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Interactions between pattern formation and domain growth.

A A Neville¹, P C Matthews, H M Byrne

¹Centre for Mathematical Medicine, School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, UK.

Bulletin of Mathematical Biology

|November 7, 2006

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This study introduces a framework for biological pattern formation in growing tissues. Rapid growth affects spatial patterns and chemical concentrations, revealing complex interactions between tissue size and pattern development.

Area of Science:

Theoretical biology
Mathematical modeling
Developmental biology

Background:

Investigating pattern formation in biological systems.
Understanding how tissue growth influences spatial patterns and chemical concentrations.

Purpose of the Study:

Develop a theoretical framework for pattern formation in growing biological tissues.
Analyze the interplay between tissue growth and chemical signaling in pattern development.

Main Methods:

Theoretical framework development.
Numerical simulations for exponential and chemically controlled growth.
Weakly nonlinear analysis of the full system.

Main Results:

Dilution effects from rapid exponential growth impact spatial patterns and chemical concentrations.

Related Experiment Videos

Complex interplay identified between chemical effects on domain size and domain size influence on pattern formation.

A pair of nonlinear equations derived for pattern amplitude and domain size.

Conclusions:

Domain growth rate is quadratically dependent on pattern amplitude, tissue growth rate functions, and chemical kinetics.
The developed framework elucidates the dynamics of pattern formation in growing biological systems.