Fig 1.
Component organization and model mechanism features.
(A) A virtual Mouse, detailed in Methods, is a concretized, coarse-grain software analogy of an actual mouse. Shading within a cross-section of a hepatic lobule illustrates idealized PP-to-PC gradients. (B) A portion (16%) of one vLobule is illustrated. A Monte-Carlo specified interconnected directed graph, which can be different (within constraints) for each vExperiment, specifies flow paths for APAP and other Compounds (see Methods). (C) A multi-layered, quasi-3D Sinusoid Segment (SS) maps to a portion of hepatic tissue. One is placed at each graph node. An SS functions during execution analogous to sinusoid components and features averaged across many actual lobules; SS dimensions are Monte Carlo-sampled to mimic lobular variability. An SS comprises a Core surrounded concentrically by five 2D grids. One space contains virtual Endothelial Cells (vECs) and another contains vHPCs. (D) Mobile Compound objects move within and between the grids in C. They enter and exit an SS via Core and Interface, percolate stochastically through accessible spaces influenced by flow parameters. Compounds that exit to the CV are returned to Mouse Body. vHPCs and vECs control Compound entry from, and exit to, adjacent spaces, and the fate of Compounds within. Each vHPC contains a variety of components needed to enable the cause-effect events. All of the preceding components are parameterized the same as in Smith et al. [8].
Fig 2.
Events that can occur within each vHPC.
Arrows indicate discrete probabilistic events (not continuous processes) that may occur during a particular simulation cycle. (A) These features and events are parameterized the same as in Smith et al. [8]. There is a direct mapping between the probability of an APAP Metabolism event and average metabolic capacity of hepatocytes at various PP-to-PC locations. Red arrow: event probability or value decreases PP-to-PC. Green arrow: event probability increases PP-to-PC. A NAPQI removal event depletes Glutathione (GSH). Once GSH falls below the vHPC’s GSH Depletion Threshold, each subsequent NAPQI removal event is paired with creation of one of two types of Damage Product, either a MitoD object (maps to mitochondrial damage products) or a nonMitoD object (maps to non-mitochondrial damage products). Amounts of MitoD and nonMitoD are amplified [8]. A MitoD or nonMitoD object may be removed, which maps to a damage mitigation process. The probability of a MitoD removal event decreases PP-to-PC, whereas the probability of a nonMitoD removal event increases PP-PC [8]. (B) The virtual counterparts of two types of damage-induced ALT externalization events are illustrated. 1) Accumulation of MitoD objects above an ALT Leakage Threshold triggers ALT leakage and subsequent ALT externalization. 2) Accumulation of nonMitoD objects above an ALT Leakage Threshold triggers ALT leakage and subsequent ALT externalization. Both ALT Leakage Threshold values are the same. 3) Both of the preceding processes may operate concurrently. The contributions 1–3 to explanations of the target data were investigated separately. Externalized ALT accumulates in Mouse Body. (C) Independent of the events in B, accumulation of MitoD above a Necrosis threshold triggers Necrosis, the same as in Smith et al. [8]. Once Necrosis is triggered, there is a delay—a Monte Carlo sampled lag time—before the vHPC becomes Necrotic (maps to cell death) and all remaining ALT is externalized. The minimum ALT Leakage lag time is less than the minimum lag time for Necrosis Triggered → Necrotic. Parameterizations within B and C are independent of a vHPC’s PP-to-PC location. Nevertheless, ALT Externalization within B and C is dependent on a vHPC’s PP-to-PC location because of the location-dependent events in A (red and green arrows). Externalized ALT exits a SS, enters the CV, and is transferred to Mouse Body the same as unmetabolized APAP. ALT in Mouse Body maps quantitatively to plasma ALT values.
Fig 3.
ALT externalization processes, validation targets, and Lobular organization.
(A) An illustration of plausible relationships between the ALT externalization processes in Table 1 and in vivo counterparts. Non-Necrotic ALT Release = (MitoD-Caused + nonMD-Caused + Dual-Cause) and maps to a structured conflation of non-necrotic damage and recovery processes that may directly or concomitantly enable ALT release, indicated by blue shading. (B) The gray area is the initial validation target range (left axis), which is based on mouse data from the four indicated reports. The minimal Similarity Criterion for an acceptable ALT release MM is that it generates ALT-in-Mouse-Body profiles that, when scaled (right axis), fall within the target range. (C) Bar heights represent the mean number of vHPCs at the indicated location within an average vLobule. The left edge corresponds to PV. The right edge corresponds CV. Moving left-to-right, the first 14 bars are located at increasing distances from PV (designated dPV) along the average PV-to-CV path. Moving right-to-left, the first 12 bars are located at increasing distances from the CV (designated dCV) along the average CV-to-PV path. Periportal band = blue bars, Mid-Zonal (M-Z) band = green bars, and Pericentral band = red bars.
Table 1.
Descriptions of four processes that may cause ALT externalization.
Fig 4.
Temporal measurements made during executions of the Parent Model Mechanism.
Average amount of MitoD (A) and nonMD (B) within PP, M-Z, and PC bands. (C) Cumulative Necrosis-Triggered and Necrotic events (dashed curves) within the three bands. vHPCs that are Necrosis-Triggered become Necrotic following a Monte Carlo sampled Necrosis interval.
Fig 5.
ALT Release characteristics and features during MM executions.
(A) Average ALT accumulation in Mouse Body from vExperiments using each of the four MMs in Table 1. (B) The values are the average amounts of ALT that have been externalized by vHPCs within the three bands (Fig 3C) during the vExperiment using the Necrotic-only MM. However, at the time measured, that ALT has not yet exited the band. (C) Average ALT amounts, as in B, from vExperiments using the MitoD-Caused MM. The relative patterns of corresponding measures from vExperiments using the nonMD-Caused and the Dual-Cause MMs are similar to those in C.
Fig 6.
Results from the MitoD-Caused MM vExperiments are scaled to match plasma ALT values from 18 individual mice.
(A) Plasma ALT values from groups of six mice are plotted at the times indicated. We targeted the 18 mice at 3, 4.5, and 6 h; they are numbered in sequence (from largest to smallest at each time). Solid curve: average amounts of ALT-in-Mouse-Body (right axis) from the MitoD-Caused MM vExperiment. Dashed curve: average amounts of ALT-in-Mouse-Body from the MitoD-CausedexLT MM vExperiment (exLT = extended lag time); in that vExperiment, the [Min, Max) distribution for the ALT Release and the Death Delay lag times are increased by 1600 s (26.67 min). Both curves: ALT amounts are scaled to plasma ALT values (left axis) using Eq 1, with S = 1.72 (IU ml-1, ALT-objects-1). (B) The validation targets are the six 3 h values (black); the other values are gray. The solid and dashed gray profiles are the same as in A. Purple profiles: the average ALT amounts from the MitoD-Caused MM vExperiment in A are scaled to match the individual plasma ALT values from mice 1 and 2 using Eq 2. Green profiles: the average ALT amounts from the MitoD- CausedexLT MM vExperiment in A are scaled to match the individual plasma ALT values from mice 3–6 using Eq 2. (C) and (D) The average amount of ALT-in-Mouse-Body from the MitoD-Caused MM vExperiment in A are scaled using Eq 2 to match the individual plasma ALT values from mice 7–12 (C) and 13–18 (D). The δi values for all 18 mice are listed in S2 Table. Statistical measures for the 12 Monte Carlo MitoD-Caused MM trials prior to scaling using Eq 1 are provided in S3 Table.
Fig 7.
Dose-response relationships from vExperiments using the MitoD-Caused MM.
Mean ALT-in-Mouse-Body amounts were recorded at 4.5 and 12 h post-Dose. The low, medium, and high Doses map directly to wet-lab doses (upper axis) of 150, 300, and 600 mg/kg, respectively. Blue diamonds: mean amounts of ALT. Whiskers for the medium, and high Doses span the range of ALT amounts for 12 Monte Carlo trials. For smaller Doses, the symbol eclipses the whiskers. Open circles: mean plasma ALT values (right axis) for three APAP doses from McGill et al. [7]; the whiskers span the range of plasma ALT values for all six mice. We map the ALT-in-Mouse-Body to plasma ALT values using Eq 1 with S = 1.72 (IU ml-1, ALT-objects-1). At 12 h, one of the six plasma ALT values is off-scale.