Defining the Role of Solid Stress and Matrix Stiffness in Cancer Cell Proliferation and Metastasis

Abstract

Solid tumors are characterized by an abnormal stroma that contributes to the development of biomechanical abnormalities in the tumor microenvironment. In particular, these abnormalities include an increase in matrix stiffness and an accumulation of solid stress in the tumor interior. So far, it is not clearly defined whether matrix stiffness and solid stress are strongly related to each other or they have distinct roles in tumor progression. Moreover, while the effects of stiffness on tumor progression are extensively studied compared to the contribution of solid stress, it is important to ascertain the biological outcomes of both abnormalities in tumorigenesis and metastasis. In this review, we discuss how each of these parameters is evolved during tumor growth and how these parameters are influenced by each other. We further review the effects of matrix stiffness and solid stress on the proliferative and metastatic potential of cancer and stromal cells and summarize the in vitro experimental setups that have been designed to study the individual contribution of these parameters.

Keywords: externally applied stress; extracellular matrix; fibroblasts; growth-induced stress; in vitro models.

Figure 1

Solid stress and stiffness are two distinct biomechanical abnormalities present in the tumor microenvironment. (A) According to the simple analogy of a spring that obeys Hooke’s law σ = E ⋅ ε, when a tumor grows and pushes the surrounding host tissue of elastic modulus E’, it results in a deformation ε₁ and a stress, σ₁. As a consequence, the host tissue returns an equal and opposite stress σ₁′, which is defined as externally applied solid stress (σ₁ = σ₁′). This externally applied stress, in combination with the growth-induced stress (σ_g), generated from mechanical interactions within the tumor, constitutes the total solid stress transmitted in the tumor interior. (B) In the case that the tumor stiffens so that E₂ is greater than E₁ (E₂ > E₁), the tumor can increase in size and the deformation ε₂ is greater than ε₁ (ε₂ > ε₁). The externally applied stress (σ₂′) and finally the total solid stress accumulated in the tumor interior are greater than that in (A) without any change in the growth-induced stress. (C) The growth-induced solid stress, however, increases during growth, while tumor stiffening might remain the same (16). In this case, the externally applied solid stress σ₃′ can be equal to σ₁′, but total solid stress increases. Therefore, the resultant stress transmitted in the tumor interior is greater than that in (A) without any change in tumor stiffness.

Figure 2

Experimental methods employed to analyze the effects of stiffness and solid stress on cancer and stromal cells in vitro. (A) Experimental setups studying the effect of ECM stiffness on cancer and stromal cells. There are two-dimensional models (2D) consisting of (i) a cell monolayer seeded on coating substrates (e.g., collagen type I or fibronectin) and three-dimensional models (3D) consisting of (ii) tumor spheroids or (iii) single cells embedded in a matrix (e.g., collagen type I, matrigel). Both models were aimed to investigate the effect of changes in extracellular rigidity on the transduction of mechanical signals into the cells as well as on the migration, invasion, proliferation and gene expression of cancer and stromal cells (B) Experimental setups studying the effect of solid stress on cancer and stromal cells. Setups include tumor spheroids that grow within (i) a polymer matrix, (ii) within elastic capsules, or (iii) in a confined polymer device. (iv,v) The setups are composed of cells seeded on the inner chamber of a transwell insert on the top of which an agarose cushion is placed or are embedded in a polymer matrix. A piston with adjustable weight applies a predefined and measurable compressive solid stress on the cells. These models provided useful information about the direct effect of solid stress on tumor growth and morphology as well as on cancer cell proliferation, migration, and gene expression. (C) A summary of in vitro and in vivo studies for the effect of solid stress in tumor progression.