Modelo de Alan Turing fornece finalmente a tão almejada fundamentação matemática da teoria da evolução???

sexta-feira, dezembro 28, 2012

Science 14 December 2012: 

Vol. 338 no. 6113 p. 1406 

DOI: 10.1126/science.338.6113.1406



Gretchen Vogel

Sixty years ago, noted mathematician Alan Turing described how two interacting chemicals diffusing through space could form interacting wave patterns. Recently, experiments have suggested that Turing's mechanisms play a role in the growth of feathers, hair follicles, the branching pattern of lungs, and even the left-right asymmetry that puts the heart on the left side of the chest. In this issue of Science, a team of biologists offer fresh evidence that this theory guides how some parts of the body develop, as Turing's model also appears to describe the pattern that leads to digit formation in the developing mouse paw.


Science 14 December 2012: 

Vol. 338 no. 6113 pp. 1476-1480 

DOI: 10.1126/science.1226804


Rushikesh Sheth1,*,†, Luciano Marcon2,3,*, M. Félix Bastida1,4, Marisa Junco1, Laura Quintana2,3, Randall Dahn5, Marie Kmita6,‡, James Sharpe2,3,7,‡, Maria A. Ros1,4,‡

+ Author Affiliations

1Facultad de Medicina, Instituto de Biomedicina y Biotecnología de Cantabria, Consejo Superior de Investigaciones Científicas–Sociedad para el Desarrollo Regional de Cantabria–Universidad de Cantabria, 39011 Santander, Spain.

2European Molecular Biology Laboratory (EMBL)–Centre for Genomic Regulation (CRG) Systems Biology Research Unit, CRG, Doctor. Aiguader 88, 08003 Barcelona, Spain.

3Universitat Pompeu Fabra, 08003 Barcelona, Spain.

4Departamento de Anatomía y Biología Celular, Universidad de Cantabria, 39011 Santander, Spain.

57322 Countrywood Lane, Madison, WI 53719, USA.

6Institut de Recherches Cliniques de Montréal, Université de Montréal, Montréal, Québec H2W 1R7, Canada.

7Institució Catalana de Recerca i Estudis Avançats, Passeig Lluís Companys 23, 08010 Barcelona, Spain.

+ Author Notes

↵† Present address: Institut de Recherches Cliniques de Montréal, University of Montréal, Montréal, Québec, Canada.

↵‡To whom correspondence should be addressed. E-mail: (M.A.R.); (J.S.); (M.K.)

↵* These authors contributed equally to this work.


The formation of repetitive structures (such as stripes) in nature is often consistent with a reaction-diffusion mechanism, or Turing model, of self-organizing systems. We used mouse genetics to analyze how digit patterning (an iterative digit/nondigit pattern) is generated. We showed that the progressive reduction in Hoxa13 and Hoxd11-Hoxd13 genes (hereafter referred to as distal Hox genes) from the Gli3-null background results in progressively more severe polydactyly, displaying thinner and densely packed digits. Combined with computer modeling, our results argue for a Turing-type mechanism underlying digit patterning, in which the dose of distal Hox genes modulates the digit period or wavelength. The phenotypic similarity with fish-fin endoskeleton patterns suggests that the pentadactyl state has been achieved through modification of an ancestral Turing-type mechanism.



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