Diffusion, Turing Patterns and Cell Polarity

SILVIA A. MENCHÓN; DOTTI, CARLOS

Congreso; Computational Cell Biology; 2010

Neuronal polarization is the process by which the recently generated neuron acquires an asymmetric shape, by the sprouting of cylindrical extensions (neurites) which are the precursors of axons and dendrites. In morphological terms, polarization stages are well defined. Initially, the cell is a sphere, hence symmetric. Then, a neurite forms in one pole of the sphere, making the neuron asymmetric. Architecturally, this is the onset of neuronal polarity. Then, other bud grows in the opposite side, and later on, more neurites emerge from different parts of the sphere, until the cell is again symmetric. In neurons in vitro, the first neurite later becomes the axon. Cell polarity can be seen like a self-organised process, in which complex mechanisms are used to establish and maintain specialised domains on the cell membrane. Here, a mathematical model for two interacting surface molecules based on Turing´s reaction-diffusion equations is presented. One of them plays the role of inhibitor as a regulator of endocytosis and the other one, the activator, stimulates exocytosis. Positions of the stationary maximums are correlated with places of symmetry breaking. Relationships between positive feedback for locally amplifying distributions of signalling molecules at the plasma membrane, lateral diffusion and endocytocis rate are established for the formation of Turing patterns.