Mathematical Models in Cellular Biophysics

Abstract: Cellular biophysics deals with, among other things, transport processes within cells. This thesis presents two studies where mathematical models have been used to explain how two of these processes occur.Cellular membranes separate cells from their exterior environment and also divide a cell into several subcellular regions. Since the 1970s lateral diffusion in these membranes has been studied, one the most important experimental techniques in these studies is fluorescence recovery after photobleach (FRAP). A mathematical model developed in this thesis describes how dopamine 1 receptors (D1R) diffuse in a neuronal dendritic membrane. Analytical and numerical methods have been used to solve the partial differential equations that are expressed in the model. The choice of method depends mostly on the complexity of the geometry in the model.Calcium ions (Ca2+) are known to be involved in several intracellular signaling mechanisms. One interesting concept within this field is a signaling microdomain where the inositol 1,4,5-triphosphate receptor (IP3R) in the endoplasmic reticulum (ER) membrane physically interacts with plasma membrane proteins. This microdomain has been shown to cause the intracellular Ca2+ level to oscillate. The second model in this thesis describes a signaling network involving both ER membrane bound and plasma membrane Ca2+ channels and pumps, among them store-operated Ca2+ (SOC) channels. A MATLAB® toolbox was developed to implement the signaling networks and simulate its properties. This model was also implemented using Virtual cell.The results show a high resemblance between the mathematical model and FRAP data in the D1R study. The model shows a distinct difference in recovery characteristics of simulated FRAP experiments on whole dendrites and dendritic spines, due to differences in geometry. The model can also explain trapping of D1R in dendritic spines.The results of the Ca2+ signaling model show that stimulation of IP3R can cause Ca2+ oscillations in the same frequency range as has been seen in experiments. The removing of SOC channels from the model can alter the characteristics as well as qualitative appearance of Ca2+ oscillations.