BioDynaMo is a biological processes simulator developed by an international community of researchers and software engineers working closely with neuroscientists. The authors have taken part in the development of the physical engine, and they are currently working on gene expression, i.e. the process by which the heritable information in a gene - the sequence of DNA base pairs - is made into a functional gene product, such as protein or RNA. Typically, gene regulatory models employ either statistical or analytical approaches, being the former already well understood and broadly used. In this paper, we utilize analytical approaches representing the regulatory networks by means of differential equations, such as Euler and Runge-Kutta methods. The two solutions are implemented in the BioDynaMo project and are compared for accuracy and performance.
@cite_22: Transendothelial migration is a crucial process of the metastatic cascade in which a malignant cell attaches itself to the endothelial layer forming the inner wall of a blood or lymph vessel and creates a gap through which it enters into the bloodstream (or lymphatic system) and then is transported to distant parts of the body. In this process both biological pathways involving cell adhesion molecules such as VE-cadherin and N-cadherin, and the biophysical properties of the cells play an important role. In this paper, we present one of the first mathematical models considering the problem of cancer cell intravasation. We use an individual force-based multi-scale approach which accounts for intra- and inter-cellular protein pathways and for the physical properties of the cells, and a modelling framework which accounts for the biological shape of the vessel. Using our model, we study the influence of different protein pathways in the achievement of transendothelial migration and give quantitative simulation results comparable with real experiments.
The work presented in @cite_22 uses differential equations in order to model changes in the concentration of proteins as well. Although, this work uses gene expression in a specific task, i.e. studying the influence of different protein pathways in the spreading of cancer cells.