Open Access Article

This Open Access Article is licensed under a Creative Commons Attribution-Non Commercial 3.0 Unported Licence

Marta
Pilz
^{a},
Karina
Kwapiszewska
*^{a},
Tomasz
Kalwarczyk
^{a},
Grzegorz
Bubak
^{a},
Dominika
Nowis
^{bc} and
Robert
Hołyst
*^{a}
^{a}Department of Soft Condensed Matter, Institute of Physical Chemistry, Polish Academy of Sciences, Warsaw, Poland. E-mail: kkwapiszewska@ichf.edu.pl; rholyst@ichf.edu.pl
^{b}Genomic Medicine, Medical University, Warsaw, Poland
^{c}Laboratory of Experimental Medicine, Centre of New Technologies, University of Warsaw, Poland

Received
10th March 2020
, Accepted 27th August 2020

First published on 28th August 2020

The efficient delivery of drugs to cells depends on their diffusion through the extracellular matrix (ECM) of tissues. Here we present a study on the diffusion of nanoprobes of radius from 1 nm to over 100 nm in the ECM of spheroids of three cell types (HeLa, MCF-7 and fibroblasts). We quantified the nanoparticle transport in the spheroids’ proliferating zone. We determined the size-dependent viscosity of the ECM. We revealed that nanoobjects up to 10 nm in radius exhibited unobstructed diffusion in the ECM, regardless of the spheroid type. The presented length-scale dependent viscosity profiles for spheroids pave the way for advanced modelling of drug administration through tissues.

The extracellular matrix is a non-cellular component of the tissues. The ECM consists of a wide diversity of molecules, including fibrous-forming proteins (e.g. collagen, elastin and fibronectin), glycoproteins, proteoglycans and glycosaminoglycans.^{9} These biomolecules form a complex network by binding to each other as well as to the cell adhesion receptors. To describe the motion of nanoprobes in such complex liquids, one can apply the length-scale dependent viscosity model.^{10,11} It uses the fluctuation–dissipation theorem to calculate the effective viscosity, η_{eff} experienced by the probe in the extracellular matrix from the measurements of its diffusion coefficient, D:

(1) |

The length-scale dependent viscosity model relies on the exponential dependence of the effective viscosity experienced by the particle moving in a complex fluid (eqn (2)).

(2) |

Here η_{eff} is the viscosity experienced by the nanosized probes, η_{0} is the viscosity of the solvent (i.e. the buffer), A is a constant of the order of 1, ξ is the correlation length – a mean half-distance between the entanglement points in a polymer matrix (dependent on the concentration of crowding agents), R_{h} is the hydrodynamic radius corresponding to the size of polymer coils creating the environment, and r_{p} is the hydrodynamic radius of the probe. Exponent a is a constant of the order of 1.

In this paper, we use the model expressed by eqn (2) to quantify the motion of biologically inert tracers in the three-dimensional models of cancer as well as non-cancerous cell culture (3D culture). 3D cell cultures are currently considered to be the most accurate in vitro tumour models, especially for the studies of the extracellular matrix.^{12–16} The extracellular space was probed by using fluorescent nanoprobes ranging in the radius from 1 to over 100 nm, encompassing the size of most therapeutic agents used in cancer treatment. Their motion within the ECM was measured using fluorescence correlation spectroscopy (FCS), as a noninvasive method successfully applied to living biological systems.^{17} This technique assumes a very small observation volume, V_{eff} (of the order of 1 fl), and the diffusion coefficient, D, is determined from the correlation function obtained from the fluctuations in the fluorescence intensity. Those fluctuations originate from small variations in the number of fluorescent particles in the V_{eff}. Eqn (2) allows for characterising the structure of the ECM providing parameters such as the interfibrillar spacing of the network (ξ), the hydrodynamic radius of the polymer creating the matrix (R_{h}) and its nanoviscosity and macroviscosity.

The spheroid formation protocol is schematically shown in Fig. 1. First, the cells (∼2 × 10^{5} ml^{−1}) were cultured in a proper complete cell medium without phenol red using Nunclon™ Sphera™ dishes (Thermo Fisher Scientific, USA) with a surface coating inhibiting cell attachment. On the third day of culture, 50% of the medium was replaced. On the fourth day, spheroids were carefully transferred onto the 8-chamber cover glass Lab-Tek® (ThermoFisher Scientific, USA) slide. The nanoprobes were introduced into the ECM 24 hours before the FCS measurements by adding them to the cell culture medium to a final concentration of ∼100 nM.

(3) |

For each tracer, at least 15 correlation functions were recorded per spheroid. The measurements were performed for 6 different spheroids. The autocorrelation function was analysed with Python using an appropriate diffusion model (ESI†) based on eqn (3) using the non-linear least squares fitting method. The standard uncertainty of the values of the autocorrelation function was calculated as the standard deviation of the average. The diffusion coefficients D[μm^{2} s^{−1}] were then calculated using the relation: D = ω^{2}/4τ_{D}.

Confocal immunofluorescence analysis was performed by plating the spheroids on the 8-chamber cover glass Lab-Tek™ slide, fixing overnight at 4 °C using the Image-iT™ fixative solution (4% formaldehyde, methanol free) (Invitrogen™, USA), permeabilising with 0.3% Triton X-100 (Sigma-Aldrich, USA) and blocking in normal goat serum (Gibco™, USA) for 4 h at room temperature. Then samples were washed and incubated overnight at 4 °C with a mouse collagen I monoclonal antibody (ThermoFisher, USA) diluted 1:2000, a mouse elastin monoclonal antibody (Abcam, UK) diluted 1:100, a mouse fibronectin monoclonal antibody (ThermoFisher, USA) diluted 1:100 or a mouse tenascin-C monoclonal antibody (ThermoFisher, USA) diluted 1:4000. Next, the spheroids were washed three times with PBS and subsequently incubated for 3 hours at room temperature in the dark with Alexa Fluor 568 goat anti-mouse IgG1 cross-adsorbed secondary antibody (ThermoFisher, USA) diluted 1:500, and was again washed three times with PBS. The cell nuclei were labelled with 15 μM Hoechst 33342 and excited using a 405 nm laser. The ECM structures were excited using a 561 nm laser.

First, we measured the diffusion coefficients of the fluorescent probes with various (from 1 nm to 110 nm) radii (r_{p}). Each probe was measured by FCS under physiological conditions in HeLa, MCF-7 and fibroblast spheroids. In Fig. 2, we show the effective viscosity experienced by the nanoprobes listed in Table 1 within all three types of spheroids. The length-scale dependent viscosity model (eqn (2)) was fitted to the data with ξ, A, a and R_{h} as free parameters. The data analysis for all three spheroid types revealed that parameter a was close to unity within 7% of uncertainty, therefore we decided to fix this parameter as 1.

Fig. 2 The logarithm of effective viscosity experienced by nanoprobes of radii r_{p} moving in the ECM of HeLa, MCF-7, and fibroblast spheroids. Error bars correspond to the standard deviations (N > 30). The fit of a length-scale dependent viscosity model (eqn (2)) is presented as a solid line. The fitting parameters are listed in Table 2. The diffusion coefficient of any inert probe within the ECM of studied cell line spheroids can be estimated from the presented length-scale dependent model. |

Sample name |
r
_{p} [nm] |
---|---|

Dextran 4.4 kDa | 1.3 ± 0.2 |

Dextran 20 kDa | 3.8 ± 0.3 |

Dextran 40 kDa | 4.9 ± 0.5 |

Dextran 155 kDa | 8.6 ± 0.7 |

S34(1) nanoparticles | 20.6 ± 1.3 |

S43(2) nanoparticles | 66.2 ± 3.1 |

S44(3) nanoparticles | 110.7 ± 3.3 |

The diffusion of probes of up to 10 nm in radius is almost unobstructed by the ECM. This implicates that probes whose r_{p} ≪ ξ experience effective viscosity similar to that of the solvent.

For tracers bigger than the correlation length r_{p} > ξ, we observe an exponential increase in the values of the effective viscosity experienced by the probe. In all examined spheroids, tracers bigger than r_{p} ≫ 90 nm (i.e. 4R_{h}) experience the effective viscosity corresponding to macroscopic viscosity. Thereby, we proved that the effective viscosity experienced by a probe undergoing motion in the ECM is a function of the hydrodynamic radius of the probe. Nanoparticles smaller than the correlation length, ξ, experienced much lower viscosity than the macroscopic one.

According to the length-scale dependent viscosity model, R_{h} corresponds to the mean value of hydrodynamic radii of obstacles creating the environment surrounding the probes. In the studied spheroids, type I collagen might be considered as the major hindrance since it is the most abundant fibrous protein within the ECM.^{21} Knowing that the radius of an individual collagen molecule r_{c} = 0.75 nm,^{22} the length of the ECM obstacles can be calculated using the relation^{23}R_{h} = L/(2s − 0.19 − 8.24/s + 12 s^{−2}), where s = ln(L/r) and L is the length of the filament. The estimated values of the length of the obstacles are comparable with the collagen monomers, whose length (250–300 nm) was previously measured by AFM.^{24}

The nanoviscosity of the ECM (η_{ECM},) as well as R_{h}, take similar values in both cancerous (HeLa and MCF-7) and non-cancerous (fibroblasts) spheroids. However, the correlation length, ξ, influencing the macroscopic viscosity value, η_{macro}, is approximately two times higher in HeLa than in the other two tested cell lines.

Next, we complemented our analyses with confocal imaging, as shown in Fig. 3 and 4.

Fig. 4 Immunochemical analysis of the ECM proteins collagen I, elastin, fibronectin, and tenascin-C was performed on HeLa, MCF-7, and fibroblast spheroids. The density of the labelled ECM fibres (in red) differs among the examined cell lines and follows the trend of change of ξ, as shown in Table 2. The observed density of fibres in MCF-7 spheroids is notably lower than in HeLa and fibroblast spheroids. Hoechst 33342 nuclear counterstain is also shown (in blue). Scale bars are 50 μm. |

By using Col-F fluorescent dye binding to elastic and collagenous fibres, we visualised the structure of the ECM within the spheroids.^{25} Additionally, we performed the immunohistochemical staining of four major extracellular matrix components: collagen type I, fibronectin, elastin, and tenascin-C. We found that the density of the labelled fibres differs among the examined cell lines and follows the trend of changes of ξ, as shown in Table 2. The observed density of fluorescent fibres in HeLa spheroids is markedly higher than in all other tested spheroids.

Parameter | HeLa spheroids | MCF-7 spheroids | Fibroblast spheroids |
---|---|---|---|

η
_{0} corresponds to the viscosity of PBS, which is 0.75 mPa s. |
|||

Nanoviscosity of the ECM matrix, η_{ECM} = Aη_{0} |
(1.29 ± 0.04) η_{0} = 0.97 mPa s |
(1.00 ± 0.03) η_{0} = 0.75 mPa s |
(1.05 ± 0.07) η_{0} = 0.79 mPa s |

Correlation length, ξ | 17.78 ± 1.73 nm | 39.72 ± 6.98 nm | 30.94 ± 7.50 nm |

Hydrodynamic radius, R_{h} |
21.93 ± 1.94 nm | 23.47 ± 3.81 nm | 26.30 ± 6.30 nm |

Obstacle length, L | 220 ± 2 nm | 240 ± 18 nm | 274 ± 40 nm |

Macroscopic viscosity of the ECM, η_{macro} |
4.43 η_{0} ≈ 3.32 mPa s |
1.81 η_{0} ≈ 1.36 mPa s |
2.46 η_{0} ≈ 1.85 mPa s |

(4) |

In eqn (4), an effective radius of a probe is defined as R_{eff}^{−2} = R_{h}^{−2} + r_{p}^{−2}. The values for R_{h} and A were taken from Table 2 (the second column, HeLa spheroids), and a = 1.

As shown in Fig. 5, in the first 3 days of HeLa spheroid culture, the average half-distance between the points of entanglement in the ECM is derived as follows: ξ = (31.59 ± 7.86) nm. After 72 h, there is around a two-fold decrease in ξ = (17.97 ± 6.65) nm, which does not change upon further maturation of spheroids. Thus, we conclude that it takes approximately 60–70 hours for the cells in the spheroids to create the network of collagen in the ECM. The occurring variation in the results (range from 72 h to 304 h of the spheroid culture) can be related to the heterogeneity of the ECM structure (for more details, please see Fig. S11 and S12 in the ESI†).

We used FCS as it is a high statistics, non-invasive method to study the internal dynamics of molecules at nanomolar concentrations in complex biological structures.^{31} Another tool that was used to study diffusion in spheroids is fluorescence recovery after photobleaching (FRAP).^{32} However, this historically older method has its drawbacks as it requires photobleaching of the studied biomatter, which can be phototoxic due to localised heating by the laser.^{33} Moreover, FRAP requires much higher concentrations of fluorophores. A technique used in similar concentration regimes to FCS is single particle tracking (SMT). SMT, performed using a new two-photon excitation microscopy TSUNAMI, allows tracking of a protein in spheroids even at a depth of ∼100 μm. But this type of system is not commercially available and probably is too expensive to be used on a regular basis to determine the diffusion of bioactive molecules within the ECM. In addition, SMT requires recordings of many tracks to obtain high statistics, which in the case of FCS can be collected in a single measurement.

Most of the prior reports on motion in the extracellular space used the collagen gel as the ECM model. For instance, Kihara et al.^{34} suspended the fibroblast cells in the collagen gels and analysed diffusion using FCS. In contrast to our results, the diffusion within the fibroblast-contracted collagen gel of molecules with r_{p} from 1 to 10 nm follows the Stokes–Sutherland–Einstein relation.^{35,36} Consequently, the D_{eff}/D_{0} ratio is constant, irrespective of the probe size. This result may be explained by the fact that for such a narrow range of molecular radii, the authors do not observe all the length scales of the hydrodynamic flow around the probe particles.

A key study of macromolecules’ diffusion in tumours was demonstrated experimentally by Pluen et al.^{32} Diffusion coefficients of FITC-conjugated particles in tumours growing in cranial windows (CW) and dorsal chambers (DC) were measured by fluorescence recovery after photobleaching (FRAP). As an outcome, it was found that D does not decrease linearly with an increasing radius of the probe. It has been suggested that an unexpectedly more significant decrease in the diffusion of larger molecules can be described by the concept of tortuosity. Here we propose a different explanation of their results. The observed reduction of the diffusion coefficient is well described by our length-scale dependent viscosity model. We used the data obtained for the tumours growing in the cranial windows (CW)^{32} to plot the dependence of the effective viscosity of the tissues on the radius of the probes, as shown in Fig. 7. The value of the correlation length for the CW tumours (obtained from the fitting of eqn (2)) is as follows: ξ = 10.17 ± 1.74 nm, which revealed that the concentration of the crowding agents is higher than that in spheroids (ξ = 19.31 ± 5.08 nm). Interestingly, we found that the hydrodynamic radius of the obstacles R_{h} = 22.98 ± 4.05 nm in the tumours is almost the same as the value obtained for the spheroids, R_{h} = 23.62 ± 5.75 nm, which clearly indicates the same size of the obstacles present in both the ECMs.

Fig. 7 The logarithm of the effective viscosity experienced by the nanoprobes of radii r_{p} moving in the CW tumours^{32} and spheroids (the average value for all 3 cell lines). The solid lines calculated from eqn (2). The error bars correspond to the maximal error calculated on the basis of standard deviations of measurements. |

Furthermore, the devised methodology allows to predict the motion of any probe particle directly from the displayed curve of the length-scale dependent viscosity. Based on the presented results and under the assumption that the effective viscosity of the ECM is the same in all parts of a tumour, we can calculate the time needed to cross a given distance by particles of any size (using the relation: t = x^{2}πηR/kT^{35}). For instance, the doxorubicin molecule (common chemotherapeutic with a radius of 0.7 nm) needs 22 seconds to pass through 200 μm of the tissue. On the other hand, the same active ingredient encapsulated in the liposome of ∼95 nm in the radius (Myocet®) requires over 8 hours (precisely 497 minutes).

It shows that diffusion can not only be significantly altered but also controlled by means of particles’ size. This outcome also correlates with markedly different pharmacokinetics of both drugs. The accumulation of bigger therapeutics in tissues and as a consequence a longer duration of their action at the target site enhances the treatment efficacy of liposomal DOX compared with the conventional doxorubicin.^{7,37}

Our method of analysis of extracellular transport using spheroids seems to be a good compromise connecting the simple approach involving artificial ECM models^{34} and the advanced investigations with the use of animals.^{32} The ECM of spheroids provides an accurate imitation of the native ECM, maintaining the simplicity of cell culturing. The structure of the ECM of the compact spheroids does not change over time, which is manifested as constant interfibrillar spacing observed over the days (Fig. 5).

An additional advantage of our approach is the possibility to test factors influencing the ECM structure. Based on the diffusivity measurements and the length-scale dependent model, we can verify the anti-fibrosis properties of any compound. It can be useful in the assessment of novel therapeutic strategies using ECM-oriented cancer treatments.^{38,39} As an example, we examined the effect of decorin on HeLa spheroids. We estimated that the effective viscosity experienced by the liposomal DOX in spheroids exposed to decorin would be over 2 times higher than in the non-treated HeLa spheroids.

The length-scale dependence of viscosity of the ECM has its impact on drug distribution in tissues. While small drug carriers (smaller than 10 nm) move freely through the ECM, larger ones encounter diffusion hindrance. Free diffusion of small molecules – revealed in our study – also lead to important questions concerning the biology of 3D cultures. The majority of works on spheroid indicate “diffusion hindrance” as a significant factor causing hypoxia and deficiency in nutrients in the necrotic core of spheroids.^{13} Our results, however, suggest that diffusion of oxygen or glucose should remain unobstructed due to their small sizes (less than 0.4 nm in radius), and there should be other, more significant factors determining their shortage in the core of the spheroids.

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## Footnote |

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d0nr01986k |

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