Question

Explain what is the Alan Turing's reaction-diffusion model of proximal-distal limb development.

Answer 1

Turing’s model of the chemical basis of pattern formation centers on the theoretical activities and interactions ofdiffusible molecules. Two types of simple molecular networks would conform to the model: an activator and an inhibitor or an activator and the depletion of its substrate.

Specifically in the context of digit development, an activator would be predicted to induce digit cartilage differentiation and also to amplify itself by positive feed-back. At the same time, the activator either produces an inhibitor of cartilage differentiation or depletes a substrate in the process of amplifying itself. In either case, if all molecules in the network are expressed equivalently with the same reaction rates, the field of tissue would be homogeneous with no cartilage condensations.

In order for a pattern of condensations to emerge, an initiating heterogeneity, is amplified by differing rates of diffusion of component molecules.

Several Turing models have proposed the identities of activators and inhibitors that are all capable of computa-tionally simulating the ordered array of digits.However, until recently, few had merged theory with experimental validation of model predictions in the intact limb.

In the most recent modeling approach experimentally pursued a prediction from previous Turing models of digit formation to identify members of key signaling pathways that are expressed in phase or out of phasewith Sox9, an HMG-box transcription factor that is an early marker and is itself required for digit chondrogen-esis. This highlighted both the in phase response to Bmp signaling and the out of phase activation of Wntsignaling and expression of the Bmp2 ligand.

In the Bmp-Sox9-Wnt (BSW) model, it is assumed from experimental data in other developmental systems, that the rate of Bmp diffusion exceeds the rate of Wnt diffu-sion. This difference in diffusion amplifies initial heterogeneity by initiating a cascade of events.

BmP induces expression of Sox9 that in turn inhibits theinhibitory effect of Wnt thus producing an autoca-talysis of activation.

However, according to the best-fit topological model, Sox9 also inhibits the production of Bmp2 mRNA, which causes a local down-regulation of Bmp signaling, attenuates the production ofSox9, and thus relinquishes the inhibition of Wnt. This restricts the amplifying effect to local islands of cells, and thus a pattern takes form where Sox9 (digit) is expressed out of phase with both Bmp2 ligand and Wnt target genes (interdigit).

On their own, these three signals form a computational pattern remarkably similar to that formed by chondro-genic nodules in micromass cultures of limb bud mesen-chyme in absence of any additional signals.

A theoretical role for Hox and Fgf activities restricts the physical space in which heterogeneity initiates a Turing pattern and organizes the pattern into digit-like stripes rather than meandering lines. The latter is predicted to occur in response to a gradient of Fgf signal from the AER that together with Hox function, coordinately decreases the inhibition and increases the activation of the Turing network to set the thickness and orientation of stripes.This causative relationship between levels of Hox and Fgf and limb size ensures that as the modeled limb scaleslarger (higher Hox and Fgf) or smaller (lower Hox andFgf), digit thickness also scales to predict that five smaller or larger digits will form as a function of limb bud size.