The predicted IA EC 50 values are shown from most toxic to least toxic.https://doi.org/10.1371/journal.pone.0306382.g001

Fig 3 .
Fig 3. Linear regression plot of observed vs. predicted mixture toxicity for binary combinations containing 3M2B.The 45-min CA EC 50 and AQ 50 values generated in this study were inserted into the equation: MX EC 50 = -233.926+ (1.063 * CA EC 50 ) + (219.256* AQ 50 ) (see Table 5) to generate the predicted 45-min MX EC 50 values for each combination.The predicted MX EC 50 values were then plotted against the observed 45-min MX EC 50 values.

Table 1 .
(Continued)Rank is listed from most to least toxic as predicted by the 45-min EC 50 for independent action (IA).b SMILES, Simplified Molecular-Input Line-Entry System notation of chemical structure.

Table 5 . Multiple linear regression equations for estimating mixture toxicity for 3M2B-containing binary mixtures a .
d standard error of the estimate e variance inflation factor https://doi.org/10.1371/journal.pone.0306382.t005