Mathematical modelling of a suspension culture microenvironment

Abstract

The aim of this work is to create a computer model for in-vitro cellular growth of neural cells. The identification of Neural Stem Cells (NSCs) began with the initial work on neural progenitors isolated from the adult rat brain in the sixties. This was followed by work done on the embryonic mammalian central nervous system (CNS) where distinct pools of neural cells were identified as having stem cell properties. Further work was done to identify NSC in the subependymal region and in the hippocampus dentate gyrus (DG), where they divide to generate progenitors. Subsequently, NSCs were cultured in-vitro as floating suspensions called neurospheres. Neurosphere culture is plagued with variances in neurosphere numbers and cellular expansion rates. This has made it difficult to benchmark the culture conditions that promote cellular proliferation. We present a neurosphere formation model that incorporates experimental data about paracrine factor stimulation in a 20000 cells/ml, N2 supplemented medium. Factor transport is modelled as a three dimensional isotropic diffusion event. Diffusion coefficients are adapted from the diffusion coefficients of similar sized molecules in the rat brain tissue. The cellular response is modelled as a factor concentration dependent response. The cellular doubling time is set at 20hrs when the conditions are ideal for division. Cellular proliferation is based on a 0.1% subset that is predetermined to form neurospheres and a further 1.3% of cells that are dependent on a critical cell surface factor concentration threshold that ensures geometric expansion rates through cellular doubling. The model?s predictions match the experimental data for neurosphere cell numbers at both high (200000 cells/ml) and low densities (2000 cells/ml). The model forms a framework to build upon for the simulation of a suspension culture that can be used to investigate other aggregate suspension cultures.