Gompertzian growth pattern correlated with phenotypic organization of colon carcinoma, malignant glioma and non-small cell lung carcinoma cell lines

Abstract

In the current study we present a Gompertzian model for cell growth as a function of cell phenotype using six human tumour cell lines (A-549, NCI-H596, NCI-H520, HT-29, SW-620 and U-251). Monolayer cells in exponential growth at various densities were quantified over a week by sulforhodamine B staining assay to produce cell-growth curves. A Gompertz equation was fitted to experimental data to obtain, for each cell line, three empirical growth parameters (initial cell density, cell-growth rate and carrying capacity - the maximal cell density). A cell-shape parameter named deformation coefficient D (a morphological relationship among spreading and confluent cells) was established and compared by regression analysis with the relative growth rate parameter K described by the Gompertz equation. We have found that coefficient D is directly proportional to the growth parameter K. The fit curve significantly matches the empirical data (P < 0.05), with a correlation coefficient of 0.9152. Therefore, a transformed Gompertzian growth function was obtained accordingly to D. The degree of correlation between the Gompertzian growth parameter and the coefficient D allows a new interpretation of the growth parameter K on the basis of morphological measurements of a set of tumour cell types, supporting the idea that cell-growth kinetics can be modulated by phenotypic organization of attached cells.

Figure 1

Illustration procedure for the SW‐620 cell line to estimate the deformation coefficient D. Phase contrast photomicrographs were analysed in NIH‐image program and two orthogonal cell diameters (r _i, r _j) were measured in both spread (a) and confluent (b) cell culture phenotypes. The cell polarity f is expressed by the ratio f = r _i/r _j. Coefficient D was obtained by the formula D = f ₀/f ₁ − 1, where f ₀ is the cell polarity of spread cells and f ₁ the polarity of confluent cells. A cell foci with heterogeneous cells in shape is shown in (c) and exemplifies the amplitude of cell distortion expressed by the cell deformation coefficient D. At least 30 cells of each line in three experiments were measured to obtain the mean ± SD presented in Table 1 for A‐549, NCI‐H596, NCI‐H520, HT‐29, SW‐620 and U‐251 cell lines. Bar in (c), 50 µm.

Figure 2

Growth curves of monolayer cells. The solid lines are the best‐fit curves of the Gompertz equation 2 and the points are experimental data of our cell panel: SW‐620 (○), HT‐29 (□), U‐251 (▵), NCI‐H520 (•), NCI‐H596 (▪) and A‐549 (▴) cell lines. The cell‐density scale is transformed logarithmically. The growth‐rate constant K derived from the best‐fit curves of each cell line is given in Table 1 and is plotted in Figure 3 along with the deformation coefficient as paired constants (K, D). Each symbol represents the average value of at least three experiments. Standard deviations were typically 10% of the mean for cell number.

Figure 3

Correlation between growth rate parameter K and deformation coefficient D. The points represent pairs of (K, D) determined from morphological measures as illustrated in Figure 1 and from the best‐fit curves presented in Figure 2 for U‐251 (a), NCI‐H520 (b), NCI‐H596 (c), HT‐29 (d), A‐549 (e) and SW‐620 (f) cell lines. The whole data set are given in Table 1, including the confidence intervals (error bars) for each parameter. The Pearson correlation coefficient of the regression equation D = u · K + m is present inside the box. The u and m‐values are empirically determined. Correlation is significant at the level of P < 0.05.

Figure 4

Model prediction of the growth curves. The transformed Gompertzian equation 5 was used to simulate cell growth (solid lines) of the SW‐620 (a), HT‐29 (b), U‐251 (c), NCI‐H520 (d), NCI‐H596 (e), and A‐549 (f) cell lines. Simulations were produced with the deformation coefficient D of each cell line presented in Table 1 and with the constants u + m of the Figure 3, in agreement with the description of equation 5. The best‐fit curves of experimental data (dotted lines) are the same as presented in Figure 2.