Non-Turing stripes and spots: a novel mechanism for biological cell clustering

doi:10.1016/j.physa.2004.03.089

Physica A: Statistical Mechanics and its Applications

Volume 341, 1 October 2004, Pages 482-494

https://doi.org/10.1016/j.physa.2004.03.089 Get rights and content

Abstract

A classical model for developmental patterning invokes a chemical ‘prepattern’ which cells read out as developmental instructions. The ‘prepattern’ arises from the Turing Instability of two reacting and diffusing chemicals, an ‘activator’ and an ‘inhibitor.’ We propose a novel developmental mechanism, based on cell–cell adhesion and cell–extracellular matrix (ECM) adhesion, which depends only on biological mechanisms and chemicals shown experimentally to be significant during patterning. In our model, condensation results from random cell diffusion biased by preferential attachment of cells to ECM and enhanced local cell–cell adhesion. We implement a two-dimensional Cellular Potts Model (CPM) simulation of condensation to explore this mechanism and discuss the parameter dependencies of the patterns. The simulation reproduces much of the density-dependent phenomenology of in vitro biological cell clustering during the developmental process of chick limb precartilage mesenchymal condensation. We study pattern formation in our model and compare it to the standard Turing mechanism. The mechanism should apply to other condensation processes besides limb chondrogenesis in vivo. The existance of an overlooked and simple mechanism which explains the observed phenomenology better than the classical picture is genuinely surprising.

Introduction

Mesenchymal condensation, in which mesenchymal cells (i.e., cells that form part of the bulk tissues rather than the epithelial surfaces) condense (i.e., coalesce) into compact clusters) is the earliest stage of organogenesis and is crucial to the development of skeletal and other mesenchymal tissues (e.g. cartilage, kidney, lung, etc.). The morphology of the condensations lays down the shape of future organs [1], [2]. In this paper we propose a novel developmental mechanism for mesenchymal condensation, based on cell–cell and cell–extracellular matrix (ECM, the loosely structured noncellular scaffolding which surrounds and supports the cells) adhesion. We use it to explain the clustering and differentiation of a previously dispersed population of mesenchymal cells during precartilage mesenchymal condensation in chick limb chondrogenesis (bone patterning and formation), a specific case of the more general developmental phenomenon. We compare the results to those the Turing mechanism produces, which Newman and others have proposed as explaining mesenchymal condensation [3].

Turing proposed a reaction-diffusion mechanism for biological pattern formation in 1952 [4] and patterns similar to Turing-type also occur in certain chemical reactions [5]. A Turing pattern results spontaneously from the reaction and diffusion of two initially homogeneous chemical substances: activator (A) and inhibitor (I), provided that I diffuses faster than A. A promotes the production of both A and I, while I inhibits the production of A. A zone of elevated concentration of A increases the concentration of I over a larger area, inhibiting A in the surrounding region and leading to an inhomogeneous spatial distribution of A and I. Basic patterns include spots, simple stripes and labyrinths, while fine tuning the parameters can produce a whole zoo of patterns.

Many explanations of biological patterning invoke the Turing mechanism, e.g. for the patterning of animal coats, feather buds and fish skin [6], [7]. In this class of models, the standard Turing mechanism establishes a chemical pre-pattern and cells interpret the pattern by differentiating only where the chemical (morphogen) concentration is above a certain threshold [1], [2]. The Turning model is incomplete in several respects: the huge inventory of molecules involved in morphogenesis includes very few which behave like classical activators or inhibitors. No activators or inhibitors are known for mesenchymal condensation. The cells do not influence the static chemical ‘prepattern’, making development into a slave process, while real cells actively reshape their environment. The model requires an additional process (e.g. selective differentiation or chemotaxis) to lock in the labile prepattern. These problems led us to look for a simple patterning mechanism that could reproduce the basic Turing patterns using only biological mechanisms proved experimentally to act during mesenchymal condensation.

Section snippets

Biology

Recent experiments show that extracellular matrix molecules and membrane-bound cell adhesion molecules, such as fibronectin (a sticky protein in the ECM) and N-CAM (a cell–cell adhesion molecule) play an important role in initiating cell clustering during precartilage mesenchymal condensation [8].

Precartilage mesenchymal cells are swarming cells that secrete a variety of complex molecules which form the ECM, the porous environment which is largely responsible for the mechanical integrity of

Methods

We implement a Cellular Potts Model (CPM) [21], [22] simulation on a two-dimensional lattice. The two-dimensional model reflects the quasi-two-dimensional micromass experiment. Our simulation produces a density dependent morphology which we compare to experimental data. We also discuss possible extensions to our model to study the formation of pattern and shape during limb chondrogenesis.

Glazier and Graner introduced the CPM to describe surface-energy-driven biological processes at the cellular

Model and simulation

We propose the following model for precartilage mesenchymal condensation in limb chondrogenesis: mesenchymal cells produce nondiffusing fibronectin and deposit it onto the substrate. Cells execute a random walk biased by their binding more strongly to fibronectin than to the substrate (haptotaxis). Fibronectin–cell surface binding upregulates the production of cell–cell adhesion molecules such as N-cadherin, increasing cells’ adhesiveness to each other. The pattern continues to evolve until the

Results

Precartilage mesenchymal condensations at medium and low culture density (Fig. 2) show very different morphologies. When the density is relatively high (Fig. 2(A)), the condensations consist of both spots and ‘finger-like’ stripes, while dots form during low density condensation (Fig. 2(B)). In Fig. 2(C) we have a cell concentration of 35%, while in Fig. 2(D) the concentration is about 15%. Both cases show reasonable agreement with experiment. Figs. 2(D and E) show the fibronectin distribution

Discussion

Our simulations show that spot and stripe patterns can result from a density dependent mechanism unrelated to the Turing mechanism. In our model, the instability arises from positive feedback in the fibronectin production. Cells tend to stay longer in regions with fibronectin, and hence become more adhesive and produce more fibronectin in those regions, further increasing the time the cells spend there. The wavelength grows continuously until cells stick and clusters cannot coalesce any more.

Acknowledgements

Grants NSF-IBN-008365, NASA-NAG2-1619 and CAPES-Brazil. The authors are grateful to Stuart Newman for his experimental instruction and discussions about the biological aspects of the work, though his interpretation of the experiments differs from ours. We thank Mark Alber, Cornelis Weijer and Gemunu Gunaratne for critical reading and comments.

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View all citing articles on Scopus

¹: Permanent address: Instituto de Fı́sica, Universidade Federal do Rio Grande do Sul, Porto Alegre, RS 91501-970, Brazil.

View full text

Non-Turing stripes and spots: a novel mechanism for biological cell clustering

Abstract

Introduction

Section snippets

Biology

Methods

Model and simulation

Results

Discussion

Acknowledgements

Dev. Biol.

Dev. Biol.

Dev. Biol.

Dev. Biol.

Principles of Development

Developmental Biology

Dynamics of skeletal pattern formation in developing chick limb

Science

The chemical basis of morphogenesis

Phil. Trans. Roy. Soc. B

Experimental evidence of a sustained standing turing-type nonequilibrium chemical pattern

Phys. Rev. Lett.

Mathematical Biology

A viable reaction-diffusion wave on the skin of Pomacanthus, a marine angelfish

Nature

All for one and one for allcondensations and the initiation of skeletal development

BioEssays

Defects in mesoderm, neural tube and vascular development in mouse embryos lacking fibronectin

Development

Fibronectin gene expression during limb cartilage differentiation

Development

TGFbeta2 acts as an “activator” molecule in reaction–diffusion model and is involved in cell sorting phenomenon in mouse limb micromass culture

Dev. Dyn.

Expression and functional involvement of N-cadherin in embryonic limb chondrogenesis

Development