A cut-cell method for simulating spatial models of biochemical reaction networks in arbitrary geometries

Abstract

Cells use signaling networks consisting of multiple interacting proteins to respond to changes in their environment. In many situations, such as chemotaxis, spatial and temporal information must be transmitted through the network. Recent computational studies have emphasized the importance of cellular geometry in signal transduction, but have been limited in their ability to accurately represent complex cell morphologies. We present a finite volume method that addresses this problem. Our method uses Cartesian-cut cells in a differential algebraic formulation to handle the complex boundary dynamics encountered in biological systems. The method is second-order in space and time. Several models of signaling systems are simulated in realistic cell morphologies obtained from live cell images. We then examine the effects of geometry on signal transduction.