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Ceccarelli, A.S.* ; Borges, A. ; Chara, O.*

Size matters: Tissue size as a marker for a transition between reaction-diffusion regimes in spatio-temporal distribution of morphogens.

R. Soc. Open Sci. 9:211112 (2022)

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The reaction-diffusion model constitutes one of the most influential mathematical models to study distribution of morphogens in tissues. Despite its widespread use, the effect of finite tissue size on model-predicted spatio-temporal morphogen distributions has not been completely elucidated. In this study, we analytically investigated the spatio-temporal distributions of morphogens predicted by a reaction-diffusion model in a finite one-dimensional domain, as a proxy for a biological tissue, and compared it with the solution of the infinite-domain model. We explored the reduced parameter, the tissue length in units of a characteristic reaction-diffusion length, and identified two reaction-diffusion regimes separated by a crossover tissue size estimated in approximately three characteristic reaction-diffusion lengths. While above this crossover the infinite-domain model constitutes a good approximation, it breaks below this crossover, whereas the finite-domain model faithfully describes the entire parameter space. We evaluated whether the infinite-domain model renders accurate estimations of diffusion coefficients when fitted to finite spatial profiles, a procedure typically followed in fluorescence recovery after photobleaching (FRAP) experiments. We found that the infinite-domain model overestimates diffusion coefficients when the domain is smaller than the crossover tissue size. Thus, the crossover tissue size may be instrumental in selecting the suitable reaction-diffusion model to study tissue morphogenesis.

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Publication type Article: Journal article

Document type Scientific Article

Corresponding Author

Keywords Morphogens ; Reaction-diffusion Model ; Morphogenesis ; Tissue Size; Pattern; Gradient; Model; Proliferation; Multiscale; Dynamics

ISSN (print) / ISBN 2054-5703

e-ISSN 2054-5703

Journal Royal Society Open Science

Quellenangaben Volume: 9, Issue: 1, Article Number: 211112

Publisher Royal Society of London

Publishing Place 6-9 Carlton House Terrace, London Sw1y 5ag, England

Non-patent literature Publications

Reviewing status Peer reviewed

Institute(s) Research Unit Sensory Biology and Organogenesis (SBO)

Grants Fondo para la Investigacion Cientifica y Tecnologica