Invadopodia are finger-like protrusions located at subcellular membrane which can lead to cancer cell invasion. The formation of invadopodia involves several steps such as actin polymerizations, degradation of extracellular matrix which produce ligand and signal stimulation that is occurred from the binding of ligand with epidermal growth factor receptor. In this paper, a mathematical model of signal transduction is investigated. Both signal and ligand are represented by Laplace equation with Dirichlet boundary condition for each region. The cell membrane is treated as free boundary surface to separate any activity that occurred in intracellular and extracellular regions. The motion of the interface is taken as gradient of  nterior signal and the cell membrane is set as zero level set function. The problem is solved numerically using finite difference scheme of upwind, interpolation and extrapolation methods. The results showed that the formation of invadopodia is formed when protrusions exist on the cell membrane.

No abstract

This research is focused on two types of finite abelian groups which are the group of integers under addition modulo , and the group of integers under multiplication modulo , where  is any positive integer at most 200. The computations of some properties of the group including the order of the group, the order and inverse of each element, the cyclic subgroups, the generators of the group, and the lattice diagrams get more complicated and time consuming as n increases. Therefore, a special program is needed in the computation of these properties. Thus in this research, a program has been developed by using Microsoft Visual C++ Programming. This program enables the user to enter any positive integer at most 200 to generate answers for the properties of the groups.