Mechanistic Computational Model of Steroidogenesis in H295R Cells: Role of Oxysterols and Cell Proliferation to Improve Predictability of Biochemical Response to Endocrine Active Chemical-Metyrapone
Miyuki Breen, *** Michael S. Breen,¿ Natsuko Terasaki,§ Makoto Yamazaki,§ Alun L. Lloyd,t and Rory B. Conolly*,1
*Integrated Systems Toxicology Division, National Health and Environmental Effects Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27711; }Biomathematics Graduate Program, Department of Mathematics, North Carolina State University, Raleigh, North Carolina 27695; ¿ Human Exposure and Atmospheric Sciences Division, National Exposure Research Laboratory, U.S. Environmental Protection Agency, Research Triangle Park, North Carolina 27711; and §Safety Research Laboratory, Mitsubishi Tanabe Pharma Corporation, Kisarazu, Chiba 292-0818, Japan
1To whom correspondence should be addressed at Office of Research and Development, National Health and Environmental Effects Research Laboratory, U.S. Environmental Protection Agency, 109 T. W. Alexander Drive, Mail B105-03, Research Triangle Park, NC 27711. Fax: (919) 541-0694. E-mail: conolly.rory@epa.gov
Received December 28, 2010; accepted June 14, 2011
The human adrenocortical carcinoma cell line H295R is being used as an in vitro steroidogenesis screening assay to assess the impact of endocrine active chemicals (EACs) capable of altering steroid biosynthesis. To enhance the interpretation and quantita- tive application of measurement data in risk assessments, we are developing a mechanistic computational model of adrenal steroidogenesis in H295R cells to predict the synthesis of steroids from cholesterol (CHOL) and their biochemical response to EACs. We previously developed a deterministic model that describes the biosynthetic pathways for the conversion of CHOL to steroids and the kinetics for enzyme inhibition by the EAC, metyrapone (MET). In this study, we extended our dynamic model by (1) including a cell proliferation model supported by additional experiments and (2) adding a pathway for the biosynthesis of oxysterols (OXY), which are endogenous products of CHOL not linked to steroidogenesis. The cell proliferation model predictions closely matched the time-course measurements of the number of viable H295R cells. The extended steroidogenesis model estimates closely correspond to the measured time-course concentrations of CHOL and 14 adrenal steroids both in the cells and in the medium and the calculated time-course concentrations of OXY from control and MET-exposed cells. Our study demonstrates the improvement of the extended, more biologically realistic model to predict CHOL and steroid concentrations in H295R cells and medium and their dynamic biochemical response to the EAC, MET. This mechanistic modeling capability could help define mechanisms of action for poorly characterized chemicals for predictive risk assessments.
Key Words: endocrine disrupting chemicals; mechanistic computational model; in vitro toxicology; metyrapone; H295R cells; steroid biosynthesis.
endocrine disrupting properties of chemicals in drinking water and pesticides. This legislation addresses the concern that various environmental chemical contaminants may alter the endocrine system of humans and wildlife with subsequent adverse outcomes and disease. Based on this legislation, an endocrine disruptor screening program (EDSP) was developed by the U.S. Environmental Protection Agency (U.S. EPA, 1998). The EDSP is designed as a two-tiered screening and testing process to identify chemicals that can interact with the endocrine system (Tier 1) and to characterize their dose- response (Tier 2). In the EDSP Tier 1 battery of screening assays (U.S. EPA, 2009), the human adrenocortical carcinoma cell line H295R was selected as an in vitro steroidogenesis assay to detect chemicals that affect steroid biosynthesis.
As a screening tool, the in vitro H295R steroidogenesis assay has several strengths. This assay can be used to evaluate the effects across the entire steroidogenesis pathway because H295R cells express all the key enzymes for steroidogenesis and have the ability to produce all the adrenocortico steroids as well as sex steroids (Gazdar et al., 1990; Rainey et al., 1994; Staels et al., 1993). The screen is rapid and inexpensive and can detect chemicals that either inhibit or induce steroidogenesis (U.S. EPA, 2009). Furthermore, this assay coupled with a mechanistic computational model supports the recommendations by the National Research Council (NRC) report regarding a vision and strategy for toxicology testing in the 21st century (NRC, 2007). The NRC report recommends the use of in vitro systems to assess mechanisms of action for a large number of chemicals while reducing the number of animals and testing cost for in vivo assays (Andersen and Krewski, 2010).
To increase the understanding and quantitative use of data from the in vitro H295R steroidogenesis assay for human
and ecological risk assessments, we are developing a mech- anistic computational model of steroidogenesis in H295R cells. We previously developed a deterministic model that describes the biosynthetic pathways for conversion of cholesterol (CHOL) to adrenocortical steroids and the kinetics for enzyme inhibition by the competitive steroido- genic enzyme inhibitor, metyrapone (MET), a model endocrine active chemical (EAC) with a well-characterized mechanism of action (Breen et al., 2010). Metyrapone is used as a clinical diagnostic test for pituitary adrenocorti- cotropic dysfunction. In the present paper, we extended the model and performed additional critical experiments to address key limitations of the previously described model.
The primary focus of the previous work was on steroid synthesis (Breen et al., 2010). The main limitation of the previous steroidogenesis model was the large underestimation and overestimation of CHOL concentrations in cells and medium, respectively. In the present paper, we addressed this limitation by investigating CHOL utilization. Because CHOL metabolism is responsible for the biosynthesis of steroids and oxysterols (OXY) (Bjorkhem, 2002; Javitt, 2008; Nishimura et al., 2005; Schroepfer, 2000), we extended the previous model by adding the pathway for OXY biosynthesis. We examined the hypothesis that metabolism of CHOL into OXY may reduce the large discrepancy between measured and model-predicted concentrations of CHOL in cells and medium.
The OXY, similar to steroid hormones, are endogenous products of CHOL. The OXY are formed in many tissues, including adrenal tissue, through CHOL oxygenation reactions mediated by different cytochrome P450 enzymes or reactive oxygen species (Adams et al., 2004; Bjorkhem, 2002; Schroepfer, 2000). The OXY possess potent regulatory functions in a broad range of biological mechanisms, including CHOL homeostasis, apoptosis, calcium uptake, and cell differentiation (Bjorkhem, 2002; Javitt, 2008; Nishimura et al., 2005; Schroepfer, 2000).
Another key limitation of the previous steroidogenesis model is the potential confounding effects of cell pro- liferation and viability on the time-course concentrations of the steroids. Because the proliferation of H295R cells can be substantial (Logie et al., 1999), we addressed this limitation by performing additional experiments and developing a cell proliferation model. Cell proliferation and viability experi- ments for control and EAC-exposed H295R cells were performed, and the data were used for parameter estimation and model evaluation. The cell proliferation model was then linked with the steroidogenesis model to control for this confounding.
The contribution of this study is the extension of a previously developed steroidogenesis model (Breen et al., 2010) by including (1) a pathway for OXY biosynthesis and (2) cell proliferation model. The extended model was evaluated with measurements of CHOL and 14 steroids in H295R cells and medium, measurements from an H295R cell proliferation and
viability assay, and OXY concentrations determined from a molecular balance formulation.
MATERIALS AND METHODS
We first describe the H295R cell proliferation and steroidogenesis experiments and the calculation of OXY concentrations. Then, we present the mathematical models for cell proliferation, pathways for OXY and steroid biosynthesis, and procedures for parameter estimation and sensitivity analysis.
H295R cell proliferation assay. We performed a cell proliferation study following the experimental method as the previously described H295R steroidogenesis assay for control and two concentrations of MET (1 and 10uM) (Breen et al., 2010). The MET concentrations were selected based on cytotoxicity and clinical data. Using a cell viability assay, no significant cytotoxicity was observed at these two concentrations after treatment for 3 days. Clinical observations show mean plasma peak concentrations of 2.2 and 16.3uM at 4 and 1 h following administration of 750 mg MET, respectively (www.pharma.us.novartis.com).
For the cell proliferation assay, 6 × 105 cells were initially incubated for 72 h (prestimuli incubation period). At poststimuli incubation periods of 0, 24, 48, and 72 h, all cells were separated and removed from six replicate wells. The number and percentage of viable cells in each well were then determined using a cell analyzer (Vi-CELL XR; Beckman Coulter, Fullerton, CA).
For statistical analysis of the cell viability data, two-way ANOVA test was used to determine differences between the mean numbers of viable cells across treatments (MET doses), using sampling times as a blocking factor to control variability due to differences across sampling time. Differences were considered significant at p ≤ 0.05.
Steroidogenesis assay with H295R cells. We performed in vitro experi- mental studies with H295R cells: a control study with samples collected at five time points (0, 8, 24, 48, and 72 h) and a MET study with two MET concentrations (1 and 10uM) with samples analyzed at four time points (8, 24, 48, and 72 h). The start time of the experiments was after changing the medium, adding stimuli for activation of steroidogenesis, and including the concentrations of MET. The details were previously described (Breen et al., 2010). Briefly, the medium and cells were separately removed from four replicate wells at each time point. The cells were sonicated in 100 ul of distilled water to produce a cell lysate, which included all the cellular membranes. The CHOL concentrations in the medium and cell lysate were measured using a commercial kit (Wako Pure Chemical Industries, Ltd, Osaka, Japan) based on a CHOL oxidase method. Steroid concentrations in the medium and cell lysate were measured using liquid chromatography/mass spectrometry for 12 steroids (pregnenolone [PREG], 17a-hydroxy-pregnenolone [HPREG], dehydroe- piandrosterone [DHEA], progesterone [PROG], 17a-hydroxy-progesterone [HPROG], androstenedione [DIONE], testosterone [T], deoxycorticosterone [DCORTICO], corticosterone [CORTICO], aldosterone [ALDO], 11-deoxycortisol [DCORT], and cortisol [CORT]) and ELISA for two additional steroids (estrone [E1] and 17ß-estradiol [E2]). The steroid concentrations were adjusted for the recovery of each steroid, with a recovery range between 81.7 and 94.1%. The quantitative ranges for CHOL and each steroid in cells and medium are provided in Supplementary Table S1.
Oxysterols calculated from measurements of cholesterol and steroids. Because no OXY measurements are available, all OXY molecules were lumped together, and the OXY concentrations were calculated based on a molecular balance formulation. To determine OXY concentrations, we made four assumptions. First, we assumed no degradation of CHOL, OXY, and steroids. This assumption is supported by other studies reporting little or no degradation of various steroids across 72 h, our experimental duration (Evans et al., 2001; Garde and Hansen, 2005; Wickings and Nieschlag, 1976). Second, we assumed no de novo synthesis of CHOL because CHOL is abundant in our experiments and is unlikely to be synthesized. Third, because OXY data are unavailable, we
assumed no OXY transport between cells and medium. Fourth, we assumed that the sum of number of CHOL, OXY, and steroid molecules is conserved across time. We determined OXY concentrations from the molecular balance equation, which equates the quantity of molecules (i.e., CHOL, OXY, and steroids) at the initial time to those at later times, as described by
Vi Cdi
cell CHOL,cell + C
d,i OXY,cell +
14 x,cell + V
x=1
d,i=1 CHOL,cell +
d,i=1 OXY,cell +
14 E x=1
C
d,i=1 x,cell
+V
med
C C CHOL,med + d,i=1
14
2
C
d,i=1
x,med
;
x=1
) (1)
where CCHOL,cell and CCHOL,med are the measured concentrations of CHOL in cells and medium at the ith time and dth MET dose (including control) for d = 1, 2, 3 (0, 1, 10uM) and i = 1, … , 5 (0, 8, 24, 48, 72 h), respectively; Cx,cell and Cx,med are the measured concentrations of steroid x in cells and medium at the ith time and dth MET dose, respectively; COXY.cell are the calculated concentrations of OXY in cells at the ith time and dth MET dose; Vien is the volume of cells at the ith time, as predicted by the cell proliferation model described below; and Vmed is the volume of medium. To solve Equation (1) for C di di=‘1 COXY.cell, the initial OXY concentrations in cells are assumed to be zero: COXY,cell = 0. We calculated OXY for one experiment because medium concentrations of El and E2 at time equals zero were below blank sample
d,i concentrations in replicate experiments. We obtained the equation for COXY,cell as
d,i ‘OXY,cell =
+ c Vmed cell
d,i=1 CHOL,cell C
d,i=1 CHOL,med d,i CHOL,cell
d,i CHOL,med +
+
2 x=1 14 C
x,med D
d,i=1 14 x=1
C
)
d,i x,med : ) (2)
Mathematical model of cell proliferation. To predict the number of viable H295R cells per well across time, Ncell(t), we developed a cell proliferation model. We assumed an exponential cell population growth as described by
Ncel(t) = Ncell(-72)ekp(++72), , (3)
where Ncell(-72) is the initial number of viable cells and kp is the proliferation rate. The least squares method was used to estimate kp with time-course data from the control experiments. By taking logs of Equation (3), we obtained a least squares estimate for kp as
K$= TI] TX, (4)
where kp is the least squares estimate of kp, X is a 25-element vector, and T’ = [0 72 96 120 144 … 72 96 120 144]. The vector X is defined as
X = 0
ln Ncell (t = 48,r=1) Ncell(-72)
ln Ncel(t=0,r=1) Ncell (-72) Ncel(-72) ) ln Ncell(t =72,r=1)
Ncel (t =24,r=1)
ln Ncell (-72)
)
)
ln Ncell (t =72,r=6) Ncel(-72)
)]: ?
for t = 0, 24, 48, 72, and r = 1, 2, … , 6, where Ncell (t, r) is the measured number of viable cells at time t and replicate r. Negative time denotes time before stimuli added to initiate steroid biosynthesis (prestimuli). Positive time denotes incubation time with stimuli (poststimuli).
The cell proliferation model was used to estimate the volume of viable cells. From Equation (3), we determined the volume of viable cells per well across time, Vcell(t), as
Vcell(t) = Vcell ( - 72)exp(+72), (6)
where Vcell(-72) is the initial volume of viable cells per well. The Vcell(-72) is obtained by multiplying Ncell(-72) by the overall mean volume of an individual H295R cell from control and the two MET concentrations (1 and 10uM), which was previously determined to be 1499 um3 (Breen et al., 2010). The overall mean volume was used since the mean volumes changed only slightly between controls and the two MET concentrations.
The Vcell(t) was used to compensate for steroid dilution in the cell lysate. We determined the concentration of steroid x in cells, Ccell.x(t), by
Cell,x(+) = Clysatex (1) ( Vysate (*). Vcell (t) ? (7) ;
where Clysate,«(t) is the measured concentration of steroid x in the cell lysate at time t and is the volume of cell lysate at time t. The Vlysate(t) is the sum of Vcell(t) and the volume of distilled water. This Vcell(t) was also used in the dynamic molecular balance equations to determine the time-course concentrations of CHOL, OXY, and the 14 steroids.
Overview of mathematical model for metabolic and transport pathways. The computational model is based on the experimental design with two compart- ments: culture medium and H295R cells (Fig. 1). The model includes two distinct metabolic pathways originating from CHOL: OXY biosynthesis and steroid biosynthesis. The OXY biosynthesis pathway includes conversion of CHOL into OXY. The steroid biosynthesis pathway includes the conversion of CHOL into 14 steroids (PREG, HPREG, DHEA, PROG, HPROG, DIONE, T, DCORTICO, CORTICO, ALDO, DCORT, CORT, E1, and E2) and the inhibition of the steroidogenic enzymes by MET.
The transport pathways for the model include cellular uptake of CHOL and MET and import and secretion of the steroids. The transport of OXY between the cells and medium is not included in the model because no data are available. The details and supporting literature data for the biological pathways of steroid biosynthesis and transport were previously described (Breen et al., 2010). Below, we first describe the details of the metabolic and transport pathways. Then, the dynamic molecular balance equations, which couple the metabolic and transport pathways, are described. The complete set of equations is provided in the Supplementary data.
Metabolic pathways. In the extended model, the conversion of CHOL into OXY is described by a first-order rate equation (Fig. 1B). The metabolic pathway that converts CHOL into the 14 steroids consists of 17 enzymatic reactions catalyzed by nine different proteins (Fig. 1A) (Payne and Hales, 2004). As described in the previous model (Breen et al., 2010), we assumed that the substrate concentration is much less than the Michaelis constant (substrate concentration that yields a half- maximal reaction rate). Thus, the rate of product formation increases linearly with substrate concentration as described by a first-order rate equation (Fig. 1B).
Various EACs can inhibit the enzymes in the steroidogenesis metabolic pathway. In this study, we examined the response of H295R cells exposed to the EAC, MET, which is a competitive inhibitor of cytochrome P450 11ß- hydroxylase (CYP11B1) (Harvey and Everett, 2003; Harvey et al., 2007). For the two CYP11B1 enzymatic reactions competitively inhibited by MET: conversion of DCORTICO to CORTICO and conversion of DCORT to CORT (Fig. 1A), the kinetic parameters k16 and k17 are divided by &CORTICO(t) = 1 + (CMET,cell(t)/k41) and @CORT(t) =1 +(CMET,cell(t)/k42), respectively, where k41 and k42 are MET inhibition constants (Fig. 1B).
Transport pathways. The model used for the transport of CHOL and the steroids between cells and medium was previously described (Breen et al., 2010). Briefly, we model the transport rate of CHOL from the medium as a first-order process (Fig. 1B). We model the secretion and uptake rates for each steroid as reversible first-order processes (k+x and k_x for secretion and uptake of steroid x, respectively) (Supplementary Fig. S1).
(5)
14 x=1
med C
d,i CHOL,med +
C x,med
d,i
¼ Vi-
cell
x=1 14 E C d,i=1 x,cell -
- 2 d,i x,cell
x=1 14
C
A
CYP11A
H295R Cells
CHOL
PREG
CYP17H
HPREG
CYP17L
DHEA
OE
3BHSD2
17BHSD1
OXY
PROG
HPROG
DIONE T
CYP21A
CYP19
DCORTICO
DCORT
E1
E2
StAR
CYP11B1
MET
CORTICO
CORT
CYP11B2
ALDO
CHOL
MET
PROG
CORTICO
HPREG
DCORT
DHEA
E1
E2
PREG
DCORTICO
ALDO
HPROG
CORT
DIONE
T
Medium
B
K2
H295R Cells
CHOL
PREG
K3
HPREG
KĄ
DHEA
Ko
K5
K6
K7
Kg
K10
OXY
PROG
Kg
HPROG
DIONE
T
K11
K12
K13
₭14
DCORTICO
K15
DCORT
E1
E2
16
K41
MET
K42
K17
CORTICO
CORT
18
ALDO
K1
919
920
921
922
923
924
940
125
926
927
928
929 9:30 931
932
CHOL
MET
PROG
CORTICO
HPREG
DCORT
DHEA
E1
E2
PREG
DCORTICO
ALDO
HPROG
CORT
DIONE
T
Medium
As described in the previous model (Breen et al., 2010), we assume no degradation of MET, and MET diffuses into the cells and reaches equilibrium with the MET concentration in the medium
CMET,cell(t) = q40CMET,med(t), (8)
where q40 is the equilibrium coefficient, and CMET,cell(t) and CMET,med(t) are the
cell and medium MET concentrations at time t, respectively (Fig. 1B). To calculate CMET,cell(t), we need to account for the Vcell(t) and Vmed. We obtained the equation for CMET,cell(t) by solving the molecular balance equation
Vcell(t)CMET,cell(t) + VmedCMET,med(t) =Vcell(t)CMET,cell(0) +Vmed CMET,med (0), (9)
for CMET,med(t) and substituted into Equation (8) with CMET,cell(0) = 0 to yield
q40 CMET,cell(t) = ( 1 +q40Vcell (t)/Vmed ) CMET,med (0). (10)
Dynamic molecular balances. The time-course of the steroids, CHOL, and OXY are described by dynamic molecular balance equations (Supplemen- tary data). The general dynamic molecular balance equations for the steroids in cells and medium are
d(Vcell(t)Cx,cell(t)) dt = Px,cell(t) - Ux,cell(t) +Ix,cell(t) -Sx,cell(t), (11)
and
dCx,med(t) dt
Vmed x,med (1) = Sxcell (t) - Ixcell(t), (12)
where Cx,med(t) is the concentration of steroid x in medium at time t; Px,cell(t) and Ux,cell(t) are the production and utilization rates of steroid x in cells at time t, respectively; Ix,cell(t) and Sx,cell(t) are the cell import and secretion rates of steroid x at time t, respectively. The first two terms on the right side of Equation (11) represent the net metabolic reaction rate of steroid x and the last two terms represent the net cellular uptake or release rate of steroid x. The time-courses of CHOL and OXY are calculated in the same manner as the time-courses of the steroids.
Quasi-equilibrium analysis. Based on the evidence that steroid transport between the cells and medium is rapid and reversible, as described in the previous model (Breen et al., 2010), we assume the steroid concentrations in the cells and medium are operating near equilibrium. Because the steroids are involved in the larger network consisting of the metabolic pathway of steroidogenesis, this is considered as quasi-equilibrium.
For quasi-equilibrium, the reversible transport rates (k+x and k_x for secretion and import of steroid x, respectively) are assumed to be much greater than the metabolic reaction rates. The concentration of steroid x in the cells and medium rapidly reaches equilibrium to yield
Cx,med (t) _k+x Cx,cell(t) k_x 9x = qx, (13)
where qx is the equilibrium constant of steroid x transport. By solving Equation (13) for Cx,med(t), we obtain an algebraic equation for each steroid in the medium as
Cx,med(t) = qxCx,cell(t). (14)
To determine the dynamic molecular balance equations for the steroids in cells for quasi-equilibrium, we sum the molecules of steroid x in the cells and medium based on Equations (11 and 12) and substitute Equation (14) for Cx,med(t) to yield
d(Vcell(t)Cx,cell(t) +Vmed Cx,med(t))_d[(Vcell(t)+Vmedqx)Cx,cell(t)] dt
= Px,cell(t) - Ux,cell (t). dt
(15)
We obtain a system of equations consisting of a differential equation for each steroid in the cells from Equation (15) as
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| dCx,cell (t) | 1 | Px,cell(t)- Ux,cell(t) -Cx,cell(t) | dVcell (t) | |
|---|---|---|---|---|
| dt | ¼ Vcell(t) + Vmedqx | dt ; | ||
| (16) | ||||
| where | ||||
| dVcell(t) = kp Vcell(-72)ekp(+72) = kpVcell(t). dt | (17) | |||
Equation (17) was obtained by differentiating Equation (6) with respect to time. The quasi-equilibrium assumption reduces the number of the model parameters to 36 parameters: 14 transport equilibrium constants (q19, q20, … , q32), 18 metabolic rate constants (k0, k2, k3, … , k18), CHOL import rate (k1), 2 enzyme inhibition constants for MET (k41 and k42), and the partition coefficient for MET (q40). These dynamic molecular balance equations for quasi-equilibrium and the 36 parameters are used in all subsequent analysis (Supplementary data).
Parameter estimation. The parameters for the transport and metabolic pathways were independently estimated using the mean concentrations from replicate experiments. For the transport pathway, the equilibrium constants (q19, q20, … , q32) were estimated with the time-course data from the control and MET studies using the least squares method. From Equation (14), we obtained a least squares estimate for qx as
qx = [Cx,cell’ Cx,cell] Cr,cell’ Cr,med, (18)
where qx is the least squares estimate of the equilibrium constant for steroid x transport, and = cd=1,i=1 ‘x,cell C x,cell . .. ad=1,i=2 cd=3,i=5 x,cell and Cx,med’ = x,med Cx,cell’ cd=1,i=2 d=1,i=1 Cx,med C d=3,i=5] … are the measured concentra- tions in the cells and medium at the ith time and dth MET dose (including x,med control), respectively.
For the metabolic pathway, the parameters (k0, k1, k2, … , k18, k41, k42) were estimated with the time-course data from the control and MET studies. The weighted least squares method was used to estimate these parameters instead of the least squares method to account for CHOL and all the steroids concentrations that vary by several orders of magnitude. Let CCHOL,cell (t; CMET,med, k) and COXY,cell (ti; CMET,med, k ) be the model-predicted concentrations of CHOL and OXY in the cells at the ith time, ti, for the dth MET dose (including control), CMET,med, with parameter set k = (ko, k1, k2, . .. , k18, k41, k42) for d= 1, … , 3, and i = 1, … , 5, respectively; Cx,cell (ti; CMET,med, k) be the model-predicted concentrations of steroid x in the cells at time t; for the MET dose, CMET,med, with parameter set k; CCHOL,cell and COXY,cell be the mean measured concentration of CHOL and calculated concentration of OXY in the cells across time, respectively; Cx.cell be the mean measured concentration of steroid x in the cells across time. Then, the weighted least squares estimate, k” = (kg, k1, k2, … , kjg, k41; k42), is the parameter values k, which minimizes the cost function ☒
J (k) ¼
3 E
1
d=1 CHOL,cell i=1
3 d=1 14 3
C Cd,i x,cell
d,i OXY,cell Cx,cell CCHOL,cell cell
ti; Cd ti; cd
MET,med
+ +
5 1 2 OXY,cell i=1 5 2 x=1d=1 “x,cell i=1 C
1 5
d,i CHOL,cell
COXY,cell k)) ti; Cd *)) 2
Parameters for the metabolic pathway were estimated with a nonlinear optimization algorithm using MATLAB R2010a (Mathworks, Natick, MA) software. The Nelder-Mead simplex method was used due to its relative insensitivity to the initial parameter values as compared with other common methods, such as Newton’s method and its robustness to discontinuities (Nelder and Mead, 1965).
Sensitivity analysis. We performed a sensitivity analysis to examine parameter uncertainty using the method previously described (Breen et al.,
2010). Briefly, the sensitivity function relates changes of the model output to changes in the model parameters. We calculated relative sensitivity functions Rx,med,ki (t) andRx,med,q; (t) with respect to parameters ki and qi, respectively, for each of the model-predicted concentrations in the medium, Cx,med, and each MET dose (including control). MATLAB was used to numerically solve the partial derivatives in Rx,med,k; (t) and Rx,med,q; (t). To rank the relative sensitivities, we calculated the L2 norm across time for each relative sensitivity function as described by
L2 norm(Rx,med,k;)
¼
V 14
Rx,med,k;(t)|2dt (20)
and
L2 norm(Rx,med,;) =|Rx,med,q:(+)2dt. (21)
RESULTS
Cell Proliferation- Estimated Parameter and Model Evaluation
The time-course measurements for the number of viable cells per well (Supplementary Fig. S2A) and percentage of viable cells per well (Supplementary Fig. S2B) are shown for each MET dose. The percentage of viable cells per well across all measurements was 91.8 ± 2.3% (mean ± SD). The mean number of viable cells measured across MET doses (control, 1, and 10uM) was not statistically different (p = 0.41). Therefore, control data were used to estimate the value of kp, which was determined to be 0.00878/h. The model-predicted number of viable cells was compared with time-course measurements from the control experiments (Fig. 2). The model predictions closely correspond to the mean time-course data.
Calculated Oxysterols
3× 106
Model-Predicted
2.5
Measured
Number of Viable Cells
2
1.5
1
0.5
0
-72
-48
-24
0
24
48
72
Time (h)
2 (19)
2
MET,med
MET,med? k)) :
A
B
Number of Molecules per Well (nmoles)
200
Measured CHOL: Control
200
180
Measured Steroids: Control
Number of Molecules per Well (nmoles)
Calculated OXY: Control
180
160
160
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
8
24
Time (h)
48
72
0
0
8
24
Time (h)
48
72
C
D
200
Number of Molecules per Well (nmoles)
Measured CHOL: MET 1AM
200
Calculated OXY: MET 1uM
180
Measured Steroids: MET 1 u.M
Number of Molecules per Well (nmoles)
180
160
160
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
0
8
24
48
72
0
8
24
48
72
Time (h)
Time (h)
Number of Molecules per Well (nmoles) m
F
200
Measured CHOL: MET 10UM
Number of Molecules per Well (nmoles)
200
Calculated OXY: MET 10UM
180
Measured Steroids: MET 10UM
180
160
160
140
140
120
120
100
100
80
80
60
60
40
40
20
20
0
0
0
8
24
48
72
0
8
24
Time (h)
48
72
Time (h)
Figure 3 shows the time-course for the sum of measured number of CHOL and steroid molecules and the calculated number of OXY molecules at each MET dose (control, 1, and 10uM). For each MET dose, the calculated number of OXY molecules monotonically increased across time. The number of OXY molecules showed no apparent pattern with increasing MET dose (Supplementary Fig. S3).
Transport Pathways for Steroids
Table 1 shows the estimated transport equilibrium parameters. As described in the previous model (Breen et al., 2010), the MET transport equilibrium, q40, could not be determined from the data because MET was not measured in the cells. Therefore, q40 was set equal to q22, the CORTICO transport equilibrium, because the partition coefficients for MET
| Parameter | Value |
|---|---|
| q19 | 0.013 |
| q20 | 0.005 |
| q21 | 0.041 |
| q22 | 0.056 |
| q23 | 0.091 |
| q24 | 0.061 |
| q25 | 0.021 |
| q26 | 0.042 |
| q27 | 0.068 |
| q28 | 0.038 |
| q29 | 0.040 |
| 930 | 0.027 |
| q31 | 0.044 |
| q32 | 0.035 |
| 940 | 0.056ª |
ªMetyrapone transport equilibrium (q40) set to CORTICO transport equilibrium (q22); see text for details.
(XLogP = 2.0) and CORTICO (XLogP = 1.9) are similar (PubChem database).
Metabolic Pathways for OXY and Steroid Biosynthesis
Table 2 shows the estimated parameters for the metabolic pathways. The convergence time for the nonlinear parameter estimation was typically around 10 min on an Intel Core 2 Duo processor using MATLAB.
| Parameters | Value | Units |
|---|---|---|
| k0 | 0.014 | Per h |
| kı | 0.016 | Per h |
| k2 | 0.011 | Per h |
| 0.757 | Per h | |
| k3 | 1.268 | Per h |
| k4 k5 k6 k7 | 0.814 | Per h |
| 11.153 | Per h | |
| 7.217 0.177 | Per h | |
| Per h | ||
| kg | 1.754 | Per h |
| kg | 0.048 | Per h |
| k10 | 6.479 | Per h |
| k11 | 12.188 | Per h |
| k12 | 0.595 | Per h |
| k13 | 0.001 | Per h |
| k14 | 0.091 | Per h |
| k15 | 0.637 | Per h |
| k16 | 0.247 | Per h |
| k17 k18 | 0.122 | Per h |
| k41 | 63.566 | nM |
| k42 | 25.208 | nM |
A
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Model-Predicted CHOL: Control
Concentration in Medium (nM)
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8
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For CHOL and OXY, we compared model-predicted concentrations with time-course data from control and MET- exposed cells (Fig. 4). Model-predicted concentrations corre- spond well to the mean time-course data for CHOL both in the
cells and in the medium and OXY in cells. For MET-exposed cells, model-predicted and measured concentrations of CHOL and calculated concentrations of OXY remained approximately unchanged from controls as MET increased.
For CHOL in medium and cells, the extended model performed remarkably better than the previous model (Breen et al., 2010). For CHOL in medium, the extended model overestimated the mean measurements by 9, 13, and 11% at 24, 48, and 72 h, respectively, whereas the previous model overestimated the mean measurements by 43, 96, and 153% at 24, 48, and 72 h, respectively. For CHOL in cells, the extended model overestimated the mean measurements by 2, 4, and 5% at 24, 48, and 72 h, respectively, whereas the previous model underestimated the mean measurements by 52, 53, and 47% at 24, 48, and 72 h, respectively.
For the 14 steroids, we compared model-predicted concentrations with time-course measurements from control and MET-exposed cells. Overall, model-predicted concentrations correspond closely to the mean time-course measurements in cells (Supplementary Fig. S4) and medium (Fig. 5) for control cells. As compared with the previous model (Breen et al., 2010), the extended model better captured the mean time-course behavior for the five steroids (PROG, HPROG, DHEA, HPREG, and PREG), which increased until 48 h and then sharply decreased at 72 h (Figs. 5B, 5C, and 5E). For these five steroids, the extended model predictions increased until 40-50 h and then decreased (Figs. 5B, 5C, and 5E), whereas the previous model predictions monotonically increased across time (Breen et al., 2010). For the other steroids in control cells, the extended model performed similar to the previous model. A detailed evaluation was reported previously (Breen et al., 2010).
For MET-exposed cells, we compared model-predicted steroid concentrations with time-course measurements. For three steroids (ALDO, CORTICO, and CORT) downstream from the enzyme inhibited by MET (CYP11B1), the model- predicted concentrations correspond well to the mean time- course measurements both in the cells (Supplementary Fig. S5) and in the medium (Figs. 6A-C). For two steroids (DCOR- TICO and DCORT) immediately upstream from CYP11B1, the model-predicted concentrations correspond closely to the mean time-course data both in the cells (Supplementary Fig. S5) and in the medium (Figs. 6D and 6E), which remained approxi- mately unchanged at 8, 24, and 48 h as MET increased and slightly increased at 72 h as MET increased. For the other nine steroids further upstream from CYP11B1, model-predicted and measured concentrations remained approximately unchanged from controls as MET increased (data not shown). For five steroids (ALDO, CORTICO, CORT, DCORTICO, and DCORT), the extended and previous models showed similar results for MET-exposed cells.
Sensitivity Analysis
Figures 7 and 8 show the relative sensitivities for the four primary steroids: ALDO, CORT, T, and E2. For ALDO, k18 was highly sensitive at each MET dose, and eight parameters were
moderately sensitive: parameters associated with transport path- ways (k1, q21, and q22), metabolic pathways (k2, k5, and k16), and MET-mediated enzyme inhibition (q40 and k41). For CORT, q27 and k17 were highly sensitive, and two parameters associated with MET-mediated enzyme inhibition (q40 and k42) were moderately sensitive. For steroids T and E2, the parameters associated with MET (q40, k41, and k42) were not sensitive, and the sensitivity of all parameters was unchanged with increasing MET dose. For T, k10 was highly sensitive, and six parameters were moderately sensitive: parameters associated with transport pathways (k1 and q29) and metabolic pathways (k2, k3, k9, and k12). For E2, six parameters were moderately sensitive: parameters associated with transport pathways (q29, q30, and q32) and metabolic pathways (k2, k13, and k15). The E1 pathway appears to be the preferred pathway for E2 synthesis because E2 was sensitive to the E1 pathway (k13 and k15) and not sensitive to the T pathway (k10 and k14). This preferred pathway result is consistent with our previous study of ovarian steroidogenesis (Breen et al., 2007). The sensitivity analysis orders the inputs by importance, identifying main contributors to the variation in the outcome of a model. Parameters with high sensitivity are more important and significant for the model output than parameters with low sensitivity.
DISCUSSION
We extended a computational model of adrenal steroido- genesis to include (1) a cell proliferation model to account for time-varying number of viable cells and (2) a metabolic pathway for biosynthesis of OXY to examine the hypothesis that metabolism of CHOL into OXY improves the model fit for CHOL. Experiments were designed and performed to evaluate the cell proliferation model. The extended model and cell proliferation experiments addressed key limitations of the previous model (Breen et al., 2010) by (1) removing the confounding effects of cell proliferation from the steroidogen- esis model, (2) reducing the large discrepancy between the measured and model-predicted concentrations of CHOL both in the medium and in the cells, and (3) allowing the steroidogenesis model to more accurately capture the observed dynamic behavior. Furthermore, the model’s predictive ability improved considerably with only a slight increase in the model complexity by adding one parameter for cell proliferation and one parameter for OXY biosynthesis.
Metabolic Pathway for Oxysterols
In the previous steroidogenesis model, we developed a steroidogenesis model and evaluated its ability to predict only the steroid concentrations for MET-exposed H295R cells (Breen et al., 2010). The present study was initiated after we discovered that (1) the differences between the model-predicted and measured CHOL concentrations both in the medium and in the cells were large and (2) the sum of the number of measured CHOL and steroids molecules was not conserved across time.
A
350
-Model-Predicted ALDO
300
Measured ALDO
Concentration in Medium (nM)
Model-Predicted E2
Measured E2
250
Model-Predicted T
Measured T
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1500
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Concentration in Medium (nM)
200
Model-Predicted HPROG
Concentration in Medium (nM)
1250
Model-Predicted DIONE
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Measured DIONE
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To explain the lack of a molecular balance in the data, we examined the hypothesis that other metabolic pathways were needed in the model. The literature shows that OXY biosynthesis is a primary pathway for CHOL metabolism, and the pathway is present in adrenal tissue. To test this hypothesis, we (1) included the OXY metabolic pathway in the extended model, (2) calculated OXY concentrations, (3) estimated model parameters, and (4) evaluated the model- predicted concentrations of CHOL, OXY, and all 14 steroids both in the cells and in the medium.
The results support our hypothesis. By including the OXY metabolic pathway, the extended model significantly improved the model fit for CHOL both in the medium and in the cells as compared with the previous model. Moreover, the model-predicted and calculated OXY concentrations closely correspond. Close correspondence of model-predicted and measured CHOL and 14 steroids supports our model assumption of no degradation of CHOL, OXY, and steroids.
Besides the pathway for conversion of CHOL to OXY, we examined alternative biologically realistic hypotheses to allow for
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Concentration in Medium (nM)
Model-Predicted CORT: MET 1AM
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Measured CORT: MET 1uM
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Measured DCORTICO: MET 10UM
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a molecular balance. One alternative hypothesis is an unaccounted form of CHOL because CHOL is distributed in various cell membranes and compartments with a high abundance in the plasma membrane, endocytic recycling compartment, and Golgi complex (Ikonen, 2008). Another alternative hypothesis is a pathway for conversion of CHOL to CHOL esters because CHOL is a biosynthetic precursor of steroid hormones, OXY, and CHOL esters in all cells (Ikonen, 2008). However, in this study, the assay used to measure CHOL concentrations in cells includes CHOL esters and all the cellular membranes and compartments that can contain CHOL and CHOL esters. Because this CHOL
measurement accounts for free, membrane-bound, and esterified CHOL, these alternative hypotheses are not supported.
Dynamic Steroid Behavior
For the previous model, the dynamic steroid predictions for all 14 steroids had the same qualitative behavior, increasing monotonically across time (0-80 h). Although the mean measured concentrations for nine steroids increased mono- tonically, the mean measurements for five steroids (PROG, HPROG, DHEA, HPREG, and PREG) increased until 48 h and then decreased at 72 h. This was a key limitation of the
A
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ALDO
☒ Control
☐ ΜΕΤ 1μ.Μ
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☐ ΜΕΤ 10μ.Μ
Relative Sensitivity
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ko
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K14
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K17
K18
919
920
92
922
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926
927
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931
932
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K41 1 K42
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CORT
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k2
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931 932
940
K41
K42
Parameter
previous model. By including cell proliferation, the extended model captures this observed time-course behavior for each steroid. One possible factor responsible for this behavior is the increasing number of enzymes due to cell proliferation. This is further evidence that the more biologically realistic features of the extended model allow for a better representation of the observed time-course behavior of steroidogenesis.
Future Applications of Extended Model
There are several potential applications for the extended model. First, the model’s better ability to predict the time-course
of CHOL concentrations both in the medium and in the cells will be critical for EAC that affect upstream metabolic (e.g., inhibition of steroidogenic enzyme CYP11A) or signaling processes, which may affect CHOL levels. Second, the more biologically realistic model may improve the accuracy for low concentration extrapolations of concentration-response curves for other EACs with environmental concentrations below experimental levels. Environmental concentrations of MET are unknown. Third, the model can be simply modified with EAC- specific enzyme inhibition constants to predict the biochemical response for other EACs that competively inhibit steroidogenic
A
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enzymes. Fourth, our in vitro model could be extended to predict the in vivo response. The steroidogenesis model would need to be linked to a multiorgan systems model, which includes the regulatory feedback of the hypothalamus-pituitary-adrenal axis, and refined based on additional experiments. This extension of the current model would require a significant research effort. Finally, with further model refinement and evaluation, the model can be used to help identify mechanisms of action for EACs by predicting the enzyme inhibition constants for poorly character- ized EACs and for screening assays that typically measure only a few steroids in the medium.
Limitations
There are some limitations to our extended model based on the model structure and assumptions and data available for model evaluation. First, the extended model structure and parameter values are based on MET concentrations at or below 10uM. At higher MET concentrations, the proliferation rate and viability of the cells can be altered and inhibition of additional steroidogenic enzymes can occur. Therefore, the extended model may not accurately extrapolate at higher MET concentrations without including a cell proliferation model and enzyme inhibition constants that are dose dependent. Second, our model
assumption of first-order enzyme kinetics, which reduced the model complexity while maintaining the model’s predictive ability, is only applicable for nonsaturable enzyme kinetics. For highly concentrated or potent EACs, first-order enzyme kinetics may need to be replaced by saturable enzyme kinetics (e.g., Michaelis- Menten). Third, transport of OXY between the cells and medium is not included in the model because the OXY data are unavailable. This may result in the overestimation of OXY in the cells. Experiments that measure the time-course of OXY are needed to further evaluate the OXY metabolic and transport pathways. Finally, the extended model structure is based on EACs that are competitive enzyme inhibitors. For EACs with different mecha- nisms of action (e.g., activating or antagonizing steroid hormone receptors and inducing steroidogenic enzymes), model refinements will be needed (Sanderson, 2006). These refinements may require additional model-guided experiments for other pathways, such as gene regulation and upstream signaling pathways.
Conclusions
We extended a previous steroidogenesis model by including a cell proliferation model and a pathway for OXY biosynthesis. The cell proliferation model, which was independently evaluated with experimental data, removed the confounding of cell proliferation from the steroid biosynthesis and its biochemical response to EAC. The inclusion of the metabolic pathway for OXY biosynthesis significantly improved the model fit for CHOL and allowed the model to capture the dynamic behavior of steroids both in the medium and in the cells. Our study demonstrates the significant improvement of the extended, more biologically realistic model to estimate CHOL and adrenal steroid concentrations both in H295R cells and in medium and their dynamic biochemical response to the EAC, MET. This mechanistic modeling capability could help define mechanisms of action for poorly characterized chemicals and mixtures for predictive risk assessments and to screen drug candidates based on steroidogenic effects in the early phase of drug development.
SUPPLEMENTARY DATA
Supplementary data are available online at http://toxsci. oxfordjournals.org/.
FUNDING
North Carolina State University/Environmental Protection Agency Cooperative Training Program in Environmental Sciences Research (Training Agreement CT833235-01-0 to M.B.) with North Carolina State University.
ACKNOWLEDGMENTS
We thank Hisham El-Masri and Daniel Villeneuve for their review comments and helpful suggestions. Although this
manuscript was reviewed by the U.S. EPA and approved for publication, it may not reflect official Agency policy. Mention of trade names or commercial products does not constitute endorsement or recommendation for use.
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