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Graduate Group in Comparative Biochemistry, University of California, Berkeley, California (L.X.G.); The University of California San Francisco/University of California Berkeley Joint Graduate Group in Bioengineering, University of California, Berkeley and San Francisco, California (C.A.H.); and Department of Bioengineering and Therapeutic Sciences, BioSystems Group, University of California, San Francisco, California (C.A.H.)
(Received December 17, 2007; accepted April 23, 2008)
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Abstract |
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; Cao et al., 2006; Dokoumetzidis et al., 2007) because there can be heterogeneity and individual differences in the levels and expression patterns of transporters and metabolic enzymes along the length of the intestine (Paine et al., 1997; Zhang et al., 1999; Mouly and Paine, 2003). Differences in intestinal transit and other factors further increase the system's complexity (Kimura and Higaki, 2002). P-glycoprotein (Pgp) and the drug-metabolizing enzyme CYP3A4 are most important in limiting intestinal absorption (Watkins, 1997; Wacher et al., 1998). Although Pgp and CYP3A4 play separate roles in restricting absorption, it is believed that they can function synergistically to increase intestinal metabolism (Gan et al., 1996; Watkins, 1997; Wacher et al., 1998; Ito et al., 1999). The idea has been that efflux would increase intestinal drug residence time and that would enable more exposure to and thus more extensive metabolism by CYP3A4. Accordingly, Kivistö et al. (2004) and others (Cummins et al., 2002, 2003) have called for methods to achieve greater insight into the joint actions of Pgp and CYP3A4. As Cummins et al. (2002, 2003) have demonstrated, it has been challenging to selectively reduce the complexity of experimental wet lab systems because interventions, such as administration of a transport inhibitor, can alter mechanisms and create new uncertainties. With such complex systems, there can exist several different, plausible mechanistic explanations for experimental observations. In such cases, it can be challenging to identify the most likely explanation. Experimentation with mechanistically realistic, in silico analogs provides a new method that can supplement wet lab options for achieving deeper insight.
The recently introduced synthetic modeling method (Grant et al., 2006; Hunt et al., 2006; Garmire et al., 2007; Tang et al., 2007; Yan et al., 2007) is intended specifically to engineer models that can be useful for gaining mechanistic insight into complex biological phenomena such as intestinal absorption of compounds that are substrates for both Pgp and CYP3A4. Such models can be constructed consistent with current knowledge using validated components. They are advanced examples of what has recently been called executable biology (Fisher and Henzinger, 2007). When simulation results mimic targeted behaviors, intestinal absorption in this case, the models can be used as objects of experimentation to explore answers to mechanistic questions that would be difficult, impossible, or unethical to answer using biological systems. Following iterative validation, the expectation has been that these models will become useful in anticipating intestinal absorption in advance of costly wet lab experiments. In this report, we present an abstract, yet mechanistically realistic, physiologically based, intestinal analog. The amounts, ratios, and locations of analogs of Pgp and drug-metabolizing enzymes (called PGP and CYP) along the length of the simulated intestine can be easily manipulated. We refer to these assembled systems as in silico intestinal devices (ISIDs).
We explored the impact on simulated passive absorption of compounds that are dual substrates of CYP and PGP. Results for six different proximal-to-distal CYP-PGP patterns are presented, along with results for different CYP/PGP ratios and absolute amounts. The locations and fates of compounds within the ISID were followed to determine the consequences of CYP-PGP interactions. Contrary to expectations, no CYP-PGP synergy was measured. Interestingly, the conditions studied (CYP and PGP having similar levels and substrate reactivates) gave rise to a small but significant degree of CYP-PGP antagonism. Increasing the PGP/CYP ratio from about 1 to 10 increased compound retention in the simulated intestinal lumen, which caused more compounds to exit the intestine but decreased, rather than increased, total metabolism. Different proximal-to-distal CYP-PGP patterns had substantial effects on measures of simulated absorption, metabolism, and extraction ratio. The changes were due more to CYP than to PGP; a pattern of decreasing proximal-to-distal CYP, for fixed amounts of PGP and CYP, dramatically increased metabolism and extraction ratios. We submit that these simulation results may have in vivo counterparts.
This study demonstrates that for this relatively simple, abstract, but mechanistically realistic ISID, the consequences of interventions, such as changing CYP patterns relative to those of PGP, can be nonintuitive initially. Having methods such as those presented to explore scenarios and plausible, mechanistic explanations, in whatever detail is needed, will help achieve deeper insight into the biological mechanisms. The ISID and the results presented expand the repertoire of experimental methods for unraveling the mechanistic details of intestinal drug absorption and in anticipating the absorption consequences of drug interactions.
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Materials and Methods |
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Model Structures and Components. The componentized structure of the ISID is illustrated in Fig. 1. It is a straightforward application of the already validated in silico transwell device (ISTD) (Garmire et al., 2007). It is an example of the synthetic modeling method (Hunt et al., 2006). The ISID is an abstract, physiologically based representation of an arbitrary length of small intestine in which the intestinal wall is represented as a monolayer of epithelial cells. It is not intended to duplicate the intestine, detail-for-detail. All ISTD components and spaces were reused here, with only the changes noted below. For convenience, an abridged description of ISTD methods follows. For additional detail, consult (Garmire et al., 2007).
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). S1 represents cylindrical intestinal luminal contents, with a radius of about 1.5 cm (Stubbs et al., 1998). S1–4 map to an epithelial monolayer, S2 maps to apical membranes, S3 corresponds to intracellular spaces, and S4 represents basolateral membranes. S5 maps to capillary blood. Each S2 to S5 space was discretized further using a two-dimensional rectangular grid containing m by n elements; the dimension m maps to the circumference of the inner intestinal wall (3
cm). The dimension n maps to the length of the small intestine (5 M) (Lin et al., 1999). The m and n values control the lower limit of spatial resolution and the precision of simulated behaviors. In this report, m = 75 and n = 4000.
The volumetric nature of elements in S1–4 is simulated by placing at each grid location a software object that acts as a container having an arbitrary but specifiable CAPACITY (a virtual volume). The effective CAPACITY of each element in S1–4 is given by a relative (with respect to radius) "height" parameter (H). For S1, H is the radius of the simulated intestinal luminal content, 1.5 cm. As discussed by Garmire et al. (2007), H for S1–4 corresponds to the typical height of the referent space in an epithelial cell monolayer. The values used are listed in Table 1. Each element is also labeled with relevant chemical properties, such as pH (in silico pH); in this report, S1-4 pH = 7.4. Tight junctions are as detailed by Garmire et al. (2007). They occupy 0.066% of S1–4 elements. A COMPOUND (also called a DRUG) is a mobile object. A stationary agent called PGP (also called TRANSPORTER) maps to a portion of all transporters that can transport drugs. A stationary agent called CYP (also called ENZYME) maps to a portion of all metabolic enzymes that can metabolize drugs. Both are discussed further below.
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During the formative project stage, it was not clear how much detail should be represented. For a given systemic phenomena, some system details are simply irrelevant. When it was unclear that a detail would be needed, we used exploratory simulation to determine when that detail would be needed. For example, we can combine collocated elements of S2, S3, and S4 and have them function as a unit that maps to a collection of intestinal epithelial cells. For the specified ISID uses, is such detail needed? We conducted exploratory experiments (data not shown) in which S2 to S4 spaces were subdivided into isolated segments; a compound within a segment of S3, for example, could not move directly into an adjacent segment of S3 without first exiting to S1 and then entering the adjacent segment through S2. Because of the effective thinness of S1–4, we found that neither course nor fine-grained segmentation influenced systemic ISID measures. Consequently, it was not used, but it can be added easily should it be needed by descendants of these ISIDs.
We added a conductor component (insert, Fig. 1) at the proximal end of S1. It has no biological counterpart. Rather, it holds and delivers the dose of COMPOUNDs to simulate dissolved drug in a volume of fluid arriving from higher in the gastrointestinal tract. The conductor has the same radius as S1. Its length was optimized to avoid any artifacts that may arise from too many COMPOUNDs entering the ISID too quickly and to minimize the lag-time effect that would result from too few COMPOUNDs entering too slowly. Except when noted otherwise, simulations were initiated with 1000 COMPOUNDs. One set of experiments used dose = 2000 COMPOUNDs to provided insight into the effects of changes in dosed amounts.
Passive Dispersion and Biased Flow in S1. Passive dispersion of COMPOUND in all directions, as described by Garmire et al. (2007), occurs in S1 to S4, whereas biased dispersion only occurs in S1 to simulate flow of intestinal contents (objects in S1 were subject to both passive dispersion and biased forward movement, as stated in the equation below). Passive dispersion involves transition between and within spaces and relocation within an element. We introduced two modifications of those movement mechanisms. 1) Once a COMPOUND appears in S5, it stays there; random movement back to S4 is not allowed. With that restriction, we mimic the "sink condition" that is usually assumed for drug entering blood from the intestine (Ingels and Augustijns, 2003). 2) In S1, we simulate flow as follows. Every COMPOUND used a rule to schedule a transition opportunity at some future time, tt; for COMPOUNDs within S1 and S3 of the ISTD (Garmire et al., 2007), that time was calculated using Einstein's one-dimensional diffusion function: tt = tc + (H - h0)2/2D. tc is the current simulation time, H is the relative "height" of elements within the space in which the COMPOUND resides (Table 1), D is the diffusion coefficient in that space (it was calculated as specified in the appendix of Garmire et al., 2007), and h0 is the COMPOUND's current location within that element. In S2, h0 = 0 at the S1 to S2 interface, and so on. In S1, the parameter h0 is the distance of a COMPOUND from the cylinder's axis. If h0 = 0, the COMPOUND is at the S1 axis, and if h0 = H1, the COMPOUND is located at the interface of S1 and S2. A COMPOUND's movement in S1 of the ISID is comprised of radial movement combined with simulated flow relative to the cylinder's surface. The cylinder's width is 2h0, and its length is n = 4000 as above. At tt, the COMPOUND calculated a new location for itself (Garmire et al., 2007). Briefly, in each simulation cycle, a new position (xt, yt) within the same space and within a fixed update interval of t =
5 s is calculated as xt = x0 +
(4Dt)(rv x sin
) and yt = y0 +(4Dt)(rv x cos + e); (x0, y0) is the center of the element in which a COMPOUND is located, rv is a random value drawn from a standard Gaussian distribution (mean = 0, S.D. = 1), is an angle drawn from the uniform distribution on (0, 2), and D is the referent compound's diffusion coefficient in the referent space. e is a bias factor added to the random walk to simulate proximal-to-distal flow along S1. When xt is larger than 2h0, the COMPOUND's destination on the circumference is determined by (xt - 2Nh0); N is the integer that makes 0 
(xt - 2Nh0) < 2. A COMPOUND is eliminated from the ISID when yt > N. In this report, we used two values of D in S3: 1.69 x 10-6 and 1.69 x 10-8 cm2/s. These D values were selected so to be comparable with those used by Ito et al. (1999).
Effects of CYP and PGP. Already validated ENZYME objects (Garmire et al., 2007) were reused here. Briefly, the enzymatic reaction algorithm is a stochastic analog of the conventional kinetic model. When scheduled, each CYP agent updates its state depending on its internal logic, the nature of, and relative location of objects in its local environment, and values drawn from a pseudorandom number generator. A CYP has two substrate-binding sites, so that self-activation and/or self-inhibition can be simulated. In this report, for simplicity, we inactivated the second site of the ENZYME objects that were validated by Garmire et al. (2007). By so doing, the ENZYME had only one active site, and as documented by Garmire et al. (2007), its metabolic properties exhibited simple Michaelis-Menten kinetics. A CYP is in one of the two states: with or without a bound COMPOUND. State changes can occur within each 0.5-s simulation cycle. Each free CYP scans the 24 elements comprising its local neighborhood (illustrated in Fig. 1) and selects the COMPOUND within that has the smallest assigned pseudorandom number. If that number is less than the CYP-COMPOUND binding probability, P1, it binds the COMPOUND. Otherwise, it ignores any COMPOUND and waits until the next opportunity. When a CYP has a bound SUBSTRATE, it decides whether to release it as a METABOLITE. The decision is based on the relationship between a new pseudorandom number and P2; if that pseudorandom number is less than P2, a METABOLITE is released. Otherwise, the CYP-COMPOUND complex will be unchanged at the start of the next simulation cycle. For simplicity, we specified that METABOLITEs inherit the physicochemical properties (PCPs) of COMPOUNDs, including the COMPOUND's CYP and PGP binding affinities and releasing probabilities listed in Table 1.
The CYP agent and its mechanism, which were detailed by Garmire et al. (2007), were general and designed to be reused for other purposes. By simply changing the logic and/or location, it can serve as an analog to some other cell component such as a transporter. The PGP agents are slightly modified versions of CYP. Only one site was used, a one-site PGP that had been validated earlier against data from in vitro model (Sheikh-Bahaei and Hunt, 2006). The logic used by each PGP to deal with objects in its S3 neighborhood is the same as that used by CYP. Once a COMPOUND or METABOLITE is bound, the complex moves to the S2-S1 interface, and the object is released into S1 randomly along the radius of the ISID. When facing S1, PGP is inactive. After releasing an object, it moves back to its original location facing S3. In that state, it is again active.
For each 0.5-s simulation cycle, extraction ratio (ER) measured the fraction of COMPOUND that was actually METABOLIZED among what was available for METABOLISM during the last simulation cycle:
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In general, the density of Pgp-type transporters increases from the jejunum to the ileum, whereas the density of drug-metabolizing enzymes decreases from the jejunum to the ileum (Mouly and Paine, 2003; Paine et al., 1997). Along the small intestine, their gene expression levels are comparable (Cao et al., 2006). To represent their relative densities, we subdivided the ISID into eight segments and randomly placed different amounts of CYP and PGP within each segment as specified in Table 2. Choice of the total amount of CYP and PGP was somewhat arbitrary but was guided by four constraints: 1) DOSE/total(CYP + PGP) 1; 2) the relative, separate trends of CYP and PGP along the eight segments in Table 2 should closely match the listed, relative gene expression levels; 3) we did not want CYP/PGP in any one segment to deviate too far from 1.0; we arbitrarily specified 0.5 < CYP/PGP < 2 within any one of the eight segments; and 4) we wanted CYP(total)/PGP (total) to be close to 1.0; we arbitrarily specified 0.8 (total CYP)/(total PGP) 1.2. Specifying CYP = 480 and PGP = 419 met those constraints, so those amounts were used for most experiments.
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Discrete Event Schedule. The ISID used discrete event simulation. Simulations are advanced by dynamically scheduling events at realistic times. Two levels of agents manage event scheduling. Each scheduling agent implements heap tree (a priority queue) data structures to ensure fast event insertion, rescheduling, and deletion (Cormen et al., 1990). At the bottom level, four scheduling agents, Transit Event Scheduler, Lateral Event Scheduler, Enzyme Event Scheduler, and Transport Event Scheduler, control the progress of COMPOUND relocation and transition into adjacent spaces, lateral movement within each space, and METABOLISM and transport. The master Schedule Event agent coordinates the activities of the other four subagents.
Software. The ISID is built from Swarm platform and libraries (http://swarm.org). We coded in Java Swarm. Doing so gave direct access to Swarm's Objective-C libraries and enabled the created software to be easily integrated with R and MATLAB version 13 (Mathworks Inc., Natick, MA). Most experiments were executed on an eight node OSCAR cluster (http://oscar.openclustergroup.org) running RedHat's Fedora 5. The distribution of the runs used MPICH 1.2.7 (http://www-unix.mcs.anl.gov/mpi/mpich1). The initial pseudorandom number seed was extracted from the machine's clock. The input data were fed automatically from the MATLAB script for sequential runs, in which an interface was linked with Java Swarm. The output data files, in Java Swarm, were automatically linked and processed using MATLAB and R. We conducted parameter tuning, graphing, data analysis, and data fitting in MATLAB version 13. We repeated most simulations 10 to 15 times; results are reported as arithmetical mean values, unless otherwise noted. We assumed that the central limit theorem holds for all observations.
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Results |
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). The simplest way to simulate proximal-distal flow in S1, the method used, is to instruct each object to move farther than it would using a simple random walk whenever a move toward the distal end of S1 is scheduled. This was done by adding an additional unitless biased walk parameter e; in Materials and Methods, it is called the biasFactor. The mean transit time through human small intestines for the 400 drugs (Yu et al., 1996) was approximately 199 min. We wanted the ISID to exhibit simulated mean transit times that were similar. Following the lead of Kalampokis et al. (1999), we made S2 impermeable to confine the dose to S1. We then explored the consequences of using different biasFactor values. Results from five of these experiments are shown in Fig. 3. When using a biasFactor of 50, 50% COMPOUNDs had exited after 199 min. Inspection of the insert in Fig. 3A also shows that the simulated maximum elimination rate for biasFactor = 50 fell between about 195 and 205 min. Thus, that biasFactor value was used for all subsequent experiments.
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During those biasFactor experiments, we monitored the amount of COMPOUND in each of the 4000 S1 elements from the proximal to the distal end. We pooled data from a sequence of 20 equally distant segments along the proximal to distal ISID. Results are summarized in Fig. 3B for biasFactor = 50. The approximate Gaussian shape of the histogram profiles along with their increasing variance with increasing simulated time is consistent with dispersion occurring during flow through a tube.
Effects of PGP and CYP on Simulated Absorption and Metabolism. We provided validation experiments for two-site, enzyme-substrate reaction mechanisms in the previous report (Garmire et al., 2007). For this report, we inactivated the second substrate-binding site. The result was a CYP object that exhibited simple Michaelis-Menten kinetics. A copy of that object was modified to represent PGP. Rather than releasing a METABOLITE, a PGP released the original COMPOUND. Before combining and experimenting with the CYP and PGP within the same ISID, we verified the function of each within the ISID using different values of P1 and P2 (Table 1) and two different levels of PGP. To simplify comparisons, exploratory simulations, identical to those in Garmire et al. (2007), were conducted to select a reference COMPOUND that would, at the conclusion of the experiment, exhibit similar values of: 1) ABSORPTION (accumulation in S5), 2) the amount of COMPOUNDs exiting the ISID from S1, and 3) LUMEN retention. A basic COMPOUND having mol wt. = 500, logP = 3 was selected. All experiments used 480 CYPs distributed along the ISID using the pattern specified in Table 2. One set of experiments used 419 PGPs distributed along the ISID as specified in Table 2, and another used 4190 distributed identically. Ten repetitions were completed for each experiment condition. The control condition, which had P1 = 0 for both CYP and PGP, simulated passive absorption; it also simulated complete inhibition of both CYP and PGP. The results are shown in Fig. 4.
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), there was no significant change in LUMEN retention. However, for the experiments in which we used 4190 PGPs (Fig. 4A), mean LUMEN retention increased from 301 to 379 COMPOUNDs. The mean amount that exited the distal end of S1 increased from 332 to 408 COMPOUNDs, whereas mean ABSORPTION decreased from 366 to 213, consistent with expectations.
Absent PGPs, activating the 480 CYPs caused about 10% of the dose to be metabolized on passing through S3 (Fig. 4B), which was sufficient for the objectives of this study. By decreasing either P1 or P2 from 1 to 0.5, metabolism decreased significantly. There are several ways to increase simulated metabolism without altering specific ISID components or their arrangements. One is to increase the local neighborhood (Fig. 1D) surveyed by each CYP during each simulation cycle.
Different, Relative PGP and CYP Patterns Can Influence ABSORPTION Dramatically. A plausible contributor to interindividual variability in oral drug bioavailability is differences in the proximal-to-distal patterns of relative densities of metabolic enzymes and transporters. We conducted experiments using the five different proximal-to-distal patterns shown in Fig. 5A to explore that issue. Total objects within the ISID in each case were the same: CYP = 480 and PGP = 419. We focused on observing the maximum differences among patterns by setting P1 = P2 = 1 for both CYP and PGP. We conducted 15 repeat experiments for each case. The results in Fig. 5 are arithmetic means.
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In all cases, the amount ABSORBED increased until about 200 min, which is the mean transit time of the simulation; thereafter, on average, no significant additional absorption occurred. The different proximal-to-distal CYP and PGP patterns caused only modest changes in amount absorbed (Fig, 5B) because passive ABSORPTION for the reference COMPOUND dominates. However, it was not surprising that relative differences in METABOLISM and extraction ratio (Fig. 6) showed clearly the influence of the different CYP and PGP patterns. The pattern for CYP dominates; switching the PGP pattern from a to b (or d to e) did not meaningfully change either cumulative METABOLISM (Fig. 6A) or extraction ratio profiles (Fig. 6B). By 60 min, at least 50% of ABSORPTION had occurred. The data document that having more CYP toward the proximal end of the ISID (cases a and b relative to case c) caused more METABOLISM. Prior to reaching an asymptote at about 200 min, cumulative METABOLITE profiles exhibit three CYP-dependent patterns (Fig. 6A). When both CYP and LUMINAL COMPOUND levels declined proximal-to-distal (a and b), we observed early, rapid METABOLITE accumulation. When CYP levels increased proximal-to-distal (d and e), early METABOLISM was least. When CYP levels were constant (pattern c), the rate of METABOLITE accumulation decreased in parallel with declining LUMINAL COMPOUND levels.
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Relative PGP and CYP Expression Levels Influence ABSORPTION and METABOLISM. Another plausible contributor to variability in interindividual, oral bioavailability is the total, relative amount of metabolic enzymes and transporters within the intestine (Paine et al., 1997; Mouly and Paine, 2003). To explore the consequences of such differences, we conducted four experiments in which PGP and CYP amounts were changed by a factor of 10, while maintaining the proximal-to-distal patterns specified in Table 2. Results from 20 replicate experiments were averaged. Note that a 10-fold difference in PGP activity can result from different amounts or from a 10-fold inhibition of PGP in one ISID case relative to another. Below, for clarity, a change in CYP or PGP amount can also mean a change in activity.
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Increasing PGP 10-fold for the same amount of CYP (changing CYP/PGP from 10:1 to 10:10 and from 1:1 to 1:10 in Fig. 8A) decreased cumulative METABOLITE formation by about 50% for both the large and smaller amounts of CYP. However, increasing PGP 10-fold for the same amount of CYP did not dramatically alter measures of extraction ratio (Fig. 8B), similar to the observations in Fig. 6B. When CYP levels were largest, having relatively more PGP caused slightly larger extraction ratio values. The effect was a consequence of how ER is defined; it is a measure of the fraction of COMPOUND that was available for METABOLISM and that was actually METABOLIZED. In these studies, PGP pumps both COMPOUNDs and METABOLITEs into the ISID LUMEN, increasing the amount of both that exits S1. The shape of the ER profile after about 25 min is a consequence of the changing ratio of CYP to PGP along the length of the ISID, as specified in Table 2.
CYP-PGP Antagonism But Not Synergy Occurred. CYP-PGP synergy occurs when the decrease in ABSORPTION due to the combined function of CYP and PGP (relative to ABSORPTION in the absence of CYP and PGP) is greater than the sum of the separate effects: the reduced ABSORPTION when each is functioning alone. When CYP/PGP = 480:419, no synergy occurred (data not shown); the results in Fig. 4 show that for that ratio, LUMEN levels of COMPOUNDs did not increase. We explored conditions that might be more conducive to synergy. Results of two conditions merit attention: CYP/PGP = 480:4190, with and without simulated, nonspecific INTRACELLULAR (S3) binding of COMPOUNDs. Nonspecific binding can be represented is several ways. We present results for one of the simplest (also used by Ito et al., 1999): decrease the COMPOUND's effective diffusion coefficient in S3. We decreased it 100-fold to 1.69 x 10-8 cm/s. Slowing INTRACELLULAR COMPOUND movement within a simulation cycle can map to multiple binding and release events in the referent. The simulation cycle was 0.5 s. The time between two, tandem-scheduled events for the same object (a CYP, PGP, or COMPOUND) was 
0.5 s. Any event in the intestine that occurs within that interval is below the ISID's current level of simulation resolution.
The following experiments all used CYP/PGP = 480:4190; for some experiments, both were active, for some other experiments, one or the other or both were deactivated. There were two sets of experiments for each of those four sets of conditions: with and without nonspecific binding. The results are means of 20 repeat experiments. When both CYP and PGP were active (P1 = 1 for both), the condition is designated CYP:PGP = +:+; when either or both were deactivated by setting P1 = 0, it is designated CYP:PGP = +:– or –:–. The expected ABSORPTION, assuming no interaction, was calculated as specified under Materials and Methods. The time profiles of mean amounts ABSORBED are plotted in Fig. 9. The box plots in Fig. 10 show results at 200 min; they demonstrate the variability, built-in uncertainty, in these ISID experiments.
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Inhibition of CYP increased ABSORPTION, as expected. The magnitude of the effect was increased with nonspecific binding (Fig. 9B). Inhibition of PGP increased ABSORPTION more when nonspecific binding was absent, whereas the combined inhibition of CYP and PGP increased ABSORPTION more in the presence of nonspecific binding. The results in Fig. 9 and Table 3 show that no synergy occurred. As stated under Materials and Methods, METABOLITEs inherited all of the PCPs of the parent COMPOUND, including PGP P1 and P2 values. However, METABOLITEs had no affinity for CYP (P1 = 0).
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Somewhat counterintuitively, the results showed a small but real degree of CYP-PGP antagonism (Figs. 9A and 10A; Table 3); the expected amount ABSORBED was less than measured ABSORPTION. The effect was enhanced with nonspecific binding within S3 (Figs. 9B and 10B; Table 3). Antagonism was a consequence of the density of COMPOUNDs being such that within one simulation cycle, a small fraction of COMPOUNDs was simultaneously in the local neighborhood of two or more binding objects, CYP and/or PGP. The probability of such an occurrence increased with increased COMPOUND densities caused by nonspecific binding. Because either CYP or PGP can bind a COMPOUND that is within their overlapping neighborhoods within a simulation cycle, the effectiveness of the loser (the one that, by chance, does not bind the target object) during that cycle is diminished.
The consequences of the events described above for dose = 1000 on the time courses of LUMEN retention, formation of total METABOLITEs, and extraction ratio are presented in Fig. 11. Nonspecific binding slightly increased LUMEN retention (Fig. 11A), in part, because there was a higher probability that a COMPOUND would return to S1 from S3, both passively and by PGP transport. Nonspecific binding in S3 increased the probability for METABOLISM. Consequently, total METABOLISM and ER values (Fig. 11, B and C) were increased. Consistent with the observations in Figs. 6 and 8, less METABOLISM but greater ER values were obtained when PGP was active.
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Might the presence of active METABOLITEs (having an affinity for PGP) have obscured evidence of synergy? To explore the possibility, we repeated the preceding experiments, eliminating that affinity for PGP (P1 = 0); the results corresponding to the data in Fig. 11A were unchanged (data not shown). The results corresponding to the data in Fig. 9, A and B, after 100 min were also unchanged.
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Discussion |
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) validated the functionality of the components in Fig. 1 but in the absence of fluid flow. The data taken from those simulations were essentially indistinguishable from wet lab data (within the range of variability of wet lab experiments). Assume that within the ISID context, the simulated flow mechanism is a reasonable, low-resolution representation of intestinal flow. We submit that the relative relationships between ISID components, their logic, and how they are plugged together are similar to the corresponding component relationships within the intestine, from the perspective of measures of metabolism, luminal retention, and absorption. That degree of similarity provides ISID face validation for the current level of granularity and establishes a semiquantitative mapping between ISID and the intestine at the mechanism level: mapping C in Fig. 12. ISID simulations are not intended to faithfully represent details occurring in the intestine during drug absorption. We claim only that similarities of form and function within the two systems, for the uses specified and from the perspective of the measurements taken, are sufficiently similar so that the ISID can be used as a surrogate of in situ intestinal absorption studies for the purposes of discovering plausible answers to mechanistic questions of the type addressed here.
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The simulation results presented here show that for the passively ABSORBED, reference COMPOUND (mol wt. = 500, logP = 3, pKa = 7.4, base), higher levels of PGP did cause LUMINAL retention (Fig. 4). The presence of more PGP for a fixed amount of CYP, in the absence of nonspecific binding, did increase exposure of drug to CYP, as measured by ER (Figs. 6B, 8B, and 11C), but total METABOLISM diminished (Figs. 6A, 8A, and 11B); it did not increase, as had been speculated in the literature. The primary effect of PGP was the increased LUMINAL retention and more COMPOUNDs exiting the INTESTINE (Figs. 7A and 11A). The explanation for increased ER values is that when PGP levels were elevated, total METABOLITE levels were reduced, but so were levels of COMPOUNDs in S3, sufficiently so that calculated ER values actually increased relative to corresponding values when PGP levels were lower. Nonspecific binding amplified the effect, in part because of the increased levels of COMPOUNDs in S3 (Fig. 11C).
No synergy was observed for the dose studied. Counterintuitively, the results in Figs. 9 and 10 and Table 3 showed that measurable CYP-PGP antagonism occurred. There may be circumstances when similar antagonism occurs between metabolic enzymes and transporters within the intestine. To date, however, there have been no reports of such antagonisms. The results of earlier simulations (Liu and Hunt, 2006) indicated that it might be interesting to explore in more detail the consequences of different placements of CYP within S3 relative to S2 and restricted orientation of CYP and, in particular, PGP.
Differences are known to exist between the proximal-to-distal mRNA expression patterns along the human intestine of members of both ABC and SLC families of transporters (Englund et al., 2006). ABSORPTION, METABOLISM, and LUMINAL retention of the reference COMPOUNDs were strikingly sensitive to changes in CYP-PGP patterns. Not surprising was that pattern b in Fig. 5 was most effective in limiting ABSORPTION because CYP and PGP levels were highest when LUMINAL levels of COMPOUNDs were also highest.
For the conditions studied, maximum amount ABSORBED was always less than 40%. That was because the S1-S2 interface was simulated as having the same area as the S4-S5 interface. Doing so does not impact the observations reported here because the relative amounts of CYP and PGP will stay the same when effective surface areas are changed. When greater absorption is needed per unit length, possibly as a consequence of simulating increased surface area, several simulation options are available, and they are being explored.
Using a steady-state equational model, Ito et al. (1999) showed that for their model, the fraction absorbed increased following inhibition of PGP for a dual CYP-PGP substrate. Furthermore, absorption in their model increased when PGP was inhibited; the effect was greater in the case of simulated intracellular binding. ISID simulations showed the same effects. Their model exhibited synergy, whereas we detected none, but then they explored a greater range of conditions and did so under steady-state conditions. Their continuous model abstracted away important details that occur at the S1-S2 and S2-S3 interfaces. They also abstracted away the discrete nature of CYP-COMPOUND and PGP-COMPOUND interactions. These abstractions effectively couple the effects of transport and metabolism within the variables of their partial differential equations. We observed CYP-PGP antagonism. Their model made no a priori allowance for that possibility. The differences in stated uses, assumptions, and in simulation results between the two models help illustrate some of the strengths and weakness of each class of models. By representing clearance measures at steady state, Ito et al. abstracted away mechanistic details occurring within spaces; they also abstracted away differences in the proximal-to-distal pattern of interacting components. However, by imposing those abstractions, Ito et al. were able to explore a far larger region of their model's parameter and behavior space than was done with the ISID, and they can make precise predictions. Because of the presence of mechanistic details, the simulation time needed for an ISID to reach steady state would be hours for the single processors we used. The ISID was developed, in part, to explore the consequences of changes in spatial and configuration changes. If that is not an intended model use, which was the case for Ito et al., then an equational model is the better choice. For additional contrasts between models of the ISID class and traditional equation-based models, see Hunt et al. (2006). It is worth recalling that all models of biological systems are, by necessity, abstractions. Consequently, whenever the subject of those abstractions becomes important to the measured properties of the model, all models that have adopted them are at risk of being wrong.
Motivated by the goal of having the ISTD (Garmire et al., 2007) and its descendants become useful tools for predicting in vitro transport properties of compounds based only on their structure, ISTDs were designed to exhibit nine capabilities. Four of those capabilities merit recall: 1) "Flexibility: it must be relatively simple to increase or decrease detail to... change usage and assumptions, without requiring significant reengineering." 2) "Reusability: device components can be designed to be autonomous and thus can be easily reconfigured to represent different cell types, experimental conditions, and compounds, alone or in combination. It must be easy to simulate and analyze outcomes of several different in silico experiments in a fraction of the time (and at a fraction of the cost) required to complete the wet lab experiments." 3) "Adaptability: in addition to flexibility and reusability, the components must be constructed so that they can be adapted to function as components in physiologically based, intestine and whole organism models." Because the ISTD cited above and its components were designed to exhibit these capabilities, it was straightforward to create and verify an ISID with minimum re-engineering by reusing already validated ISTD components. The conductor in Fig. 1 was new. However, the S1 to S5 spaces, along with the tight junction components from the ISTD, were reused with only the minor modifications detailed under Materials and Methods. The COMPOUNDs used in ISTD experiments were also used in these ISID experiments. PGP and its enabling algorithms were simplified versions of the ISTD's dual substrate ENZYME. 4) The fourth capability addresses the hypothesized mappings in Fig. 12: "observables in silico are designed to be consistent with in vitro observables. Doing so enables clear mappings between in vitro and in silico components and mechanisms." The ISID is mechanistically realistic in part because it too exhibits these capabilities. Using the ISID to achieve greater insight into plausible mechanisms of intestinal absorption facilitates thinking more deeply about the far more complex referent system. ISID components can easily evolve over time. That bodes well for ISID's future uses and heuristic value. An example of a future use would be combining it with the in silico liver (Yan et al., 2007) to gain deeper insight into the complexities of bioavailability and thereby be better positioned to improve bioavailability predictions with the available, limited data.
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The work was abstracted in part from a dissertation presented by L.X.G. to the Graduate Division, University of California, Berkeley, CA, in partial fulfillment of the Ph.D. degree.
Article, publication date, and citation information can be found at http://dmd.aspetjournals.org.
ABBREVIATIONS: Pgp, P-glycoprotein; ISID, in silico intestinal device; ISTD, in silico transwell device; PCP, physicochemical property; ER, extraction ratio.
Address correspondence to: C. Anthony Hunt, Department of Bioengineering and Therapeutic Sciences, University of California, 513 Parnassus Avenue, S-926, San Francisco, CA 94143-0446. E-mail: a.hunt{at}ucsf.edu
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