Estudo matemático sobre o surgimento de função de células coordenadas em um tecido: mero acaso, fortuita necessidade ou design inteligente?

segunda-feira, fevereiro 06, 2017

Emergence of function from coordinated cells in a tissue

Indika Rajapakse a,1,2 and Stephen Smale b,1,2

Author Affiliations

a Department of Computational Medicine and Bioinformatics, Medical School, Department of Mathematics, University of Michigan, Ann Arbor, MI 48105;

b Department of Mathematics, University of California, Berkeley, CA 94720

Contributed by Stephen Smale, December 22, 2016 (sent for review November 4, 2016; reviewed by Sayan Mukherjee and Jean-Jacques Slotine)


A basic problem in biology is understanding how information from a single genome gives rise to function in a mature multicellular tissue. Genome dynamics stabilize to give rise to a protein distribution in a given cell type, which in turn gives rise to the identity of a cell. We build a highly idealized mathematical foundation that combines the genome (within cell) and the diffusion (between cell) dynamical forces. The trade-off between these forces gives rise to the emergence of function. We define emergence as the coordinated effect of individual components that establishes an objective not possible for an individual component. Our setting of emergence may further our understanding of normal tissue function and dysfunctional states such as cancer.


This work presents a mathematical study of tissue dynamics. We combine within-cell genome dynamics and diffusion between cells, so that the synthesis of the two gives rise to the emergence of function, akin to establishing “tissue homeostasis.” We introduce two concepts, monotonicity and a weak version of hardwiring. These together are sufficient for global convergence of the tissue dynamics.

diffusion emergence genome dynamics monotonicity tissue dynamics


1I.R. and S.S. contributed equally to this work.

2To whom correspondence may be addressed. Email: or

Author contributions: I.R. and S.S. designed research, performed research, contributed new reagents/analytic tools, analyzed data, and wrote the paper.Reviewers: S.M., Duke University; and J.-J.S., Massachusetts Institute of Technology.

The authors declare no conflict of interest.

Freely available online through the PNAS open access option.