Tag Archives: Dnm1

We develop a multispecies continuum model to simulate the spatiotemporal dynamics

We develop a multispecies continuum model to simulate the spatiotemporal dynamics of cell lineages in solid tumors. such as Dkk and SFRPs). We find that the progression of the tumors and their response to treatment is controlled by the spatiotemporal dynamics of the signaling processes. The model predicts the development of spatiotemporal heterogeneous distributions of the feedback factors (Wnt Dkk and TGFβ) and tumor cell populations with clusters of stem cells appearing at the tumor boundary consistent AM 1220 with recent experiments. The non-linear coupling between the heterogeneous expressions of growth factors and the heterogeneous distributions of cell populations at different lineage stages tends to create asymmetry in tumor shape that may sufficiently alter otherwise homeostatic feedback so as to favor escape from growth control. This occurs in a setting of invasive AM 1220 fingering and enhanced aggressiveness after standard therapeutic interventions. We find however that combination therapy involving differentiation promoters and radiotherapy is very effective in eradicating such a tumor. is the fraction of the daughter cells that progress to the next stage). When the sooner the extinction). Note that no reference is made by this characterization to cell division symmetry. From the population standpoint it does not matter whether a value of tumor spheroids showing cancer stem cells at the spheroid boundary. The green color (online) denotes the accumulation of ZsGreen-ODC and marks the location of what are believed to be AM 1220 cancer stem cells (Vlashi et … Figure 4 Heterogeneous spatial patterning of Wnt signaling activity (a) and the Wnt-inhibitor Dkk (b) in tumor spheroids. In (a) two single-cell-cloned colon cancer spheroids (scale bars are 20 μm) are shown using phase contrast (left) AM 1220 fluorescence … Using a mathematical model Lander AM 1220 et al. (2009) and Lo et al. (2009) demonstrated that feedback regulation of the that reduce the self-renewal … For each cell type a conservation equation of the form denotes the volume fraction of the cell type J is a generalized diffusion denotes the source or mass-exchange terms and us is the mass-averaged velocity of the solid components. Although each cell type could move with its own velocity here we assume that cells move with the mass-averaged velocity which is equivalent to assuming that the cells are closely packed (Wise et al. 2008). Using a variational argument the flux is derived from an adhesion energy that accounts for interactions among the cells. We assume for simplicity that tumor cells prefer to adhere to one another rather than the host and thus we write the adhesion energy as (Wise et al 2008) = +++denotes the solid tumor volume fraction is a measure of cell-cell adhesion and effectively controls the stiffness of the tumor/host interface like a surface tension. The parameter models longer-range interactions among the components and introduces a finite thickness (proportional to + = 1. Thus the tumor and host domains and the tumor-host interface may be written as Ω(((() < 1/2} and Σ(to be a double-well potential which is minimized when = 1 (tumor) or = 0 (host). The fluxes for the tumor components can be given by (Wise et al. 2008) is a mobility is the chemical potential which is equal to the variational derivative of the adhesion energy is the cell-motility which contains the combined effects of cell-cell and cell-matrix adhesion is the solid or oncotic pressure generated by cell proliferation and the remaining term is the contribution from cell-cell adhesion forces. This constitutive AM 1220 law assumes that the tumor can be treated as a viscous inertialess fluid and also models flow through a porous media. {Again other constitutive laws may be found in Lowengrub et al.|Other constitutive laws Dnm1 may be found in Lowengrub et al again.} (2010) and Cristini and Lowengrub (2010). Note that cell-cell adhesion arises in the model from two sources—the fluxes in the conservation equation (3) and the extra forces in the velocity equation (4). Overall these equations guarantee that in the absence of mass sources the adhesion energy is {non-increasing|nonincreasing} in time as the fields evolve (thermodynamic consistency). Further because of the double well potential in the adhesion energy 0 and 1 are energetically favored states of the volume fraction of the total tumor = 0 ) the conservation equations may be summed to.