Tuning payload delivery in tumour cylindroidsusing gold nanoparticlesByoungjin Kim1, Gang Han2, Bhushan J. Toley1, Chae-kyu Kim2, Vincent M. Rotello2 and Neil S. Forbes1*

Nanoparticles have great potential as controllable drug delivery vehicles because of their size and modular functionality.Timing and location are important parameters when optimizing nanoparticles for delivery of chemotherapeutics. Here, weshow that gold nanoparticles carrying either fluorescein or doxorubicin molecules move and localize differently in anin vitro three-dimensional model of tumour tissue, depending on whether the nanoparticles are positively or negativelycharged. Fluorescence microscopy and mathematical modelling show that uptake, not diffusion, is the dominantmechanism in particle delivery. Our results indicate that positive particles may be more effective for drug delivery becausethey are taken up to a greater extent by proliferating cells. Negative particles, which diffuse more quickly, may performbetter when delivering drugs deep into tissues. An understanding of how surface charge can control tissue penetration anddrug release may overcome some of the current limitations in drug delivery.

Inefficient delivery limits the efficacy of many chemotherapeutictreatments1–5. Overcoming delivery limitations requires precisecontrol of interstitial diffusion and cellular uptake. Tumours typi-

cally have irregularly formed vasculature, with large intervessel dis-tances and heterogeneous populations of cells6. These populationsare often unresponsive to standard therapy because of their distancefrom blood vessels and resistance to molecular uptake3,7. Thislimited efficacy prevents complete cell clearance per drug cycle,which can eventually lead to tumour regrowth, metastatic diseaseand poor treatment outcomes1–3,8,9.

Colloidal gold nanoparticles have great potential to overcomedelivery limitations because of their biocompatibility, low toxicity,small size and tunable surface functionalities10,11. Functionalitycan be tuned by modifying the composition of functional moleculesin the mixed monolayer on the surface of gold nanoparticles12–14. Incancer cell cultures, surface properties have been shown to regulatecellular uptake, intracellular release and distribution in subcellularcompartments15–18. Modification of the surface properties of goldnanoparticles therefore has the potential to control accumulationin tumours, and the locations at which drug payloads are released.

Three-dimensional in vitro tumour models provide an importanttool for the optimization of efficient intratumoural drug delivery.Multicellular tumour cylindroids provide a unique platform withwhich to systematically monitor extracellular diffusion, cellularuptake and molecular release from nanoparticles in real time(Fig. 1a). Tumour cylindroids are spheroids constrained betweentwo parallel surfaces19,20. The geometry of cylindroids allows onlyradial diffusion from the peripheral edge to the centre, simplifyinganalysis. Through the optically accessible cross-section, local concen-trations of nanoparticles and dyes can be measured with standardfluorescence microscopy. Importantly, cylindroids consist of hetero-geneous cell populations arranged relative to their distance from theperipheral edge: cells in the periphery are predominantly proliferat-ing, and cells in the centre are mostly apoptotic and necrotic19–24.This radial organization mimics the distribution of cells aroundblood vessels in tumours in vivo (Fig. 1b)24,25.

We predict that different surface charges can control the pen-etration of nanoparticles and the location of cellular uptake and

release. Thioalkylated fluorescein-labelled gold nanoparticles(2 nm core diameter, 6 nm overall with ligand) with positive andnegative surface charges were synthesized (Fig. 1c) and administeredto cylindroids. Fluorophore concentrations were measured as func-tions of time and radial position. The diffusion of gold nanoparticlesin an extracellular matrix (Matrigel) was measured in a linear cell-free chamber. A mathematical model was developed to discriminatebetween fluorescence from particles and released fluorescein, and tocalculate the rates of cellular uptake/release (Fig. 1d) as a function ofposition in the cylindroids. The determined parameters were used topredict the dynamics of particle transport and release from bloodvessels in a conceptualized tumour (Fig. 1b). Positive and negativegold nanoparticles conjugated with doxorubicin (DOX) were simi-larly synthesized, and our results show that surface charge can beused to control tissue penetration and drug release.

Uptake of fluorescent gold nanoparticlesNanoparticles were synthesized with gold cores protected bymixed monolayers14,26 to provide tunable probes for delivery. Themonolayers on these particles consisted of thioalkylated fluoresceinisothiocyanate (FITC–SH) and either thioalkyl tetra(ethylene gly-col)lyated trimethyl ammonium or thioalkyl tetra(ethylene glycol)-lyated carboxylic acid to create cationic (p-FITC–AuNP) andanionic (n-FITC–AuNP) gold nanoparticles (Fig. 1c), respectively27.The surface zeta potentials of p-FITC–AuNP and n-FITC–AuNPwere measured to be þ30 and 236 mV, respectively.

The fluorescence intensities of p-FITC–AuNP, n-FITC–AuNPand free fluorophore (FITC–SH) were used to calibrate the fluor-escence intensity and determine the FITC-SH loading ratio oneach gold core. Fluorescence intensities were linearly proportionalto concentration (Fig. 2a). Conjugation to gold cores quenchesFITC–SH fluorescence. Treatment with potassium cyanide torecover quenched fluorescence increased the intensities of thep-FITC–AuNP and n-FITC–AuNP solutions by factors of 4 and2.4, respectively (Fig. 2a). The ratio of released ligand to freeligand fluorescence indicates that the loading ratios were 7.5 and8.3 for p-FITC–AuNP and n-FITC–AuNP, respectively.The linear relationship between intensity and concentration

1Department of Chemical Engineering, University of Massachusetts, Amherst, Massachusetts 01003-9303, USA, 2Department of Chemistry, University ofMassachusetts, Amherst, Massachusetts 01003-9303, USA. *e-mail: forbes@ecs.umass.edu

ARTICLESPUBLISHED ONLINE: 11 APRIL 2010 | DOI: 10.1038/NNANO.2010.58

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Figure 1 | Schematic showing the delivery of payload by gold nanoparticles. a, Delivery of payload (green ovals) into tumour cylindroids by gold nanoparticles

(gold circles). Cells containing released FITC–SH are in green. Viable cells are shown with smooth, solid boundaries, and necrotic cells have irregular, dashed

boundaries. Dashed arrows indicate diffusion and cellular uptake. In cylindroids, nanoparticles are present in the medium outside the boundary of the cell mass.

b, Intratumoral delivery by gold nanoparticles following extravasation from the vessel lumen (red circles). c, Mixed monolayer-protected gold nanoparticles

loaded with thioalkylated FITC or doxorubicin (DOX). d, Cellular uptake and FITC–SH release by thiol-mediated replacement reactions.

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concentration. Dotted lines represent linear least-squares fitting results. For all components, fluorescence intensity was linearly proportional to concentration.

b,c, Differential interference contrast (DIC) and confocal green fluorescent images of cells in monolayer culture incubated with cationic (b) and anionic

(c) gold nanoparticles. Scale bars, 50 mm.

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indicates that self-quenching did not have a large effect over thisconcentration range.

In monolayer cell culture, all FITC–SH release from nanoparticlecores was intracellular (Fig. 2b,c). Intracellular release of FITC–SH ismediated by cytoplasmic thiol compounds, of which reduced gluta-thione (GSH) is the most abundant28. Similar selectivity would beobserved in vivo, because the intracellular concentration of glutathione(�1–10 mM) is considerably higher than that in plasma (�2 mM)29,30.After removal of media containing FITC–AuNP, stronger green fluor-escence was observed across the cells treated with p-FITC–AuNP(Fig. 2b) compared with n-FITC–AuNP (Fig. 2c). This observationindicates that cellular uptake and dissociation were greater for cationicgold nanoparticles, potentially mediated by interactions of the particleswith serum proteins.

Cellular uptake and release in cylindroids was dependent on par-ticle surface charge and radial position (Fig. 3). Intra- and extracellularfluorescence was measured in cylindroids in real time using fluor-escence microscopy (Fig. 3a,c,e). A clear morphological boundarycould be observed between the inner and outer regions of the cylin-droids (Fig. 3a,c,e), which have been shown to contain viable andapoptotic microenvironments, respectively19,20,24. In the outerregion, cationic particles produced more fluorescence than free

FITC and anionic particles (Fig. 3a–f). For positive particles, the flu-orescence intensity in the outer region increased with time, and even-tually the entire cylindroid became fluorescent (Fig. 3a,b). For negativeparticles, the fluorescence intensity in the outer region did not increase(Fig. 3c) and remained unchanged after 11 h (Fig. 3d). This preferen-tial uptake of cationic gold nanoparticles by proliferating cells wassimilar to the difference observed in the monolayer cultures(Fig. 2b,c). In the inner region, fluorescence appeared at earlier timepoints than in the outer region and appeared regardless of surfacecharge (Fig. 3a–d). Images acquired at 4 and 8 h (seeSupplementary Information) were spatially similar but fainter thanthose at 11 h. In cylindroids incubated with free FITC, strong fluor-escence appeared only in the inner region (Fig. 3e), and the intensityprofiles remained unchanged for 11 h after treatment (Fig. 3f). Theenhanced cellular uptake of positive particles by proliferating cellsmay be caused by electrostatic interaction with the net negativesurface charge of the plasma membrane31,32, which has also beenobserved in liposomal and polymeric delivery systems33–35.

Particle charge had a pronounced effect on the dynamics of particleuptake and fluorophore release (Fig. 3g,h). These dynamics wereobserved by averaging the behaviour in the inner and outer regions,which were defined as annuli 175–200 mm from the centre and

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Figure 3 | Release of FITC–SH from AuNPs in tumour cylindroids. a–f, Green fluorescence images (a,c,e) and corresponding intensity profiles (b,d,f) of

cylindroids treated with nanoparticles. Fluorescence images were acquired after incubation with p-FITC–AuNP (a), n-FITC–AuNP (c) and FITC (e) for 11, 21

and 46 h. Dotted circles indicate cylindroid edges. Scale bar, 300mm. Fluorescence intensity profiles are shown at 11, 21, 38 and 46 h (b,d). g,h, Change of

average fluorescence intensities over time in the inner and outer regions of the cylindroids (indicated by grey bars in b and d) after incubation with p-FITC–

AuNP (g) and n-FITC–AuNP (h). Errors are standard error of the mean (n¼ 3). i, Blue fluorescence image of a cylindroid incubated with OPA for 18 h. Scale

bar, 200 mm. j, Green confocal fluorescence microscope image of the outer region of the cylindroid treated with p-FITC–AuNP. Scale bar, 20 mm.

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25–50 mm from the periphery of three cylindroids (grey bars inFig. 3b,d). In cylindroids treated with positive particles, fluorescenceintensities increased monotonically (Fig. 3g). The behaviour was con-siderably different for cylindroids treated with negative particles, inwhich the fluorescence intensity saturated with time and eventuallyreached a plateau (Fig. 3h). Comparing inner and outer regions, thetime-dependent behaviour of cellular uptake/release was functionallysimilar for both particle types (Fig. 3g,h).

Two possible causes for the early appearance of fluorescenceat the centre of the cylindroids following nanoparticleadministration (Fig. 3a–d) can be suggested: first, an increased rateof uptake by apoptotic/necrotic cells or, second, an increased rate offluorophore dissociation due to higher thiol concentrations. The dyeo-phthaldialdehyde (OPA) reacts non-enzymatically with aminoacids and their derivatives in the presence of thiol compounds; thishas been widely used to measure intracellular glutathione concen-tration36,37. Staining with OPA showed that the concentration ofthiol compounds was higher in the outer region and decreasedtoward the centre of the cylindroids (Fig. 3i). This location of cellularthiol compounds was opposite to the pattern of fluorescence fromnanoparticles (Fig. 3a–d). We have previously shown that centres ofcylindroids are composed of apoptotic and necrotic cells19,20,24, andthese cells preferentially take up particles when compared to viable

cells (Supplementary Fig. S2a–c) because they have lost membraneintegrity19,20. Together, these observations demonstrate that cellularuptake is the dominant mechanism. If dissociation, and not uptake,were the limiting mechanism, then fluorescence from released fluoro-phore would have been greater in the periphery than in the centre.

Ligand dissociation was expected to be entirely intracellularbecause of the higher levels of glutathione relative to the extracellu-lar environment. Confocal microscopy was used to verify that extra-cellular dissociation did not occur (Fig. 3j). Following incubationwith nanoparticles for 36 h, FITC–SH release was observed primar-ily inside cells (Fig. 3j). Intracellular localization of dissociation wasconsistent across the diameter of the cylindroids; fluorescence wasobserved only inside cells in both the inner and outer regions.Furthermore, the observed fluorescence patterns were conserved inthe z-direction (away from the objective), supporting the use of epi-fluorescent microscopy for quantitative penetration measurements.

Uptake of doxorubicin nanoparticlesTo further probe the potential therapeutic applications of engineerednanoparticles, we fabricated particles featuring a doxorubicin prodrugtethered through an acid-labile hydrazone linkage to a thiol ligand(Fig. 1c). Similar to FITC–AuNP, a positive surface charge dramati-cally enhanced uptake of DOX–AuNP into proliferating peripheral

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Figure 4 | Doxorubicin release in cylindroids. a–c, Red fluorescence images and the corresponding radial intensity profiles of cylindroids treated with

positive DOX–AuNP (a), negative DOX–AuNP (b) and free DOX (c). Dotted circles indicate cylindroid edges. Scale bars, 200mm. d,e, Ratio of average

fluorescence intensities in the outer region to those in the inner region of the cylindroids, 30 h after treatment (d) and as a function of time (e). Errors are

standard error of the mean, and significance was determined using Student’s t-test (*P , 0.05; n¼ 3).

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cells when compared to negative particles and free drug (Fig. 4). Incylindroids, positive particles delivered more doxorubicin than nega-tive particles (Fig. 4a,b). With regard to position, positive particlesdelivered significantly more doxorubicin to viable cells in the cylin-droid periphery when compared to negative particles and free drug,which were preferentially taken up by dead cells at the cylindroidcentre (P , 0.05; Fig. 4d). This charge-dependent localization wasconsistent over the 46 h of the experiment (P , 0.05; Fig. 4e),during which the concentration of particles and free drug increasedwithin the cylindroids (Fig. 4a–c, radial profiles). The similarity ofthese results with the FITC results (Fig. 3) supports the predictionthat nanoparticles with positive surface charges will outperform nega-tive particles for most applications, and confirms that charged goldnanoparticles have the potential to overcome drug penetration bar-riers and deliver clinically relevant anticancer drugs.

Diffusion of nanoparticles in matrix materialIn addition to regulating cellular uptake, surface charge also signifi-cantly affects the diffusivity of gold nanoparticles in the extracellularmatrix. Diffusivity in the extracellular matrix was modelled using acell-free diffusion chamber, which confined Matrigel betweena trench cut in a polycarbonate block and the bottom surface of awell plate (Fig. 5a). In this model, diffusion occurred in only onedirection: from the exposed surface to the centre of the trench.Concentrations of FITC and FITC–AuNP were measured as afunction of time and location by acquiring a series of fluorescenceimages along the longitudinal direction every 2 h.

Intensity gradients decreased from the edge towards the centre ofthe Matrigel trench, and the slope of the gradients diminished withtime (Fig. 5b,c). Diffusion coefficients were determined by non-linear least-squares fitting of the intensity gradients to a Fickiandiffusion model (Fig. 5c). The diffusion coefficient for FITC was(42+2) × 1027 cm2 s21, which was larger than both gold nano-particles by an order of magnitude (Fig. 5d). Simulations with this

diffusion coefficient matched the concentration profiles seen inthe cylindroids (Fig. 3), suggesting that diffusion alone controlledthe delivery of free FITC. Anionic gold nanoparticles had a largerdiffusion coefficient, (9.0+0.1)× 1027 cm2 s21, than cationic nano-particles, (7.6+0.1) × 1027 cm2 s21 (P , 0.005; n¼ 3; Fig. 5d).

The lower diffusion coefficient of positive particles suggests thatelectrostatic interactions with negatively charged macromolecules inthe matrix slowed particle diffusion. The major components of theextracellular matrix in tumours and spheroids are collagen and pro-teoglycans38–40. Matrigel is derived from tumour matrix materials41,which are negatively charged under physiological conditions31.Because cationic and anionic particles have similar molecularweights and hydrodynamic radii, it is likely that electrostatic inter-actions with the matrix are the primary cause of the differencebetween the diffusion coefficients.

Three mechanisms control the timing and location of drug deliv-ery into tumours using nanoparticles: diffusion, cellular uptake andligand dissociation. Our results indicate that, of the three, cellularuptake is the dominant mechanism. In all cylindroids, fluorescenceappeared early in their centres (Fig. 3). If diffusion were the limitingmechanism, fluorescence would first appear at the outside edge andprogress into the centre. The measured diffusion coefficients in thematrix material (Fig. 5d) confirm that diffusion can account for therapid appearance of particles in the cylindroid centres.

Modelling diffusion and cellular uptake/releaseA descriptive mathematical model was developed to interpret thecoupled effects of extracellular diffusion (Fig. 1b) and cellularuptake/release (Fig. 1d) on molecular nanoparticle delivery. Themodel framework was designed to show how dynamic nanoparticlemeasurements in cylindroids provide preliminary information aboutnanoparticle behaviour under physiological conditions. The modelconsisted of two transient partial differential equations, one forgold nanoparticles, and the other for free intracellular fluorophore.

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b, Green fluorescence images acquired from the bottom of the loading module 4 and 24 h after adding particles. Dotted lines at both ends indicate the

Matrigel edges. Scale bar, 500mm. c, Fluorescence intensity profiles in Matrigel along the x-axis as a function of time (symbols) and intensity profiles

generated by fitting to a Fickian diffusion model (solid lines). d, Comparison of diffusion coefficients of FITC, cationic and anionic gold nanoparticles in

Matrigel (*P , 0.005; n¼ 3).

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Concentration profiles for particles and released ligand were pre-dicted using in vitro calibrations of ligand release (Fig. 2a). Basedon confocal microscopy results (Fig. 3j), all ligand dissociation wasmodelled as an intracellular reaction. Internalization of FITC–AuNPsand release of FITC–SH were modelled as a single reaction with radially

dependent forward (k1) and reverse (k2) rate constants (Fig. 1d andSupplementary Fig. S2). Nanoparticle diffusion coefficients werederived from measured diffusivities in Matrigel (Fig. 5).

The modelling results fit the experimental data well, and predictthat positively charged particles will outperform negative particles

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Figure 6 | Rate constants of cellular uptake and predictions of particle and ligand distribution in tumours. a,b, Fluorescence intensity profiles measured in

fluorescence images of cylindroids (symbols) and those predicted by the mathematical model (solid lines). Concentrations were normalized by the maximum

concentration of FITC–AuNP in the cylindroids. c, Independent concentration profiles of fluorophore bound to nanoparticles (FITC–AuNP) and released

fluorophore ligand (FITC–SH) predicted by the computation model. d, Comparison of forward (k1) and reverse (k2) rate constants in different regions. Errors

are standard error of the mean, and significance was determined using Student’s t-test (*P , 0.05). e,f, Modelled concentrations of FITC–AuNPs and released

FITC–SH as a function of distance from blood vessels of a hypothetical tumour. Clearance half-life of FITC–AuNPs was assumed to be 3 h. g, Average

concentrations of FITC–AuNPs in the regions 10–70mm (proliferating) and 75–120mm (quiescent) from the blood vessel wall as a function of time.

h, Average concentrations of released FITC in deep tumour regions (1.0–1.5 mm) as a function of time.

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for most, but not all applications (Fig. 6). The modelling results(solid lines in Fig. 6a,b) capture a number of key characteristics ofthe fluorescent patterns shown in Fig. 3 and the experimental datapoints (symbols, Fig. 6a,b). First, a higher fluorescence was observedin the inner regions than in the outer at early time points. Second,positive particles showed a monotonic increase in fluorescence, andthis increase was more pronounced in the outer regions. Third,negative particles displayed saturation of fluorescence. By separatingthe fluorescence contributions from free and bound fluorophore, themodelling results indicate that particle diffusion was rapid, and theappearance of free fluorophore by uptake and dissociation con-trolled overall fluorescence (Fig. 6c). Calculated kinetic ratessuggest that viable cells had a higher net uptake of positive particlesbecause of a lower export rate (k2) in both inner and outer regions(P , 0.05; n¼ 3; Fig. 6d). For negative particles, the forward rateconstant was only larger in the inner region (P , 0.05; n¼ 3; Fig. 6d).

Modelling predictions were based on a hypothetical tumour forwhich the geometry was inverted: particles diffused from a bloodvessel (0 , r , 5 mm) into tumour tissue (r . 5 mm). Because oftheir greater diffusion coefficient, negative particles penetrateddeeper into the interstitium at all times (Fig. 6e). However, the con-centration of released intracellular ligand was greater for positiveparticles, because of their larger net uptake rate (Fig. 6f). This pre-dicts that deep penetration of negative particles may be mitigated bythe elevated interstitial fluid pressures often observed in tumoursin vivo42–44. For both particles, the concentration of releasedligand reached a maximum between 20 and 30 h (Fig. 6f ).Regions of proliferating (10–70 mm) and quiescent (75–120 mm)cells were defined based on single cell analysis performed incylindroids24. The average concentrations of released ligand forpositive particles in the proliferating and quiescent regions weremore than 11-fold and 8-fold greater at all times, respectively(Fig. 6g). Deep in the tissue (.1 mm) the concentration of releasedligand was greater for negative particles at later times (.20 h;Fig. 6h). These results suggest that positive particles will releasemore ligand to most cells at all times (Fig. 6f,g) and thereforewould be advantageous for most applications. Complementarily,negative particles would have an advantage in delivering drugsdeep into tissue (Figs 5d,6h) and would be useful for treatingtumours with large intervessel spacing and high hypoxic tolerance.

ConclusionsUsing a combination of experimental in vitro tumour models andmathematical modelling, we have shown that, under most circum-stances, positively charged nanoparticles improved delivery of pay-loads to the majority of cells in tumours, whereas negatively chargedparticles would perform better when delivering drugs deep intotissues. Positive particles had significantly higher uptake and dis-sociation by viable cells, whereas negative particles diffused at afaster rate. Both positive and negative particles penetrated tissuesrapidly, and for both, the rate of cellular uptake and dissociationwas slower than extracellular diffusion. The mathematical modelssuggested that the rate of cellular uptake of both particles was fastin apoptotic and necrotic tissues. Furthermore, the uptake kineticsof positive particles is irreversible, but is reversible for negative par-ticles over the timescales investigated. The ability to tune surfacecharge to control tissue penetration and drug release makes goldnanoparticles a flexible and powerful drug delivery vehicle.

Experiments and MethodsSynthesis and characterization of mixed monolayer-protected goldnanoparticles. Pentanethiol-coated gold nanoparticles were synthesized accordingto the method reported by You and colleagues45 and as described in theSupplementary Information. Zeta potentials were measured in triplicate using aMALVERN Zetasizer Nano ZS for 0.8 mM nanoparticles in phosphate bufferedsaline (PBS; pH¼ 7.8, 20 mM potassium phosphate, 100 mM sodium chloride).Fluorescence intensities of p-FITC–AuNP, n-FITC–AuNP and FITC–SH were

measured at 0.5 and 1.0 mM in Dulbecco’s Modified Eagle’s Medium (DMEM) byfluorimetry (SPECTRAmax GEMINI XS, Molecular Devices) to calibrate thefluorescence intensity and determine the FITC–SH loading ratios.

FITC–AuNP and DOX–AuNP uptake and ligand release in monolayer culture.LS174T human colon carcinoma cells were grown in DMEM (1 g l21 glucose)supplemented with 10% fetal bovine serum at 37 8C with 5% CO2 in a humidifiedincubator. Cells in monolayer cultures were incubated with 1 mM FITC–AuNPs for6 h, and were washed with PBS three times before image acquisition. Confocalfluorescence microscope images were acquired with a Zeiss LSM510 microscopeequipped with a ×25 objective lens. A 488-nm argon laser was used for excitation,and emission was acquired at 505 nm (long pass).

FITC–AuNPs and DOX–AuNPs in cylindroids. Cylindroids were prepared fromspheroids as described previously19,20 and in the Supplementary Information. Afterequilibration, cylindroids were treated with 125 mM FITC, 1 mM FITC–AuNP,1 mM DOX, or 1 mM DOX–AuNP. Transmitted and fluorescence images wereacquired with an Olympus IX71 microscope with a ×10 objective at 0, 11, 21, 38,46 h after treatment. Radial fluorescence intensity profiles in the cylindroids weregenerated using a customized script in ImageJ (NIH Research Services Branch).Average fluorescence intensities were determined for two annular regions:175–200 mm from the centre (inner) and 25–50 mm from the periphery (outer). Forconfocal fluorescence microscopy, cylindroids were prepared in 35-mmglass-bottomed culture dishes. Images were acquired with a Zeiss LSM510microscope equipped with a ×63 oil-immersion objective. A 488-nm argon laserwas used for excitation, and emission was acquired at 505 nm.

Thiol compounds in cylindroids. The distribution of GSH was determined bymeasuring the fluorescence intensity of OPA derivatives. OPA reacts with aminoacids in the presence of thiol compounds to form fluorescent derivatives36,37.Cylindroids were incubated with 250 ml of 100 mM OPA in PBS. Transmitted andfluorescence images were acquired 4, 18 and 36 h after treatment. Samples wereexcited at 350 nm and measured at 460 nm.

Extracellular diffusion of FITC–AuNP. Diffusion of gold nanoparticles wasmeasured in Matrigel in a loading module (Fig. 5a) as described in theSupplementary Information. The loading module was prepared by making a channel(3.1 × 0.5 × 6.2 mm3; W × H × L) in the top of a polycarbonate block (9.6 × 4.8 ×6.2 mm3). Before loading, the well plate was plasma-treated for 5 min and sterilizedwith UV for 4 h. The module was loaded with 12 ml Matrigel, which was allowed togelate at 37 8C for 5 min. Pre-warmed DMEM (2.0 ml) was added to each well and,after 2 h, was replaced with DMEM containing 1 mM FITC–AuNP. Transmitted andgreen fluorescence images were acquired every 2 h for 36 h. Spatial concentrationprofiles were obtained by averaging pixel values across the width of the channel.Diffusion coefficients of FITC, p-FITC–AuNP and n-FITC–AuNP weredetermined by fitting measured fluorescence intensities to a mathematicaldiffusion model. Numerical solutions were calculated using finite elements, andbest-fit diffusion coefficients were determined by nonlinear least-squaresoptimization in Matlab (MathWorks).

Mathematical modelling of particle diffusion and cellular uptake in cylindroids.Internalization of gold nanoparticles from the extracellular space and glutathione-mediated replacement were represented with a one-step reversible reaction:

FITC−AuNPOk1

k2

FITC−SH + AuNP

where k1 and k2 are forward and reverse reaction constants. Coupled conservationequations for FITC–AuNPs and released FITC–SH incorporated expressions forextracellular nanoparticle diffusion and the kinetics of particle uptake and ligand release:

∂Cparticle

∂t= Deff

r· ∂∂r

r∂Cparticle

∂r

( )− fv k1Cparticle − k2Cligand

( )(1)

∂Cligand

∂t= k1Cparticle − k2Cligand (2)

From confocal measurements, the cell volume fraction fv was found to be 0.48. Theeffective nanoparticle diffusion coefficients Deff were derived from the Matrigelexperiments. Reaction rates were assumed to be functions of position as described inthe Supplementary Information. This model was solved using finite elements and fit tomeasured fluorescence concentrations by nonlinear least-squares optimization inMatlab. Calculated fluorescence values were determined from the sum of the volume-fraction-weighted particle (FITC–AuNP) and released ligand (FITC–SH)concentrations. Calculated rate constants were reported as average values insidethe inflection point, r , Rt (inner) and between the inflection point and the edge,Rt , r , 1 (outer). Significance was determined using unpaired Student’s t-testswith unequal variance. Particle diffusion and ligand release was modelled in a

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hypothetical tumour as described in the Supplementary Information. In this model, theblood was assumed to be well mixed, and particles were cleared with a 3-h half-life46.

Received 24 December 2009; accepted 1 March 2010;published online 11 April 2010

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AcknowledgementsThe authors gratefully acknowledge financial support from the National Institutes ofHealth (grant nos 1R21CA112335-01A and 1R01CA120825-01A1) and the NationalScience Foundation (grant no. DMI-0531171).

Author contributionsN.F. and V.R. conceived and designed the experiments. B.K., G.H., B.T. and C.K. performedthe experiments. G.H. synthesized the FITC nanoparticles. C.K. synthesized the DOXnanoparticles. B.K. performed all cell and cylindroid experiments with FITC nanoparticlesand wrote all mathematical models. B.T. performed all cylindroid and cell experiments withDOX nanoparticles. B.K., B.T. and N.F. analysed the data. V.R. contributed materials. B.K.and N.F. co-wrote the paper. All authors discussed the results and commented onthe manuscript.

Additional informationThe authors declare no competing financial interests. Supplementary informationaccompanies this paper at www.nature.com/naturenanotechnology. Reprints andpermission information is available online at http://npg.nature.com/reprintsandpermissions/.Correspondence and requests for materials should be addressed to N.S.F.

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