Topology of the heterogeneous nature of the extracellular matrix on stochastic modeling of tumor-induced angiogenesis

The functional cross talk between cancer cells and cancer associated fibroblasts from a cancer mechanics perspective

The function of biological tissues in health and disease is regulated at cellular level and is highly influenced by the physical microenvironment, through the interaction of forces between cells and ECM, which are perceived through mechanosensing pathways. In cancer, both chemical and physical signaling cascades and their interactions are involved during cell-cell and cell-ECM communications to meet requirements of tumor growth. Among stroma cells, cancer associated fibroblasts (CAFs) play key role in tumor growth and pave the way for cancer cells to initiate metastasis and invasion to other tissues, and without recruitment of CAFs, the process of cancer invasion is dysfunctional. This is through an intense chemical and physical cross talks with tumor cells, and interactive remodeling of ECM. During such interaction CAFs apply traction forces and depending on the mechanical properties, deform ECM and in return receive physical signals from the micromechanical environment. Such interaction leads to ECM remodeling by manipulating ECM structure and its mechanical properties. The results are in form of deposition of extra fibers, stiffening, rearrangement and reorganization of fibrous structure, and degradation which are due to a complex secretion and expression of different markers triggered by mechanosensing of tumor cells, specially CAFs. Such events define cancer progress and invasion of cancer cells. A systemic knowledge of chemical and physical factors provides a holistic view of how cancer process and enhances the current treatment methods to provide more diversity among targets that involves tumor cells and ECM structure.

Tumor proliferation and diffusion on percolation clusters

We study in silico the influence of host tissue inhomogeneity on tumor cell proliferation and diffusion by simulating the mobility of a tumor on percolation clusters with different homogeneities of surrounding tissues. The proliferation and diffusion of a tumor in an inhomogeneous tissue could be characterized in the framework of the percolation theory, which displays similar thresholds (0.54, 0.44, and 0.37, respectively) for tumor proliferation and diffusion in three kinds of lattices with 4, 6, and 8 connecting near neighbors. Our study reveals the existence of a critical transition concerning the survival and diffusion of tumor cells with leaping metastatic diffusion movement in the host tissues. Tumor cells usually flow in the direction of greater pressure variation during their diffusing and infiltrating to a further location in the host tissue. Some specific sites suitable for tumor invasion were observed on the percolation cluster and around these specific sites a tumor can develop into scattered tumors linked by some advantage tunnels that facilitate tumor invasion. We also investigate the manner that tissue inhomogeneity surrounding a tumor may influence the velocity of tumor diffusion and invasion. Our simulation suggested that invasion of a tumor is controlled by the homogeneity of the tumor microenvironment, which is basically consistent with the experimental report by Riching et al. as well as our clinical observation of medical imaging. Both simulation and clinical observation proved that tumor diffusion and invasion into the surrounding host tissue is positively correlated with the homogeneity of the tissue.

Extracellular regulation of VEGF: isoforms, proteolysis, and vascular patterning

The regulation of vascular endothelial growth factor A (VEGF) is critical to neovascularization in numerous tissues under physiological and pathological conditions. VEGF has multiple isoforms, created by alternative splicing or proteolytic cleavage, and characterized by different receptor-binding and matrix-binding properties. These isoforms are known to give rise to a spectrum of angiogenesis patterns marked by differences in branching, which has functional implications for tissues. In this review, we detail the extensive extracellular regulation of VEGF and the ability of VEGF to dictate the vascular phenotype. We explore the role of VEGF-releasing proteases and soluble carrier molecules on VEGF activity. While proteases such as MMP9 can 'release' matrix-bound VEGF and promote angiogenesis, for example as a key step in carcinogenesis, proteases can also suppress VEGF's angiogenic effects. We explore what dictates pro- or anti-angiogenic behavior. We also seek to understand the phenomenon of VEGF gradient formation. Strong VEGF gradients are thought to be due to decreased rates of diffusion from reversible matrix binding, however theoretical studies show that this scenario cannot give rise to lasting VEGF gradients in vivo. We propose that gradients are formed through degradation of sequestered VEGF. Finally, we review how different aspects of the VEGF signal, such as its concentration, gradient, matrix-binding, and NRP1-binding can differentially affect angiogenesis. We explore how this allows VEGF to regulate the formation of vascular networks across a spectrum of high to low branching densities, and from normal to pathological angiogenesis. A better understanding of the control of angiogenesis is necessary to improve upon limitations of current angiogenic therapies.

How changes in extracellular matrix mechanics and gene expression variability might combine to drive cancer progression

Changes in extracellular matrix (ECM) structure or mechanics can actively drive cancer progression; however, the underlying mechanism remains unknown. Here we explore whether this process could be mediated by changes in cell shape that lead to increases in genetic noise, given that both factors have been independently shown to alter gene expression and induce cell fate switching. We do this using a computer simulation model that explores the impact of physical changes in the tissue microenvironment under conditions in which physical deformation of cells increases gene expression variability among genetically identical cells. The model reveals that cancerous tissue growth can be driven by physical changes in the microenvironment: when increases in cell shape variability due to growth-dependent increases in cell packing density enhance gene expression variation, heterogeneous autonomous growth and further structural disorganization can result, thereby driving cancer progression via positive feedback. The model parameters that led to this prediction are consistent with experimental measurements of mammary tissues that spontaneously undergo cancer progression in transgenic C3(1)-SV40Tag female mice, which exhibit enhanced stiffness of mammary ducts, as well as progressive increases in variability of cell-cell relations and associated cell shape changes. These results demonstrate the potential for physical changes in the tissue microenvironment (e.g., altered ECM mechanics) to induce a cancerous phenotype or accelerate cancer progression in a clonal population through local changes in cell geometry and increased phenotypic variability, even in the absence of gene mutation.

Modified Gompertz equation for electrotherapy murine tumor growth kinetics: predictions and new hypotheses

BACKGROUND

Electrotherapy effectiveness at different doses has been demonstrated in preclinical and clinical studies; however, several aspects that occur in the tumor growth kinetics before and after treatment have not yet been revealed. Mathematical modeling is a useful instrument that can reveal some of these aspects. The aim of this paper is to describe the complete growth kinetics of unperturbed and perturbed tumors through use of the modified Gompertz equation in order to generate useful insight into the mechanisms that underpin this devastating disease.

METHODS

The complete tumor growth kinetics for control and treated groups are obtained by interpolation and extrapolation methods with different time steps, using experimental data of fibrosarcoma Sa-37. In the modified Gompertz equation, a delay time is introduced to describe the tumor's natural history before treatment. Different graphical strategies are used in order to reveal new information in the complete kinetics of this tumor type.

RESULTS

The first stage of complete tumor growth kinetics is highly non linear. The model, at this stage, shows different aspects that agree with those reported theoretically and experimentally. Tumor reversibility and the proportionality between regions before and after electrotherapy are demonstrated. In tumors that reach partial remission, two antagonistic post-treatment processes are induced, whereas in complete remission, two unknown antitumor mechanisms are induced.

CONCLUSION

The modified Gompertz equation is likely to lead to insights within cancer research. Such insights hold promise for increasing our understanding of tumors as self-organizing systems and, the possible existence of phase transitions in tumor growth kinetics, which, in turn, may have significant impacts both on cancer research and on clinical practice.