Mathematical Modeling of Biological Systems

Abstract

Mathematical and computational models are increasingly used to help interpret biomedical data produced by high-throughput genomics and proteomics projects. The application of advanced computer models enabling the simulation of complex biological processes generates hypotheses and suggests experiments. Appropriately interfaced with biomedical databases, models are necessary for rapid access to, and sharing of knowledge through data mining and knowledge discovery approaches.

Tumor spheroids accelerate persistently invading cancer cells

“…We hypothesized that the gradients imposed by the spheroid would result in an apparent bias in the cell trajectories i.e. following a BPRW model, as previously suggested 17 . Specifically, we anticipated this bias to be a repulsive field in the direction of the spheroid and decaying as 1/ | r |, where r is the radial vector.…”

“…its presence changes the external environment but has no intrinsic effect on the cell – the effect of the spheroid can be modeled by adding an external bias term in the Ornstein-Uhlenbeck process. The resulting model is a biased PRW (BPRW) model whose bias amplitude decreases with the distance from the spheroid 17 .…”