Regulation of Cell Proliferation and Migration in Glioblastoma: New Therapeutic Approach

Abstract

Glioblastoma is the most aggressive brain cancer with the poor survival rate. A microRNA, miR-451, and its downstream molecules, CAB39/LKB1/STRAD/AMPK, are known to play a critical role in regulating a biochemical balance between rapid proliferation and invasion in the presence of metabolic stress in microenvironment. We develop a novel multi-scale mathematical model where cell migration and proliferation are controlled through a core intracellular control system (miR-451-AMPK complex) in response to glucose availability and physical constraints in the microenvironment. Tumor cells are modeled individually and proliferation and migration of those cells are regulated by the intracellular dynamics and reaction-diffusion equations of concentrations of glucose, chemoattractant, extracellular matrix, and MMPs. The model predicts that invasion patterns and rapid growth of tumor cells after conventional surgery depend on biophysical properties of cells, dynamics of the core control system, and microenvironment as well as glucose injection methods. We developed a new type of therapeutic approach: effective injection of chemoattractant to bring invasive cells back to the surgical site after initial surgery, followed by glucose injection at the same location. The model suggests that a good combination of chemoattractant and glucose injection at appropriate time frames may lead to an effective therapeutic strategy of eradicating tumor cells.

Complex, non-monotonic dose-response curves with multiple maxima: Do we (ever) sample densely enough?

“…circadian clocks, cell cycle oscillators) and space (e.g., periodic waves of Dictyostelium cells aggregation, embryonic patterning). [19][20][21][22] However, theoretical models -for example those of eukaryotic cell cycle regulation 23 or of effects of glucose concentration on glucose-regulated miRNA levels in tumor cells 24 -show that some parameters of a system of metabolic reactions mutually linked by regulatory feedback relationships may also exhibit complex, non-monotonic responses as a function of parameters other than time or space, such as e.g. cell size or concentration of one of the systems components.…”

Chronic Inflammation in the Epidermis: A Mathematical Model

“…Oscilla(on In Figure 12, we investigate the effect of constant drug injection on the dynamics of the DDE system (52)- (55) in the presence of large time delays (τ 1 = τ 2 = 3.5). Figure 12C) significantly enhances the immune activity and eliminates both harmful and beneficial pathogens (B s 1 = 0, B s 2 = 0).…”

“…Hybrid approaches may be used to take into account these intracellular signaling pathways in addition to the mechanical interactions of cells with microenvironment for detailed proteolytic activities, growth and invasion at the cellular level and viscoelastic response of the whole tissue [23,[53][54][55][56][57]. Yet a more comprehensive understanding of the role of the microenvironment in epidermal homeostasis may lead to the development of new therapeutic agents.…”

Optimal control strategies of eradicating invisible glioblastoma cells after conventional surgery

“…We extend the model of miR-451-AMPK core control system developed in [25] and related works [26,27] to include regulation by glucose and influence of drug use and thus additional components are added. Figure 1a shows the conceptual model dynamics adapted from Godlewski et al [7] with possible drugdriven intervention of inhibitory pathways of miR-451 from the AMPK complex.…”

“…Thus, the core control system of miR-451 and AMPK complex plays an integral role in the regulation of balance between proliferation and invasion of glioma cells. Kim et al [25][26][27] developed a mathematical model that shows how the dynamics of the core miR-451-AMPK control system affects cell proliferation and migration in glioblastoma. It provides an explanation for up-and downregulation of miR-451 in response to high and low glucose levels and known mutual antagonism between miR-451 levels and AMPK complex activities [7].…”