SAMPLE POTE CY ESTIMATIO REVISITED: REASO S A D OPTIO S FOREMPLOYI G A LI EARIZED POTE CY ESTIMATIO MODEL
Baston, D.S.1, Elskens, M.1, Denison, M.S.2, Goeyens, L., and Baeyens, W.1
1. Department of Analytical and Environmental Chemistry, Vrije Universiteit Brussels, Brussels Belgium.
2. Department of Environmental Toxicology, Meyer Hall, University of California, Davis, CA 95616.
Abstract
Exposure of humans and wildlife to HAH compounds through food and feed is a concern in recent years with theEuropean Union and the USA implementing legislation to monitor exposure. These widespread persistentenvironmental contaminants have varied species and tissue specific biological effects including but not limited
to: birth defects, tumor promotion, lethality, endocrine disruption, and other effects. Biological samples, inrecent years, are exhibiting low level concentrations of HAH compounds pushing the lower limits of detection
and quantification. One of the tools used for screening of biological samples is the CALUX bioassay, we havegenerated Mid and Low-Range linearized models from sigmoid dose curves providing an increased lower range
for detection of HAHs. The EC50 values of these models correlate well with the historically used sigmoidal
models with well structured dose response curves.
Introduction
Halogenated aromatic hydrocarbons (HAHs) are, at some level, a part of every day life, they are ubiquitous in
the environment1. It is important to understand the level of exposure and consequently the risk experienced by
the presence of these compounds due to their potential for significant biological effects: eg. endocrine disruption,
immunotoxicity, induction of numerous enzymes, birth defects, as well and others2. Identification andquantitation of halogenated aromatic hydrocarbons (HAHs), such as polychlorinated dioxins (PCDDs),polychlorinated furans (PCDFs), and biphenyls has typically been performed by high resolution instrumental
methods (i.e. GC/HRMS), the long term gold standard, however biological relevance is difficult to establish.
Multiple inexpensive and rapid bioanalytical methods have been developed in the last decade1, these methods
allow interpretation of biological response, expressed as Bioanalytical Equivalents (BEQs), to quantities ofHAHs and other HAH-like compounds extracted from various matrices, including but not limited to, soil,sediment, fly ash, food and feed, and biological samples including blood, milk, and fat. In contrast toenvironmental samples, biological samples appear to be decreasing in concentration as a result of legislation andregulatory actions controlling major HAH sources3.
CALUX, a well defined detection system used for screening purposes, is an AhR-based cell bioassay systemcapable of responding to individual compounds, such as TCDD, PCB 77, other HAHs, and, beta-Naphthaflavone
as well as complex mixtures extracted from various environmental and biological matrices. The potency ofindividual compounds as well as complex mixtures is based upon induction of luciferase reporter gene
expression compared to expression of luciferase from TCDD standards, the most potent AhR agonist. Typicalenvironmental samples yield complete or full receptor-dependent sigmoidal dose curves with upper and lower
plateaus and a linear mid-section, however biological samples typically have low concentrations, not conduciveto a complete dose curve and more often relegated to analysis of a single point making the potency difficult toestimate with confidence at the lower end of the sigmoidal standard curve. Resultant Bioanalytical Equivalents(BEQs), estimated from the TCDD EC50 and a sample potency from the CALUX bioassay are compared withanalytical Toxicity Equivalents (TEQs) derived from Toxic Equivalency Factors (TEFs) established by the WHOin 20064.
Implementing the use of screening tools for HAHs in biological matrices at low levels is significantly important
given the various levels of environmental contamination potentially leading to low level contamination of food,the source for 90% of the general population intake5, ultimately leads to exposure of humans and wildlife.
Screening of biological samples is usually performed with a single point as opposed to the usual multipoint
environmental sample extract dose curve. Above and beyond the biological difficulties/implications withestimating potencies at low induction levels, sometimes there may not be any alternatives to determining theVol. 71, 2009 / Organohalogen Compounds page 002048

potency of a sample from a single point induction can be difficult at low induction levels. We present here twodifferent linearized models, a low-range linear model and a mid-range linear model, both based upon thesigmoidal dose response curve designed with the purpose of estimating potencies for low HAH concentrations inbiological samples, in contrast to estimation models for environmental samples6. Both curves are capable ofestimating and EC50, the low-range model is capable of estimating in the range of 6% - 60% where the midrange model utilizes a range of 25% - 90%. Both models are derived from one sigmiodal dose response curve,current results from tests with standard curves and individual EC50 data indicates an excellent correlation
between EC50 potency estimations from the two linear models as well as correlating well with EC50 potency
estimations from nonlinear regression models and the sigmoidal model and from Sigma Plot. The ease of use andpresentation of multiple correlative potencies is an important step towards providing more accurate data whenscreening biological samples for compliance with current EU regulations6.
MethodsCell Culture, Chemical Treatment and CALUX Analysis. Standard curves were generated using two different
stably transfected CALUX cell lines, H1L6.1c3 and the recently developed G3 cell line were grown aspreviously described9. The inducing potency of each sample was evaluated in a range finding study, followed bya ten-point dose curve.8-10 Cells in a 96-well microplate format were incubated with various standard solution
concentrations for 24 hours, treatment solution was discarded appropriately, the cells were rinsed, lysed andluciferase activity determined using a Promega Glomax luminometer using 50l of lysis buffer, 50 l ofluciferin with a 5.6 second lag time after luciferin addition and prior to integration. Integration time for theH1L6.1c3 cell line was set at 5.0 sec and integration time for the H1L7.5c1 cell line was 3.0 sec.
Statistical Evaluation of Standard Curves
Triplicate concentrations were used for each of a ten point standard curve. Multiple standard curves were diluted
in DMSO from one series of 26 standard dilutions. The solutions were applied to multiple plates containing boththe H1L6.1C3 cell line and the new G3 Cell line (H1L7.5). In all 32 standard curves were generated, thelinearized model and the Sigma Plot version of the 4 Parameter Hill plot were used to estimate EC50 values, 4 in
all for each curve.
Estimation of EC50 values for TCDD standard curves and sample extract dose curves was achieved using twodifferent mathematical models: 1) the model 4-parameter Hill plot from the Sigma plot program offered bySystat; 2) a linear transformation function established optimizing the R^2 value for two different functions: a
mid-range (25% to 90%) and low-range function (6% to 60%). These functions were developed from establishedstatistical protocols.
Results and Discussion
Potency estimation of low concentration samples is confounded by two different, independent mathematicalissues when using nonlinear regression models: 1) statistical error at low concentrations prevents precise
estimation of potency based upon response from the data and 2) the uncertainty changes from an additive error toa multiplicative error when back calculating from potency to response, this rearrangement can be observed whentransforming Equation A to Equation B. The Mid-range and Low-range linear models, based upon Equation C, atransformation of the error observed with each data point in the sigmoid plot, increase the precision, bydecreasing data point error, of the potency estimation at low concentrations by minimizing the error associatedwith the data points.
To provide potency values from single point analysis of low concentration samples two linear models werecreated, a Mid-Range model capable of estimating potencies between 25% and 90% and a Low-Range model
capable of estimating potencies for single point samples between 6% and 60%. Using a ten point TCDD standard
curve we established the criteria for these models where the confirmatory data is the generation of correlative
EC50 values from non-linear regression models and the two new linear regression models.
The process of providing accurate potency estimations at low concentrations and hence low induction using theMid-range and Low-range is dependent upon the correlation of each of the models EC50 values. Review of data

Vol. 71, 2009 / Organohalogen Compounds page 002049

used to properly estimate EC50 values with reasonable agreement there is needed a minimum of ten points tocreate a standard curve which satisfies enough criteria in all of the models to establish agreement between EC50values. Specifically, the concentrations of TCDD standards are best distributed in a 2:1:4:1:2 manner where there
are two concentrations which define both the upper and lower plateaus, single points falling in the transition
region and four points within the middle section of the curve. In relation to the range of values for each linear
model the four points in the middle of the sigmoid curve are four points which are common to both the Midrange and Low-range linear models, the range of percent induction can be defined by the upper boundary of theLow-range linear model and lower boundary of the Mid-Range linear model, 25% to 60% of maximal induction.
Furthermore, each of the individual points fall within the transition portion between the mid section and each of
the upper and lower plateaus; between 6% and 25% for the lower transitional point and between 60% and 90%
for the upper transitional point. The two sets of points defining the upper and lower plateaus are below 6% andabove 90%. Data from two of the curves is presented in Table 1 with the resultant EC50 data provided in Table 2.
The mathematical process in fitting the Mid- and Low-range linear curves can be described as seen in the set offigures A1 – A4 and B1 – B4 where Figures A1 – A4 are for data that work with the two models and figures B1– B4 are for data that does not work with the two models. Figures A1 and B1 the overall uncertainty in theexperimental RLU values has a positive slope or as the experimental RLU values increase so does the percentage
induction. Figures A2 and B2 illustrate the nonlinear regression fit using the 4 parameter Hill function as
described by equation A above. Figures A3 and B3 are the linear transformation of the nonlinear data from
Figures A2 and B2 (the equation in fact encompasses both the Mid- and Low-range models). Figures A4 and B4
show the residual plot expressed as a z-score (standard residuals). If the model correctly evaluates the data it isexpected that |z| > 2 in less than 5% of the cases and |z| > 3 in less than 0.3% of the cases. The latter indicatesunacceptably poor performance in terms or accuracy while for a satisfactory model performance |z| ≤ 2 isrequired.
It was clear that the increased response of the H1L7.5c1 cell line rendered insufficient data points at low
concentrations of the TCDD standards used for the H1L6.1c3 cell line. Studies are currently underway toevaluate the linear models using a greater number of lower concentration TCDD standards.
References:
1. Simonich SL, Hites RA. Science 1995;269:1851.
2. Denison MS, Zhao B, Baston DS, Clark GC, Murata H, Han, D-H, (2004) Talanta 63:1123.
3. Bayens W, Verstraete F, Goyens L, (2004) Talanta 63:1095
4. Van den Berg M, Birnbaum LS, Denison M, De Vito M, Farland W, Feeley M, Fiedler H, Hakansson H,Hanberg A, Haws L, Rose M, Safe S, Schrenk D, Tohyama C, Tritscher A, Tuomisto J, Tysklind M, Walker
N, Peterson RE, Toxicol Sci 2006;93:223
5. Baeyens W, Leermakers M, Elskens M, Van Larebeke N, De Bont R, Vanderperren H, Fontaine A, Degroodt
J.-M, Goeyens L, Windal I, (2007) Arch. Environ. Contam. Toxicol. 52:563
6. Windal I, Van Wouwe N, Eppe G, Xhrouet C, Debacher V, Bayens W, De Paul E, and Goeyens L, (2005)
Environ Sci Technol 39:1741
7. Brown DJ, Orelien J., Gordon JD, Chu AC, Chu MD, Murata HJ, Kayama F, Denison MS, Clark GC (2007)
Environ Toxicol Chem 41:4354.
8. Rogers JM, Denison MS (2000) In Vitro Molec Toxicol 13:67.
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10. Chen Y-H, Tukey RH (1996) J Biol Chem 271:26261.

m ⋅ (ln x )nEquation A.

y = y0 +k n + (ln x )n+ εyBasic Sigmoid model employed to estimate potency values (εγ is the residual (error) term).

Vol. 71, 2009 / Organohalogen Compounds page 002050

1 

y − y 0 )⋅ k n  n  '(x = exp  ⋅ε m − y + y 0   xEquation B.

Restructured Sigmoid equation for potency estimation of a sample as a function of response either RLU values
or percent maximal induction.

y* = y p = s ⋅ x + i + εy*Equation C.

Linearizing equation for the Mid-range and Low-Range sections of the complete sigmoidal TCDD Dose curve,
the linearized equations to be used for estimating potency of low concentration samples or single point analysis
when sample concentrations are thought to be low.

pM
1000000
9928, 95436,73535,22951,9
1966,01572,81179,6587,49,7A1-A4Avg % RLU
10084,278,559,957,038,732,224,917,32,4

Std Dev
2,44,43,2
4,5
6,6
5,92,82,30,90,3

pM
37117,37843,84838,63535,22951,92259,81179,6783,3
97,79,7B1-B4Avg % RLU
10085,470,156,553,4
40,926,620,63,92,0

Std Dev
3,75,62,60,2
1,5
1,90,90,80,20,1

Table 1. Subset of 32 different TCDD Standard Curve data. Provided for illustration of standard concentrations
used to establish response within the boundaries as described in the text.

A1-A4B1-B4NLR
EC50 Std Err
2798,2266.94299,2653.4

Mid-Range
EC50 Std Err
2749,2162.23850,892.4

Low-Range
EC50 Std Err
2895,6185.33671,751.4

Sigma Plot
EC50 Std Err
2700,4213,03054,1218,0

Table 2. Estimated values potency values generated from the two different nonlinear models and the Mid- andLow-Range linearized models exhibiting the potency data.

Vol. 71, 2009 / Organohalogen Compounds page 002051

A1Std Dev vs. % RLU
7A2YFIT vs Y
1206y = 0,9937x + 0,1309R2 = 0,9916

100

580
sdYFIT

4360

240

1200020406080

10001200204060RLU

80100120YA3Non-linear regression

A4Residuals
1,5110100

1,090
0,570z-scores

% RLU

80
60
50
40
30

0,012345678

9 10 11 12 13 14 15 16 17 18 19 20-0,5-1,0-1,520-2,0

10
0
1,E+001,E+01

1,E+02

1,E+03 1,E+04
TCDD pM/well

1,E+051,E+06-2,5

1,E+07

Observ ations

Figures A1-A4: Statistical representation of bioassay data used to generate the Mid- and Low-Range potency
estimation models with statistically correlative EC50 values.
B1

Std Dev vs. % RLU

B3

YFIT vs Y

6120

5100

4

y = 0,9901x + 0,0977
R2 = 0,987

80

sdYFIT

360

240
1

20
0020

40

60

80

100

120

0-1

020

40

60

RLUResiduals

B2

Non-linear regression

120

2,5

110

2,0100

120

B4

1,590
80

1,070

0,5z-scores

% RLU

10060
50
40

0,0-0,512

3456789 10 11 12 13 14 15 16 17 18 19 20-1,030-1,5201001,E+00

80Y-2,01,E+01

1,E+02

1,E+03 1,E+04
TCDD pM/well

1,E+051,E+061,E+07-2,5
Observations

Figures B1-B4: Statistical representation of bioassay data used to generate the Mid- and Low-Range potency
estimation models generating non-correlative EC50 values.

Vol. 71, 2009 / Organohalogen Compounds page 002052