Figure 3. Pattern generation through Turing-like mechanisms.

The Turing mechanism shows that a two component system can generate a spatially heterogeneous pattern when the diffusion coefficients are significantly different, as shown in (A). The two basic mechanisms of pattern formation in a two component system are the activator-inhibitor mechanism (B) and the substrate-depletion mechanism (C), as described in the text. Both panels show the connection diagrams for the respective mechanism above and a possible biological implementation below. (D) The yeast bud-site selection and polarization mechanism offers a unique example of parallel Turing mechanisms in biology. As shown in panel (i), the WT GTPase Cdc42 displays a polarized response corresponding to the presumptive bud site, as do the two mutant versions of Cdcd42 i.e. Q61L (constitutively GTP bound form) and D57Y (constitutively GDP bound form) [146]. The membrane bound polarized profile of a cell with the Cdc42-Q61L mutation (ii) is plotted in (iii) [80]. The formation of the incipient bud can be divided into two parallel phases (iv). The initial symmetry-breaking phase involves the formation of a cluster of activated Cdc42, which can occur without the presence of actin or microtubule machinery, and requires a positive feedback mechanism involving Cdc42, its GEF Cdc24 and the scaffold protein Bem1 (which binds both Cdc24 and Cdc42GTP). In particular, this polarization depends on the cycling of Cdc42 between the GDP and GTP bound forms. The second phase involves an actin mediated positive feedback involving polarized secretion of vesicles (containing proteins like Cdc42 or Cdc24) along actin cables leads to an ensuing phase of growth and protrusion. This mechanism does not depend on Bem1 and Cdc24 and leads to the polarized distribution of the Q61L and D57Y mutants. Mathematical models of each of these phases display polarization through inherently Turing-based mechanisms. Panel (v) shows a model of the initial actin-independent phase which leads to a polarized Cdc42 distribution as shown in (vi) [147]. Mathematical modeling shows that a combination of lateral diffusion of Cdc42, its endocytosis and its polarized secretion as part of a positive feedback (increased presence of Cdc42 leads to increased probability of actin cable formation and decreased actin cable detachment) as shown in panel (vii) can lead to a polarized distribution of Cdc42 as shown in panel (viii) [80]. (Panels (i) and (iv) reprinted with permission from [146], copyright Wedlich-Soldner et al., 2004, originally published in The Journal of Cell Biology, doi:10.1083/jcb.200405061. Panels (ii), (iii), (vii), (viii) reprinted from [80] with permission from Elsevier. Panels (v) and (vi) reprinted with permission from [147].)