open access

https://doi.org/10.14943/83505

https://hdl.handle.net/2115/69109

A logic-based dynamical theory for a genesis of biological threshold

英語

Chaotic functional map

1996-11-01

Department of Mathematics, Hokkaido University

Hokkaido University Preprint Series in Mathematics

359

1-34

Motivating the study of constructing a formal neuron in computer, we propose a logic-based dynamical theory for a genesis of biological threshold which specific pro­ teins like ion channel proteins or their network can be responsible for. By viewing such a protein or a protein network as a computation machine, the statements concerning the states of reaction chains which eventually activate or inactivate the protein are treated. Introducing dynamical systems, associated with an inference process on the statements with continuous truth values, we investigate invariant characters of such a dynamics, thereby we obtain a sigmoidal function for an invariant distribution func­tion of the truth values. The domain of solutions of functional equations regarded as a representation of the self-description of proteins or protein networks as a machine indicates the emergence of threshold, namely the realization of dyadic value, 0 or 1, b􀁃d on the continuous truth values takes place. The results obtained may highlight the mechanism of neuronal threshold in the framework different from population dy­namics. The derived dynamical systems may also provide a simple model of" demon" rectifying the thermal fluctutions to drive unidirectional movements.

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