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A simpler version of Turing model for experimental biology Kondo, Shigeru


The reaction-diffusion model presented by Alan Turing has recently been supported by experimental data and accepted by most biologists. However, scientists have recognized shortcomings when the model is used as the working hypothesis in biological experiments, particularly in studies in which the underlying molecular network is not fully understood. Temporal models mainly utilize the diffusion of the ligand molecules as the basis of nonlocal interaction. However, recent studies have shown that the nonlocal signals are often transfered by other cellular behavior. Therefore, the mathemtaical model need to be flexible. To address some such problems, I would like to proposes a new simpler version of the Turing model.

This simpler model is not represented by partial differential equations, but rather by the shape of an activation-inhibition kernel. Therefore, it is named the kernel-based Turing model (KT model). Simulation of the KT model with kernels of various shapes showed that it can generate all standard variations of the stable 2D patterns (spot, stripes and network), as well as some complex patterns that are difficult to generate with conventional mathematical models. The KT model can be used even when the detailed mechanism is poorly known, as the interaction kernel can often be detected by a simple experiment and the KT model simulation can be performed based on that experimental data. These properties of the KT model complement the shortcomings of conventional models and will contribute to the understanding of biological pattern formation.

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