Mathematical modeling of drug-induced receptor internalization in the HER2-positive SKBR3 breast cancer cell-line

Abstract

About 20% of breast cancer tumors over-express the HER2 receptor. Trastuzumab, an approved drug to treat this type of breast cancer, is a monoclonal antibody directly binding at the HER2 receptor and ultimately inhibiting cancer cell growth. The goal of our study was to understand the early impact of trastuzumab on HER2 internalization and recycling in the HER2-overexpressing breast cancer cell line SKBR3. To this end, fluorescence microscopy, monitoring the amount of HER2 expression in the plasma membrane, was combined with mathematical modeling to derive the flux of HER2 receptors from and to the membrane. We constructed a dynamic multi-compartment model based on ordinary differential equations. To account for cancer cell heterogeneity, a first, dynamic model was expanded to a second model including two distinct cell phenotypes, with implications for different conformational states of HER2, i.e. monomeric or homodimeric. Our mathematical model shows that the hypothesis of fast constitutive HER2 recycling back to the plasma membrane does not match the experimental data. It conclusively describes the experimental observation that trastuzumab induces sustained receptor internalization in cells with membrane ruffles. It is also concluded that for rare, non-ruffled (flat) cells, HER2 internalization occurs three orders of magnitude slower than for the bulk, ruffled cell population.

Figure 1

Analysis of membrane-bound HER2 level on SKBR3 cells. (A) Membrane-bound HER2 on SKBR3 cells were labeled with an Affibody-quantum dot (QD) to visualize the locations of HER2. Light microscopic image from the QD fluorescence channel acquired for a control group of SKBR3 cells without drug incubation. The typical HER2 distribution, as found in the bulk cancer cells, is characterized by higher HER2 densities (appearing in orange and yellow) on membrane ruffles and at the cell periphery than in flat regions. Three rare flat/resting cells lacking membrane ruffles are marked with asterisks. The QD fluorescence signal is shown in false color (red hot LUT) to better discern the HER2 distribution patterns. (B) Overlay of the original red fluorescence channel image, with the corresponding direct interference contrast (DIC) channel image, yielding additional information of the membrane topography. These overlay images were used to manually mark all individual cells, except incompletely imaged cells at the image borders and small spherical cells. The marking resulted in distinctly coloured regions of interest each defining the area used for the measurement of total membrane-bound HER2 per cell, as calculated from the intensity in the QD-channel image. Scale bars: 100 μm.

Figure 2

Trastuzumab incubation reduces membrane-bound HER2 levels, and changes the cell membrane topography by abolishing membrane ruffles. Shown are images of the QD-fluorescence channel measuring membrane-bound HER2 represented in false color. (A) SKBR3 cells were first incubated for 10 min at 37 °C to label all membrane-bound HER2 with the Affibody, followed by 5 min of incubation with 10 μg/mL of trastuzumab at 37 °C, fixation, and QD labeling. Compared to control cells (see Fig. 1A), the 5 min drug incubation led to a loss of the typically higher HER2 densities on the cell peripheries and on membrane ruffles, as reflected by the absence of membrane areas with orange and yellow color. (B) Results of a pulse-chase experiment in which the Affibody-labeled cells were first incubated with trastuzumab as in A, but for 20 min, followed by wash steps and a 2 h chase period in medium at 37 °C, prior to fixation and QD labeling. Compared to A, the level of membrane-bound HER2 has reduced, membrane ruffles have completely disappeared, and a fraction of the cells have reacted by marked constriction. (C) Extension of the drug incubation to 1 h (without a subsequent chase time) leads to further reduction of membrane HER2 levels. (D) The depicted SKBR3 cells were first incubated for 60 min with trastuzumab, and then labeled with Affibody. This led to similar changes as shown in (C), thus, no reversal of the drug effect by reappearing/recycled HER2 was found. The images were recorded and represented with the same settings. Scale bars: 100 μm.

Figure 3

Testing of HER2 recycling model. (A) Schematic representation of the recycling model. The Affibody binding process is not shown. The processes represented in grey color were found negligible and removed for the final fitting results. (B) Experimental data points and trajectories of the final fit of the recycling model, normalized by dividing by the scaling constant s_c. (C) Fluxes with relevant contributions in the final fit of the recycling model for the condition with 60 min trastuzumab treatment, normalized by s_c. The sign of the flux was chosen such that the backward processes (disassociation and recycling) are negative while all other processes give positive fluxes.

Figure 4

Normalized HER2 bound QD fluorescence intensity distribution. Shown is the difference in trastuzumab induced HER2 removal from the membrane between bulk cells, characterized by more than one membrane ruffle per cell (upper graphs), and flat cells, with no or only one membrane ruffle per cell (lower graphs). The main data set (left side) depicts the early reactions after 2 min (orange), and 5 min (green) of drug incubation, compared to control cells without drug incubation (blue). The validation dataset (right), determined after 60 min of drug incubation, shows a marked shift of the median of the ruffled bulk cell population towards median values of the flat cell population, indicating a more than 50% reduction of membrane-bound HER2 within the bulk subpopulation. The mean HER2 signal distribution of the control flat cells started at already lower mean intensity values, compared to the ruffled cells. At early time points these cells exhibited only small, negligible shifts towards lower intensity values, after 60 min this subpopulation completely failed to show a difference towards the untreated flat cell population.

Figure 5

Testing of extended model including SKBR3 cancer cell heterogeneity. (A) Schematic representation of the model with ruffled and flat receptor populations on the membrane. (B) Fitted model trajectories with data points. (C) Model trajectories separated for the contributions of ruffled and flat regions for the control and 60 min trastuzumab treatment conditions.