Cell position. Edge. Core Mean Std. Deviation

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1 Diameter (um) 20 *** Edge Cell position Core Mean Std. Deviation Edge Core Supplementary Figure S1: Measuring cell diameter. Cell diameters were obtained by ImageJ using fluorescent images and drawing a line through the centre of the cell from the perimeter of the spheroid towards the centre. *** t-test, p <

2 a imaging chamber entrance b dam c Supplementary Figure S2: Characterization of microfluidic device. (a) Scheme of the device showing various dimensions and highlighting specific regions such as the entrance (h: 250µm, w: 600µm), imaging chamber (h: 250µm, w: 1200µm) and the dam (h: 25µm). COMSOL Computational Fluid Dynamics (CFD) simulation values at the imaging chamber prior to the dam. (b) Reynolds number and velocity in the imaging chamber. (c) Pressure drop and shear stress in the imaging chamber.

3 Supplementary Figure S3: Characterization of Nanoparticles. Each graph contains the UV- Vis spectra (black) and emission spectra (red) after excitation at 618 nm (dotted line). The inset of each graph contains a TEM image of the nanoparticles. Scale bars = 100µm

4 Accumulation (A.U.) Accumulation (A.U.) Fluorescence vs. Media (A.U.) Fluorescence vs. Media (A.U.) Fluorescence vs. Media (A.U.) Fluorescence vs. Media (A.U.) a Slice #4 Slice #5 Slice #6 Slice # Radial depth ( m) Radial depth ( m) Radial depth ( m) Radial depth ( m) b 0.15 c Time (min) Time (min) Supplementary Figure S4: Quantification of NP accumulation. (a) For each time point, we selected 4 images at different z-axis planes between 30 and 70 µm to determine nanoparticle accumulation. To quantify tissue fluorescence, the spheroid contour was traced (yellow line) at in ImageJ and a macro (developed in-house) was produced to quantify the average fluorescent intensity at 1.38 µm radial increments. These values were normalized to the fluorescence of the media (white squares). This figure illustrates 4 different images of the same spheroid at different z-axis planes (above) and the corresponding fluorescence vs. radial depth (below). (b) Sample

5 data of fluorescence accumulation in the spheroid. Dotted line included to highlight background fluorescence at t=0 (when NPs enter the imaging chamber). Values represent the average of 4 different z-axis images and the standard deviation for one representative spheroid. (c) Final accumulation data after t=0 background has been subtracted. Data shows presents the average accumulation for five spheroids treated with 40 nm PEG NPs.

6 rate constant (min -1 ) in out NP (nm) Supplementary Figure S5: Rate constants for accumulation of PEG-NPs Average NP accumulation in spheroids at each time point in Figure 2c was fit using Equation 6 and rate constants were calculated (see Methods section).

7 Accumulation (A.U.) nm 70 nm nm 150 nm Time (min) Supplementary Figure S6: Efflux of PEG-NPs. Data was obtained by flushing spheroids with blank imaging buffer at 50µl h -1 for 30min. Because there was no external fluorescence to normalize values, all data was obtained as a percentage of t=0 min. These values were then multiplied by the final accumulation value of the spheroid before flushing.

8 Supplementary Figure S7: Silver staining and electron microscope images of PEG-NPtreated spheroids. (a, b) Representative images of spheroids treated for 1h with 25nM 40nm PEG-NPs. Scale bar = 100 µm (c) Transmission electron microscope image of spheroids treated with 25nM 40nm PEG-NPs with cells outlined in dotted lines. Scale bar = 500 µm

9 Supplementary Figure S8: Distribution of Tf protein in the spheroid. (a) Fluorescent intensity of spheroid with Tf protein at 50 µl h -1 for 60 min; scale bar = 100 µm. (b) Overlay of fluorescent and differential interference contrast images of spehroids treated with Tf protein; scale bar = 10 µm. (c) Mean fluorescent intensity at various radial distances in spheroids treated with Tf protein at 50 µl h -1 for 0, 15, 30 or 60 min.

10 Supplementary Figure S9: Blocking Tf receptors on spheroids. Images of spheroids treated with 25nM Tf-NP with or without 6.41µM Tf for 30min at 50µl h -1. Although fluorescence in the ECM is still present after blocking, a decreased accumulation of Tf-NPs is observed in the tissue. Fluorescence distribution also shows a decrease of Tf-NP in the tissue after 30 min.

11 a cell b cell c d cell cell cell e f g h cell cell cell cell Supplementary Figure S10: TEM images of spheroids incubated with Tf-NPs for 1h. (a-d) shows Tf-NPs (arrows) interacting with the cell membrane (dotted line); (e-h) shows Tf-NPs (arrows) trapped in the ECM. All scale bars = 100µm.

12 Mean NP Intensity (A.U.) a b c Radial depth ( m) Supplementary Figure S11: Silver stained images of spheroids incubated with Tf-NPs for 1h. (a, b) Representative images of spheroids treated for 1h with 25nM 40nm PEG-NPs. (c) Tf- NP distribution from silver stained spheroids. Image threshold was set to visualize the position of the silver stain and distribution was quantified (data presented as mean intensity ± s.e.m., n= 9).

13 Reservoir Fluorescence (A.U.) Penetration Ratio Reservoir Fluorescence (A.U.) Penetration Ratio a cell layers (~12 um) spheroid L3 L2 L1 L1 = reservoir or binding site barrier L2/L1 ratio L3/L2 ratio b c d e PEG reservoir ul/h 450 ul/h PEG ratios 1.0 L2/L1 (50ul/h) L3/L2 (50ul/h) L2/L1 (450ul/h) 0.8 L3/L2 (450ul/h) Tf binding site barrier ul/h 450 ul/h Tf ratios L2/L1 (50ul/h) L3/L2 (50ul/h) L2/L1 (450ul/h) L3/L2 (450ul/h) Time (min) Time (min) Time (min) Time (min) Supplementary Figure S12: Flow rate controls the concentration of NPs in the first layer of the tissue. (a) Scheme of spheroid showing that accumulation can be subdivided into multiple cell layers (L1, L2, L3, etc.) To determine whether faster flow rates can increase the penetration depth of NPs, we can look at the ratios between L2 vs. L1 or L3 vs. L2. (b) Accumulation of PEG-NPs in the first layer or reservoir. (c) Accumulation ratios between the two adjacent layers demonstrate that flow rate does not change the ratios. (d) Accumulation of Tf-NPs in the first layer or reservoir. (e) Accumulation ratios between the two adjacent layers demonstrate that flow rate does not change the ratios. Data for each time point is presented as the mean ± s.e.m. (n=3).

14 Fluorescence (A.U.) AuNPs Supn't Pellets time (min) Supplementary Figure S13: Stability of Tf-NPs in media. Desorption of fluorescent Tf protein from the Tf-NPs. Tf-AuNPs were incubated with imaging media for up to 1h and sample fluorescent was measured (AuNPs), then samples were centrifuged and fluorescence of the supernatant and pellets (resuspended in imaging media) were measured. If protein was desorbing, fluorescence would increase in the AuNP or in the supernatant measurements.

15 a b c Supplementary Figure S14: Quantifying interstitial flow rates. Representative images showing milestones of the media exchange rate at the appearance (a), mid-way (b) and disappearance (c) of characteristic tail showing the replacement of non-fluorescent media in the spheroid s interstitial spaces with 10 kda Dextran-568-labelled media.

16 Supplementary Figure S15: Modeling flow through the interstitial channels. This illustrates the various flow efficiencies through the different orientations of interstitial channels.

17 Supplementary Figure S16: Scheme of mathematical model for rate constants. Basic singlecompartment depiction to develop a mathematical model that predicts the time-dependent level of NPs that enter and exit the spheroid. The rates at which the NPs enter and leave the spheroid depend on the concentrations of the NP dose (C D ) and NP inside the spheroid (C S ) as well as the rate constants into(k IN ) and out of (k OUT ) the spheroid.

18 Supplementary Table S1: Characterization of in vitro nanomaterials. The hydrodynamic diameter and polydispersity index as obtained from dynamic light scattering. Surface HD (nm) PDI zeta (mv) TEM Dose (nm) 40nm PEG-NP 5kDa mpeg ± ± Tf-NP holo-tf ± ± nm PEG-NP 100nm PEG-NP 150nm PEG-NP 10kDa mpeg ± ± kDa mpeg ± ± kDa mpeg ± ±

19 Supplementary Table S2: Characterization of in vivo nanomaterials. The hydrodynamic diameter and polydispersity index as obtained from dynamic light scattering. Surface HD (nm) PDI zeta (mv) TEM 50nm PEG- NP 50 nm Tf-NP 100nm PEG- NP ~15% 10kDa PEG- Alexafluor750 ~85% 5kDa mpeg ~3% OPSS-PEG-5k-holo-Tf ~15% 10kDa PEG- Alexafluor750 ~82% 5kDa mpeg ~15% 10kDa PEG- Alexafluor750 ~85% 5kDa mpeg ± ± ± ± ± ± 8.66

20 Supplementary Table S3: Interstitial flow rates. These values were calculated using the mathematical model described in the Methods section. Q (µl h -1 ) Q S (µl h -1 ) Q IS_Channel (µl h -1 ) V= Q IS_Channel A -1 (µm s -1 ) x x x x x