A physiologically based in silico kinetic model predicting plasma cholesterol concentrations in humans.

Increased plasma cholesterol concentration is associated with increased risk of cardiovascular disease. This study describes the development, validation, and analysis of a physiologically based kinetic (PBK) model for the prediction of plasma cholesterol concentrations in humans. This model was directly adapted from a PBK model for mice by incorporation of the reaction catalyzed by cholesterol ester transfer protein and contained 21 biochemical reactions and eight different cholesterol pools. The model was calibrated using published data for humans and validated by comparing model predictions on plasma cholesterol levels of subjects with 10 different genetic mutations (including familial hypercholesterolemia and Smith-Lemli-Opitz syndrome) with experimental data. Average model predictions on total cholesterol were accurate within 36% of the experimental data, which was within the experimental margin. Sensitivity analysis of the model indicated that the HDL cholesterol (HDL-C) concentration was mainly dependent on hepatic transport of cholesterol to HDL, cholesterol ester transfer from HDL to non-HDL, and hepatic uptake of cholesterol from non-HDL-C. Thus, the presented PBK model is a valid tool to predict the effect of genetic mutations on cholesterol concentrations, opening the way for future studies on the effect of different drugs on cholesterol levels in various subpopulations in silico.

structure), mathematical formulation of the model, model calibration, and model validation. After development, a sensitivity analysis was performed to obtain more insight into the factors that determine plasma cholesterol concentrations.

Conceptual model development
The conceptual model for the human PBK model was modifi ed from the conceptual model for the mouse ( 11 ). Briefl y, the mouse model was constructed as follows: relevant knockout mouse models were screened for altered plasma cholesterol levels compared with the levels in the wild-type mouse. If the alteration was more than 2-fold (up or down) compared with the wild-type, the corresponding gene was marked as a key gene. Based on the function of a subset of 12 of these key genes that code for metabolic enzymes producing or consuming cholesterol and transport proteins transporting cholesterol, metabolic and transport reactions were included in the mouse conceptual model ( 11 ). The conceptual model for the human was developed from the mouse model by adding human-specifi c features (see Results). In view of the sparsity of data available to calibrate and validate the model, the number of pools and fl uxes in the model was kept to a minimum to avoid overparametrization. As a consequence, FC and CE pools were not distinguished in plasma non-HDL and in the periphery. Also, in the intestine, luminal and enterocytic pools were not distinguished (i.e., the aggregate pools were used).

Mathematical model formulation
As the second step in the model development, the conceptual model was converted to mathematical equations. Similar to the mouse model, the human model was formulated as a set of differential equations, each describing the time behavior of one of the cholesterol pools in the conceptual model as a function of the reaction rates.
Equations were slightly altered compared with the mouse model: for the human model, reaction rates were expressed as mmol/man/day, where "man" refers to a standard human, leading to more simple equations ( 12 ). For practical reasons, reaction rates (expressed by i ) were numbered according to the numbering in Fig. 1 . All symbols of variables and parameters that were used to defi ne the model are given in Table 1 . The differential equations, one for each cholesterol pool in the model, are given in Table 2 (Eq. 1-8). Eq. 1, for example, can be interpreted as follows: the change in time of the concentration of hepatic free cholesterol is determined by the balance of the rates of the reactions producing ( 1 , 5 , 10 , 13 ) and consuming ( 14 , 17 , 18 , 19 ) hepatic free cholesterol. In a kinetic model, the reaction rates are calculated using kinetic equations that express the reaction rate as a function of concentrations and kinetic parameters. Most reactions in our model represent a set of lumped enzymatic and/or transport reactions. Often, such a composite reaction can be conveniently represented by a kinetic equation that contains apparent rate constants and apparent K M values. A general solution is to use Michaelis-Menten kinetics as a prototype kinetic expression for biological reactions. In the present approach, to keep the number of parameters as limited as possible, it was assumed that the reactions operate in the linear part of a Michaelis-Menten kinetic curve (substrate concentration much lower than the apparent K M ) or in the saturated part (substrate concentration much higher than the apparent K M ). At low substrate concentrations, Michaelis-Menten kinetics effectively reduce to fi rstorder kinetics (Eq. 9; Table 2 ). At high substrate concentrations, Michaelis-Menten kinetics reduce to zero-order kinetics (i.e., the reaction becomes independent of the substrate concentration) (Eq. 10; Table 2 ). transfer protein (CETP), which is present in humans and other primates but absent in mice and other rodents ( 14 ). CETP transfers cholesterol ester (CE) from HDL to LDL, thereby greatly infl uencing the distribution of cholesterol over the different plasma fractions (HDL-C and non-HDL-C). The importance of the CETP gene is illustrated by the observation that a specifi c mutation in this gene causes a 10% increase in HDL-C levels ( 15 ). The pharmaceutical industry has recognized the importance of this gene, resulting in the development of CETP modulators that aim to increase the concentrations of HDL-C (16)(17)(18).
Apart from this qualitative difference, there are many quantitative differences between mouse and human with respect to parameters that infl uence cholesterol turnover, such as dietary intake, transport and synthesis rates of cholesterol, and organ sizes ( 13,19 ). Some of these differences persist even after correcting for differences in body mass. For example, according to Dietschy and Turley ( 13 ), the amount of cholesterol absorbed from the diet per kilogram of body mass is 30 mg cholesterol/kg body mass/day in the mouse, compared with only 5 mg cholesterol/kg body mass/day for human. Consequently, translationally modifying the available mouse model for human subjects is not straightforward. This study describes this translation, as well as a validation of the resulting model, by simulating human mutations and comparing the model predictions on HDL-C and non-HDL-C in plasma concentrations with experimental data reported in literature.

MATERIALS AND METHODS
The development of the in silico model was subdivided into the following steps: development of a conceptual model (model    ( 20,21 ). Therefore, the rate of this reaction was dependent on HDL-CE and non-HDL-CE. It was assumed that the reaction rate was linear with respect to both concentrations as given by Eq. 11 ( Table 2 ).
The kinetic formats of reactions 1-20 were obtained from the previously defi ned mouse model. Instead of developing one optimal model, the mouse model consists of a set (ensemble) of eight submodels, each having a different combination of fi rst-and zero-order kinetics for the various reactions. The model prediction is calculated as the average of the predictions of the submodels. These eight submodels have been selected from a larger set of 65,536 alternative submodels. Each of the suitable submodels has been selected on the basis of a correct prediction of a higher or lower plasma cholesterol level of fi ve knockout mouse strains compared with the wild-type controls ( 12 ). For the human situation, not enough data were available to apply an identical selection procedure. Therefore, it was decided to use the kinetic formats of the reactions 1-20 in the eight submodels for the mouse also for the corresponding reactions in the human model. Thus, the eight mouse submodels were converted to eight human submodels, retaining the kinetic orders of reactions 1-20 and adding reaction 21. As in the mouse model, the human model prediction was defi ned as the average of the predictions of the resulting eight submodels. The predicted TC concentration was calculated as the sum of all three types of plasma cholesterol (non-HDL-C, HDL free cholesterol [HDL-FC], and HDL-CE), whereas the predicted HDL-C concentration was calculated as the sum of HDL-FC and HDL-CE. Literature data on reaction rates and pool sizes were taken from a wide range of experiments including cannulations, dietary surveys, and in vitro tests, as explained in detail below. Regarding reaction rates, we concentrated on data from experiments that had directly assessed rates that were attributable to a specifi c reaction in our model.

Model calibration
As usual in PBK modeling ( 3,19 ), the model was developed for a standard human, for which we chose the 70 kg "reference man" as defi ned by the International Commission on Radiation Protection ( 19 ). Thus, data on 70 kg adult male subjects were taken as much as possible. In case the data were obtained from subjects with different body masses, reaction rates were normalized per unit of organ volume and multiplied by the organ mass of the reference man to obtain the reaction rate for the standard human.
If a specifi c submodel a rate was calculated for a fi rst-order reaction, the corresponding rate constant was calculated using the pool sizes and steady-state reaction rates according to Eq. 12 ( Table 2 ). In the case of a zero-order reaction, the corresponding rate constant was calculated according to Eq. 13 ( Table 2 ). To calculate the rate constant of reaction 21, Eq. 14 was used ( Table 2 ).

Model validation
To validate the model, the model was used to predict the plasma cholesterol concentrations of humans carrying genetic mutations, and these predictions were compared with experimental data obtained from literature. A genetic mutation was simulated by a model run with a case-specifi c set of parameters different from the normal situation, as follows. The rate constants for the reactions primarily affected by the given mutation were multiplied with a specifi c parameter (f mut ), according to Eq. 15, 16, or 17 ( Table 2 ). This multiplication refl ects the impact of the mutation on the reaction rate constant (i.e., fold reduction or increase). All other parameters were assumed to be unaffected by the given mutation. The values for f mut for each individual mutation were defi ned based on literature data as described in the Results section.  [12][13][14], for simulation of the effect of human mutations (Eq. [15][16][17], and sensitivity analysis (Eq. 18) Model predictions were derived as follows: the differential equations (Eq. 1-8) were solved by numerical integration with the normal concentrations as initial values. Integration was performed using routine ode15s as implemented in MATLAB version 7.5 (R2007b) with the appropriate parameter value(s) for each subject (normal or mutant). The simulation was performed until steady state of all cholesterol pools in the model was achieved. Model predictions were defi ned as these steady-state concentrations.

Model validation
As a model validation, 10 genetic variations known to affect cholesterol metabolism were simulated, and model predictions for TC, HDL-C, and non-HDL-C were compared with experimental data. The 10 mutations included mutations that cause familial hypercholesterolemia (FH), fi sh eye disease, Smith-Lemli-Opitz syndrome (SLOS), and other diseases. Details on all 10 mutations (numbered with roman digits) are given in Table 4 and are explained below. In the list of 10 mutations, two genes were included twice (APOB and LCAT), both as homozygote and as heterozygote variant.
Each mutation was simulated by multiplying the rate constant of the reaction affected with a specifi c parameter f mut defi ned for that mutation (see Eq. 15-17; Table 2 ). The parameter f mut is generally defi ned as the ratio of the value of a specifi c variable in carriers of the mutation to the value of that specifi c variable in controls. The specifi c affected variables for all mutations are given in Table 4 . The parameter f mut for the simulation of a bile acid synthesis defect in the gene CYP7A1 (mutation X), for example, was defi ned as the ratio of the bile acid contents of the stools from carriers of the mutation to that in controls. The affected individuals had 5% of the amount of bile acids in their stools compared with healthy controls ( 24 ). The value of f mut was, therefore, set to 0.05 ( Table 4 ). Values of the parameter f mut range from 0.00 for the SLOS mutation and the homozygote LCAT mutation to 0.65 for a variant of the CETP gene, implying that the list contained mutations that cause both mild and severe phenotypes.
Model predictions and experimental data are given in  Table 4 ), the model correctly predicted whether the TC, HDL-C, and non-HDL-C concentrations were decreased, increased, or relatively unchanged by the mutations. The average relative deviations between model predictions and experimental data were 36%, 49%, and 43% for TC, HDL-C, and non-HDL-C, respectively. This is considered successful within the present state-of-the-art of PBK modeling, where quantitative predictions may generally be correct within one order of magnitude (25)(26)(27)(28). These model predictions are generally within the experimental error margin given the small patient groups sizes (generally n < 20).

Model analysis
An important step in modeling is model analysis, which is the step in which novel biological insight can be obtained. Model sensitivity analysis was performed to analyze which cholesterol concentrations were most affected by which biological reactions. Fig. 5 presents the sensitivity coeffi cients (SC) (Eq. 18) that express the sensitivity of the eight concentrations in the model toward changes in the kinetic parameters of each of the 21 reactions. A positive SC indicates that an increase in the reaction rate constant resulted in an increase of the predicted concentration. A negative SC indicates that an increase in the reaction rate constant resulted in a decrease of the predicted concentration. Some

Sensitivity analysis
To identify which reactions had a large infl uence on the eight predicted cholesterol pools in the model, a sensitivity analysis was performed. Percent changes in reaction rates were related to percent changes in tissue and plasma cholesterol pools. One by one, each kinetic constant was increased by 1% (leaving all other kinetic constants unchanged), and the model was used to predict the effect of this increase on all eight cholesterol pools that fi gured in the model. This analysis includes the response of all reactions in the model to the change in this kinetic constant. The effect of the increase in parameter of rate i on pool j was expressed in a sensitivity coeffi cient (SC) as defi ned in Eq. 18. The SC of the model was defi ned as the average of the SCs calculated with the eight submodels.

Model development and calibration
The human PBK model was formulated as differential equations (Eq. 1-8; Table 2 ) and rate equations (Eq. 9-11; Table 2 ) based on the conceptual model given in Fig. 1 . The model was calibrated using compartmental volumes, steady-state cholesterol concentrations, and rates of cholesterol-involving reactions derived from literature. A detailed description of how data were derived, transformed into the correct units, and scaled to the 70 kg "reference man" as defi ned by the International Commission on Radiation Protection ( 19 ) can be found in the supplementary material. Concerning plasma cholesterol, the total plasma cholesterol concentrations were 5.25 mM for TC and 1.19 mM for HDL-C as was obtained from an inventory of data from 8809 US adults ( 22 ). Plasma cholesterol not present in the HDL-C pool (4.03 mM) was considered to be present in the non-HDL-C pool. The total HDL-C concentration (HDL-C, 1.19 mM) consists of HDL-FC and HDL-CE. The HDL-FC:HDL-CE ratio was 1:3 as obtained from Groener et al. ( 23 ). This ratio was applied to the HDL-C data above to obtain the HDL-FC and HDL-CE concentration, resulting in 0.30 mM for HDL-FC and 0.89 mM for HDL-CE. No distinction was made between non-HDL-free cholesterol and non-HDLcholesterol ester (i.e., only the total [non-HDL-C] was considered).
A summary of the results is presented in Table 3 . Several steady-state reaction rates were not directly obtained from data but instead were calculated from the other reaction rates using mass balances as indicated in Table 3 Table 3 , which indicates that the data, taken from various sources, were mutually consistent.
cholesterol esterifi cation (reaction 9), and hepatic cholesterol transport was only sensitive to HDL (reaction 17; Fig.  5 ). Fig. 5 indicates that some reactions strongly infl uenced many concentrations. The rate of hepatic uptake of cholesterol from non-HDL (reaction 5) infl uenced concentrations responded to changes in many different rate constants (e.g., hepatic-free cholesterol [Liv-FC]), whereas other concentrations were sensitive to changes in only a few reactions. HDL-FC, for example, was only sensitive (SC < Ϫ 0.25 or SC > 0.25) to changes in HDL-associated Sum of the uptake rates of non-HDL-C (reactions 5 and reaction 7) was calculated with the LDL-C balance: ν 5 ss + ν 7 ss = ν 21 ss + ν 6 ss + ν 11 ss . The ratio between hepatic ( ν 5 ss ) and extrahepatic uptake ( ν 7 ss ) in the human was assumed to be identical to that ratio in the mouse ( 60   (again |SC| > 0.25) four of the eight pools. In contrast, intestinal cholesterol synthesis (reaction 3) or intestinal cholesterol transport to HDL (reaction 16) did not infl uence any concentration.
An increased free cholesterol concentration (Liv-FC and Int-FC) is associated with membrane damage and cytotoxicity ( 29 ). This model analysis might, therefore, be relevant to predict cytotoxicity: if a reaction highly affects one of these pools, then substances that alter the activity of that reaction may induce cell death.  Table 4 .   TABLE 4. Description of the 10 human mutations used for model validation. The table includes the name of the gene carrying the mutation, the plasma cholesterol levels (TC, HDL-C, and non-HDL-C) of the subjects carrying the mutations (expressed as fold increase relative to the control group), the number of the reaction(s) affected by specifi c mutations, the severity of the affection expressed as f mut (Eq. [15][16][17], and the name of the variable used to determine f mut . Reaction numbers correspond to numbers in Fig. 1  non-HDL (reaction 21), and hepatic uptake of cholesterol from non-HDL (reaction 5). The model predicted ( Fig. 6, right panel) that non-HDL-C was highly dependent on hepatic uptake of cholesterol from non-HDL (reaction 5) and mainly on hepatic transport of cholesterol to HDL (reaction 17) and hepatic cholesterol esterifi cation (reaction 19).
In general, as seen in Fig. 6 , sensitivity coeffi cients for TC were more similar to those for non-HDL-C than to those for HDL-C because only a small fraction of plasma cholesterol is present in HDL-C.
Finally, this sensitivity analysis revealed that, according to the model, there are several effi cient ways to lower non-HDL-C concentrations and increase HDL-C concentrations simultaneously by modulating only one single reaction ( Fig.  6, middle and right panels). The most potent reactions Of special interest for the purpose of the present model are the SC values for cholesterol concentrations in plasma (TC, HDL-C, and non-HDL-C) that are correlated with the risk for coronary heart disease ( 10 ). Sensitivity coeffi cients for the infl uence of the different reactions on these concentrations are given in Fig. 6 .
Hepatic uptake of cholesterol from non-HDL (reaction 5), hepatic transport of cholesterol to HDL (reaction 17), and hepatic cholesterol esterifi cation (reaction 19) were the reactions that showed the largest infl uence on TC (i.e., resulting from the combined infl uence of these reactions on HDL-C [   Table 4 . NA, no data available.  Table 4 . NA, no data available.
genetic, nutritional, and pharmaceutical effects on plasma cholesterol levels.
As all models, our model is a compromise between simplicity and complexity ( 37 ). A too simple model is not useful to simulate multiple interventions because such a model will lack the targets of at least part of these interventions. A too complex model is not useful either because insuffi cient experimental data will be present to defi ne the parameters (calibration) or to validate the model.
One of the important necessary simplifi cations made was to restrict the description of lipoprotein metabolism to cholesterol alone. As a consequence, no distinction was made between different fractions of non-HDL-C (i.e., LDL, IDL, and VLDL) in the present model. Including a more detailed mechanistic description of lipoprotein metabolism is a highly complex task that will necessitate to, for example, include the link between cholesterol metabolism and triglyceride metabolism. Although signifi cant progress in this fi eld is being made ( 4,38,39 ), this was considered too ambitious for the present stage of model development.
As a consequence of these necessary simplifi cations, rates derived from model-based interpretation of stable isotope tracer data were unsuited for model calibration because the structure of well-established isotopic tracer kinetic models ( 33 and references therein) did not match with the present model due to different aggregations of reactions. A factor further hampering the use of these data is that the tracer analysis considers bidirectionality of fl uxes, whereas our PBK model formulation had to be limited to unidirectional (i.e., net) fl uxes to keep the number of parameters at a minimum. As a result, using the isotopic fl ux data for calibration of the PBK model was not possible.
The following two examples illustrate some of the difficulties arising from the different structures of the present PBK model vs. the established tracer kinetic models described in Schwartz et al. ( 33 ): ( 1 ) The tracer kinetic model assumes all cholesterol to be synthesized in the liver, whereas in the present PBK model the liver contributed only 10% of total cholesterol synthesis, in line with data from Dietschy and Turley ( 40 ). ( 2 ) Schwartz et al. ( 33 ) reported that the liver does not take up HDL-CE, whereas the corresponding reaction (reaction 10) in the PBK model carries a considerable fl ux (2.93 mmol/man/day), seem to be hepatic uptake of non-HDL-C (reaction 5) and CE transfer from HDL to LDL (reaction 21). The fi rst reaction is targeted indirectly by statins ( 30 ). The latter reaction is targeted by CETP inhibitors, a drug class of which several members (e.g., dalcetrapib) were recently tested in clinical trials ( 16,31,32 ).

DISCUSSION
In silico models have been used for various purposes in the study of cholesterol metabolism, such as in the interpretation of isotope-labeling studies ( 4-6, 33 ), in the analysis of the regulatory pathway of cholesterol synthesis ( 34 ), or in making predictions of the effect of genetic mutations or food and drug interventions ( 35,36 ). These models, however, could predict the effect of a few genetic mutations only. The aim of this study was to develop a model that can be applied in the prediction of a wide variety of  considerably in this regard. Human sebum secretion rates from forehead skin are reported to lie between 1.3 and 3.3 mg/10 cm 2 /3 h ( 42 ). NMR studies indicate that the molar fractions of CE and squalene in sebum are 0.03 and 0.28, respectively, with the other constituents being triglycerides, fatty acids, and wax esters ( 43 ). With a total body area of approximately 2 m 2 , taking into account the molar weights of the different constituents and assuming uniform secretion rates, an upper bound for the total CE and squalene fl ux may be as high as 2.5 mmol/man/day. Although this estimation seems to support the possibility that peripheral cholesterol loss may be as high as the model calibration suggests, independent validation experiments are necessary to confi rm the hypothesis that sebum excretion is a possible explanation for the missing peripheral cholesterol excretion.
Another item is the transfer of FC from liver to HDL ( ν 17 , 6.91 mmol/man/day), which in the present analysis greatly exceeded total hepatic uptake of HDL-FC and HDL-CE combined ( ν 10 + ν 13 , 4.50 mmol/man/day), whereas in Schwartz et al. ( 33 ) the reverse was observed (i.e., more liver uptake of HDL-C than transfer from liver to HDL). However, in Schwartz et al. ( 33 ), this net fl ux is the difference between very high fl uxes (> 46 mmol/man/ day) that operate in both directions. Thus, both models indicate a large contribution to plasma HDL coming from the liver. This has also been observed in animal studies and in our previous mouse work ( 12 ).
These observations indicate that, although the fl ux distribution in our model deviated strongly from that seen in established isotope tracer studies for reasons discussed above, supporting evidence for the PBK model structure and fl ux predictions can be found in the literature.
The key question is whether the model is valid for its intended use to predict changes in plasma cholesterol concentrations following different dietary regimens, pharmacological treatments, or genetic variation. Indeed, the PBK model was able to predict the effects of 10 human mutations ( Figs. 2-4 ), including a mutation in the LDLR gene (mutation I, responsible for FH) and the DHCR7 gene (mutations IX, responsible for SLOS). While simulating this latter syndrome, negative concentrations were predicted for several submodels. This must be due to the fact that these submodels retain zero-order kinetics (i.e., saturated Michaelis-Menten kinetics) when under the extreme conditions associated with blocked cholesterol synthesis in SLOS ( 44 ), cholesterol concentrations are lowered to such an extent that fi rst-order kinetics would be more appropriate.
Model predictions for TC deviated on average less than 40% from experimentally observed values, which is relatively good compared with the current state of the art for PBK models of exogenous substances (26)(27)(28)45 ). This is all the more remarkable because the model was obtained via a relatively straightforward translational adaptation of our previously developed mouse model.
The only case where a large deviation between model predictions and experimental data (HDL-C concentration) were seen is in LCAT defi ciency: mutation VIII. The model which is more in line with the statement of Rinninger et al. ( 41 ) based on data obtained with primary hepatocytes (i.e., "high-density lipoprotein cholesteryl esters were selectively taken up by hepatocytes and are hydrolyzed independently from the classical lysosomal catabolic pathway"). Thus, although the two models differ markedly in structure, supporting evidence for the PBK model structure can also be found in the literature. This suggest that valuable insights could be obtained from future work that would analyze structure variations in both models while taking calibration data for both models into account. For instance, one could investigate whether directing ν 5 and ν 10 into liver CE and adding a pathway that is the reverse of ν 19 to represent lysosomal hydrolases is equivalent (in terms of outcomes and conclusions) to directing them into the liver FC pool as in the present PBK model. Likewise, different alternative structures of the tracer kinetic models may be investigated that are more in line with the PBK model. Such models could, for example, incorporate constraints on net fl uxes derived from the PBK model in the isotopic tracer data analysis.
The level of complexity of the model described here was apparently an acceptable compromise because the model could successfully be calibrated from literature data by fl ux balancing with only a limited set of assumptions (see supplementary information). Nevertheless, the consequences of the implemented calibration procedure may be a point for further attention. Data used were from a variety of different unconnected studies that used different experimental protocols and methods, often applied to very small groups of subjects of different weight and age. This carries the inherent risk of data inconsistencies and potentially large infl uences of individual variation. Although this risk was mitigated as much as possible by scaling all data to a 70 kg reference man, questions may remain as to the impact of the calibration on the predictions by the model. The sensitivity analysis gives some insight in this issue (i.e., from Fig. 6 it appears that variation of reactions 6, 11, and 16 will have little infl uence on the plasma cholesterol predictions of the model). Although a full variability analysis would be required to cover this issue, this was not feasible because data are too sparse to give a statistically meaningful estimate and to validate the analysis, but we generally saw a 25% variation across any dataset. Rather, we discuss in the following sections some specifi c results that seem at variance with established cholesterol fl ux analysis literature (33 and references therein). Peripheral cholesterol loss (reaction 12) was 2.62 mmol/man/day, which is comparable to the sum of net bile acid loss (1.03 mmol/ man/day) and net fecal cholesterol loss (1.85 mmol/ man/day), which are generally considered the main routes for cholesterol loss from the body. Beyond skin sloughing and steroid hormone production, one could ask which candidate processes could carry this fl ux. Because the estimation of total cholesterol synthesis is based on in vivo squalene isotopic labeling data, we do not consider a mistake in this estimation as a possible explanation for the missing peripheral cholesterol excretion. Rather, we hypothesize that sebum production might contribute We conclude that the approach of fi rst developing a computational PBK model for the mouse and then translating it into a human model as described in this paper resulted in an accurate model for the prediction of plasma cholesterol concentrations in humans. Sensitivity coefficients derived from the model correlated well with recent independent GWAS data on plasma cholesterol. Because the model correctly predicted key features of the effect of increased dietary cholesterol intake and of statin treatment and CETP inhibition, we expect that the model can also be used to predict the effects of a wider variety of pharmacological and dietary interventions on plasma cholesterol levels in humans, which will be the subject of further work.
predicted an increase in HDL-C, whereas a decrease is observed in reality ( Fig. 3 ). This increase is in the form of HDL-FC and not in HDL-CE (data not shown). The resulting shift in CE/FC ratio predicted by the model is in fact similar, as seen in the literature ( 46 ). A possible explanation for the deviation between model predictions and experimental data is that, in reality, a maximum of HDL-FC might exist. If this maximum is reached, the transport of free cholesterol to HDL (reactions 8, 16, and 17) will be inhibited, thereby causing HDL-C lowering. The model in its present form does not take this into account.
As shown in Fig. 6 , the model predicted that an increased dietary intake of cholesterol (reaction 4) will lead to an increased TC level, an increased non-HDL-C level, and a slightly lowered HDL-C level. This is in agreement with fi ndings in nutritional studies (see meta-analysis in Ref. 47 ). The model also predicted that non-HDL-C is mostly affected by hepatic cholesterol esterifi cation (reaction 19) and hepatic uptake of cholesterol from LDL (reaction 5). This confi rms that the liver is a dominant organ in determining the plasma cholesterol levels ( 13 ).
A decrease in hepatic cholesterol synthesis (reaction 1) resulted in a decrease of the non-HDL-C ( Fig. 6 , right panel) and in an increase of HDL-C. This is in agreement with the outcome of statin-mediated inhibition of hepatic cholesterol synthesis ( 48 ). In reality, statin therapy will also cause an up-regulation of the LDLR and thereby the activity of hepatic non-HDL-C uptake, increasing the non-HDL-C lowering effect.
A decrease in the activity of CETP (reaction 21) had a larger relative effect on HDL-C than on non-HDL-C ( Fig. 6 ). This is in agreement with the outcome of torcetrapibmediated CETP inhibition ( 49 ) and CETP mutations (mutation VI, Table 4) . Taken together, these fi ndings illustrate that the described model can indeed be helpful to predict effects of dietary and pharmaceutical interventions.
A recent genome-wide association study (GWAS) has found 95 SNPs that correlated with altered TC, HDL-C, LDL-C, or triglycerides concentrations ( 50 ). At least 19 of these SNPs were near genes that are involved in one or more of the reactions in the model. The gene ABCA1, for example, is involved in the transport of cholesterol to HDL (reactions 8, 16, and 17).
We compared effect sizes of the 19 SNPs given by Teslovich et al. ( 50 ) with the sensitivity coeffi cients of associated reactions ( Fig. 6 ) by Spearman correlation and found a positive correlation between our fi ndings and the ones reported by Teslovich et al. ( 50 ) for HDL-C, LDL-C, and TC (all P < 0.05) (data not shown). This is an additional validation of the present model and implies that the developed model is useful to study the implications of genetic variations on cholesterol metabolism.
The GWAS study ( 50 ) also reports several SNPs correlating with cholesterol concentrations in plasma near genes that could not be directly linked to a specifi c reaction in our model ( Fig. 1 ), like in HNF4A, CILP2, and ANGPTL3. This absence of a direct link is the result of essential simplifi cations needed to construct the model.