the capacity of drugs to inhibit the bile salt export pump ( bsep ) has been correlated with clinical drug  induced liver injury ( dili ) .
furthermore , known inhibitors of bsep and other bile acid ( ba ) transporters have been implicated in the case studies of dili .
glibenclamide has been associated with lobular liver injury in the clinic , bosentan has been associated with many cases of hepatotoxicity and carries a black - box warning for hepatotoxicity , and troglitazone was withdrawn from the market due to idiosyncratic dili .
currently marketed bsep inhibitors , such as lapatinib , have been given black - box warnings due to issues with liver toxicity .
interestingly , bsep inhibitors often have additional proposed mechanisms for hepatotoxicity , and this can often confound our understanding of how these drugs cause dili . understanding the effects of bsep inhibitors on ba metabolism and processing will prove crucial in understanding the importance of bsep inhibition in clinical dili .
while much is understood qualitatively about the basics of ba homeostasis , there are still many aspects of ba transport about which little quantitative information exists . for example , regulation of transporter activity by the farnesoid - x receptor ( fxr ) and other nuclear receptors generally responsible for ba synthesis has been demonstrated , and chenodeoxycholic acid ( cdca ) and its amide conjugates have been shown to decrease ba synthesis and trigger fxr .
however , to our knowledge , fxr response and transporter activity have not been linked quantitatively to ba concentrations within hepatocytes .
secondary bas , such as lithocholic acid ( lca ) and deoxycholic acid ( dca ) , are synthesized in the gut by intestinal bacteria , but to our knowledge , the rates of synthesis and the population variability of this synthesis have not been quantified in any species .
transporter kinetic and inhibition studies have used ( or focused on ) taurocholic acid , a metabolically stable model ba , but similar studies rarely have been performed on other bas .
furthermore , while certain ba species , such as lca and cdca , are more cytotoxic than other bas , the effect that intrahepatic concentrations of these bas have on hepatocytes remains to be elucidated . while bsep transporter expression variability in humans has been quantified , and underlying diseases have been shown to affect transporter expression , the significance of this variability has not been explored fully .
the process of constructing a mathematical model of ba - induced dili can be helpful in determining which data gaps should be filled first for maximum impact . while any mechanistic model of ba - induced dili will be lacking in quantitative accuracy due to the significant data gaps , mechanistic modeling can be used to qualitatively describe elements of the system that would be more or less likely to contribute to ba - mediated dili . in this study
, we use dilisym ( www.dilisym.com ) , a mechanistic mathematical model of dili , to explore the nature of ba homeostasis and its disruption by ba transporter inhibitors .
dilisym has been used previously to assess the efficacy of different n - acetylcysteine treatment regimens in acetaminophen - overdosed patients and to understand the species differences in methapyrilene toxicity using in vitro metabolism data . for this study
, we have constructed a module of ba homeostasis within dilisym for rats and humans ; information on the data used to construct this module is available in the supplementary materials online .
we have also collected novel in vivo data from the rats treated with the bsep inhibitor glibenclamide and used these data to ensure the reasonability of the dilisym model .
we also compared the human representation in dilisym to serum ba data in humans after acetaminophen overdose .
this model was used to explore the changes in intrahepatic ba concentrations that are predicted to occur in humans when a ba transporter inhibitor is administered .
finally , a sample population was used to determine which system parameters have the most influence on the magnitude of the intrahepatic ba changes that occur after dosing with a ba transporter inhibitor and would thus be the system components that would be most useful to be illuminated by future experiments .
the bsep and na - taurocholate - cotransporting polypeptide inhibitor glibenclamide , when administered orally to rats , causes an increase in total plasma bas ; this increase in ba concentrations is associated with high systemic exposure to glibenclamide , but is not observed at lower exposure levels . figure 1 shows the results from the single - dose studies .
glibenclamide is notoriously poorly absorbed ; as such , the systemic exposure for each individual rat is more important than the dose administered . at concentrations below a cmax of 10,000  ng / ml
, there was little correspondence between glibenclamide concentrations and serum ba fold change , suggesting that the variability in ba processing among rats exceeds the effects of transporter inhibition at these exposure levels .
rats with glibenclamide cmax > 10,000  ng / ml generally displayed a higher concentration of bas , albeit over a wide range .
as shown in figure 1 , the simulated population ( simpops ) covers the range of ba increases observed in the experimental rat data at each maximum simulated concentration tested , validating our model .
figure 2 summarizes the results of the multiple - dose ( 300 , 750 , and 1,500  mg / kg ) studies where individual ba species were measured .
serum data from day 1 are plotted in figure 2 ; each data point represents an individual rat .
serum cdca and lca concentrations increased very soon after glibenclamide dosing with a return to the baseline predosing value by the end of 24  h ; serum cdca amide conjugates did not appear to change after glibenclamide dosing . on day 7 , plasma concentrations of glibenclamide did not vary widely in animals treated with the three different dose levels ( data not shown ) ; as a result , a single simulation was conducted on a rat simpops at a simulated drug  exposure level similar to that observed in the rats in vivo .
the results of this simulation were compared to the experimental data for lca , cdca , and cdca  amide conjugates in figure 2 .
the simulated population showed similar dynamics to those observed in vivo ; the simulated rats exhibited a mild increase in bas between 1 and 2  h after dosing and returned to baseline values by 24  h. for unconjugated cdca , the simulated rat population covered the range of observed responses ; for lca , the simulated responses covered the bulk of the experimental data but missed the highest ba concentrations , while for cdca  amide , our simulated population covered a much wider range than the experimental data , likely due to a wider range of initial cdca  amide concentrations in the rat simpops .
figure 2 demonstrates that dilisym provides a good approximation of the range of ba increases that were observed after administration of a transporter inhibitor . as data detailing the effect of ba transporter inhibitors on ba concentrations in humans were scarce , the model was validated in humans by comparing the response of the system after acetaminophen dosing to serum ba data from the clinic .
acetaminophen is not a bsep inhibitor , so in this case , ba elevations are due to hepatocyte necrosis .
our baseline human model had a similar response to that demonstrated by james et al .
, that is , little to no ba elevations in serum when injury was minimal , small but significant increases when there was moderate injury , and large elevations when the injury was severe .
the small human simpops also exhibited a similar range of ba concentration changes to the patients reported in the james study . with
the model structure validated using the rat and human experimental data , we proceeded to simulate a bsep inhibitor in our baseline human model .
the difference in liver ba area under the curves ( aucs ) over the course of simulated drug administration in the presence and absence of the theoretical inhibitor is given in table 1 .
in all zones of the liver , increases were observed in the auc of bulk bas , cdca  amide conjugates , and lca  sulfate conjugates .
meanwhile , the auc of unconjugated cdca and unconjugated lca actually decreased , while the auc of amide - conjugated lca remained about the same .
the changes in ba concentrations with inhibitor as a function of the zonality of the liver were also examined using dilisym ( table 1 ) . in the periportal region , where most bas are concentrated ,
however , in the centrilobular region , all ba species except for unconjugated lca increased significantly . for cdca 
amide and lca  sulfate conjugates , the increases in auc were far greater than those predicted in the periportal region . however , the absolute centrilobular auc remained lower than the absolute periportal auc for all ba species .
the large model human population was used to understand the sensitivity of the model parameters to ba accumulation .
the most important variables for the accumulation of each ba species in simulated human liver are shown in table 2 .
since the baseline human model simulations suggested that cdca  amide and lca  sulfate were the most likely ba species to accumulate in the liver , we assessed the correlation between changes in system parameters and increases in cdca  amide and lca  sulfate concentrations .
the sensitivity analysis suggested that bsep expression , as represented by cdca  amide canalicular transport vmax , was the most important variable for cdca  amide accumulation , while the magnitude of lca synthesis in the gut was the most important variable for lca  sulfate accumulation .
amide accumulation when cdca  amide canalicular efflux vmax changes compared to when the canalicular transport regulation scaling factor changes ( which roughly corresponds to the magnitude of the response of ba transporter expression to fxr activation ) , as seen in figure 4 , is particularly instructive .
when cdca  amide canalicular efflux vmax was varied , the baseline cdca  amide concentration of the individual changed ; however , the percentage increase in cdca  amide concentration after administration of the inhibitor was approximately constant across the variable range .
in contrast , when the canalicular regulation scaling factor was varied , the baseline concentration of cdca  amide remained the same ( although meal fluctuations were more pronounced with less regulation ) , while the percentage increase in cdca  amide concentration was much higher when canalicular transport regulation was lower .
the novel in vivo data included herein demonstrate the importance of considering population variability and individual characteristics in any model of ba homeostasis and its disruption .
the variability between rats shrouded the detection of changes in ba due to low concentrations of glibenclamide ( cmax : 50010,000  ng / ml ) and the resultant transporter inhibition .
the lack of an apparent exposure / response effect in the individual ba data is due to the population variability . even with higher doses of glibenclamide
, when an exposure / response relationship was observed , we found that there was a wide range of responses , as measured by a fold increase in ba concentrations , among the rats with glibenclamide cmax higher than 10,000  ng / ml .
few rats reached the higher drug - exposure levels ; further experiments , perhaps using a more readily absorbed formulation of glibenclamide , could help illuminate this effect .
the variability in the results also makes model validation difficult , as our ability to reproduce the experimental conditions ( including individual rats ' initial plasma and liver ba concentrations ) within the context of a simulation is challenging ; while our model is reasonably validated , further experimentation in this area will continue to improve our representation .
our results suggest that due to the population variability inherent in the ba system , a baseline model is of limited utility for predicting the response of rats ( or patients ) to ba transporter inhibitors .
a baseline model is useful for gleaning interesting information about the basic behavior of the system , but quantitative predictions of ba increases and decreases should not be based on the behavior of a baseline ba model .
constructing an appropriate population for the human model is , therefore , of the utmost importance for the prediction of ba - mediated dili . to that end
, we used the ba model to identify the most important parameters that are likely to vary among individuals .
these parameters should be included in the creation of a reasonable population for the prediction of ba toxicity .
the model suggests that the end - product ba conjugates are the ba species that are most likely to accumulate in the liver .
this is likely due to the fact that the conjugation of bas is fairly rapid in the liver , and these pathways do not easily saturate .
previous research has placed the km for ba amidation in the 1 mmol / l range , which is several orders of magnitude higher than typical in vivo unconjugated ba concentrations . as a result of the predicted accumulation of ba conjugates in the liver , ba amide and sulfate conjugates are potential liver toxicophores ; the toxicity of these molecules should be explored and quantified with future experimentation .
centrilobular cells , which generally have a lower ba concentration than their periportal counterparts , have a much higher predicted relative accumulation of all ba species .
in fact , the auc of unconjugated bas was predicted to increase in the centrilobular zone , even though the same bas ' auc decreased in the periportal zone . despite the differential
ba changes in the two zones , the absolute auc of bas in the centrilobular zone was predicted to remain lower than the periportal zone .
however , if centrilobular cells are more sensitive to ba toxicity than periportal cells , an increase in ba concentrations could lead to zonal centrilobular toxicity . indeed , some case reports of liver injury due to glibenclamide demonstrate centrilobular injury .
the investigation of the differential effects of bas on centrilobular and periportal liver cell toxicity would be another interesting and worthwhile experiment .
simulations using a model population provided further insight into the most valuable experiments that could be performed to improve our understanding of ba - mediated dili . among the many system unknowns varied within the model population , the most important variables included lca synthesis in the gut and the regulatory response to ba accumulation . therefore , quantifying lca synthesis in the gut in addition to changes in bsep expression and activity with increasing hepatocyte ba concentrations would be important and impactful experiments . the importance of bsep expression levels to ba accumulation in hepatocytes , for example , could be quantified using existing animal or in vitro models .
the modeling also revealed the importance of transporter expression levels on the behavior of the system ; however , it is important to note a key difference between the behavior of the system when these expression levels are varied and its behavior when the regulatory response is varied .
when transporter expression levels  especially canalicular transporter levels  are decreased , the baseline ba concentration in the liver increases ; the percentage increase in bas after dosing the inhibitor remains somewhat constant .
varying the magnitude of the regulatory response ( fxr activation ) , by contrast , does not have a large effect on baseline ba concentrations in the liver ; however , the percentage increase in bas after inhibitor dosing is highly variable .
both transporter expression levels and the magnitude of the regulatory response are expected to vary within a population ; however , only the variability in transporter expression levels may be apparent in untreated individuals .
this result suggests both the promise and the limitations of prescreening individuals for certain risk factors before prescribing known bsep inhibitors .
it includes ( i ) the synthesis and metabolism of bas in hepatocytes , ( ii ) the basolateral and canalicular active transport of bas , ( iii ) the release of bas from the gallbladder in humans , ( iv ) the synthesis of secondary bas and deconjugation of bas in the gut , ( v ) the recirculation of bas from the gut and subsequent active uptake by the liver , and ( vi ) the regulatory effects of bas on transporter expression and ba synthesis .
the model contains representations of lca and cdca and its conjugates , the ba species most frequently linked to toxicity in in vitro experiments , and a  bulk  ba representation that contains the other bas .
a more detailed description of the ba homeostasis model and its parameterization is presented in the supplementary materials online . to represent ba dynamics in humans , the model was optimized to the known profile of bas in serum published by trottier et al . , as well as to overall concentrations of bas in the liver measured by setchell and garca - caaveras et al .
there were 47 system variables that were either unknown or expected to vary within the human population that were fit to the ba profile ; a list of the variables used in the optimization is provided in the supplementary materials online .
the optimization of the model based on the published ba profile was performed in a manner similar to the simpops method outlined in previous publications , wherein a genetic algorithm was used to generate values of variable parameters that lead to model outcomes ( in this case , ba profiles ) that are within the range of experimental data . using this optimization method allowed the selection of a population of 2,400 individuals with reasonable baseline ba concentrations for the large human sample population .
a smaller , 10-parameter , 331-individual simpops was also constructed for the purpose of model validation . while the large population was given artificially wide
parameter ranges for the purpose of the sensitivity analysis , the small human sample population was constructed with more constrained parameter ranges for the purpose of approximating a plausible population of humans . for example , the transporter vmax ranges included four orders of magnitude in the large population , but were constrained to ranges suggested by transporter expression profiles from meier et al . in the small population .
a population of 191 rats using a more limited 11 variable set ( supplementary table s4 online ) was generated .
this population was intended to represent rats with both plausible serum ba concentrations and plausible values for the parameters that were varied .
the baseline rat model was optimized to the ba profile from the control rats in the present experiment , and the simpops was constructed around this baseline .
details on the simulations performed for the model validation and for the model exploration can be found in the supplementary materials online .
multivariate analysis on the population sample was performed using jmp 9 from sas ( cary , nc ) .
multiple - dose glibenclamide study in rats for the ba - profiling experiments , 16 male 8- to 9-week - old cd-1 rats from charles river laboratories ( raleigh , nc ) weighing between 200 and 300  g were randomized into four groups of four animals each .
these groups were administered daily doses of either the vehicle control ( 0.5% hydroxypropylmethylcellulose /0.1% tween 80 in water ) or glibenclamide ( sigma - aldrich , st louis , mo ) in vehicle via oral gavage for 7 days at three dose levels ( 300 , 750 , and 1,500  mg / kg / day ) .
rats underwent a viability check twice per day , and detailed clinical observations were taken at least twice over the course of the study .
blood was drawn for serum ba profiles at 1 , 3 , 6 , and 24  h after dosing on day 1 and day 7 , and glibenclamide concentrations were measured for toxicokinetic analysis using the same blood samples from day 7 .
clinical and anatomic pathology data were collected from the animals , and these results are reported in the supplementary materials online .
the serum ba concentrations from day 1 were used for comparison to the simulation results .
ba profiling in serum was performed using liquid chromatography  tandem mass spectrometry analysis at glaxosmithkline ( ware , uk ) .
bas in liver tissue 24  h after the final dose also were profiled ; results from this analysis , as well as the liquid chromatography  tandem mass spectrometry analytical method , are presented in the supplemental materials online . this study was conducted in accordance with the glaxosmithkline policy on the care , welfare and treatment of laboratory animals and was reviewed by the institutional animal care and use committee .
for this experiment , doses of glibenclamide were administered every 24  h for 7 days .
systemic exposure data were compared to simulation results for day 7 ; day 1 ba data were compared to simulated ba concentrations on day 1 .
short - term glibenclamide studies in rats for the short - term studies , male han wistar rats ( substrain alpkhsdbrlhan : wist ; astrazeneca , macclesfield , uk ) of 1012-week age ( 300400  g ) were used .
details on the treatment of the rats used in this study are available in the supplemental materials online .
two experiments were performed in which total plasma ba concentrations and glibenclamide plasma concentrations were determined .
glibenclamide ( sigma - aldrich ) was formulated as a solution or suspension in hydroxypropyl--cyclodextrin ( acros organics , distributed by fisher scientific , loughborough , uk ) in aqueous 0.2  mol / l na2co3/nahco3 buffer ( ph 10 ) . in the first experiment ( 29 animals ) , four groups of five animals received a single dose via oral gavage of 50 , 250 , and 500  mg / kg glibenclamide or 10% ( w / v ) hydroxypropyl--cyclodextrin vehicle alone , and blood samples were taken at 1 , 6 , and 24  h after dosing ; an additional three animals per glibenclamide - treated group received a single dose of 50 , 250 , and 500  mg / kg glibenclamide , and blood samples were taken at 1 , 3 , 6 , 12 , and 24  h after dosing . in the second experiment
( 20 animals ) , two groups of five animals each received two oral doses of 250 and 500  mg / kg glibenclamide in 20% ( w / v ) hydroxypropyl--cyclodextrin vehicle at 0 and 4  h , and blood samples were taken predose and at 0.5 , 1 , 2 , and 4  h after dosing ; blood samples from an additional five animals per glibenclamide - treated group were taken predose and 1  h after dosing to increase the dataset for this time point .
 bile salt export pump ( bsep ) inhibition has been proposed to be an important mechanism for drug - induced liver injury ( dili ) . 
 modeling can prioritize knowledge gaps concerning bile acid ( ba ) homeostasis and thus help guide experimentation . 
 a submodel of ba homeostasis in rats and humans was constructed within dilisym , a mechanistic model of dili . in vivo experiments in rats with glibenclamide 
 were conducted , and data from these experiments were used to validate the model . 
 the behavior of dilisym was analyzed in the presence of a simulated theoretical bsep inhibitor . 
 bsep inhibition in humans is predicted to increase liver concentrations of conjugated chenodeoxycholic acid ( cdca ) and sulfate - conjugated lithocholic acid ( lca ) while the concentration of other liver bas remains constant or decreases . on the basis of a sensitivity analysis , 
 the most important unknowns are the level of bsep expression , the amount of intestinal synthesis of lca , and the magnitude of farnesoid - x nuclear receptor ( fxr)-mediated regulation . 
Introduction
Results
Discussion
Methods
Author Contributions
Conflict of Interest
Study Highlights
Supplementary Material