Self-Organizing Waves and Patterns of Proteins in Biological Cells
Anders Carlsson (Washington University)
Self-organized patterns, such as traveling waves and symmetry-breaking distributions of chemical species, demonstrate how simple laws of motion can lead to complex behaviors in physical systems. Such patterns result from a combination of positive and negative feedback effects with different time scales. The talk will discuss the example of waves of the protein actin in biological cells. Actin, the most abundant intracellular protein in mammals, occurs either as an isolated protein in solution, or in the form of filaments which have mechanical rigidity and are crosslinked into a gel. Recent experiments have shown that filamentous actin forms spontaneous waves that cause protrusion of the cell membrane. Such waves may serve as a “clock” that helps a cell explore its environment. A theoretical model of actin waves will be presented, based on the three-dimensional structure of the gel formed by actin filaments, interacting reciprocally with proteins in the cell membrane. Implementation of this model shows that positive feedback is inherent in the growth process of the actin gel, while negative feedback arises from the actin-membrane interaction. As the concentration of key proteins in the cell is varied, the model predicts phase transitions between different phases including traveling waves or patches, and static symmetry-breaking polarization of the cell.