Estrutura de desvios de otimização em sistemas biológicos

Structure of deviations from optimality in biological systems

Alfonso Pérez-Escuderoa,b,c,1, Marta Rivera-Albaa,b and Gonzalo G. de Polaviejaa,b,1
- Author Affiliations

aInstituto Cajal, Consejo Superior de Investigaciones Científicas, Avenida Dr. Arce 37, 28002 Madrid, Spain;
bDepartment of Theoretical Physics and Instituto “Nicolás Cabrera” de Física de Materiales, Universidad Autónoma de Madrid, 28049 Madrid, Spain; and
cInstituto de Óptica “Daza de Valdés”, Consejo Superior de Investigaciones Científicas, Serrano 121, 28006 Madrid, Spain
Edited by Stanislas Leibler, The Rockefeller University, New York, NY, and accepted by the Editorial Board September 20, 2009 (received for review May 18, 2009)

Abstract

Optimization theory has been used to analyze evolutionary adaptation. This theory has explained many features of biological systems, from the genetic code to animal behavior. However, these systems show important deviations from optimality. Typically, these deviations are large in some particular components of the system, whereas others seem to be almost optimal. Deviations from optimality may be due to many factors in evolution, including stochastic effects and finite time, that may not allow the system to reach the ideal optimum. However, we still expect the system to have a higher probability of reaching a state with a higher value of the proposed indirect measure of fitness. In systems of many components, this implies that the largest deviations are expected in those components with less impact on the indirect measure of fitness. Here, we show that this simple probabilistic rule explains deviations from optimality in two very different biological systems. In Caenorhabditis elegans, this rule successfully explains the experimental deviations of the position of neurons from the configuration of minimal wiring cost. In Escherichia coli, the probabilistic rule correctly obtains the structure of the experimental deviations of metabolic fluxes from the configuration that maximizes biomass production. This approach is proposed to explain or predict more data than optimization theory while using no extra parameters. Thus, it can also be used to find and refine hypotheses about which constraints have shaped biological structures in evolution.

Caenorhabditis elegans Escherichia coli evolution neuroanatomy optimization

Footnotes

1To whom correspondence may be addressed. E-mail: gonzalo.polavieja@cajal.csic.es or alfonso.perez.escudero@cajal.csic.es

Author contributions: A.P.-E. and G.G.d.P. designed research; A.P.-E. performed research; A.P.-E., M.R.-A., and G.G.d.P. analyzed data; and A.P.-E. and G.G.d.P. wrote the paper.

The authors declare no conflict of interest.

This article is a PNAS Direct Submission. S.L. is a guest editor invited by the Editorial Board.

This article contains supporting information online at www.pnas.org/cgi/content/full/0905336106/DCSupplemental.

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