Modeling and Simulation of Intracellular Drug Transport and Disposition Pathways with Virtual Cell

Abstract

The development of computational approaches for modeling the spatiotemporal dynamics of intracellular, small molecule drug concentrations has become an increasingly important area of pharmaceutical research. For systems pharmacology, the system dynamics of subcellular transport can be coupled to downstream pharmacological effects on biochemical pathways that impact cell structure and function. Here, we demonstrate how a widely used systems biology modeling package - Virtual Cell - can also be used to model the intracellular, passive transport pathways of small druglike molecules. Using differential equations to represent passive drug transport across cellular membranes, spatiotemporal changes in the intracellular distribution and concentrations of exogenous chemical agents in specific subcellular organelles were simulated for weakly acidic, neutral, and basic molecules, as a function of the molecules' lipophilicity and ionization potentials. In addition, we simulated the transport properties of small molecule chemical agents in the presence of a homogenous extracellular concentration or a transcellular concentration gradient. We also simulated the effects of cell type-dependent variations in the intracellular microenvironments on the distribution and accumulation of small molecule chemical agents in different organelles over time, under influx and efflux conditions. Lastly, we simulated the transcellular transport of small molecule chemical agents, in the presence of different apical and basolateral microenvironments. By incorporating existing models of drug permeation and subcellular distribution, our results indicate that Virtual Cell can provide a user-friendly, open, online computational modeling platform for systems pharmacology and biopharmaceutics research, making mathematical models and simulation results accessible to a broad community of users, without requiring advanced computer programming knowledge.

Keywords: Computational Biology; Drug Disposition; Pharmacokinetics; Pharmacology; Simulation and Modeling; Systems Biology; Systems Pharmacology; Virtual Cell.

Figure 1

Suspended cell model (A) and transcellular model (B) and their corresponding Virtual Cell BioModels (C and D, respectively).

Figure 2

Reaction diagram and Reactions tab describing the transport kinetics of molecules between different intracellular compartments. A) Reaction Diagram showing Bt_Outside being transported across Plasmalemma into Cytoplasm, and subsequently Bt_Cytoplasm being transported across Mito_mem into Mitochondria. The Flux term (flux_OC) is further defined in the Reaction tab. B) Reaction tab allowed users to set up the kinetics of each transport reaction, with a reaction name, structure location, and kinetic type. In this example, the passive diffusion from Outside to Cytoplasm was named flux_OC, as shown in the Object Properties tab. The flux J_oc given in the first line was defined by the user, and all the variables in this expression automatically appeared beneath, to allow further inputs by the user.

Figure 3

Navigation panel and Simulations tab defining simulation conditions and parameter values. This screen shot shows navigation panel on the left hand side of the BioModel: Baik & Rosania 2013 JPP – 01 Suspension model no lysosome. Applications were defined based on Geometry and Simulations. The Simulation tab included individual parameter windows that could be changed from default values using the editing function. As an example, mitochondrial membrane potential (Emm), drug type (c=−1 for acid, c=1 for base, and c=0 for neutral), and ionization constants (pK_a) were scanned using combinations of multiple input parameter values. The Annotation and Simulation settings also showed the step sizes used in the calculations. Clicking on the green arrowhead at the upper right corner ran the simulation by submitting the equations generated by Virtual Cell to a remote solver.

Figure 4

Examples of simulation results made with scanning input parameters, varying Emm and pKa values for neutral, basic and acidic compounds, as specified in Figure 3. For visualizing simulation results, Virtual Cell allowed users to graph plots with user-defined X- or Y-axes, to compare the effect of different parameter variables. After choosing the parameter options in the lower panel, Virtual Cell displayed combinations of multiple simulation results in a single plot. Simulation results could also be exported as raw values in various formats, for plotting and visualization with other software packages.

Figure 5

Simulation results showing changes in drug concentrations in cytosol (left column) and mitochondria (right column) for molecules with logKow of −2, 0 and +2, for a suspended cell incubated with a homogeneous extracellular drug concentration. A) Time course plot showed changes in concentration of a weakly basic molecule (ionized species charge = +1). B) Similar plot for a neutral (unionizable) molecule. C) Similar plot for a weakly acidic molecule (ionized species charge = −1).

Figure 6

Simulation results capturing the influx and efflux of a weakly basic molecule from cells, showing concentration changes in extracellular and intracellular compartments, modeled using the transcellular transport model (BioModel: Baik & Rosania 2013 JPP – 02 Transcellular model no lysosome). A) Time course changes showed drug influx into the cell and other intracellular compartments, after setting initial concentrations to 10 µM in the apical and 0 µM in the cytosolic, mitochondrial and basolateral compartments. B) Time course changes showing drug efflux from the cell and other intracellular compartments, after setting initial concentrations to 1000 µM in cytosol and mitochondria, and 0 µM in apical and basolateral compartments.

Figure 7

Simulation results showing changes in the mitochondrial concentrations of a weakly basic lipophilic molecule dosed in the apical compartment, modeled with a transcellular transport model (BioModel: Baik & Rosania 2013 JPP – 03 Transcellular model with lysosome). For comparing the transport kinetics of molecules sensitive to mitochondrial potential, we used three different pKa values (pKa = 5: purple line; pKa = 7: green line; pKa = 9: gold line). Time course plot showed the rapid mitochondrial drug accumulation of weakly basic molecules. The molecule with a pKa = 9 was the most sensitive to Emm changes, as expected.

Figure 8

Virtual Cell can facilitate the work of pharmaceutical scientists and systems pharmacologists (Blue Boxes). With Virtual Cell, scientists are able to build and modify computational models (Orange Box), without being experts in computer programming. Virtual Cell’s modular software components (Green Boxes) and object driven menus greatly facilitate the modeling process, without requiring computer coding skills.