Yangjin Kim

MicroRNA regulation of a cancer network: Consequences of the feedback loops involving miR-17-92, E2F, and Myc

The transcription factors E2F and Myc participate in the control of cell proliferation and apoptosis, and can act as oncogenes or tumor suppressors depending on their levels of expression. Positive feedback loops in the regulation of these factors are predicted—and recently shown experimentally—to lead to bistability, which is a phenomenon characterized by the existence of low and high protein levels (“off” and “on” levels, respectively), with sharp transitions between levels being inducible by, for example, changes in growth factor concentrations. E2F and Myc are inhibited at the posttranscriptional step by members of a cluster of microRNAs (miRs) called miR-17-92. In return, E2F and Myc induce the transcription of miR-17-92, thus forming a negative feedback loop in the interaction network. The consequences of the coupling between the E2F/Myc positive feedback loops and the E2F/Myc/miR-17-92 negative feedback loop are analyzed using a mathematical model. The model predicts that miR-17-92 plays a critical role in regulating the position of the off–on switch in E2F/Myc protein levels, and in determining the on levels of these proteins. The model also predicts large-amplitude protein oscillations that coexist with the off steady state levels. Using the concept and model prediction of a “cancer zone,” the oncogenic and tumor suppressor properties of miR-17-92 is demonstrated to parallel the same properties of E2F and Myc.

A mathematical model for pattern formation of glioma cells outside the tumor spheroid core.

Glioblastoma is the most common and the most aggressive type of brain cancer. The median survival time from the time of diagnosis is approximately one year. Invasion of glioma cells from the core tumor into the surrounding brain tissue is a major reason for treatment failure: these migrating cells are not eliminated in surgical resection and cause tumor recurrence. Variations are seen in number of invading cells, and in the extent and patterns of migration. Cells can migrate diffusely and can also be seen as clusters of cells distinct from the main tumor mass. This kind of clustering is also evident in vitro using 3D spheroid models of glioma invasion. This has been reported for U87 cells stably expressing the constitutively active EGFRVIII mutant receptor, often seen expressed in glioblastoma. In this case the cells migrate as clusters rather than as single cells migrating in a radial pattern seen in control wild type U87 cells. Several models have been suggested to explain the different modes of migration, but none of them, so far, has explored the important role of cell-cell adhesion. The present paper develops a mathematical model which includes the role of adhesion and provides an explanation for the various patterns of cell migration. It is shown that, depending on adhesion, haptotactic, and chemotactic parameters, the migration patterns exhibit a gradual shift from branching to dispersion, as has been reported experimentally.

Mechanistic modeling of the effects of myoferlin on tumor cell invasion

Myoferlin (MYOF) is a member of the evolutionarily conserved ferlin family of proteins, noted for their role in a variety of membrane processes, including endocytosis, repair, and vesicular transport. Notably, ferlins are implicated in Caenorhabditis elegans sperm motility (Fer-1), mammalian skeletal muscle development and repair (MYOF and dysferlin), and presynaptic transmission in the auditory system (otoferlin). In this paper, we demonstrate that MYOF plays a previously unrecognized role in cancer cell invasion, using a combination of mathematical modeling and in vitro experiments. Using a real-time impedance-based invasion assay (xCELLigence), we have shown that lentiviral-based knockdown of MYOF significantly reduced invasion of MDA-MB-231 breast cancer cells in Matrigel bioassays. Based on these experimental data, we developed a partial differential equation model of MYOF effects on cancer cell invasion, which we used to generate mechanistic hypotheses. The mathematical model predictions revealed that matrix metalloproteinases (MMPs) may play a key role in modulating this invasive property, which was supported by experimental data using quantitative RT-PCR screens. These results suggest that MYOF may be a promising target for biomarkers or drug target for metastatic cancer diagnosis and therapy, perhaps mediated through MMPs.

miR451 and AMPK mutual antagonism in glioma cell migration and proliferation: a mathematical model.

Glioblastoma multiforme (GBM) is the most common and the most aggressive type of brain cancer; the median survival time from the time of diagnosis is approximately one year. GBM is characterized by the hallmarks of rapid proliferation and aggressive invasion. miR-451 is known to play a key role in glioblastoma by modulating the balance of active proliferation and invasion in response to metabolic stress in the microenvironment. The present paper develops a mathematical model of GBM evolution which focuses on the relative balance of growth and invasion. In the present work we represent the miR-451/AMPK pathway by a simple model and show how the effects of glucose on cells need to be “refined” by taking into account the recent history of glucose variations. The simulations show how variations in glucose significantly affect the level of miR-451 and, in turn, cell migration. The model predicts that oscillations in the levels of glucose increase the growth of the primary tumor. The model also suggests that drugs which upregulate miR-451, or block other components of the CAB39/AMPK pathway, will slow down glioma cell migration. The model provides an explanation for the growth-invasion cycling patterns of glioma cells in response to high/low glucose uptake in microenvironment in vitro, and suggests new targets for drugs, associated with miR-451 upregulation.

Interaction of Tumor with Its Micro-environment: A Mathematical Model

This paper is concerned with early development of transformed epithelial cells (TECs) in the presence of fibroblasts in the tumor micro-environment. These two types of cells interact by means of cytokines such as transforming growth factor (TGF-β) and epidermal growth factor (EGF) secreted, respectively, by the TECs and the fibroblasts. As this interaction proceeds, TGF-β induces fibroblasts to differentiate into myofibroblasts which secrete EGF at a larger rate than fibroblasts. We monitor the entire process in silico, in a setup which mimics experiments in a Tumor Chamber Invasion Assay, where a semi-permeable membrane coated by extracellular matrix (ECM) is placed between two chambers, one containing TECs and another containing fibroblasts. We develop a mathematical model, based on a system of PDEs, that includes the interaction between TECs, fibroblasts, myofibroblasts, TGF-β, and EGF, and we show how model parameters affect tumor progression. The model is used to generate several hypotheses on how to slow tumor growth and invasion. In an Appendix, it is proved that the mathematical model has a unique global in-time solution.

Transformed epithelial cells and fibroblasts/myofibroblasts interaction in breast tumor: a mathematical model and experiments

It is well known that tumor and its microenvironment, or stroma, interact with each other and that this interaction plays a critical role in tumor initiation, growth, and metastasis. This interaction consists of complex relations between tumor cells, stromal cells such as fibroblasts, epithelial cells and immunocytes, the vascular system, the extracellular matrix, and cytokines secreted by the cells. Understanding these relationships may lead to new therapeutic approaches to cancer. In the present paper, we consider tumor-stroma crosstalk in a simple in vitro situation which involves interaction between tumor epithelial cells from breast cancer and a microenvironment consisting of just fibroblasts. The two populations of cells are separated by a semi-permeable membrane that allows only cytokines to cross over. We develop a mathematical model that includes two critical growth factors: TGF-β, produced by the tumor cells, and EGF, secreted by the fibroblasts. The TGF-β modifies the microenvironment by transforming fibroblasts into myofibroblasts. Myofibroblasts secrete higher concentrations of EGF than fibroblasts, thereby, increasing the proliferation of tumor cells. Thus already in this simple setup one sees a mutual interaction between tumor cells and their microenvironment. We conducted experiments which show good agreement with the model’s simulations, hence confirming the model’s ability to predict aspects of tumor cell behavior in response to signaling from fibroblasts.

Regulation of Th1/Th2 cells in asthma development: A mathematical model

Airway exposure levels of lipopolysaccharide (LPS) determine type I versus type II helper T cell induced experimental asthma. While high LPS levels induce Th1-dominant responses, low LPS levels derive Th2 cell induced asthma. The present paper develops a mathematical model of asthma development which focuses on the relative balance of Th1 and Th2 cell induced asthma. In the present work we represent the complex network of interactions between cells and molecules by a mathematical model. The model describes the behaviors of cells (Th0, Th1, Th2 and macrophages) and regulatory molecules (IFN- γ, IL-4, IL-12, TNF-α) in response to high, intermediate, and low levels of LPS. The simulations show how variations in the levels of injected LPS affect the development of Th1 or Th2 cell responses through differential cytokine induction. The model also predicts the coexistence of these two types of response under certain biochemical and biomechanical conditions in the microenvironment.

Tumor cells proliferation and migration under the influence of their microenvironment.

It is well known that tumor microenvironment affects tumor growth and metastasis: Tumor cells may proliferate at different rates and migrate in different patterns depending on the microenvironment in which they are embedded. There is a huge literature that deals with mathematical models of tumor growth and proliferation, in both the avascular and vascular phases. In particular, a review of the literature of avascular tumor growth (up to 2006) can be found in Lolas (G. Lolas, Lecture Notes in Mathematics, Springer Berlin / Heidelberg, 1872, 77 (2006)). In this article we report on some of our recent work. We consider two aspects, proliferation and of migration, and describe mathematical models based on in vitro experiments. Simulations of the models are in agreement with experimental results. The models can be used to generate hypotheses regarding the development of drugs which will confine tumor growth.

Strategies of eradicating glioma cells: a multi-scale mathematical model with MiR-451-AMPK-mTOR control.

The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR-451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multi-scale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatio-temporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR-451-AMPK-mTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.

Qualitative Network Modeling of the Myc-p53 Control System of Cell Proliferation and Differentiation

A kinetic model of a molecular control system for the cellular decision to proliferate or differentiate is formulated and analyzed for the purpose of understanding how the system can break down in cancer cells. The proposed core of this control system is composed of the transcription factors Myc and p53. The network of interactions between these factors involves negative and positive feedback loops that are linked to pathways involved in differentiation, cell cycle, and apoptosis. Understanding the dynamics of the Myc-p53 control system is aided by the postulate that there exists a cancer zone defined as a range of oncogenic Myc activities where the probability of initiating cancer is high. We propose that an essential role of p53 is to prevent the system from entering or staying too long in the cancer zone by downregulating Myc or, when Myc activity somehow becomes too high, by inducing apoptosis, cell cycle arrest, or differentiation. Kinetic modeling illustrates how deletions or aberrations in PTEN, MDM2, and ARF (genes implicated in various cancers, including glioma) affect the Myc-p53 control system. In addition, computer simulations demonstrate how this control system generates different cellular phenotypes characterized by rates of cellular differentiation and proliferation.