Chemoaffinity hypothesis proposes that axons differentially recognize chemical cues displayed by target matching cells, and this selective recognition is the basis for establishing proper functional neuronal connections. This hypothesis proposed by the neuropsychologist Roger Wolcott Sperry (August 20, 1913 - April 17, 1994), based on classic experiments performed with frogs.
In the early 1940, Roger Sperry performed a series of experiments on the visual system of frog. In his experiments, the eye of a frog is severed from the original connection to the tectum, and then rotated 180o and re-implanted. The retinal ganglion cells are able to re-generate axons that project back to the tectum, and re-establish functional synapses. Insterestingly, this rotation of the eye resulted in a subjectively inverted visual world for these frogs: when attracted by a fly in its upper visual field, the frog always lunges downwards. This inappropriate behavior strongly implied that the frog behaves as if its entire visual world is inverted.
These experiments led to the conclusions that when original optic connections were severed, the regenerating axons of the retina grow back to their original location in the tectum and re-established these well-organized connections. Based on these conclusions, Sperry proposed that spatial gradients of chemical cues expressed by tectal cells likely mediate this process during development, i.e. each optic fiber and each tectal neuron possessed chemical cues that uniquely determined their neuronal type and position and that optic fibers could utilize these labels to selectively navigate to their predeterined target cell. This inference was subsequently formulated into a general explanation of how neurons form well-organized connections during development and became known as the chemoaffinity hypothesis.
Major Reference: Meyer, R. L., 1998, Roger Sperry and his chemoaffinity hypothesis, Neuropsychologia, 36, 957-980