MBI Publications

MBI Publications for Yangjin Kim (23)

  • Y. Kim and H. Othmer
    A hybrid model for tumor spheroid grown in vitro I: Theoretical development and early results
    Math. Models Methods in Appl ScisVol. 17 (2007) pp. 1773-1798

    Abstract

    Tumor spheroids grown in vitro have been widely used as models of in vivo tumor growth because they display many of the characteristics of in vivo growth, including the effects of nutrient limitations and perhaps the effect of stress on growth. In either case there are numerous biochemical and biophysical processes involved whose interactions can only be understood via a detailed mathematical model. Previous models have focused on either a continuum description or a cell-based description, but both have limitations. In this paper we propose a new mathematical model of tumor spheroid growth that incorporates both continuum and cell-level descriptions, and thereby retains the advantages of each while circumventing some of their disadvantages. In this model the cell-based description is used in the region where the majority of growth and cell division occurs, at the periphery of a tumor, while a continuum description is used for the quiescent and necrotic zones of the tumor and for the extracellular matrix. Reaction-diffusion equations describe the transport and consumption of two important nutrients, oxygen and glucose, throughout the entire domain. The cell-based component of this hybrid model allows us to examine the effects of cell–cell adhesion and variable growth rates at the cellular level rather than at the continuum level. We show that the model can predict a number of cellular behaviors that have been observed experimentally.
  • Y. Kim, S. Lawler, M. Nowicki, E. Chiocca and A. Friedman
    A mathematical model of Brain tumor: pattern formation of glioma cells outside the tumor spheroid core
    J Theo BiolVol. 260 (2008) pp. 259-371 (Submitted)

    Abstract

  • B. Aguda, Y. Kim, M. Piper-Hunter, A. Friedman and C. Marsh
    MicroRNA Regulation of a Cancer Network: Consequences of the Feedback Loops Involving miR-17-92, E2F, and Myc
    PNASVol. 105 No. 50 (2008) pp. 19678-19683

    Abstract

  • B. Aguda, Y. Kim, M. Piper-Hunter, A. Friedman and C. Marsh
    MicroRNA Regulation of a Cancer Network: Consequences of the Feedback Loops Involving miR-17-92, E2F, and Myc
    PNASVol. 105 No. 50 (2008) pp. 19678-19683

    Abstract

    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.
  • M. Stolarska, Y. Kim and H. Othmer
    Multiscale models of cell and tissue dynamics
    Phil. Trans. Roy. Soc.Vol. 367 (2009) pp. 3525-3553

    Abstract

  • Y. Kim and K. Boushaba
    A PDE mathematical model for the regulation of tumor dormancy based on enzyme kinetics
    DCDS-S (2009) (Submitted)

    Abstract

  • Y. Kim, S. Lawler, M. Nowicki, E. Chiocca and A. Friedman
    A mathematical model of Brain tumor: pattern formation of glioma cells outside the tumor spheroid core
    J Theo BiolVol. 260 (2009) pp. 259-371

    Abstract

    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 wildtype 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.
  • M. Stolarska, Y. Kim and H. Othmer
    Multiscale models of cell and tissue dynamics
    Phil. Trans. Toy. Soc.Vol. 367 (2009) pp. 3525-3553

    Abstract

    Cell and tissue movement are essential processes at various stages in the life cycle of most organisms. The early development of multi-cellular organisms involves individual and collective cell movement; leukocytes must migrate towards sites of infection as part of the immune response; and in cancer, directed movement is involved in invasion and metastasis. The forces needed to drive movement arise from actin polymerization, molecular motors and other processes, but understanding the cell- or tissue-level organization of these processes that is needed to produce the forces necessary for directed movement at the appropriate point in the cell or tissue is a major challenge. In this paper, we present three models that deal with the mechanics of cells and tissues: a model of an arbitrarily deformable single cell, a discrete model of the onset of tumour growth in which each cell is treated individually, and a hybrid continuum-discrete model of the later stages of tumour growth. While the models are different in scope, their underlying mechanical and mathematical principles are similar and can be applied to a variety of biological systems.
  • Y. Kim and A. Friedman
    Interaction of tumor with its microenvironment : A Mathematical Model
    Bulletin of Mathematical BiologyVol. 72 No. 5 (2010) pp. 1029-1068

    Abstract

  • Y. Kim and A. Friedman
    Interaction of tumor with its microenvironment: A Mathematical Model
    Bulletin of Mathematical BiologyVol. 72 No. 5 (2010) pp. 1029-1068

    Abstract

    This paper is concerned with early development of transformed epithelial cells (TECs) in the presence of fibroblasts in the tumor microenvironment. These two types of cells interact by means of cytokines such as transforming growth factor (TGF-beta) and epidermal growth factor (EGF) secreted, respectively, by the TECs and the fibroblasts. As this interaction proceeds, TGF-beta 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-beta, 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.
  • Y. Kim, J. Wallace, F. Li, M. Ostrowski and A. Friedman
    Transformed Epithelias cells (TEC) and fibroblasts/myofibroblasts interaction in Breast Tumor: A Mathematical Model and Experiments
    Journal of Mathematical BiologyVol. 61 No. 3 (2010) pp. 401-421

    Abstract

    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-beta, produced by the tumor cells, and EGF, secreted by the fibroblasts. The TGF-beta 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.
  • Y. Kim and S. Lim
    The role of the microenvironment in tumor invasion
    2009 Proceedings of the Fourth SIAM Conference on Mathematics for Industry (2010) pp. 84-92

    Abstract

    Fibroblasts and myofibroblasts in the tumor microenvironment are important players in tumor growth and metastasis because of their unique ability to coordinate events which increase cell proliferation and invasion especially in breast cancer. It has been experimentally shown that fibroblasts play an important role in promoting tumor growth. Our study illustrates a model in which tumor cells are able to communicate with these fibroblasts/myofibroblasts through proteinases for active invasion toward stroma near breast ducts.
  • Y. Kim, A. Friedman, J. Wallace, F. Li and M. Ostrowski
    Transformed Epithelial cells (TEC) and fibroblasts/myofibroblasts interaction in Breast Tumor: A Mathematical Model and Experiments
    Journal of Mathematical BiologyVol. 61 No. 3 (2010)

    Abstract

  • M. Eisenberg, Y. Kim, R. Li, W. Ackerman, D. Kniss and A. Friedman
    Modeling the effects of myoferlin on tumor cell invasion
    Proc Natl Acad Sci USAVol. 108 No. 50 (2011) pp. 20078-20083

    Abstract

  • B. Aguda, Y. Kim, H. Kim, A. Friedman and H. Fine
    Qualitative network modeling of the MYC-p53 control system of cell proliferation and differentiation
    Biophysical JournalVol. 101 No. 9 (2011) pp. 2082-2091

    Abstract

  • Y. Kim, S. Roh, S. Lawler and A. Friedman
    miR451 and AMPK mutual antagonism in glioma cells migration and proliferation
    PLoS OneVol. 6 No. 12 (2011)

    Abstract

  • Y. Kim and K. Boushaba
    An enzyme kinetics model of tumor dormancy, regulation of secondary metastases
    Discrete and Continuous Dynamical Systems-SVol. 4 No. 6 (2011) pp. 1465-1498

    Abstract

    In this paper we study 1 dimensional (1D) and 2D extended version of a two compartment model for tumor dormancy suggested by Boushaba et al. [3]. The model is based on the idea that the vascularization of a secondary tumor can be suppressed by inhibitor originating from a larger primary tumor. It has been observed emergence of a polypoid melanoma at a site remote from a primary polypoid melanoma after excision of the latter. The authors observed no recurrence of the melanoma at the primary site, but did observe secondary tumors at secondary sites five to seven centimeters from the primary site within a period of one month after the excision of the primary site. 1D and 2D simulations show that when the tumors are sufficiently remote, the primary tumor will not influence the secondary tumors while, if they are too close together, the primary tumor can effectively prevent the growth of the secondary tumors, even after it is removed. The sensitivity analysis was carried out for the 1D model. It has been long observed that surgery should be followed by other treatment options such as chemotherapy. 2D simulation suggests a possible treatment options with different dosage schedule after a surgery in order to achieve better clinical outcome.
  • Y. Kim, M. Stolarska and H. Othmer
    The Role of the Microenvironment in Tumor Growth and Invasion
    Progress in Biophysics and Molecular BiologyVol. 106 (2011) pp. 353-379 (Submitted)

    Abstract

    Mathematical modeling and computational analysis are essential for understanding the dynamics of the complex gene networks that control normal development and homeostasis, and can help to under- stand how circumvention of that control leads to abnormal outcomes such as cancer. Our objectives here are to discuss the different mechanisms by which the local biochemical and mechanical microenvironment, which is comprised of various signaling molecules, cell types and the extracellular matrix (ECM), affects the progression of potentially-cancerous cells, and to present new results on two aspects of these effects. We first deal with the major processes involved in the progression from a normal cell to a cancerous cell at a level accessible to a general scientific readership, and we then outline a number of mathematical and computational issues that arise in cancer modeling. In Section 2 we present results from a model that deals with the effects of the mechanical properties of the environment on tumor growth, and in Section 3 we report results from a model of the signaling pathways and the tumor microenvironment (TME), and how their interactions affect the development of breast cancer. The results emphasize anew the complexities of the interactions within the TME and their effect on tumor growth, and show that tumor progression is not solely determined by the presence of a clone of mutated immortal cells, but rather that it can be ââ?¬Ë?community-controlledââ?¬â?¢.
  • A. Friedman and Y. Kim
    Tumor cells proliferation and migration under the influence of their microenvironment
    Mathematical Biosciences and EngineeringVol. 8 No. 2 (2011) pp. 373-385

    Abstract

    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 [8] (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 de- scribe 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.
  • Y. Kim and H. Othmer
    A hybrid model of tumor-stromal interactions in breast cancer
    Bull. Math. Biol. (2012) (Submitted)

    Abstract

  • Y. Kim, S. Lee, Y. Kim, Y. Kim, Y. Gho and H. hwang
    Regulation of Th1/Th2 cells in asthma development A mathematical model
    J. Math. Biol. (2012) (Submitted)

    Abstract

  • Y. Kim and S. Roh
    A hybrid model of cell proliferation and migration in glioblastoma
    Discrete and Continuous Dynamical Systems -B (2012) (Submitted)

    Abstract

  • Y. Kim and K. Boushaba
    A mathematical model of tumor dormancy and secondary metastasis
    Systems of Tumor Dormancy (2012) (Under Revision)

    Abstract

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