Confermati i modelli matematici delle forme naturali, ideati 60 anni fa da Alan Turing

Perché il nostro cuore è a sinistra e il fegato a destra? Come si formano le strisce di zebre e tigri? E le chiazze del leopardo? Alan Turing nel 1952 ipotizzò che le posizioni e le ripetizioni di colori e forme nei sistemi biologici fossero generate da sostanze che si comportano da attivatori e inibitori.
Un gruppo di ricercatori di Harvard ha scoperto che Nodal e Lefty, due proteine implicate nella regolazione dell'asimmetria nei vertebrati, combaciano con il modello descritto da Turing 60 anni fa.
In questo modello denominato Gierer-Meinhardt si dimostra che le interazioni tra inibitore e attivatore possono portare a una grande varietà di modelli. Negli ultimi 20 anni sono state scoperte numerose coppie attivatore-inibitore e si è riscontrato che manipolandole viene modificata la dislocazione e la forma dei disegni durante lo sviluppo. Nello studio, pubblicato su Science (online il 12 Aprile 2012), Alexander Schier, docente di biologia molecolare e cellulare a Harvard, e i suoi collaboratori Patrick Müller, Katherine Rogers, Ben Jordan, Joon Lee, Drew Robson e Sharad Ramanathan, hanno dimostrato che Nodal e Lefty sono alla base del sistema di attivazione-inibizione, e che la proteina che funge da attivatore (Nodal) si muove molto più lentamente rispetto alla proteina che si comporta da inibitore (Lefty).

In uno studio pubblicato su Nature Genetics (online il 19 Febbraio 2012) un gruppo di ricercatori del King's College di Londra, guidati da Jeremy B A Green, aveva fornito di fatto la prima prova sperimentale che conferma la teoria di Turing per modelli biologici come le strisce della tigre e le macchie del leopardo. I ricercatori hanno identificato i morfogeni coinvolti in questo processo: FGF (fattore di crescita dei fibroblasti) e Shh (Sonic Hedgehog). E hanno dimostrato che all'aumentare o al diminuire dell'attività di questi morfogeni lo schema delle creste presenti all'interno della bocca (nel palato) segue gli andamenti previsti dalle equazioni di Turing.

Andrea Mameli www.linguaggiomacchina.it 27 Settembre 2012

Differential Diffusivity of Nodal and Lefty Underlies a Reaction-Diffusion Patterning System

Patrick Müller, Katherine W. Rogers, Ben M. Jordan, Joon S. Lee, Drew Robson, Sharad Ramanathan, Alexander F. Schier
Published Online April 12 2012
Science 11 May 2012:
Vol. 336 no. 6082 pp. 721-724
DOI: 10.1126/science.1221920

Abstract

Biological systems involving short-range activators and long-range inhibitors can generate complex patterns. Reaction-diffusion models postulate that differences in signaling range are caused by differential diffusivity of inhibitor and activator. Other models suggest that differential clearance underlies different signaling ranges. To test these models, we measured the biophysical properties of the Nodal/Lefty activator/inhibitor system during zebrafish embryogenesis. Analysis of Nodal and Lefty gradients revealed that Nodals have a shorter range than Lefty proteins. Pulse-labeling analysis indicated that Nodals and Leftys have similar clearance kinetics, whereas fluorescence recovery assays revealed that Leftys have a higher effective diffusion coefficient than Nodals. These results indicate that differential diffusivity is the major determinant of the differences in Nodal/Lefty range and provide biophysical support for reaction-diffusion models of activator/inhibitor-mediated patterning.

Periodic stripe formation by a Turing mechanism operating at growth zones in the mammalian palate
Andrew D Economou, Atsushi Ohazama, Thantrira Porntaveetus, Paul T Sharpe, Shigeru Kondo, M Albert Basson, Amel Gritli-Linde, Martyn T Cobourne, Jeremy B A Green.
Nature Genetics 44, 348–351 (2012) doi:10.1038/ng.1090
Published online: 19 February 2012

Abstract

We present direct evidence of an activator-inhibitor system in the generation of the regularly spaced transverse ridges of the palate. We show that new ridges, called rugae, that are marked by stripes of expression of Shh (encoding Sonic hedgehog), appear at two growth zones where the space between previously laid rugae increases. However, inter-rugal growth is not absolutely required: new stripes of Shh expression still appeared when growth was inhibited. Furthermore, when a ruga was excised, new Shh expression appeared not at the cut edge but as bifurcating stripes branching from the neighboring stripe of Shh expression, diagnostic of a Turing-type reaction-diffusion mechanism. Genetic and inhibitor experiments identified fibroblast growth factor (FGF) and Shh as components of an activator-inhibitor pair in this system. These findings demonstrate a reaction-diffusion mechanism that is likely to be widely relevant in vertebrate development.

Figure 1: New rugal stripes appear in the palate at regions of growth.

(a) In situ hybridization for Shh in the developing palatal shelves from mice at E12.0 to E14.5 (right, anterior; up, medial) showing the sequential addition of new rugae (white arrowheads) anterior to ruga 8 (r8; black arrowhead). Scale bar, 500 μm. (b) Schematic showing the sequential addition of rugae with growth. (c) Inter-rugal intervals measured at E13.5 and E14.5 along a line drawn from the point where the palatal shelf meets the posterior of the primary palate parallel to the midline of the head (dotted line). Scale bar, 200 μm. (d) Ratios of the lengths of the inter-rugal intervals at E14.5 and E13.5, indicating high levels of growth between r8 and ruga 5 (r5) and elevated growth between r5 and ruga 4 (r4), with little growth anterior to r4. Error bars, s.d. Colors in the histogram in d correspond to those for different inter-rugal intervals in c. (e) Growth anterior to ruga 2 (r2). Colored dotted lines show the orthogonal distance from Shh expression at r2 to the anterior shelf edge (black dotted line) at the base of the shelf (blue), medial edge of the stripe of Shh expression (red) and midway between (yellow). Growth in more medial regions correlated with the appearance of Shh expression at ruga 1 (r1) at the anterior edge. Scale bar, 200 μm.

Figure 2: Rugal stripe patterning size is scaled with growth inhibition and is branched when an established stripe is excised.

(a) Schematic of a lateral inhibition hypothesis for rugal spacing. Curves represent levels of inhibitor produced by rugae, and the dashed line represents the inhibitory threshold. Growth between rugae would allow the level of inhibition to fall below the threshold (asterisk), permitting the formation of a new ruga (dashed rectangle). (b,c) Rugal stripes of Shh expression on palatal shelves cultured for 0, 24 and 48 h after explant from littermates at E12.5 (b) and E13.5 (c), showing the addition of rugae without anteroposterior growth at closer spacing than the equivalent stripes in vivo. (d) Schematic representing the predicted effect of removing a ruga under a lateral inhibition model. Removing the anterior edge of the palatal shelf by cutting posterior to ruga 2 (vertical dashed line) removes inhibition from this ruga, allowing inhibition to fall below the threshold at the cut edge (asterisk) and leading to the formation of a new ruga (dashed rectangle). (e–g) Experimental results differed greatly from those predicted under a lateral inhibition model. Posterior palatal shelves cut adjacent to ruga 2 and cultured for 48 h with the anterior edge immediately fixed (f,g, two examples; right, uncultured anterior pieces) were analyzed by Shh in situ hybridization, which revealed branches to ruga 3 at curves in the ruga (black arrowheads), which was not seen in uncut controls (e). (Dashed line in e represents where the cut is in cut shelves.) (h,i) Branches to stripes were readily replicated in reaction-diffusion simulations generated using Turing equations as described². Compare the pattern in circles in h and i (two examples) with those at arrowheads in f and g. For all specimens: right, anterior; up, medial.

Figure 3: Sprouty and Shh loss-of-function mutants implicate FGF and Hedgehog signaling in rugal patterning.

Palates of postnatal day 0 (P0) mice viewed from the oral side with the anterior side up. (a–d) Increased FGF signaling in Spry1^−/−; Spry2^−/− mice resulted in disorganized and compacted rugae (b, detail in d) compared to wild-type (WT) animals (a, detail in c). Rugal phenotype can be distinguished despite cleft palate in these mutants. (e–h) Downregulation of Shh in K14-Cre; Shh^fl/fl mice resulted in a similar phenotype of disorganized, compacted rugae (f, detail in h) compared to wild-type controls (e, detail in g). Scale bar in a, 1 mm (a,b,e,f); scale bar in c, 0.3 mm (c,d,g,h).