Effect of Small-Molecule Modification on Single-Cell Pharmacokinetics of PARP Inhibitors

This article is featured in Highlights of This Issue, p. 765

Heterogeneous drug distribution is a well-known phenomenon in the delivery of therapeutics to tumors (1–6), and the manipulation of delivery has a direct impact on clinical treatment of tumors (7). Variable delivery also has a pivotal but often less appreciated role in the development of targeted imaging agents (8–11). Despite the importance and impact of this heterogeneity on therapeutic outcome and imaging agent design, the study of the underlying causes is complicated by the complex and variable tumor microenvironment (4). At the whole tumor level, heterogeneous vascularization and blood flow (12), gradients in oxygen (13), nutrients (14), and waste products (15), multiple cell types (16), genetic (17), and epigenetic (18) variability in protein expression (19) all contribute to complex patterns in distribution. At the cellular level, heterogeneity can be due to differences in MDR expression levels among different clones (20), mosaic tumors (17), different cell states (18), nutrient supply (21), and acquired drug resistances, among others. Ultimately, the final distribution is determined by both these tumor characteristics and the drug-specific properties, such as molecular weight, charge, lipophilicity, target, and nontarget binding.

The study of small-molecule distribution has been complicated by a lack of high spatial and temporal resolution methods for tracking molecules in tumors. The two most common ex vivo methods are autoradiography of tritiated or other radiolabeled compounds and organ-based detection using liquid chromatography/mass spectrometry (LC/MS). Typically, these experiments provide data over several hours with tissue level distribution (6, 22–25) and an upper limit of sampling rate of minutes with cellular resolution. The relatively fast distribution of some drugs has required that in vitro methods, such as multilayered cells or tumor spheroids (26–30), be developed to measure transport parameters. In vivo methods lack the high spatial and temporal resolution necessary for many of these drugs. Mathematical models have also played a large role due to their ability to easily decouple the drug- and tumor-specific effects and aid in experimental design (31–35). However, for small-molecule drugs, the tissue, cellular, and subcellular experimental data for mathematical model validation is often lacking, providing a significant obstacle to the use of these models.

Given the challenges associated with studying small-molecule distribution in tumors, in concert with the recent technologic advances in intravital and preclinical tumor biology research (36–38), we have been developing new imaging techniques to follow drugs at higher spatial and temporal resolution in the tumor microenvironment. For example, we have derived therapeutic drug precursors with BODIPY FL to develop companion imaging drugs (39–41). This has led to new insight into the pharmacokinetics of some drugs at the single cell level in vivo. However, the attachment of the different fluorochromes also offers the unique opportunity to study variable pharmacokinetics given differences in the physiochemical and fluorescent properties (Fig. 1). In particular, using a relatively small footprint BODIPY FL on one molecule and a larger BODIPY 650 fluorophore on another, the two drugs can be used to study molecular effects in the same tissue without complicating local environment factors.

In this article, we use two different PARP inhibitor companion imaging drugs to investigate the specific effects of molecular weight and lipophilicity on target versus nontarget localization and tumor vessel permeability. The physiochemical properties have a significant effect on cellular uptake and wash-out kinetics, tumor vessel permeability, and target versus off-target ratio. A mathematical model is developed using a finite element mesh to predict the distribution in the tissue with in vivo imaging data used to validate the results.

Unless otherwise noted, all reagents were purchased from Sigma-Aldrich and used without further purification. BODIPY FL and BODIPY 650/665 succinimidyl ester were purchased from Invitrogen. Olaparib (AZD2281) was purchased from Selleck Chemicals. 4-[[4-Fluoro-3-(piperazine-1-carbonyl)phenyl]methyl]-2H-phthalazin-1-one and olaparib-BODIPY FL were synthesized as described elsewhere (40–42). High-performance liquid chromatography-electrospray—mass spectrometry (HPLC-ESI-MS) analyses and HPLC purifications were performed on a Waters LC-MS system. For liquid chromatography-electrospray—mass spectrometry (LC-ESI-MS) analyses, a Waters XTerra C18 5 μm column was used. For preparative runs, an Atlantis Prep T3 OBDTM 5 μm column was used. High-resolution ESI mass spectra were obtained on a Bruker Daltonics APEXIV 4.7 Tesla Fourier Transform mass spectrometer (FT-ICR-MS) in the Department of Chemistry Instrumentation Facility at the Massachusetts Institute of Technology (Boston, MA). Proton nuclear magnetic resonance (¹H NMR) spectra were recorded on a Varian AS-400 (400 MHz) spectrometer. Chemical shifts for protons are reported in parts per million (ppm) and are referenced against the dimethyl sulfoxide lock signal (¹H, 2.50 ppm). Data are reported as follows: chemical shift, multiplicity (s = singlet, d = doublet, t = triplet, m = multiplet), coupling constants (Hz), and integration.

Triethylamine (11 μL, 78 μmol) was added to a solution of BODIPY 650/665 succinimidyl ester (5.0 mg, 7.8 μmol) and 4-[[4-fluoro-3-(piperazine-1-carbonyl)phenyl]methyl]-2H-phthalazin-1-one (5.7 mg, 15.6 μmol) in dimethyl sulfoxide (500 μL). The reaction mixture was stirred for 2 hours at room temperature and purified via HPLC to yield the title compound as a blue solid (5.5 mg, 6.1 μmol, 78%). ¹H NMR (400 MHz, DMSO-d₆) δ = 12.59 (s, 1H), 11.45 (s, 1H), 8.30–8.25 (m, 1H), 8.11 (t, ³J_HH = 5.2, 1H), 7.95 (d, ³J_HH = 7.7, 1H), 7.88 (t, ³J_HH = 7.3, 1H), 7.82 (t, ³J_HH = 7.5, 1H), 7.58–7.04 (m, 16H), 6.37 (m, 1H), 4.52 (s, 2H), 4.32 (s, 2H), 3.62–3.12 (m, 10H), 2.34–2.23 (m, 2H), 1.51–1.43 (m, 4H), 1.29–1.22 (m, 2H); ¹⁹F NMR (376 MHz, DMSO-d₆) δ = −120.2 (s, 1F), −142.3 (q, J_BF = 34 Hz, 2F); LC-ESI-MS(+) m/z (%) = 875.5 [M-F]⁺ (100), 894.5 [M+H]⁺ (35), 917.5 [M+Na]⁺ (15); LC-ESI-MS(−) m/z (%) = 893.4 [M-H]⁻ (100); HRMS-ESI [M+H]⁺ m/z calculated for [C₄₉H₄₇BF₃N₈O₅]⁺ 895.3709, found 895.3732 [M+H]⁺.

Plasma protein binding was measured using rapid equilibrium dialysis plates from Pierce according to the manufacturer's instructions. Briefly, each probe was diluted to a 10 μmol/L concentration in 300 μL of mouse serum and allowed to equilibrate at 37°C on a shaker for 4 hours with 100 μL of PBS. After equilibration, samples from each compartment were mixed with additional plasma or PBS so the final buffer was 50% PBS and 50% plasma (to minimize protein binding effects on fluorescence). The fluorescence was measured using a Tecan Safire plate reader.

PARP enzymatic activity was measured following the manufacturer's instructions for the universal PARP colorimetric assay kit from Trevigen. Briefly, increasing concentrations of olaparib, olaparib-BODIPY FL, or olaparib-BODIPY 650 (0–4 μmol/L) were added to histone-coated strip wells in a 96-well plate. Inhibitors were then preincubated for 10 minutes at room temperature with 0.5 U/well recombinant human PARP. Wells were then incubated for 1 hour with PARP cocktail and then washed twice with PBS containing 0.1% Triton X-100 and twice with PBS. Streptavidin-HRP was then added to each well and incubated for 1 hour. Wells were again washed twice with PBS-0.1% Triton X-100 and twice with PBS. The colorimetric reaction was developed upon addition of TACS-Sapphire for 15 minutes, followed by reaction termination with 0.2 mol/L hydrochloric acid (HCl). Absorbance was measured on a TECAN Sapphire2 plate reader and enzyme inhibition curves were fit using nonlinear regression dose-response inhibition equations from GraphPad (Prism).

For cell and xenograft experiments, HT-1080 cells were purchased from American Type Culture Collection in February of 2006. Cells were resuscitated in February of 2012 for experiments; no authentication was done by the authors. The cells were grown in Dulbecco's modified Eagle medium supplemented with nonessential amino acids, 10% FBS, and 1% penicillin-streptomycin. These cells contain large nuclei and highly vascularized xenografts ideal for measuring subcellular distribution in vivo. Live cell imaging was done using an inverted Deltavision deconvolution microscope with a 40× objective (Applied Precision Instruments) and equipped with a 37°C heated stage and 5% CO₂ live cell imaging setup. Media and solutions with probes were prewarmed to 37°C before addition through an access window. The appropriate dichroic mirrors and filters were used for imaging BODIPY FL and BODIPY 650 fluorescence.

Xenografts were imaged as previously described (40), and all animal experiments were carried out in accordance with guidelines from the Institutional Subcommittee on Research Animal Care. Briefly, dorsal skin window chambers were surgically implanted in 6- to 8-week-old nude mice. Approximately 3 to 4 million cells were suspended in a 50% Matrigel and 50% PBS solution and injected under the fascia and allowed to grow for 1 to 2 weeks. When tumors were vascularized and reached 1 to 2 mm in size, mice were anesthetized using 1% to 2% isoflurane in 2 L/min oxygen and a tail vein catheter was inserted. The mouse was moved to a heated microscope stage where the vital signs were continuously monitored. Angiosense-750 (Perkin Elmer) or 250 μg of 500-kDa amino-dextran labeled with Pacific Blue NHS ester (Life Technologies) was injected via tail vein and used to visualize the vasculature. Once the region of interest was selected, a time-lapse imaging sequence was initiated, followed by tail vein injection of the probe. Seventy-five nanomoles of probe was formulated in 30 μL of 1:1 dimethylacetamide:solutol solution and 112.5 μL of PBS and sonicated.

Permeability measurements were taken using a single vessel method (43). Briefly, a time-lapse imaging sequence (sequential scans every 10 seconds) was started before injection. After intravenous delivery of 75 nmol of both probes, regions of interest inside the vessel and outside the vessel were drawn to measure the plasma concentration and extravascular concentration over time. Taking into account the plasma fraction and protein binding (since the permeability is measured relative to the free drug concentration in the plasma), the permeability was calculated for each region. These measurements were repeated at several locations within a field of view for a minimum of 3 mice.

Details of the mathematical model can be found in the supporting material, but briefly, the plasma concentration was set to a biexponential decay as measured in vivo. Because of high plasma protein binding, this concentration was held constant throughout the length of the vessels in agreement with theoretical (3) and experimental results (40). The product of the permeability and free drug concentration gradient across the vessel wall was set equal to the diffusive flux in the tissue for the boundary conditions. In the tissue, the rapid immobilization by nonspecific protein binding and cellular uptake was assumed to be linear, so the effective diffusion coefficient was adjusted by the bound to free ratio (44). Free drug entered the nucleus and bound the target at a rate equal to that measured in cell culture. The wash-out kinetics were set to those in cell culture. These rates are a combination of transport to the target protein and binding/dissociation, so they are not necessarily equal to the intrinsic association/dissociation kinetics of the drug.

Structure function studies during drug development show tolerance for a large number of substitutions at the cyclopropyl ring in olaparib (42). The charge neutral BODIPY dyes were used to ensure membrane permeability required to access the nuclear target protein. The structure and properties of the drugs are listed in Fig. 1 and Table 1. Enzyme inhibition assays of olaparib-BODIPY FL and olaparib-BODIPY 650 showed nmol/L IC₅₀ values and expected decreasing affinities as cyclopropane substitutions increase in bulk size (40).

After validating target binding of the two agents, the ability of the drugs to localize to the nucleus in vitro was investigated. HT-1080 cells were incubated with 1 μmol/L of each drug in real time using an inverted microscope and glass coverslip bottom dishes. Using an epifluorescence microscope, images were acquired every second to capture the rapid uptake (half-life 71 seconds for olaparib-BODIPY FL) and wash-out of the small-molecule companion imaging drug. After the drug accumulated within cells, they were washed twice and incubated with fresh media (without drug). PARP1 is located in the nucleus with a higher concentration in the nucleolus, enabling rapid identification of target bound drug by drawing subcellular regions of interest. Figure 1C shows the cells immediately after the drug was removed (no wash). Both drugs accumulated significantly in the perinuclear region, most likely the endoplasmic reticulum. Within five minutes of washing, the nonspecific staining of the endoplasmic reticulum with the BODIPY FL drug disappeared, while the target specific nuclear staining remained. However, the larger BODIPY 650 version required over 2 hours of washing to reduce the endoplasmic reticulum staining, although the target-specific labeling remained. The uptake and wash-out kinetics for the cells were measured and fit to uptake and clearance curves (Supplementary Materials and Methods).

On the basis of the target affinity and assuming passive transport across the plasma membrane, a simple model of nuclear versus endoplasmic reticulum uptake was developed to capture the relative cellular uptake. Specific nuclear uptake was saturable based on the affinity and estimated nuclear concentration of PARP of 3 μmol/L (Supplementary Table S1). Using the relative concentration of the nucleus and free drug concentration, a linear (nonsaturable) uptake in the endoplasmic reticulum was assumed, which is consistent with equilibrium models of small molecules partitioning into lipid membranes (45, 46). From these estimates, low concentrations of the BODIPY FL drug would specifically stain the nucleus, while the BODIPY 650 version would not obtain a higher concentration in the nucleus at equilibrium based on the higher uptake in the endoplasmic reticulum relative to the lower affinity and specific binding. Because the BODIPY FL version starts to wash out in seconds, cells were imaged in the presence of drug in the media (no washing). As the endoplasmic reticulum concentration is higher than free drug in solution, it is still possible to obtain a cellular image using wide-field microscopy under these conditions (Fig. 2). As predicted by the cell kinetic study, the 10 and 100 nmol/L concentrations gave a higher nuclear signal for the BODIPY FL drug, but the 1 μmol/L concentration resulted in a higher endoplasmic reticulum signal. The higher lipophilicity and ER uptake and the lower affinity of the BODIPY 650 labeled drug resulted in higher ER signal at all concentrations, even though nuclear-specific staining could be obtained by washing the cells. Note that the overall intensity of the images varied dramatically, so the exposure times are different, but the relative intensity behaved as expected.

Recent advances in intravital microscopy techniques allow us to measure subcellular drug concentrations at many frames per minute. This improvement in time resolution prompted us to measure the distribution of the BODIPY FL and BODIPY 650 conjugated olaparib after intravenous injection. Vascular permeability is one of the most important parameters determining the relationship between tumor physiology and drug uptake, and this value can vary by over 5 orders of magnitude between large nanoparticles and small molecules such as oxygen (3). Using intravital microscopy in dorsal window chambers of HT-1080 xenografts, the permeability was measured simultaneously for both drugs in tumor blood vessels. In all cases, the permeability of the BODIPY FL drug was higher than the BODIPY 650 drug despite similar plasma protein binding for both (Fig. 3A). Plotting this data alongside a compilation of permeability for proteins and nanoparticles (32), the olaparib-BODIPY 650 permeability (0.46 ± 0.27 μm/s) follows the same trend as these hydrophilic molecules that primarily extravasate along a paracellular path (Fig. 3B). However, the BODIPY FL version has a much higher permeability (4.7 ± 2.5 μm/s) than would be expected for this trend. The molecular weight of these drugs only differs by 255 g/mol and plasma protein binding is not statistically significantly different, but the permeability difference is significant (P = 0.001). Given the rapid cellular uptake and wash-out kinetics of the BODIPY FL drug, we hypothesize that the transcellular route for extravasation is significant for a molecule of this size. For reference, oxygen is not shown on the graph but has been estimated at 5 × 10⁻² cm/s with a radius of approximately 0.3 nm. Plasma clearance was qualitatively similar between the two agents, although the peak concentration was higher for the larger drug. The dose for both drugs was 75 nmol, so it is likely that the rapid cellular uptake of BODIPY FL drug (1.2 minutes half-life in vitro) lowered the concentration before the initial 1 minute time point (Table 1).

Given the challenges of measuring drug distribution within tumors, mathematical models play an important role in predicting the impact of variability in drug properties and the tumor microenvironment (32, 47, 48). To take advantage of the insight provided by this modeling, we used a finite element model of drug distribution to compare uptake of both drugs. For comparison with experimental results, a vascular probe was injected to define the vessels within the microscopic field of view (Supplementary Fig. S1), and a Delaunay triangulation algorithm was used to create a mesh in the extravascular space. Because of the high plasma protein binding of these drugs, the blood flow rate through each vessel has a negligible impact (3), so the plasma concentration was set equal to the systemic concentration. The experimentally measured permeability, nonspecific uptake ratio, and target binding were used in the simulations to predict the distribution at various times after injection. The lower nonspecific uptake and faster washout of the olaparib-BODIPY FL is predicted to give nuclear-specific labeling as seen in the in vivo microscope image after intravenous injection of the companion imaging drug (Supplementary Fig. S1). The higher nonspecific uptake and slower cellular wash-out of the olaparib-BODIPY 650 is predicted to result in higher nonspecific uptake at 218 minutes than nuclear bound drug (Supplementary Fig. S1), which was validated with the intravital image (Fig. 4). The experimental results validate the model predictions, where the nuclear target bound drug is less than the nonspecific cellular uptake, even though wash-out in vitro was shown to result in nuclear-specific labeling (Fig. 1).

The finite element simulation was able to capture the differences in subcellular uptake seen with the in vivo experiments at long time points after the diffusion gradients had dissipated. To further validate the model, the simulation results were compared at earlier times after injection (Fig. 5). Minutes after injection, the drug diffuses away from the vessels, and the olaparib-BODIPY FL shows approximately equal nonspecific and nuclear targeting at 8 minutes in both the simulation (top) and in vivo microscope image (bottom). By 25 minutes, the nonspecific uptake has cleared enough to identify individual nuclei in the image. In contrast, the higher nonspecific uptake of the olaparaib-BODIPY 650 results in poorer distribution and much higher nonspecific uptake early after injection. Because of the higher plasma signal (Table 1), the confocal microscope settings must be reduced to not saturate the blood vessel signal, resulting in less apparent signal in the tissue. However, the drug does not penetrate as far as the olaparib-BODIPY FL in the experimental image (bottom). By 25 minutes, the olaparib-BODIPY 650 simulation shows increased penetration but still a higher nonspecific signal than target signal (top). By this time, the blood signal has diminished enough to distinguish the high perinuclear signal for olaparib-BODIPY 650.

Heterogeneous delivery of imaging probes and therapeutics to tumors is a complex problem that limits the design, development, and efficacy of these agents. While significant progress has been made in understanding the distribution of macromolecules and nanoparticles (4, 32, 49, 50), the techniques for studying small-molecule distribution lack the subcellular spatial resolution and high sampling rate for directly observing the pertinent rates in vivo. In this work, we take advantage of the development of fluorescent drug conjugates that retain their cellular specificity and enzyme inhibition (Fig. 1) while allowing the simultaneous imaging of multiple drugs with different physiochemical properties in vivo. The different fluorophores enable the imaging of multiple probes in the same tumor microenvironment, isolating the effect of drug properties from highly variable tumor physiology. This technique has allowed us to measure the kinetics of two small-molecule drugs that bind their target with unprecedented temporal and spatial resolution.

As one specific example, this methodology allows the direct imaging of small-molecule drug permeability across the tumor vasculature. Historically, this property was measured in isolated perfused tissues to determine the physiologic permeability surface area product. However, without a simultaneous estimate of surface area, which can vary over an order of magnitude in tumors, the results cannot be used for tumor predictions where the permeability of tumor blood vessels is often higher than in healthy tissue (43). Fluorescence imaging can overcome this limitation by direct visualization of extravasation in the relevant tumor microenvironment, and previous results shed light on important trends, such as the increase in permeability with decreasing size (51, 52). Taking advantage of the fast sampling rate afforded by intravital fluorescence microscopy, we were able to measure significant differences in tumor vessel permeability given small changes in the structure of companion imaging drugs. These values are critical for predictive modeling of therapeutics and imaging agent design, but there is a paucity of data in the literature for in vivo small-molecule drug permeability. While it is generally accepted that macromolecules have limited uptake due to low permeability and oxygen and some small-molecule drugs readily cross the endothelium, the transition between these two regimes (permeability limited versus diffusion or blood flow limited uptake) is not well defined. Our data here indicate that the transition between the two regimes occurs for lipophilic small-molecule drugs between 500 and 1,000 Da, which has important implications for combination therapies with angiogenesis inhibitors that normalize the tumor vasculature (7). Our results here are consistent with the hypothesis that drugs with slow cellular uptake and washout have lower vascular permeability. The permeability of olaparib–BODIPY 650 matches the predicted value based on a two-pore model that only accounts for paracellular extravasation of macromolecules, while olaparib-BODIPY FL has a higher permeability and much faster cellular uptake and washout. In addition, previous observations for olaparib-BODIPY FL (40) show that the vascular permeability of this molecule is the same in tumor vessels and mouse ear vessels. The paracellular extravasation of macromolecules is increased in tumors due to the action of VEGF and inflammatory molecules that increase permeability, and the lack of difference between these locations indicates that paracellular transport is not significant for olaparib-BODIPY FL.

The olaparib scaffold is an ideal inhibitor for these studies given the high target expression of PARP (typically 10⁶ proteins per cell; ref. 53) and distinct subcellular distribution pattern. Target expression is localized to the nucleus while nonspecific uptake occurred in the perinuclear region including the endoplasmic reticulum (Fig. 2). It is therefore easy to identify nonspecific versus target-specific uptake. This pattern of nonspecific uptake is not surprising for a lipophilic neutral molecule, which accumulates in the membrane, but the method allowed us to measure the in vivo kinetics of uptake into the different subcellular compartments. The ER distribution is in contrast to weak bases that are trapped in lysosomes upon protonation and positively charged small molecules that accumulate in the mitochondria (45). Given the lipophilic nature of these drugs, it was assumed that the nonspecific uptake was nonsaturable and linear with concentration (Fig. 2), and the resulting prediction of uptake agreed with the cellular results. The observed subcellular distribution is important for cellular transport and metabolism, with p450 enzymes and transporters, such as p-glycoprotein, located within certain cellular compartments. The complex interplay with charge, pKa, molecular weight, and tissue physiology (e.g., anti-VEGF therapy) will be explored in future work.

Understanding the impact of physiochemical properties on tumoral distribution is important for both drug and imaging agent development. Empirical methods, such as Lipinski's rule of 5 (54) or limits on physiochemical properties (e.g., using neural networks ref. 55) can provide guidance, but outliers and counter examples exist (56). For example, canertinib, an irreversible EGFR tyrosine kinase inhibitor (TKI), obeys all the “rule of 5” criteria but failed in clinical trials (57). The next generation variant, dacomitinib, violates one of the rules but has shown better phase II results (58, 59). A more precise method for predicting pharmacokinetic and pharmacodynamic requirements is needed.

An understanding of the transient changes in concentration after dosing is even more important for the development of imaging agents. While many therapeutics benefit from continuous dosing, allowing a steady state or pseudo–steady state to develop, imaging agents are typically delivered as a single bolus dose. In several studies of radiolabeled EGFR TKIs, ¹⁸F-gefitinib provided insight into the distribution of this clinically approved drug (9). However, it failed to localize based on EGFR target expression. A more hydrophilic radiolabeled EGFR TKI (60) did distribute differentially to higher expressing tumors. Interestingly, the predicted logP of these compounds (using the same software in all cases) is 5.6 for gefitinib and 4.4 for the radiolabeled PEGylated EGFR TKI. These are similar to the 6.0 value for olaparib-BODIPY 650 and 4.0 for olaparib-BODIPY FL reported here, which are also both able to hit their target but distribute differently. Although these results cannot be extrapolated to all agents, it may provide an “upper limit” around a logP of ∼5 for target specific retention. The lower limit is not explored in this work, although successful hypoxia imaging agents have logP values around 0 to 1 (61) while negative logP values, such as Oregon Green tetrazine (39) cannot penetrate cells to reach their target. Clearly, the molecular weight and hydrophilicity must be low enough to allow access to intracellular targets. It is also important to note in these examples that while some goals of therapeutic and imaging agent development are aligned (e.g., high affinity and specificity), others are at odds (rapid systemic clearance of imaging agents to reduce background versus sustained systemic levels of therapeutics to reduce dosing).

A deeper understanding of drug distribution for both small-molecule agents and biologics is required as the lines between these two discrete fields become blurred. For example, Navitoclax, a “small-molecule” inhibitor of Bcl-2 family proteins is almost 975 Da in size, a molecular weight likely required for its disruption of protein–protein interactions. Smaller biologics include imetelstat (MW = 4610), a telomerase inhibitor, and stapled peptides (∼2 kDa) such as BH3 domains (62), among many others. These new agents may present complex pharmacokinetic behavior that do not follow small molecule or biologic drug development patterns. A better mechanistic understanding of distribution, including the influence of blood flow, permeability, diffusion, cellular uptake, and target binding (3) will enable more rapid development of these types of drugs. Unfortunately, simple extrapolation of some experiments, such as the permeability of molecules less than 1 nm in Fig. 3B, can provide misleading results since charge and protein binding can have a large effect on the paracellular versus transcellular routes of extravasation. Future work is required to make better predictions of drug uptake based on molecular properties.

Mathematical modeling will continue to play an increasing role in predicting the distribution of novel drug and imaging agents. With multiple simultaneous rates occurring during experiments, including plasma clearance, extravasation, diffusion, target binding, and metabolism, it becomes difficult to experimentally isolate the effect of any one parameter; however, this can easily be done with a validated model. This joint theoretical and experimental approach helped elucidate the effect of dose on antibody uptake (8), and the required timing after injection of hypoxic imaging agents (63). Even the clinically widespread fluorodeoxyglucose (FDG) agent shows blood flow–dependent uptake at early times followed by glucose metabolism dependent localization at later times (64), an effect captured by mathematical models (3). The development of agents based on iterative synthesis and animal experiments is labor and cost intensive. Mathematical models provide a rapid and cost-effective way of focusing synthesis on desirable molecular properties to obtain sufficient uptake and distribution for therapeutics or efficient target binding and clearance for imaging agents. They can also be combined with pharmacodynamic models for prediction of therapeutic outcome. The mechanistic framework can be scaled to humans by changing the plasma clearance rates and concentration, thus providing insight into the distribution in the clinic, which is currently unobtainable by other methods. Finally, mathematical modeling and simulations also help in interpretation of experimental and clinical results.

In conclusion, a combination of novel fluorescent drug conjugates and in vivo imaging experiments have provided insight into the cellular and tumoral heterogeneity of small-molecule drugs. The lipophilic PARP inhibitors studied here show a sharp transition in both cellular uptake and permeability between a 640-Da probe with a clogP of 4 and a 895-Da probe with clogP of 6. These measurements can be used to develop predictive mathematical simulations that help in understanding drug distribution in vivo at the preclinical and clinical stage, in designing better imaging agents and therapeutics, and in interpreting experimental results.

No potential conflicts of interest were disclosed.

Conception and design: G. Thurber, T. Reiner, R. Weissleder

Development of methodology: G. Thurber, T. Reiner, R. Kohler

Acquisition of data (provided animals, acquired and managed patients, provided facilities, etc.): G. Thurber, T. Reiner, K. Yang, R. Kohler

Analysis and interpretation of data (e.g., statistical analysis, biostatistics, computational analysis): G. Thurber, T. Reiner, K. Yang, R. Weissleder

Writing, review, and/or revision of the manuscript: G. Thurber, T. Reiner, K. Yang, R. Kohler, R. Weissleder

Administrative, technical, or material support (i.e., reporting or organizing data, constructing databases): G. Thurber

Study supervision: R. Weissleder

This work was supported in part by NIH Grants P50 CA086355, R01 EB010011, and K01 DK093766.

This work was supported by NIH Grants P50 CA086355 (to R. Weissleder), R01 EB010011 (to R. Weissleder), and K01 DK093766 (to G.M. Thurber).

The costs of publication of this article were defrayed in part by the payment of page charges. This article must therefore be hereby marked advertisement in accordance with 18 U.S.C. Section 1734 solely to indicate this fact.