Modelling of glioblastoma growth by linking a molecular interaction network with an agent-based model

In this work, a mathematical model of malignant brain tumour growth is presented. In particular, the growth of glioblastoma is investigated on the intracellular and intercellular scale. The Go or Grow principle of tumour cells states that tumour cells either migrate or proliferate. For glioblastoma, microRNA-451 has been shown to be an energy dependent key regulator of the LKB1 (liver kinase B1) and AMPK (AMP-activated protein kinase) pathway that influences the signalling for migration or cell division. We introduce a mathematical model that reproduces these biological processes. The intracellular molecular interaction network is represented by a system of nine ordinary differential equations. This is put into a multiscale context by applying an agent-based approach: each cell is equipped with this interaction network and additional rules to determine its new phenotype as either migrating, proliferating or quiescent. The evaluation of the proposed model by comparison of the results with in vitro experiments indicates its validity.