Design of optimized hypoxia-activated prodrugs using pharmacokinetic/pharmacodynamic modeling

Abstract

Hypoxia contributes to resistance of tumors to some cytotoxic drugs and to radiotherapy, but can in principle be exploited with hypoxia-activated prodrugs (HAP). HAP in clinical development fall into two broad groups. Class I HAP (like the benzotriazine N-oxides tirapazamine and SN30000), are activated under relatively mild hypoxia. In contrast, Class II HAP (such as the nitro compounds PR-104A or TH-302) are maximally activated only under extreme hypoxia, but their active metabolites (effectors) diffuse to cells at intermediate O2 and thus also eliminate moderately hypoxic cells. Here, we use a spatially resolved pharmacokinetic/pharmacodynamic (SR-PK/PD) model to compare these two strategies and to identify the features required in an optimal Class II HAP. The model uses a Green's function approach to calculate spatial and longitudinal gradients of O2, prodrug, and effector concentrations, and resulting killing in a digitized 3D tumor microregion to estimate activity as monotherapy and in combination with radiotherapy. An analogous model for a normal tissue with mild hypoxia and short intervessel distances (based on a cremaster muscle microvessel network) was used to estimate tumor selectivity of cell killing. This showed that Class II HAP offer advantages over Class I including higher tumor selectivity and greater freedom to vary prodrug diffusibility and rate of metabolic activation. The model suggests that the largest gains in class II HAP antitumor activity could be realized by optimizing effector stability and prodrug activation rates. We also use the model to show that diffusion of effector into blood vessels is unlikely to materially increase systemic exposure for realistic tumor burdens and effector clearances. However, we show that the tumor selectivity achievable by hypoxia-dependent prodrug activation alone is limited if dose-limiting normal tissues are even mildly hypoxic.

Keywords: PR-104; bystander effect; extravascular drug transport; hypoxia-activated prodrugs; pharmacokinetic/pharmacodynamic modeling; rational drug design; tirapazamine; tumor hypoxia.

Figure 1

Hypoxia-activated prodrug strategies. (A) Schematic representation of complementary cell killing achieved by radiation in combination with a high-$K_{{\mathrm{O}}_{\mathrm{2}}}$ HAP and a low-$K_{{\mathrm{O}}_{\mathrm{2}}}$ HAP that generates active metabolites that diffuse out of prodrug-activating zones to kill neighboring cells (bystander). (B) Examples of Class I (SN30000) and Class II (PR-104A) HAP are shown.

Figure 2

Schematic representation of a generalized HAP PK/PD model. Transfer of prodrug and effector between the extracellular and the intracellular compartment is defined by rate constant k_tN, where N refers to each compound. In the extracellular compartment compounds can diffuse as defined by their diffusion coefficients D_N (double-headed arrows). Prodrug activation (defined by k_metP) is restricted to the intracellular compartment and is O₂-dependent (see Eq. 3). For an effector that confers cytotoxicity by way of reacting irreversibly with its target (case 1, e.g., DNA-alkylating agents) the model assumes that potency a scales with reactivity of the effector (k_metE), while in case 2 (e.g., a reversible inhibitor) a is independent ofk_metE.

Figure 3

Virtual tissue microregions used for SR-PK/PD modeling. Oxygenation in the FaDu tumor microregion [990 μm × 810 μm × 150 μm; (A)] and the cremaster muscle region [1100 μm × 1000 μm × 240 μm; (B)] was modeled using the O₂ transport parameters reported in Table 1. (A,B) Show contour plots of O₂ (in mm Hg) in a mid-plane section of the microregions, superimposed with the whole microvascular network projected into one plane. The dimensions of the mapped cremaster muscle network are not cuboidal and O₂ concentrations were only computed for tissue points <50 μm away from any vessel (approximately indicated by a white line). (C–F) Show frequency histograms of distances to the nearest blood vessel (C), vessel diameters (D), blood flow rates (E), and O₂ concentrations (F). The red column in (F) represents the fraction at 0–0.13 μM O₂ (i.e., below the $K_{{\mathrm{O}}_{\mathrm{2}}}$ value for a representative Type II HAP).

Figure 4

Dependence of PK/PD in the FaDu tumor microregion on prodrug activation rate constant k_metP,max. SR-PK/PD model simulations for HAP with $K_{{\mathrm{O}}_{\mathrm{2}}}$ = 0.13 μM (A–C) and a 10-fold higher $K_{{\mathrm{O}}_{\mathrm{2}}}$ of 1.3 μM (D–F) are shown as a function of O₂ concentration using a k_metP,max of 0.001 s⁻¹ (blue), 0.01 s⁻¹ (black), 0.1 s⁻¹ (red), or 1 s⁻¹ (green). (A,D) Intracellular prodrug AUC (AUC_iP). (B,E) Survival probability after HAP exposure or 15 Gy radiation (gray) in the absence of bystander effects. (C,F) Survival probability with bystander effects. For no-bystander simulations, the rate constant for membrane transfer of the effector k_tE was set to 0 and effector potency was set to a lower value of 0.0414 μM⁻¹h⁻¹, to achieve similar average tumor cell kill as in the bystander case. All remaining parameters were as reported in Table 2.

Figure 5

Impact of the prodrug activation rate constant, k_metP,max, on overall cell killing in the tumor microregion of low-K_O2 (red) and high-K_O2 (green) HAP with and without bystander effects. Average log cell kill in the tumor microregion by HAP without radiation (A) and additional to radiation (B). The latter was calculated as the difference between overall log cell kill by prodrug + radiation and log cell kill by radiation alone. (C) Average HAP-mediated killing in a hypothetical normal tissue in which cells are assumed to have the same intrinsic sensitivity as tumor cells, based on simulations in a microvascular network of a mapped rat cremaster muscle region. (D) Tumor:normal tissue ratio of cell killing.

Figure 6

Dependence of HAP-induced cell killing additional to radiation on k_metP,max and the membrane transfer rate constant k_tP. (A) Class I HAP; (B) Class II HAP. Simulations for Class I HAP (no-bystander) were performed as described in the legend of Figure 4.

Figure 7

Modulation of effector diffusion properties for a class II HAP. SR-PK/PD model simulations using the base model (Table 2), with modulation of the following effector parameters: (A–C) the extracellular diffusion coefficient D_E, using a 10-fold higher value for the membrane transfer rate constant k_tE; (D–I) membrane transfer rate constant k_tE, with (D–F) or without (G–I) blood vessel permeability to the effector. Left panels show survival probability (as a function of O₂ in the FaDu tumor microregion) after 15 Gy radiation (gray) or HAP (black: base model; red and blue: 10-fold higher and lower parameter value, respectively). Middle panels show average monotherapy activity (black, solid lines) and killing additional to radiation (white, dashed lines) in the tumor region. Right panels show the tumor:normal tissue ratio of cell killing.

Figure 8

Modulation of effector stability for a class II HAP. SR-PK/PD model simulations using the base model (Table 2), or modulation of the rate constant for loss of effector k_metE. (A–C) Case 1 where survival probability is proportional to reactivity (k_metE); (D–F) Case 2 where survival probability is independent of k_metE. See legend of Figure 7 for description of graphs.

Figure 9

Impact of different parameter modulations on effector washout. Graphs show the net transport of effector across the vessel walls in the FaDu tumor microregion, normalized to the volume of the region, as estimated by the SR-PK/PD model with modulation of (A) k_metP,max, (B) k_metE, (C) k_tE, and (D) D_E, with unmodulated parameters held at their default values from Table 2, except in (D) where 10-fold higher values for k_tE was used.

Figure 10

Pharmacokinetics of PR-104H and its reduction product PR-104M in NIH-III nude mice. Concentrations of PR-104H (filled symbols) and PR-104M (open symbols) in plasma (A) and liver (B) following i.v. administration of 10 μmol/kg PR-104H, with linear regression lines. At each time point different symbols represent data from individual mice.

Figure 11

Simulation of PR-104M, the second active metabolite of PR-104A, in the tumor microregion. PR-104M AUC was calculated in the FaDu tumor microregion with oxygenation as shown in Figures 3A,F, using our previously published PR-104 SR-PK/PD model (35) at a PR-104 dose of 562 μmol/kg with inflow AUC of PR-104H and PR-104M set to 0 to distinguish the impact of reduced metabolites formed in the tumor. (A) Simulation for an HCT116/WT tumor. (B) Simulation for a HCT116/sPOR#6 tumor (20× higher prodrug activation rate constant). The AUC (in micromoles hour) is shown in color scale in the whole FaDu microvascular network projected into one plane, and in a mid-plane section of the microregion (as a contour plot). White arrows indicate vessels with high concentrations of active metabolite.