2013, 18(4): 969-1015. doi: 10.3934/dcdsb.2013.18.969

A hybrid model for cell proliferation and migration in glioblastoma

1. 

Department of Mathematics, Konkuk University, Seoul, South Korea

2. 

Department of Mathematics, University of Michigan, Ann Arbor, MI 48109, United States

Received  February 2012 Revised  April 2012 Published  February 2013

Glioblastoma is the most aggressive type of brain cancer with the median survival time of one year. A particular microRNA, miR-451, and its counterpart, AMPK complex are known to play a key role in controlling a balance between rapid proliferation and aggressive invasion in response to metabolic stress in the microenvironment. The present paper develops a hybrid model of glioblastoma that identifies a key mechanism behind the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells. We focus on the core miR-451-AMPK control system and show how up- or down-regulation of components in these pathways affects cell proliferation and migration. The model predicts the larger window of bistable systems when there exists a time delay in the inhibitory pathway from CAB39/LKB1/STRAD/AMPK to miR-451. Delayed down-regulation of miR-451 along this pathway would let glioma cells stay longer in the proliferative stage despite relatively low glucose levels, making it a possible therapeutic target. Analysis of the model predicts the existence of a limit cycle with two time delays. We then study a hybrid model for the biomechanical interaction between invasive and proliferative cells, in which all cells are modeled individually, and show how biophysical properties of cells and core miR-451-AMPK control system affect the growth/invasion patterns of glioma spheroids in response to various glucose levels in the microenvironment. The model predicts that cell migration not only depends on glucose availability but also on mechanical constraints between cells. The model suggests that adhesion strength between cells plays an important role in cell shedding from the main core and the disruption of cell-cell adhesion is a pre-requisite for glioma cell invasion. The model also suggests that injection of glucose after surgery will increase visibility of individual migratory cells and the second surgery may eradicate the remaining cancer cells, preventing regrowth of the invisible migratory glioma cells.
Citation: Yangjin Kim, Soyeon Roh. A hybrid model for cell proliferation and migration in glioblastoma. Discrete & Continuous Dynamical Systems - B, 2013, 18 (4) : 969-1015. doi: 10.3934/dcdsb.2013.18.969
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