Polypeptide Hormones and Receptors: Participants in and Products of a Two Parameter, Dissipative, Measure Preserving, Smooth Dynamical System in Hydrophobic Mass Energy
Loss of a complex Fourier spectrum and the emergence of a single periodic mode indicate loss of information transport capacity, desensitisation, in the dynamics of signal-sensitive neurobiological systems. These findings are consistent with coding theorems requiring the growth rate of orbits (topological entropy) of a channel to be equal to or exceed that of its source of information. The problem becomes that of developing a coding scheme consistent with protein motions characteristic of chaotic dynamical systems.
Integrating the Cartwright-Littlewood differential equation representing forced dissipation in hydrophobic free energy in the parameter regions of its homoclinic bifurcations, digitising the resulting time series, and autocovariance and Fourier transformation generated a full range of polypeptides resembling those found in the brain.
Using the same analytic scheme, similar patterns in hydrophobic broad bands were found between several neuroendocrine polypeptide ligands and their protein receptors.
KeywordsHomoclinic Orbit Homoclinic Bifurcation Polypeptide Hormone Homoclinic Tangency Spiral Mode
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