A morphogenic matrix was the cellular and quantum structure of a Changeling which allowed them to assume various shapes, sizes, weights, and forms.

Although capable of shape-shifting in almost any temperature, a Changeling's morphogenic matrix was most malleable at temperatures of 17 °Celsius. This determination was arrived at by Dr. Mora Pol after weeks of studying the shape-shifting abilities of Odo. (DS9: "The Begotten")

A Changeling's morphogenic matrix could be destabilized through exposure to polaron radiation, forcing a Changeling to revert to his natural, gelatinous state. In 2373, Federation officers from Deep Space 9 attempted to use polaron radiation on a Changeling whom they believed was impersonating Klingon Chancellor Gowron. (DS9: "Apocalypse Rising")

When an infant Changeling was discovered later that year, Dr. Julian Bashir determined that the baby Changeling had been subjected to tetryon radiation. After purging the radioactive isotopes, Bashir noted that the infant's morphogenic matrix still had a small degree of instability. The infant ultimately died when its morphogenic matrix destabilized. (DS9: "The Begotten")

Upon encountering another Changeling named Laas in 2375, a medical scan by Bashir revealed that Laas' morphogenic matrix had not been infected with the morphogenic virus which had infected the rest of the Great Link. (DS9: "Chimera")

In 2375, Bashir "borrowed" a sample of Odo in order to study the Changeling's morphogenic matrix in an attempt to synthesize organic tissue with the ability to change form. It was during the study of the matrix that Bashir learned that Odo had been infected with the same morphogenic disease that was affecting the rest of his people. (DS9: "When It Rains...")

The writers of the show intentionally left the mechanism Changelings use to alter their mass unaddressed, since they didn't have a satisfactory answer. They did have behind-the-scenes theories, though. Robert Hewitt Wolfe proposed that Changelings could store parts of their mass in a subspace "pocket." (AOL chat, 1997)
According to the script for "The Begotten", morphogenic was pronounced as "MORE-foe-jen-ick". [1]

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