Introduction

In the realm of cancer research, chemical stimuli, such as nutrients diffusing from blood vessels and catabolite gradients from the tumour core, play a pivotal role in cancer invasion1,2,3,4. The presence of a stimulus can drive tumour invasion through morphological instability5,6, leading to the separation of cell clusters and the subsequent metastatic spread of cells from the primary tumour7,8,9.

Chemotaxis, the process of cells migrating in response to concentration gradient generated by soluble molecules, has garnered significant attention in the literature, especially given its prognostic and therapeutic potential in cancer10,11,12. Cell movement in response to gradients of molecules is extensively studied by using different methods, including 2D or 3D in vitro assays, ex vivo assays and mathematical models, referred to as in silico models13,14,15,16,17,18,19,20.

2D models fail to recapitulate the organization of tumour microenvironment because of the lack of biological features of a native tumour microenvironment, normally found in 3D models, e.g., cell–cell interactions, extracellular matrix (ECM), chemical concentration gradients, eventual vascularization and necrosis within the tumour21,22,23. Most importantly, the lack of encapsulated cells within 3D ECM-based matrices, as well as the absence of cell–cell interactions, could influence biological findings.

From this standpoint, 3D cell culture models have emerged as a promising platform to mimic some features of solid tumours24. An increasingly diffused 3D model is represented by tumour spheroids, i.e., tightly bound multicellular aggregates composed of hundreds to thousands of cells, able to mimic non–vascularized cancer masses22,24,25. 3D spheroids are able to accurately mimic some features of solid tumours, such as their spatial organization, gene expression patterns, physiological responses, secretion of soluble molecules and drug resistance mechanisms24. As solid tumours, multicellular spheroids, being characterized by nutrients and catabolite gradients (increasing and decreasing from outer to inner regions, respectively), have an internal structure that comprises different cell layers: a necrotic core, an internal quiescent zone and an external proliferating region26. Thanks to their unique characteristics, multicellular tumour spheroids are broadly used as in vitro models of proliferation and invasion assays of cancer cells, as well as drug studies.

Several experimental approaches have been proposed over the years to investigate, both qualitatively and quantitatively, tumour cell progression in response to chemotactic stimuli: the Boyden assay27,28 and its modified methods29,30,31,32, the under-agarose assay33, and microfluidic devices21,34,35,36. Although simple, these approaches suffer from many limitations and disadvantages, e.g., inability for real–time monitoring of morphology and migration response of biological system (especially for the Boyden assay), inaccurate control of chemical stimuli, especially for long time experiments, and consumption of a large amount of expensive bioactive factors. In addition, most of the microfluidic methods require accurate active pumping to generate a chemotactic gradient, making their handling quite complicated37.

In this paper, we propose an in vitro tumour invasion assay for studying the invasion of tumour cells in response to chemotactic stimuli with the aim to overcome most of the abovementioned technical limitations and drawbacks. Our method employs tumour spheroids seeded in a 3D collagen gel to mimic the ECM due to its significance as the primary structural component, offering several advantageous properties, including biocompatibility and biodegradability, making it suitable for diverse medical and biological applications35. This low-cost and reusable setup is designed for generating stable external chemical stimuli, even in long-term experiments38. In addition, this chemotaxis chamber is compatible with Time–Lapse Microscopy (TLM) imaging, allowing real–time monitoring of cell dynamic evolution.

The in vitro experimental approach here proposed investigates the role of transport phenomena, in particular diffusive flows, on tumour morphological instability. In detail, gradients of fetal bovine serum (FBS) are generated in the chemotaxis chamber in order to investigate the invasiveness potential of multicellular spheroids of CT26 mouse colon carcinoma cells. It is known that FBS contains a number of chemoattractant molecules, including growth factors, making it a relevant model system for studying the chemical cues influencing cancer cell behaviour35,39. Specifically, two different gradients of FBS molecules are generated starting from two different FBS solutions (10% and 100% FBS). These two experimental conditions are referred in this study as ∇C 10% and ∇C 100%, respectively. As a control, uniform concentration of FBS at 10% is employed to mimic standard cell growth conditions, referred to as ISO 10%. Furthermore, the dynamic behaviour of tumour cell spheroids in a nutrient-depleted environment, specifically with FBS at 0%, is also investigated and referred to as ISO 0%. Utilizing an image analysis software, the morphological response of tumour spheroids is quantified by measuring the evolution of area over time and observing single cells invading the surrounding ECM. This analysis aims to establish a correlation between the experimentally measured degree of invasion and the imposed nutrient gradient.

Particularly, the imposed chemical stimulus, specifically the diffusive flow of nutrients, is quantified using a finite element in silico model of the experimental system, based on the Fickian diffusion model. Glucose, one of the major components of cell culture medium, has been used as a reference molecule to model the concentration gradient in the chemotaxis chamber, since it is a key component of FBS.

Materials and methods

In this section, methodologies employed to investigate the dynamics of tumour cell invasion in response to chemotactic stimuli are detailed. Our experimental approach utilizes CT26 mouse colon carcinoma cells and incorporates spheroid formation techniques to accurately replicate the tumour mass. Central to our study is the use of a custom-designed chemotaxis chamber, which allows to create a controlled and reproducible chemoattractant gradient. The following subsections offer an in-depth description of the methodologies employed, ranging from cell culture and spheroid preparation to the design and functioning of the chemotaxis chamber, as well as detailed procedures for experimental setup, imaging, and statistical analysis.

Cell cultures and spheroids formation

CT26 mouse colon carcinoma cells (ATCC CRL-2638) were cultured in Dulbecco’s Modified Eagle Medium (DMEM, Invitrogen), enriched with 10% fetal bovine serum (FBS, Invitrogen) and antibiotics (100 μg/mL streptomycin and 100 U/mL penicillin; Gibco BRL). The cells were maintained in a humidified atmosphere with 5% CO2 at 37 °C, and the medium was refreshed every two days.

CT26 spheroids were prepared according to the classical agarose protocol40. Briefly, the wells of a 48-well plate (Nunclon Δ Multidishes, flat-bottom, ThermoScientific, Nunc 150687) were coated with agarose solution 1% in water (Ultrapure agarose, Invitrogen, Carlsbad, CA). Agarose solution was let polymerize at room temperature. The non-adhesive concave surface provided by agarose gel promotes the collection of cells, seeded at a concentration of 2∙103 cells per well, in the meniscus and cell–cell adhesion establishment. The 48–well plate was then incubated under typical cell culture conditions for ~ 7 days in order to obtain compact cell spheroids. Further details are reported in a previous paper41.

Chemotaxis chamber

Chemotaxis assays were performed using a specialized chamber38,42, which is depicted in Fig. 1A. The chamber consists of a single metal block, which was securely glued on top of a microscope glass slide (24 × 24 mm) using a wax-Vaseline mixture (1:1 by weight). A porous membrane (0.22 µm pore size, MF-Millipore), held in place between two metal frames, was used to divide the chamber into two distinct compartments, one serving as a reservoir for the chemoattractant solution (chemoattractant reservoir) and the other containing the collagen gel seeded with cell spheroids (sample well). The total length of the chamber, including the chemoattractant reservoir (0.5 cm), membrane section (0.2 cm), and sample well (1 cm), is approximately 1.7 cm, with a width of approximately 0.6 cm. During the assay, the chemoattractant molecules diffused from the chemoattractant reservoir across the porous membrane, thus generating a concentration gradient in the collagen gel filling the sample well. This design allows for the precise control and monitoring of chemotactic responses in a defined and stable gradient environment.

Figure 1
figure 1

(A) Top view of the chemotaxis chamber, allowing to perform two assays in parallel. The sample well (upper compartment) and the chemoattractant reservoir (lower compartment) are created by two metal frames sandwiching a porous membrane. (B) Scheme of one section of the chemotaxis chamber used for numerical simulation: on the top the sample well embedded with cell spheroids (black dots), in the centre the porous membrane through which the diffusion of the molecules takes place, on the bottom the chemoattractant reservoir. An individual spheroid is delineated by a dashed line box as an example, with an accompanying image provided thereafter. (C) Image of a cell spheroid embedded in collagen gel. The edge of the spheroid and the edge of the necrotic core are marked (outer and inner white circles, respectively); the direction of the gradient is also shown. (D) Image of a cell spheroid in collagen gel with some single cells escaping from the spheroids underlined in black. The spheroid is subdivided into 3 different directions (north, south and sides) according to the angular region in which they are. The x and y axis, as well as the angles, are also reported according to the way they have been defined in the analysis. The direction of the gradient is the same reported for (C).

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Experimental design and setup

The assays were performed in a three-dimensional collagen gel composed of 2 mg/mL collagen I solution (BD Biosciences) mixed with 10 × PBS and DMEM; 1 M NaOH was added to adjust the pH of the solution to approximately 7.

For chemotaxis assays (∇C 10% and ∇C 100%), 170 µL of collagen gel solution, not containing any cell spheroid, were added in the sample well of the chamber. An incubation time of 20 min at room temperature allowed to achieve 50% polymerization of the collagen solution43. Then, 200 µL of collagen gel solution, containing about 10 cell spheroids, were poured on top of the half polymerized collagen gel layer. The spheroids were carefully spaced to avoid coalescence or chemotaxis from nutrients derived from neighbouring spheroids. The complete polymerization of the collagen solution was allowed at room temperature for 40 min. Gravity induced sedimentation of cell spheroids, which resulted to be embedded in the collagen gel at a fixed quota, corresponding to the interface between the two layers of collagen gel. Afterward, chemoattractant solution was added to the proper compartment of the chamber, i.e. the chemoattractant reservoir.

In the assays here proposed, FBS was used as nutrient source since it contains a large number of chemoattractant molecules, including growth factors, stimulating cell migration39. In order to stimulate cell spheroids with different chemotactic stimuli, different chemoattractant concentrations were used. Specifically, the chemoattractant reservoir was filled with a solution of FBS 10% (vol/vol) in DMEM (referred as ∇C 10%), or 100% (referred as ∇C 100%).

A control experiment in nutrient-depleted conditions (0% FBS) was also carried out, following the same protocol in the preparation of collagen gel embedded with spheroids. In this assay (ISO 0%), DMEM without FBS was used in the chemoattractant reservoir.

Reliability of chemotaxis conditions was confirmed by comparison with an isotropic control condition, ISO 10%, mimicking standard cell culture condition. In this assay, collagen solution (300 µL) without cell spheroids was added to the entire chamber, where the two compartments were merged together without adding the two metal frames and the membrane. After half polymerization of the collagen solution at room temperature for 20 min, 400 µL of collagen gel solution, supplemented with 10% (vol/vol) FBS and containing about 20 spheroids were poured on the top. Collagen solution was allowed to polymerize at room temperature for 40 min.

In all assays, cell culture medium was added to the sample well at the proper composition (depending on the experimental condition), after collagen polymerization, to prevent gel dehydration.

Chemoattractant stimuli simulations

To accurately quantify the chemoattractant concentration profile within the chemotactic chamber, finite element analysis was employed. This approach enabled to estimate the specific chemotactic stimulus felt by each spheroid along various directions. In particular, the diffusion and consumption of glucose, which is one of the components of FBS (\(6.94\text{ mol}/{\text{m}}^{3}\)), was simulated.

The chemotaxis chamber was modelled in 2D using COMSOL Multiphysics® 5.5 Software (https://www.comsol.it), as reported in Fig. 1B. Nutrient concentration was confined to a 2D simulation due to the experimental setup where spheroids were positioned between two layers of matrix, resulting in approximately the same z-position for all spheroids.

The chamber geometry was divided into three sections, corresponding to the chemoattractant reservoir, the membrane and the collagen gel embedded with cell spheroids. The spheroids were placed in the collagen gel compartment according to the experiments. The mesh was set extremely dense with triangular unstructured elements; this type of mesh is flexible and can adapt well to complex geometries, allowing for increased precision without significantly affecting computational time. For boundary and initial conditions: \(\forall \text{ t}>0 :{\text{C}}_{\text{A}}={\text{C}}_{0}\text{ for x}=0\text{ and }{\text{ C}}_{\text{A}}\) = 0 for \(\text{x}\to \infty ;\) \(\forall \text{ t}\le 0: {\text{C}}_{\text{A}}=0\text{ for x}=0\), as in our previous work41.

To simulate the diffusion of glucose in the ∇C 100% condition, an initial glucose concentration of 6.94 mol/m3 was considered, while 10% of the value (0.694 mol/m3), was used in the ∇C 10% condition.

In the section corresponding to the chemoattractant reservoir, the diffusion of glucose follows the classic Fickian diffusion model:

$$\frac{\partial {\text{C}}_{\text{g}}(\text{x},\text{t})}{\partial \text{t}}= -{\text{D}}_{\text{g}}\frac{{\partial }^{2}{\text{C}}_{\text{g}}(\text{x},\text{t})}{\partial {\text{x}}^{2}}$$
(1)

where Cg is the concentration of diffusing molecule, t is time, x is the spatial direction along which the diffusion occurs, and Dg is the diffusion coefficient of glucose in water (9.25∙10–6 cm2⁄s).

In the section corresponding to the porous membrane, glucose diffuses according to free Fickian diffusion in a porous medium. The diffusivity of glucose in the membrane, 3.24∙10–6 cm2/s, was calculated starting from the diffusivity of glucose in water, considering the empty fraction and the tortuosity of the membrane, according to data provided by the manufacturer.

In the section corresponding to collagen gel, glucose diffuses according to free Fickian diffusion as well. Preliminary calculations of glucose gradients were obtained approximating the collagen matrix, where the glucose diffuses, to a semi-infinite medium38,41,42. The diffusion coefficient of glucose in the collagen gel (Dg,coll = 7.63∙10–6 cm2/s) was determined scaling with the molecular weight the diffusion coefficient of FITC-dextran (10 KDa) in collagen gel (2∙10–6 cm2), which was experimentally measured38,42. Concerning cell spheroids, they were divided in two domains, corresponding to the necrotic core and the outer rim of live proliferating cells. In the domain corresponding to the necrotic core only diffusion takes place, following the classic Fickian diffusion model in spherical coordinates:

$$\frac{\partial {\text{C}}_{\text{g}}}{\partial \text{t}}= \frac{{\text{D}}_{\text{g},\text{s}}}{{\text{r}}^{2}}\frac{\partial }{\partial \text{r}}\left(\frac{{\text{r}}^{2}\partial {\text{C}}_{\text{g}} }{\partial \text{r}}\right)$$
(2)

In the proliferating shell, both glucose diffusion and consumption occur:

$$\frac{\partial {\text{C}}_{\text{g}}}{\partial \text{t}}= \frac{{\text{D}}_{\text{g},\text{s}}}{{\text{r}}^{2}}\frac{\partial }{\partial \text{r}}\left(\frac{{\text{r}}^{2}\partial {\text{C}}_{\text{g}} }{\partial \text{r}}\right)-\text{R}$$
(3)

Here, \(\text{r}\) is the radius of the spheroids and Dg,s is the diffusivity of glucose in cell spheroids (1.24∙10–6 cm2/s) 44. The latter one is calculated considering that Dg,s = F∙Dg,coll, where \(\text{F}\) is the fraction of tissue volume that is extracellular space (~ 16.2%)44. Glucose uptake by the cells of the proliferating rim follows Michaelis–Menten kinetics \(\left(\text{R}=\frac{{\text{V}}_{{\rm max}}{\text{C}}_{{\rm g}}}{{\text{K}}_{{\rm m}}+{\text{C}}_{{\rm g}}}\right)\), with a VMAX of 10–2 mol/m3/s and KM of 8 mol/m344. We assumed that the glucose uptake of colon carcinoma cells occurs at a rate (1∙10–2 mol⁄m3/s) that is lower than brain tumour cells and normal brain cells45, which consume glucose at a rate of 1∙10–1 mol⁄m3s and 2.5∙10–2 mol⁄m3s, respectively44. Values of each parameter used in the finite element analysis are reported in Table 1.

Table 1 Values of each parameter used in the finite element analysis in order to calculate concentrations gradients and estimate the chemotactic stimulus for each domain of the chamber and for all conditions investigated.
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Chemoattractant concentration profile was obtained for the experimental conditions under investigation (ISO 0%, ISO 10%, ∇C 10% and ∇C 100%, on rows in the Fig. 2). The concentration of glucose (C), normalized with respect to the value at the centre of spheroid (C0), and the specific gradient (SG) in close proximity to the spheroid are reported as function of the gradient direction (y-axis), normalized with respect to the initial position of the spheroid (y0). For each experimental condition, the profiles are reported for four time points (18, 24, 36 and 44 h). As shown in Fig. 2, in all conditions the concentration profile decreases along the y/y0-axis and evolves in time, due to the transient bulk diffusion from the chemoattractant reservoir. Moreover, a notable drop is concentration is visible in correspondence of the spheroid position, due to nutrient consumption by the spheroid. Variations along the x-axis are negligible compared to the y-axis41 (data not reported for the sake of brevity).

Figure 2
figure 2

Numerical simulation of the concentration profile near a spheroid, normalized with respect to the value at the centre of the spheroid (C/C0), and the specific gradient (SG, cm−1) of the nutrient (glucose) for all experimental conditions here investigated (ISO 0, ISO 10%, ∇C 10, ∇C 100%). C/C0 and SG are reported as function of the main direction (gradient direction, y/y0) for different time values (18, 24, 36 and 44 h).

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A direct comparison of all conditions investigated shows that C/C0 variation for ∇C 10% and both ISO conditions are slightly negligible respect to the ∇C 100% condition (along a distance − 2R0 the normalized concentration C/C0 value is 1.05 ∇C 100%, while changes in the range 1–1.02 for other conditions investigated, at a fixed time of 18 h). Similar result is observed about SG (1.4 cm−1 for ∇C 100%, 0.34 cm−1 ∇C 10%, ~ 0 cm−1 for ISO conditions along a distance − 2R0 at 18 h).

This study validates our understanding of the four conditions investigated, confirming the reliability of our control condition (ISO 10% condition). Additionally, the results obtained from the numerical simulations revealed that the concentration gradients in the North direction are comparable to those calculated in the South direction at the spheroid interface. This aspect will be considered in the evaluation of cell migration (see section "Migration effect").

Imaging by Time-Lapse Microscopy

Time–Lapse imaging was performed by using an inverted microscope (Nikon Eclipse Ti, 10 × /0.3-N.A. dry objective; Nikon Instruments) equipped with a motorized stage (Märzhäuser) and climate control system (The Brick; Life Imaging Systems). The microscope and the videocamera (CoolSNAP HQ2; Photometrics) were driven by Metamorph software (Molecular Devices, https://it.moleculardevices.com). The frequency of acquisition was 1 frame every 30 min, and the total experimental length was 44 h. Several spheroids (typically more than five for each experimental condition) in the chemotaxis chamber were imaged periodically scanning five layers separated by a 50 μm distance along the focus (z) direction (z-stack) within the collagen gel.

Image analysis

To quantify the impact of chemical stimuli on cell spheroid evolution, the size of cell spheroids and their necrotic core (As and Ac, respectively) were measured at different time points by using an image analysis software (Image Pro Plus 6.0, Media Cybernetics, https://mediacy.com/image-pro), distinguishing between two regions based on variations in mean light intensity, where the necrotic core appeared darker and the outer section appeared lighter47,48. The contour of the spheroids and of its necrotic core were manually drawn, as shown in the Fig. 1C, on the diametral plane of the z-stack (image 3/5) at six time steps (0, 8.5, 17, 26, 34.5 and 43.5 h), equally spaced along the entire experiment length. The viable rim δ of the spheroids was also defined as the difference between the diameter of the spheroid and the diameter of its necrotic core.

To investigate cell invasion, the number of cells moving from the spheroids and invading the 3D matrix was determined by manually counting single cells using the same image analysis software. Cells were grouped based on their position relative to the chemoattractant flow, defining three distinct spheroid regions with respect to the angle of position (θ):

  • North: section of the spheroid edge corresponding to the angular region included between 45° and 135°, i.e., opposite with respect to the source of chemoattractant;

  • South: section of the spheroid edge corresponding to the angular region included between 225° and 315°, i.e., facing the source of chemoattractant;

  • Sides: two lateral sections of the spheroid, orthogonal to the direction of the chemotactic gradient, corresponding to the angular regions included between 135° and 225°, and 315° and 45°.

The three sections are delineated by white dashed lines in Fig. 1D.

In order to better quantify the effect of chemical stimulus on cell invasiveness, two parameters were defined: (Ns + Nn)/Nside and Ns/Nn where Nn, Ns and Nside are the cells number invading the surrounding in correspondence of the north, south and side regions of the spheroids, respectively. In detail, (Ns + Nn)/Nside allowed to compare the invasion effect along the gradient direction (Ns + Nn) and in the orthogonal direction (Nside). If this parameter is equal to 1, cells invade isotropically, i.e. equally along the gradient direction and in the orthogonal direction; (Ns + Nn)/Nside > 1 suggests that cells preferentially invade along the direction of the chemoattractant flow. Ns/Nn was quantified to compare the invasiveness in the direction of the chemoattractant source (Ns) to the invasion of cells from the opposite side of the spheroid (Nn). If this parameter is equal to 1, cells invade equally towards the chemoattractant source and in the opposite direction, with no difference with respect to the source position; Ns/Nn > 1 corresponds to a preferential invasion of cells toward the chemoattractant source, thus suggesting that there is chemotactic effect.

The impact of each chemical stimulus and the degree of invasiveness were further quantified by measuring the distances travelled by individual cells into the surrounding matrix in the three direction defined with respect to the chemoattractant flow (North, South and Sides, as previously mentioned). Specifically, the (x, y) position of each cell was tracked to determine the distance \((=\sqrt{{(\text{x}}^{2}+{\text{y}}^{2})})\) from the interface of the spheroid at time 0. The distance was measured at various time points throughout the analysis.

Statistical analysis

In our study, a minimum of five spheroids were analysed for each of the four conditions investigated (ISO 0%, ISO 10%, ∇C 10%, and ∇C 100%). Data are presented as the mean ± standard error of the mean (SEM). Comparisons among data obtained for the four experimental conditions under investigation were performed using one-way analysis of variance (ANOVA) and the Bonferroni correction, in order to counteract the multiple comparisons problem. Results were considered statistically significant in the case of a p value < 0.05 (further details of specific p values are reported in figure captions).

Results

The chemotaxis assay proposed in this study is used as a systematic in vitro validation of the Diffusional Instability Model. In the assays here proposed, the growth and invasiveness of CT26 tumour spheroids are stimulated using FBS as a chemoattractant. We validate the model by examining two experimental conditions, ∇C 10% and ∇C 100%, and comparing these with two different isotropic control conditions, ISO 0% and ISO 10%. The experimental results are detailed in the following section, providing a comprehensive analysis of model's efficacy in replicating the complexities of tumour spheroid behaviour under various chemotactic stimuli.

Microscopy investigation

In Fig. 3, representative phase contrast microscopy images of CT26 tumoral spheroids are reported as a function over time and across different experimental conditions. The images are organized into columns, each representing a distinct time point from the start of the experiment (t = 0, 8.5, 17, 26, 34.5, and 43.5 h). The rows display the varying experimental conditions: ISO 0%, ISO 10%, ∇C 10%, and ∇C 100%. In each row, a spheroid, representative of a specific experimental condition, is shown at the respective time intervals.

Figure 3
figure 3

Representative phase-contrast microscopy images showing the morphological response of CT26 spheroids at six different time points (0, 8.5, 17, 26, 34.5, and 43.5 h) for four different conditions (ISO 0%, ISO 10%, ∇C 10% and ∇C 100%). Images in each row of the panel are relative to a single spheroid, taken as a representation of a given experimental condition. Scale bar: 200 \(\mu\) m.

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A preliminary visual analysis of the Time-Lapse images reveals that the CT26 spheroids exhibit a tendency to grow and invade the surrounding matrix in ISO 10%, ∇C 10%, and ∇C 100% conditions. This behaviour is particularly pronounced in the most stimulating condition, ∇C 100%, where a significant increase in spheroid area is observed. Additionally, in this condition, many cells exhibit invasive motility, migrating away from the spheroid into the 3D collagen gel, thereby mimicking invasive behaviour in living tissues.

In the ∇C 10% condition, the spheroid does not show significant morphological changes during the whole experiment and only a few cells leave the spheroid. In fact, in this condition cells experience low chemical stimulus.

The reliability of these observations is reinforced by comparison with the control conditions (ISO 10% and ISO 0%). In ISO 10%, mimicking the standard growth condition for cells, the spheroid significantly grows over time and many cells leave the spheroid invading the surrounding. The behaviour of cell spheroids in ∇C 100% appears to be similar to ISO 10% control condition, thus suggesting that in ∇C 100% chemotactic conditions cells are highly stimulated, inducing both growth of the spheroids and invasion of cells in the surrounding matrix.

Under isotropic stress condition ISO 0%, mimicking lack of nutrients, no significant change is observed in the area of the spheroid and only few cells leave the spheroid.

Growth effect

Image analysis was utilized to conduct a quantitative assessment of the experimental observations preliminarily noted in the images. In Fig. 4, the evolution of spheroid and core area, normalized to their value at t = 0 h, AS/AS0 and AC/AC0 respectively, is reported as a function of time (Fig. 4A and B, respectively) for both ISO (on the left) and \(\nabla\) C (on the right) conditions. The evolution of the viable rim, δ, defined as the difference between spheroid and necrotic core diameter, is also reported as a function of time (Fig. 4C).

Figure 4
figure 4

(A) Temporal evolution of the CT26 spheroid area, normalized to its value at t = 0 h (AS/AS0), for ISO 0 and ISO 10% (left panels), and \(\nabla\) C 10 and \(\nabla\) C 100% (right panels). (B) Temporal evolution of the CT26 spheroid necrotic core area, normalized to its value at t = 0 h (AC/AC0), for the same conditions as A. (C) Temporal evolution of the CT26 spheroid viable rim thickness (δ [μm]) for all conditions investigated. The error bars represent the standard error of the mean of measurements at each time point (t [h]).

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No significant differences can be detected in the morphological responses of cell spheroids in ISO 0% and \(\nabla\) C 10% settings. In fact, in both conditions, the area of the spheroid is quite constant over time and does not change significantly at the end of the experiment compared to its value at t = 0 h. A/A0 at 48 h is 1.02 for ISO 0% and 1.03 for \(\nabla\) C 10%, suggesting that the nutrient levels are probably not sufficient to promote spheroid growth. Accordingly, the necrotic core area of the spheroids increases over time (1.20 × and 1.50 × for ISO 0% and \(\nabla\) C 10% conditions, respectively) due to the lack of nutrients. Therefore, the viable rim decreases over time. These findings suggest that in ISO 0% and \(\nabla\) C 10% conditions the spheroids growth is not stimulated.

In IS0 10% and \(\nabla\) C 100%, instead, a growth of the spheroids can be detected. Specifically, under the ISO 10% condition, both spheroid and core areas significantly increase over time (1.90 × and 1.52 × at 43.5 h, respectively), indicating favourable cell growth conditions. As a result, with the spheroid expansion exceeding that of the core, the viable rim δ of the spheroids increases over time (reaching 115.03 ± 8.83 µm at 43.5 h). In the \(\nabla\) C 100% setting, an increment in spheroid area is observed up to 36 h, similar to ISO 10% condition. However, a stabilization of spheroid area is observed after 36 h. A similar trend is observed for the core area, which increases during 36 h and then seems to reach a plateau value. As result, in this case, the viable rim increases over time, reaching a lower value compared to isotropic condition (94.2 ± 8.9 µm and 115.03 ± 8.83 µm for \(\nabla\) C 100% and IS0 10%, respectively). These findings suggest that in ISO 10% and \(\nabla\) C 100% conditions the chemical stimulus is capable to induce the growth of cell spheroids and, more specifically, the increase of the viable rim, δ.

Migration effect

To assess the impact of the chemoattractant stimulus on the invasion of single cells from the spheroid in the surrounding matrix, cells leaving the spheroids were counted and reported as function of the invasion direction respect to the chemoattractant gradient direction. In Fig. 5, the migration response to the chemical stimulus is reported using polar plots for isotropic and chemotaxis conditions (ISO 0% and ISO 10% in the first row, \(\nabla\) C 10% and \(\nabla\) C 100% in the second row) at a fixed time (26 h, half of the entire experimental duration). Each panel features the morphological response of a specific spheroid, representative of its respective experimental condition, at the selected time step. Notably, the phase contrast microscopy image of a CT26 tumour spheroid is placed at the centre of each polar plot, denoting the spheroid's centre.

Figure 5
figure 5

Polar plots showing the distribution of cell migration from the spheroid under four experimental conditions. The top row illustrates the cell distribution for ISO at 0% (left) and 10% (right), while the bottom row shows the distribution for \(\nabla\) C at 10% (left) and 100% (right). Each plot represents the morphological response of a representative spheroid at 26 h time point. The spheroid image is centrally placed within each polar plot to visually correlate cell positions with their distance and angular orientation from the spheroid's center. The radial axis indicates the distance from the spheroid in micrometers (µm), and the angular axis represents the direction of cell migration in degrees.

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As shown, for the ISO 0% a limited number of cells migrate from the spheroid, likely due to the absence of serum providing insufficient stimulus for invasion into the surrounding gel. Conversely, a relevant number of cells leave the spheroid in the ISO 10% setting and, from a visual inspection, without any preferential direction, as would be expected in an isotropic environment.

In the case of \(\nabla\) C 10% condition, only few cells leave the spheroid, probably due to the low concentration of nutrients. On the other hand, in \(\nabla\) C 100% condition, where the concentration of nutrients is higher, a larger number of cells is observed to migrate away from the spheroid. Moreover, at a visual inspection, these cells seem to invade the collagen matrix predominantly in the direction of the chemoattractant source; in fact, there are more cells in the lower section of the chart in Fig. 5. This directional preference underscores the influence of the chemotactic gradient on cell migration, providing a clear depiction of how varying chemoattractant levels can steer the invasive behaviour of tumour cells.

In order to quantify the invasion and migration abilities of cells under different conditions, the cells migrating away from the spheroids at different time steps were counted. In Fig. 6A, the total number of invading cells (Ntot) is reported at different time steps for the experimental settings under investigation. Across all four conditions – ISO 0%, ISO 10%, ∇C 10%, and ∇C 100%—a gradual increase in the number of invading cells is observed over time. In the ISO 0% condition, the invasion level is relatively low, with an average of only about 30 cells invading by 43.5 h, as illustrated in Fig. 6A. This observation aligns with the limited stimulus provided to the cells in this environment. The ∇C 10% condition shows a slightly higher level of invasion, with approximately 78 cells invading in 43.5 h. This suggests that, although the stimulus is stronger than in the ISO 0% condition, it is likely not strong enough to promote significant spheroids growth (as shown in Fig. 4). However, it is sufficient to induce some degree of single-cell invasion. For the \(\nabla\) C 100%, the number of invading cells is higher (at 43.5 h, the average number of cells is 127) compared to ISO 0% and \(\nabla\) C 10% conditions, suggesting that cells experience a stimulus that is strong enough to escape from the spheroid and invade the surrounding matrix. However, the stimulus is not as strong as in ISO 10% condition, in which the number of invading cells is much higher in respect to the other three conditions (at 43.5 h, the average number of invading cells is 294). This condition represents a good positive control, highlighting that the growth factors contained in the serum were effectively stimulating cell invasion into the surrounding matrix.

Figure 6
figure 6

(A) Total number of cells (Ntot) migrating from the spheroids over time, presented for all experimental conditions. Significant differences (p value < 0.05) are noted for each data point at times greater than 8.5 h. (B) \(({N}_{s}+{N}_{n})/{N}_{side}\) reported for each experimental condition at 26 and 44 h, indicating mid and end of the experimental duration. (C) Chemotactic index \({N}_{s}/{N}_{n}\) evaluated at 26 and 44 h for all experimental settings. Error bars represent the standard error of the mean (*p < 0.05, **p < 0.005,***p < 0.0005).

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To evaluate if the chemotactic gradient is able to induce preferential cell invasion along the gradient direction, the number of cells migrating from the spheroids along the direction of the concentration gradient and the orthogonal direction were compared, by defining the parameter \(({\text{N}}_{\text{s}}+{\text{N}}_{\text{n}})/{\text{N}}_{\text{side}}\). As shown in Fig. 6B, in the two isotropic conditions (ISO 0% and ISO 10%), no evident preferential direction of invasion can be detected, as indicated by \(({\text{N}}_{\text{s}}+{\text{N}}_{\text{n}})/{\text{N}}_{\text{side}}\) maintaining a value close to 1 throughout the experiment. In contrast, in chemotaxis conditions, \(({\text{N}}_{\text{s}}+{\text{N}}_{\text{n}})/{\text{N}}_{\text{side}}\) is higher than 1, indicating a preference for invasion in the direction of the gradient. Specifically, for \(\nabla\) C 10% the value is approximately 1.07 and 1.21 at 26 and 43.5 h, respectively. This suggests a gradual preference for invasion along the gradient, becoming more pronounced over time as the chemoattractant diffuses. A similar result is observed for \(\nabla\) C 100% condition; in fact, \(({\text{N}}_{\text{s}}+{\text{N}}_{\text{n}})/{\text{N}}_{\text{side}}\) is approximately 1.31 and 1.18 at 26 and 43.5 h, respectively, with a more marked effect observed in conditions with higher chemoattractant concentrations.

To further investigate preferential cell invasion towards the chemoattractant source, a chemotactic index was defined as \({\text{N}}_{\text{s}}/{\text{N}}_{\text{n}}\). In Fig. 6C, this chemotactic index is reported as a function of time for two key time points: 26 h (halfway through the experiment) and 43.5 h (the end of the experiment), across all four conditions under investigation. At 26 h, \({\text{N}}_{\text{s}}/{\text{N}}_{\text{n}}\) is approximately 1 for both isotropic conditions (ISO 0% and ISO 10%), which aligns with expectations, given the lack of a directional gradient in these settings. In contrast, for the ∇C 10% condition, the ratio is slightly greater than 1 (i.e. 1.13), while for ∇C 100%, it is significantly higher than 1 (i.e. 1.84). These findings indicate that in the chemotaxis conditions, a higher number of cells migrate towards the chemoattractant source, particularly in the case of a stronger chemical stimulus (∇C 100%). This trend is also evident at the 44 h time point. This result aligns with numerical simulations, which revealed comparable concentration gradients in both the South and North directions.

To more accurately quantify the impact of the chemical stimulus on cell invasion into the surrounding matrix, the distances traveled by individual cells was measured, as an indicator of chemotaxis. These findings are presented in Fig. 7. Generally, in both ISO 10% and ∇C 100% conditions, cells travel longer distances compared to the other two experimental settings – approximately twice as far as those in ISO 0% and ∇C 10% conditions. This increased mobility of the cells can be attributed to the higher concentration of nutrients detected by the cells in these environments. Interestingly, in the chemotaxis conditions (∇C 10% and ∇C 100%), the distances traveled by the cells in various directions (south, north, and sides) are found to be almost uniform, as shown in Fig. 7A. This suggests that the chemical stimulus does not significantly affect the distance traveled by the cells in various direction, while it is able to prompt a directional invasion from the spheroid. To highlight the differences between ∇C 10% and ∇C 100% conditions more clearly, we reported in Fig. 7B the distance traveled by cells in the south direction, i.e. the the direction of the chemoattractant source. At 43.5 h, the distance covered in the ∇C 100% condition is significantly greater (approximately 146.64 µm) compared to that in the ∇C 10% condition (about 55.10 µm), reflecting the influence of the stronger chemical stimulus.

Figure 7
figure 7

(A) Distance travelled by single cells in each direction (south, north and side) as defined in section "Image analysis", for all experimental conditions as function of time. (B) Distance travelled by single cells in south direction for \(\nabla\) C 10% and \(\nabla\) C 100% as function of time.

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Conclusions

Tumours exhibiting morphologic instability often display invasive behaviours such as fingering, branching, and fragmentation, driven by differential proliferation along concentration gradients. These spatially heterogeneous behaviours pose significant challenges in understanding tumour dynamics5.

This study successfully addresses the knowledge gap regarding the influence of diffusive gradients of nutrients on cancer growth and cell migration. Our approach, employing the CT26 mouse colon carcinoma cell line, and a chemotaxis chamber, enables a detailed observation of morphologic instability of tumour spheroid driven by differential diffusive nutrient gradients, i.e. FBS. In the assay here presented, we imposed different concentration profiles to tumour spheroids embedded in a 3D collagen matrix. Two experimental conditions (∇C 10% and ∇C 100%) are explored by imposing nutrient depletion, in the presence of anisotropic diffusive flow of FBS, mimicking the presence of a nearby vessel as source of nutrients. Two isotropic control conditions are also considered. In ISO 10% setting, a uniform concentration of FBS at 10% is employed to mimic standard cell growth conditions, whereas in ISO 0% setting, a nutrient-depleted environment (FBS 0%) is created. In both ISO 10% and ISO 0% no preferential direction is imposed.

Within the tumour mass the presence of heterogeneous nutrient distribution places cells on the outer edge in favourable conditions respect to the core of the tumour mass. To overcome these diffusion limitations, tumour spheroids evolve from a compact mass to a structured and fractured morphology, with fingering growth and separation of single cells invading the surrounding 3D matrix.

Our results show a higher number of cells leaving the mass when exposed to higher diffusive gradients (∇C 100% condition), exhibiting a preferential direction along the gradient (south and nord in our terminology). The distance travelled by cells invading the surrounding tissue is higher in conditions of greater nutrient availability (∇C 100% and ISO 10% settings, where the effective concentration of FBS is comparable), but appears to be independent to the direction, also in the presence of gradients. The results suggest that the invasion of cells is driven by the gradient, while the intensity of invasiveness is driven by nutrient concentration. More information about single-cell chemotaxis, including the persistent random walk model and chemotactic index, can be found in our previous work38,42.

We confined nutrient concentration to a 2D simulation due to the experimental setup where spheroids were positioned between two layers of matrix, resulting in approximately the same z-position for all spheroids. Consequently, we focused our attention on the diametral plane, where experimental data are available and considered it to be the most relevant. However, we are aware of the limitations of 2D models and intend to transition to 3D in future studies to gain a more comprehensive understanding of the 3D environment. This will involve correlating the z-position of each spheroid and, consequently, the precise value of nutrient concentration with its impact on cell behaviour. In future analyses, we plan to evaluate the consumption of other nutrients, growth factors, and oxygen.

Our research not only provides new insights into tumour spheroid dynamics but also offers a robust methodology for studying tumour invasion, not only for in vitro systems such as spheroids but also for ex vivo systems such as organoids or biopsies. The application of this assay in drug testing and therapy development could be particularly impactful, especially in targeting nutrient-dependent pathways of tumour progression and bridge the gap between theoretical models and mathematical prediction and clinical practice.