Figure 1.
The steps in cancer metastasis.
The steps in the metastatic process can be grouped into two phases: dissemination and colonization. For a cancer cell (A) to be disseminated into the body through the blood stream, it must dissociate (B) from a primary tumour, migrate (C) to a blood (or lymph) vessel, enter and traverse the vessel wall (D) and be released (E) into the blood flow. It can then be carried (F) to a different part of the body. Colonization at that new location requires that it arrest on the vessel wall (G), pass through the wall (H), migrate (I) to a suitable niche (dashed ellipse) where it settles (J) and grows into a secondary tumour (K), receiving nutrients through new vessels formed by angiogenesis (dotted outline). This article focuses on the dissemination phase.
Figure 2.
Cell actions that produce net boundary (interfacial) tensions.
(A) Contraction of microfilaments (red curves) and cell membranes (black curves) tends to cause the interface between cells B and C to shorten, while cell-cell adhesion systems (orange and blue dots) tend to make it elongate. The result of the joint action of these and other sub-cellular structural components is a net interfacial tension γBC (Fig. 3B). (B) Invadopodia (as from cell E) can push through where the extra-cellular matrix (orange curves) has been dissolved. If attachments are made to neighbouring cells (short black lines) and the invadopodium contracts like a lamellipodium, the tension γDF along the interface between cells D and F becomes elevated.
Figure 3.
Construction of the finite element model.
(A) Biochemical networks regulate the construction of signaling and structural proteins and lead to assembly and regulation of mechanical components. These mechanical components (especially actomyosin and adhesion systems) generate net interfacial tensions γ along the cell edges [41], [42] (B). Cancer cells (type “C”) generate invadopodia which push their way between the normal cells (labelled as type “N”). They then contract with a force assumed to be q times the tension γNN that acts along the boundaries of the surrounding cells. In the finite element model, the edge forces are generated using rods that lie along each edge and that have zero stiffness but carry a constant tension γ that is specific to the cell types that form the boundary. The viscosity µ of the contents of the cells is modeled using a series of orthogonal dashpots [46], only one set of which is illustrated in the figure.
Figure 4.
A simulation of the complete dissemination phase.
All of the steps in the dissemination process are demonstrated in this simulation. In this simulation as in the others reported here unless noted otherwise, γNN = γTT = γWW = 10, γNT = 20, γNW = γWB = 50, γCT = 40, γCN = γCW = 20, q = 2. The starting configuration is shown in (A). The metastasis journey begins when a single cell in the tumour becomes sufficiently discriminated from its neighbours that Equation (2) is satisfied (see text). It is then pushed out of the tumour by interfacial tension differences (B) until at (C), its contact with the tumour becomes vanishingly small. Changes in cell signalling associated with loss of contact with the primary tumour or contact only with stromal cells or detection of chemotactic gradients are then assumed to initiate invadopodia that are oriented toward a nearby blood vessel and that pull the cell toward it (D). The migrating cell encounters the outside surface of the blood vessel (E) and continues to advance by invadopodium action until it makes contact with the blood stream (F). A further programming change in the cell occurs (γCN increases to 60) and it is pushed into the blood stream (G) and released there (γCW increases to 80) (H) by surface and interfacial tension differences akin to those that pushed the cell out of the primary tumour. See also Movie S1.
Figure 5.
Part (A) shows a series of simulations in which the strength of the tension along the cancer cell-tumour boundary takes on a variety of values from γCT = 10 to 50. The case with γCT = 50 is the only one that satisfies Equation (2) and it is the only one that successfully escapes the tumour. In (B), the activated cells are assisted by invadopodia and cells with γCT as low as 30 are able to escape.
Figure 6.
When a migrating cell arrives at a blood vessel, invadopodia of suitable strength (A) or surface tension differences (B) can pull it into the vessel and bring it in contact with the blood stream (C). Further details are given in the text. At that point, invadopodia can no longer pull the cell forward and interfacial tensions must drive further advancement (D–F). Eventually, the cell is in contact only with the inner layer of the blood vessel and if γCW is sufficiently strong that Equation (3) is satisfied, the CW boundary will shorten (G) to zero length and the cancer cell will be released into the blood stream (H).