Mathematical modeling of the metastatic process

Mathematical modeling in cancer has been growing in popularity and impact since its inception in 1932. The first theoretical mathematical modeling in cancer research was focused on understanding tumor growth laws and has grown to include the competition between healthy and normal tissue, carcinogenesis, therapy and metastasis. It is the latter topic, metastasis, on which we will focus this short review, specifically discussing various computational and mathematical models of different portions of the metastatic process, including: the emergence of the metastatic phenotype, the timing and size distribution of metastases, the factors that influence the dormancy of micrometastases and patterns of spread from a given primary tumor.Comment: 24 pages, 6 figures, Revie

An approach for the identification of targets specific to bone metastasis using cancer genes interactome and gene ontology analysis

Metastasis is one of the most enigmatic aspects of cancer pathogenesis and is a major cause of cancer-associated mortality. Secondary bone cancer (SBC) is a complex disease caused by metastasis of tumor cells from their primary site and is characterized by intricate interplay of molecular interactions. Identification of targets for multifactorial diseases such as SBC, the most frequent complication of breast and prostate cancers, is a challenge. Towards achieving our aim of identification of targets specific to SBC, we constructed a 'Cancer Genes Network', a representative protein interactome of cancer genes. Using graph theoretical methods, we obtained a set of key genes that are relevant for generic mechanisms of cancers and have a role in biological essentiality. We also compiled a curated dataset of 391 SBC genes from published literature which serves as a basis of ontological correlates of secondary bone cancer. Building on these results, we implement a strategy based on generic cancer genes, SBC genes and gene ontology enrichment method, to obtain a set of targets that are specific to bone metastasis. Through this study, we present an approach for probing one of the major complications in cancers, namely, metastasis. The results on genes that play generic roles in cancer phenotype, obtained by network analysis of 'Cancer Genes Network', have broader implications in understanding the role of molecular regulators in mechanisms of cancers. Specifically, our study provides a set of potential targets that are of ontological and regulatory relevance to secondary bone cancer.Comment: 54 pages (19 pages main text; 11 Figures; 26 pages of supplementary information). Revised after critical reviews. Accepted for Publication in PLoS ON

Lack of correlation of stem cell markers in breast cancer stem cells

BACKGROUND: Various markers are used to identify the unique sub-population of breast cancer cells with stem cell properties. Whether these markers are expressed in all breast cancers, identify the same population of cells, or equate to therapeutic response is controversial. METHODS: We investigated the expression of multiple cancer stem cell markers in human breast cancer samples and cell lines in vitro and in vivo, comparing across and within samples and relating expression with growth and therapeutic response to doxorubicin, docetaxol and radiotherapy. RESULTS: CD24, CD44, ALDH and SOX2 expression, the ability to form mammospheres and side-population cells are variably present in human cancers and cell lines. Each marker identifies a unique rather than common population of cancer cells. In vivo, cells expressing these markers are not specifically localized to the presumptive stem cell niche at the tumour/stroma interface. Repeated therapy does not consistently enrich cells expressing these markers, although ER-negative cells accumulate. CONCLUSIONS: Commonly employed methods identify different cancer cell sub-populations with no consistent therapeutic implications, rather than a single population of cells. The relationships of breast cancer stem cells to clinical parameters will require identification of specific markers or panels for the individual cancer

Cellular shear adhesion force measurement and simultaneous imaging by atomic force microscope

This paper presents a sensitive and fast cellular shear adhesion force measurement method using an atomic force microscope (AFM). In the work, the AFM was used both as a tool for the imaging of cells on the nano-scale and as a force sensor for the measurement of the shear adhesion force between the cell and the substrate. After the cell imaging, the measurement of cellular shear adhesion forces was made based on the different positions of the cell on the nano-scale. Moreover, different pushing speeds of probe and various locations of cells were used in experiments to study their influences. In this study, the measurement of the cell adhesion in the upper portion of the cell is different from that in the lower portion. It may reveal that the cancer cells have the metastasis tendency after cultured for 16 to 20 hours, which is significant for preventing metastasis in the patients diagnosed with early cancer lesions. Furthermore, the cellular shear adhesion forces of two types of living cancer cells were obtained based on the measurements of AFM cantilever deflections in the torsional and vertical directions. The results demonstrate that the shear adhesion force of cancer cells is twice as much as the same type of cancer cells with TRAIL. The method can also provide a way for the measurement of the cellular shear adhesion force between the cell and the substrate, and for the simultaneous exploration of cells using the AFM imaging and manipulatio

Dunning rat prostate adenocarcinomas and alternative splicing reporters: powerful tools to study epithelial plasticity in prostate tumors in vivo

Using alternative splicing reporters we have previously observed mesenchymal epithelial transitions in Dunning AT3 rat prostate tumors. We demonstrate here that the Dunning DT and AT3 cells, which express epithelial and mesenchymal markers, respectively, represent an excellent model to study epithelial transitions since these cells recapitulate gene expression profiles observed during human prostate cancer progression. In this manuscript we also present the development of two new tools to study the epithelial transitions by imaging alternative splicing decisions: a bichromatic fluorescence reporter to evaluate epithelial transitions in culture and in vivo, and a luciferase reporter to visualize the distribution of mesenchymal epithelial transitions in vivo

Hakai reduces cell-substratum adhesion and increases epithelial cell invasion

[Abstract] Background. The dynamic regulation of cell-cell adhesions is crucial for developmental processes, including tissue formation, differentiation and motility. Adherens junctions are important components of the junctional complex between cells and are necessary for maintaining cell homeostasis and normal tissue architecture. E-cadherin is the prototype and best-characterized protein member of adherens junctions in mammalian epithelial cells. Regarded as a tumour suppressor, E-cadherin loss is associated with poor prognosis in carcinoma. The E3 ubiquitin-ligase Hakai was the first reported posttranslational regulator of the E-cadherin complex. Hakai specifically targetted E-cadherin for internalization and degradation and thereby lowered epithelial cell-cell contact. Hakai was also implicated in controlling proliferation, and promoted cancer-related gene expression by increasing the binding of RNA-binding protein PSF to RNAs encoding oncogenic proteins. We sought to investigate the possible implication of Hakai in cell-substratum adhesions and invasion in epithelial cells. Methods. Parental MDCK cells and MDCK cells stably overexpressing Hakai were used to analyse cell-substratum adhesion and invasion capabilities. Western blot and immunofluoresecence analyses were performed to assess the roles of Paxillin, FAK and Vinculin in cell-substratum adhesion. The role of the proteasome in controlling cell-substratum adhesion was studied using two proteasome inhibitors, lactacystin and MG132. To study the molecular mechanisms controlling Paxillin expression, MDCK cells expressing E-cadherin shRNA in a tetracycline-inducible manner was employed. Results. Here, we present evidence that implicate Hakai in reducing cell-substratum adhesion and increasing epithelial cell invasion, two hallmark features of cancer progression and metastasis. Paxillin, an important protein component of the cell-matrix adhesion, was completely absent from focal adhesions and focal contacts in Hakai-overexpressing MDCK cells. The expression of Paxillin was found to be regulated by a proteasome-independent mechanism, possibly due to the decreased abundance of E-cadherin. Conclusions. Taken together, these results suggest that Hakai may be involved in two hallmark aspects of tumour progression, the lowering cell-substratum adhesion and the enhancement of cell invasion.Xunta de Galicia; PS09/24Xunta de Galicia; 10CSA916023P

Two-scale Moving Boundary Dynamics of Cancer Invasion:Heterotypic Cell Populations Evolution in Heterogeneous ECM

This book contains a collection of original research articles and review articles that describe novel mathematical modeling techniques and the application of those techniques to models of cell motility in a variety of contexts. The aim is to highlight some of the recent mathematical work geared at understanding the coordination of intracellular processes involved in the movement of cells. This collection will benefit researchers interested in cell motility as well graduate students taking a topics course in this area.

Long-Term Sphere Culture Cannot Maintain a High Ratio of Cancer Stem Cells: A Mathematical Model and Experiment

Acquiring abundant and high-purity cancer stem cells (CSCs) is an important prerequisite for CSC research. At present, researchers usually gain high-purity CSCs through flow cytometry sorting and expand them by short-term sphere culture. However, it is still uncertain whether we can amplify high-purity CSCs through long-term sphere culture. We have proposed a mathematical model using ordinary differential equations to derive the continuous variation of the CSC ratio in long-term sphere culture and estimated the model parameters based on a long-term sphere culture of MCF-7 stem cells. We found that the CSC ratio in long-term sphere culture presented as gradually decreased drift and might be stable at a lower level. Furthermore, we found that fitted model parameters could explain the main growth pattern of CSCs and differentiated cancer cells in long-term sphere culture

miR-200 Enhances Mouse Breast Cancer Cell Colonization to Form Distant Metastases

BACKGROUND: The development of metastases involves the dissociation of cells from the primary tumor to penetrate the basement membrane, invade and then exit the vasculature to seed, and colonize distant tissues. The last step, establishment of macroscopic tumors at distant sites, is the least well understood. Four isogenic mouse breast cancer cell lines (67NR, 168FARN, 4TO7, and 4T1) that differ in their ability to metastasize when implanted into the mammary fat pad are used to model the steps of metastasis. Only 4T1 forms macroscopic lung and liver metastases. Because some miRNAs are dysregulated in cancer and affect cellular transformation, tumor formation, and metastasis, we examined whether changes in miRNA expression might explain the differences in metastasis of these cells. METHODOLOGY/PRINCIPAL FINDINGS: miRNA expression was analyzed by miRNA microarray and quantitative RT-PCR in isogenic mouse breast cancer cells with distinct metastatic capabilities. 4T1 cells that form macroscopic metastases had elevated expression of miR-200 family miRNAs compared to related cells that invade distant tissues, but are unable to colonize. Moreover, over-expressing miR-200 in 4TO7 cells enabled them to metastasize to lung and liver. These findings are surprising since the miR-200 family was previously shown to promote epithelial characteristics by inhibiting the transcriptional repressor Zeb2 and thereby enhancing E-cadherin expression. We confirmed these findings in these cells. The most metastatic 4T1 cells acquired epithelial properties (high expression of E-cadherin and cytokeratin-18) compared to the less metastatic cells. CONCLUSIONS/SIGNIFICANCE: Expression of miR-200, which promotes a mesenchymal to epithelial cell transition (MET) by inhibiting Zeb2 expression, unexpectedly enhances macroscopic metastases in mouse breast cancer cell lines. These results suggest that for some tumors, tumor colonization at metastatic sites might be enhanced by MET. Therefore the epithelial nature of a tumor does not predict metastatic outcome