Pattern formation and morphogenesis

The term pattern is a rather vague notion to denote the arrangement of certain abstract elements. According to our subjective feeling there is no clear distinction between the terms structure and pattern . Temporal, spatial and spatio-temporal structures in thermochemical systems might be the result of the interaction of chemical components by diffusion and chemical reactions. 

Since chemical reactions and diffusion processes are the consequences of the interactions among chemical constitutents, chemical patterns may be interpreted at the molecular level. A certain, but closely limited, class of biological patterns may be described in biochemical terms. Adopting the spirit of the hierarchical approach, patterns at higher than molecule levels may be formulated as the products of interactions among higher than molecule (e.g. cell) constituents. 

Two points have to be emphasised here. First, the interactions in higher than molecule populations can be formally described by models similar to those used in thermodynamics (i.e reaction-diffusion equations). Second, these interactions are just thermodynamic effects, often due to chemical reactions and diffusion. For example, the spatio-temporal patterns of interacting cells due to cellular communication are based partly upon the chemical nature of the communication (and partly on the topological arrangement of the cell population). 

From the biological point of view, numerous specific mechanisms have been suggested to explain pattern formation, such as induction , lineage , prepattern , positional information and polar co-ordinate models. All these mechanisms were required to explain the question how can genetic information be translated in a reliable manner to give specific and different 

Development-controlling prepattern mechanisms have been modelled in reaction-diffusion context. In the celebrated paper of Turing (1952) a model was presented in terms of reaction-diffusion equations to show how spatially inhomogeneous arrangements of material might be generated and maintained in a system in which the initial state is a homogeneous distribution. Two components were involved in the model, and the reactions were described by linear differential equations. The model in one spatial dimension s is  

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In addition to the direct utility of mathematical models in the analysis of complex chemical systems a unified conceptual framework is offered to the mathematical treatment of problems of chemical kinetics and related areas in biomathematics. Biochemical control processes, oscillation and fluctuation phenomena in neurochemical systems, coexistence and extinction in populations, prebiological evolution and certain ecological problems of Lake j Balaton can be treated in terms of this framework. Though the main body of/ the book deals with spatially homogeneous systems, spatial structures in chemical systems, pattern formation and morphogenesis related to reaction-diffusion models are also mentioned briefly. 

Preface, Pattern Formation and Morphogenesis I - Fractal Phenomena... 

Reif, W.-E. (1976) Morphogenesis, pattern formation and function of the dentition of Heterodontus (Selachii) , Zoomorphologie, 83, 1 7. 

In the present chapter, we have not discussed cell-cell interaction and have restricted our study only to a production process of a single cell. Of course, cells start to interact with each other, as the cell density is increased through the cell division. Indeed, including the cell-cell interaction to the present cell model with reaction network, cell differentiation and morphogenesis of a cell aggregate are studied [15,16]. Through instability of intracellular dynamics with cell-cell interaction, cell differentiation, irreversible loss of plasticity in cells, and robust pattern formation process appear as a general course of development with the increase of the cell number. Relevance of minority control and deviation from universal statistics to such multicellular developmental processes will be an important issue to be studied in the future. 

Alan Turing s paper entitled The Chemical Basis of Morphogenesis [440] ranks without doubt among the most important papers of the last century. In that seminal work Turing laid the foundation for the theory of chemical pattern formation. Turing showed that diffusion can have nontrivial effects in nonequilibrium systems. The interplay of diffusion with nonlinear kinetics can destabilize the uniform steady state of reaction-diffusion systems and generate stable, stationary concentration patterns. To quote from the abstract,... 

While the focus of this chapter, and of genetic research into morphogenesis, is on the chemical pattern formation underlying growth, plants have unique mechanical characteristics which can also affect form. 

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