Towards a morphogenetic field model


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Why a morfogenetic field theory? Motivation

Thirty years ago Lynn and Tucker studied the biological mechanisms responsible for defining organelles position inside cells. This class of studies were the observational and experimental support of the ‘morphogenetic field’ notion. In the present project we study the morphogenetic field evolution yielding from an initial population of cells to different unicellular organisms as well as specialized eucariotic cells. Both types of cells were represented as
Julia sets and Pickover biomorphs, simulating Darwinian natural selection with a simple genetic algorithm.

A morphogenetic field has been defined as a plane
A with points representing the locations where cells are differentiated or sub-cellular components (or organelles) organized, being the plane A an tissue or cell, respectively. The region A representing the morphogenetic field assumes two X, Y orthogonally diffusing chemicals modeled as the real and imaginary components on the complex plane where a biomorph (a cell and its organelles) is differentiated and evolved. We found that Pickover cells show a higher diversity of size and form than those populations of cells evolved as Julia sets. Another novelty is the way that cellular organelles and cell nucleus fill the cell depending on cell definition as Julia set or Pickover biomorph.

Our findings support the existence of some attractors representing the functional and stable form of a cell. The morphogenetic field is attracted towards one or another attractor depending on the environment modeled by a particular fitness function. The model promotes the view of Waddington, Goodwin and D’Arcy Thompson that considers organisms as dynamical systems that evolve through a ‘master plan’ of transformations.


Modeling the zebra strip pattern

One of the classical problems of morphogenesis is to explain how patterns of different animals evolved resulting in a consolidated and stable pattern generation after generation. In this paper ( Int. J. Appl. Math. Comput. Sci., 2004, vol. 14(3): 351-361) we simulated the evolution of two hypothetical morphogens, or proteins, that diffuse across a grid modeling the zebra skin pattern in an embryonic state, composed of pigmented and nonpigmented cells. The simulation experiments were carried out applying a genetic algorithm (Transl.: Spanish) to the Young cellular automaton: a discrete version of the reaction-diffusion equations proposed by Turing in 1952. In the simulation experiments we searched for proper parameter values of two hypothetical proteins playing the role of activator and inhibitor morphogens. Our results show that on molecular and cellular levels recombination is the genetic mechanism that plays the key role in morphogen evolution, obtaining similar results in the presence or absence of mutation. However, spot patterns appear more often than stripe patterns on the simulated skin of zebras. Even when simulation results are consistent with the general picture of pattern modeling and simulation based on the Turing reaction-diffusion, we conclude that the stripe pattern of zebras may be a result of other biological features (i.e., genetic interactions, the Kipling hypothesis) not included in the present model.

Motivation | Morphogenetic field evolution | Mandelbrot and Julia sets | Biomorph fitness | References | Site Map


R. Lahoz-Beltra, N. Selem Mojica, C. Perales-Gravan, J. Navarro, P.C. Marijuán | lahozraf@bio.ucm.es

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