Physical models of life: diffusion, osmotic growths and artificial cells

The phrase 'diffusive wave' appears in two senses in the held texts. James (1890) used it for the spread of reflex effects through the body. He argued that emotions blunt with repetition faster than other feelings, partly because this wave tends always to become narrower¹. Leduc (1911) used 'diffusion waves' for periodic rings formed by diffusion in gelatine. He said these rings illustrate colour diffraction, and he also used them as diagrams of refraction at a spherical surface between two media⁴. The two uses share a word, not a mechanism.

Verworn (1899) described a gelatine drop in which tannin unites with the gelatine at the surface. New layers are laid down, so the membrane thickens². Leduc (1911) grew cells from a fragment of calcium chloride. The fragment surrounds itself with an osmotic membrane, water enters, and a transparent spherical cell results³. Leduc reported that such cells could grow out of the liquid into the air by one or two centimetres³. Timiriazeff (1912) used a collodion bladder holding tannin in an iron salt solution. The salt is converted to ink inside, so equilibrium is never reached. The cell absorbs all the salt⁵.

Bayliss (1915) reported a 1913 study of nerve fibres by polarised light. The medullary sheath showed double refraction like that of liquid crystals of the glycero-phosphatides⁶. Thompson described liquid crystals as fluids whose molecules move freely yet carry a directive force. Lehmann named this force Gestaltungskraft, and it gives the molecules a definite configuration or polarity⁷.

Newman (2019) treated convergent extension in tissues as the counterpart of a liquid-crystal droplet departing from a sphere. In both cases alignment of elongated elements causes the change⁸. Craddock, Tuszynski and Hameroff (2012) proposed that interference of periodic reaction-diffusion waves in cytoplasm could account for scale-free information patterns in biological systems, including the brain⁹. This is a suggestion, not a measurement. The passages do not show the earlier authors and these later ones agreeing on what such models prove.