"Stability Analysis of a Bulk–Surface Reaction Model for Membrane Protein Clustering"
Protein aggregation on the plasma membrane (PM) is of critical importance to many cellular processes such as cell adhesion, endocytosis, fibrillar conformation, and vesicle transport. Lateral diffusion of protein aggregates or clusters on the surface of the PM plays an important role in governing their heterogeneous surface distribution. However, the stability behavior of the surface distribution of protein aggregates remains poorly understood. Therefore, understanding the spatial patterns that can emerge on the PM solely through protein–protein interaction, lateral diffusion, and feedback is an important step toward a complete description of the mechanisms behind protein clustering on the cell surface. In this work, we investigate the pattern formation of a reaction–diffusion model that describes the dynamics of a system of ligand–receptor complexes. The purely diffusive ligand in the cytosol can bind receptors in the PM and the resultant ligand–receptor complexes not only diffuse laterally but can also form clusters resulting in different oligomers. Finally, the largest oligomers recruit ligands from the cytosol using positive feedback. From a methodological viewpoint, we provide theoretical estimates for diffusion-driven instabilities of the protein aggregates based on the Turing mechanism. Our main result is a threshold phenomenon, in which a sufficiently high recruitment of ligands promotes the input of new monomeric components and consequently drives the formation of a single-patch spatially heterogeneous steady state.
Massey U Palmerston North
"Spatiotemporal dynamics in spontaneous excitable cells"
Pacemaker dynamics is the spontaneous excitation-contraction coupling in muscle cells. It may arise as a result of interaction between ion fluxes through the voltage-gated ion channels. In this work, we consider a model of electrically coupled pacemaker smooth muscle cells to investigate the formation of spatiotemporal patterns. We analyse the behaviour of an isolated smooth muscle cell using numerical bifurcation analysis. By modulating model parameters, the result reveals transitions between Type I and II excitabilities in the parameter space. Numerical simulations of our model show that the pattern can bifurcate from been stable to spatiotemporal chaos.
"Evaluation of a mathematical model for estradiol effect on membrane excitability of detrusor smooth muscle cell"
The urinary bladder is composed of detrusor smooth muscle (DSM) cell to perform contraction, triggered by the intracellular calcium concentration after the generation of the action potential (AP). The DSM cells display enhanced spontaneous APs during the overactive bladder state. Estradiol, which is a natural sex hormone, has been suggested to be beneficial in the treatment of overactive bladder. This study aims in investigating the quantitative analysis of estradiol on membrane excitability of DSM cells. To simulate the estradiol effect, conductances of calcium- and voltage-dependent potassium channels (BK channels) were increased by 40% of its control value in a published DSM model cell. We found that the resting membrane potential (RMP) was more negative (─ 53 mV) than the control (─ 50 mV) value. The peak amplitude of the AP due to estradiol treatment was also significantly decreased. Similar to in the control condition, we have implemented the voltage clamp protocol to investigate the whole cell outward current. Under the effect of the estradiol, the amplitude of outward current was greatly increased due to BK channel. These findings are consistent with the experiment in guinea pig and rat DSM cells. The future investigation would provide some insight towards the modulating role of voltage-gated Ca2+ current in DSM cells due to estradiol treatment.