Figure 1.
Interactions taken into account in the study.
Two cell types are considered: cancer cells and osteoclasts. Osteoclasts positively affect cancer cells by providing space for tumor growth. Parathyroid hormone-related protein (PTHrP) produced by metastasizing cancer cells induces the expression of receptor activator of nuclear factor kappa-B ligand (RANKL) in bone tissue. RANKL in turn is a potent stimulator of osteoclasts and bone resorption. Osteoprotegerin (OPG) is a decoy receptor of RANKL which binds and eliminates RANKL.
Figure 2.
Active osteoclasts () resorb bone (
) along the gradient (red) of the RANKL field (
), and move from left to right. The tumor (
) invades the space previously resorbed by active osteoclasts. Cancer cells produce PTHrP (
), which diffuses and induces the expression of additional RANKL by osteoblastic bone cells. Cancer cells also produce OPG (
) which diffuses, inhibits RANKL, and hence modifies the RANKL–gradient.
Table 1.
Variables and parameters in model (6).
Figure 3.
The set of initial conditions used for all simulations of the study. The initial RANKL field consists of host–tissue RANKL only, and is of constant concentration . The initial profile of active osteoclasts (OC) is placed in the middle of the domain. Initially, there is no tumor present. Not shown above are the following fields: the bone tissue is intact, i.e.
, and the OPG and PTHrP concentrations are uniformly zero. Note that the initial conditions are consistent with the choice of periodic boundary conditions.
Figure 4.
Host tissue RANKL and systemic OPG.
A Starting from the initial conditions described in Figure 3, the RANKL concentration, osteoclast population density (OC) and tumor density (Tumor) are shown at 30, 60 and 90 days, respectively. The outcomes for three different values of the host-RANKL level are shown. The computational domain is 15 mm long, but since the fields are symmetric, only the right half is shown. The y-axes have the following units: RANKL in pmol/mm; OC in cells/mm; tumor density is normalized between 0, when there is no tumor per unit length, and 1, when the unit space is fully occupied by tumor. The resorption fronts of osteoclasts either reach wave-like propagation (
) or die out (
). B Starting from the initial conditions described in Figure 3, the evolution of the RANKL concentration, osteoclast population density (OC) and tumor density (Tumor) is shown after 45 and 90 days, respectively. The initial host-RANKL level is
, and between 20 and 90 days, a uniform source of OPG is administered at
(green) and
(blue), respectively. Compared to the control at
(red), the respective tumor burdens are reduced.
Figure 5.
A Starting from the initial conditions described in Figure 3, the RANKL and OPG concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown after 30, 60 and 90 days, respectively. The growing tumor produces OPG at rates (green) and
(blue), with a control case
(red). Length of domain is
, and only the right halves of the symmetric fields are shown. Scales are as in Figure 4, and OPG is in pmol/mm. B Left: zoom in on RANKL at 90 days in panel A. Right: the RANKL gradients are obtained by taking the spatial derivatives of the respective fields. C The simulation described in panel A is repeated for different initial RANKL levels
, and different levels of OPG production by cancer cells
. After 90 days, the following quantities are shown: distance traveled by osteoclasts (Distance), total number of active osteoclasts (OC), and total tumor mass (Tumor).
Figure 6.
Direct RANKL production by tumor.
Starting from the initial conditions described in Figure 3, the RANKL concentration, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 30 and 60 days, respectively. The initial host-tissue level of RANKL is . For
, RANKL is produced by the tumor at varying rates
. Length of domain is
, only the right halves of the symmetric fields are shown, the units of the y-axes are as in Figure 4.
Figure 7.
A Starting from the initial conditions described in Figure 3, the PTHrP and RANKL concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 45 and 90 days, respectively. The initial host–tissue level of RANKL is . For
, tumor produces PTHrP at rates
. Length of domain is
, only the right halves of the symmetric fields are shown, the units of the y-axes are as in Figure 4, and PTHrP has units
. B The simulations in A were repeated for the initial host tissue level of RANKL
.
Figure 8.
PTHrP and OPG production by tumor.
A Starting from the initial conditions described in Figure 3, the PTHrP, RANKL and OPG concentrations, the osteoclast population density (OC) and the tumor density (Tumor) are shown at 30, 60 and 90 days, respectively. The initial RANKL level is . The growing tumor produces PTHrP at a fixed rate
, and three different levels of tumor-derived OPG production
are considered. Length of the domain is 15 mm, only the right halves of the symmetric fields are shown. Units of the y-axes are as in Figure 7, and the OPG field has units of
. B The simulation described in panel A is performed for varying values of
and
, and the total tumor mass at 90 days is presented.
Figure 9.
OPG, RANKL and PTHrP expression in prostate cancer.
Data from nine gene expression data sets [47]–[55] were combined and analyzed. A–C Expression of OPG (A), RANKL (B) and PTHrP (C) are shown in the box-plots where the lower whisker indicates the 1st percentile, the limits of the box indicate the 25th and 75th percentiles, and the upper whisker indicates the 99th percentile. Statistical significance is indicated by ,
, calculated using one-way ANOVA. D–F Data for the metastatic prostate samples were analyzed for the correlation in the expression of OPG and PTHrP (D), OPG and RANKL (E), and RANKL and PTHrP (F).