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Updated: Apr 8, 2026

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix

Planar Gradient Diffusion System to Investigate Chemotaxis in a 3D Collagen Matrix

Published on: June 12, 2015

Contribution to an effective design method for stationary reaction-diffusion patterns.

István Szalai¹, Judit Horváth¹, Patrick De Kepper²

¹Laboratory of Nonlinear Chemical Dynamics, Institute of Chemistry, Eötvös Loránd University, P.O. Box 32, H-1518 Budapest 112, Hungary.

Chaos (Woodbury, N.Y.)

|June 29, 2015

Summary

Alan Turing predicted reaction-diffusion patterns. A new design method, developed in 2009, has since enabled five new pattern-producing reactions, expanding experimental possibilities.

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Area of Science:

Chemical kinetics
Mathematical modeling
Pattern formation

Background:

Alan Turing predicted stationary reaction-diffusion patterns in 1952.
Experimental demonstrations were limited until the 1990s.
A 2009 design method significantly increased pattern-producing reactions.

Purpose of the Study:

To evaluate the patterning capacity of Rabai's model for pH-driven Landolt type reactions.
To explore this capacity under conditions mimicking open spatial reactors.
To compare numerical predictions with experimental observations.

Main Methods:

Numerical studies of Rabai's model.
Exploration of experimentally attainable parameters controlling time and length scales.
Comparison of model predictions with existing experimental data.

Main Results:

The study numerically explored the patterning capacity of a specific reaction model.
Predictions were made based on parameters controlling reaction dynamics.
Agreements and differences between model predictions and experimental observations were analyzed.

Conclusions:

The methodical approach for assessing patterning capacity was further investigated.
Rabai's model, based on proton binding to polymers, is crucial for many observed patterns.
Numerical studies provide insights into reaction-diffusion pattern formation in realistic reactor conditions.