Singh et al carried out a studies in 1994 to find the changes in the composition of GAG during normal palatogenesis in the rat. These are their findings...

The GAG found in the palatal shelves are hyaluronic acid, heparan sulphate and chondroitin-4-sulphate. The GAG composition varies with the stage of palatal development. However, the significant changes in the amount and composition of GAG in the shelves occur after shelf elevation and are in association with histogenesis. The time of maximal GAG synthesis is in the post-elevation, early histogenesis stage.

Overall, the amount and composition of the various GAG does not differ much between pre-elevation and post-elevation stages. This suggests that changes in GAG relate more to histogenesis than to production of a shelf-elevating force. 

There is however a decrease in hyaluronic acid immediately after elevation. Hyaluronic acid starts at a level of 45% before elevation and decreases to about 30% after elevation. It is possible that the production of greater amounts of it prior to elevation could be the major influence at this stage of morphogenesis and its decrease after elevation may reflect that this task has been completed. 

Also, despite the apparent lack of change in amount and composition of GAGs during pre and post elevation, there may be differences in the rates of synthesis and degradation in these stages. Slower rates before elevation would allow a greater degree of  hydration, therefore a greater shelf volume and pressure to be achieved and this may contribute to an elevating force. The GAG activity after elevation may be required to maintain the shelf in its new position.

As the sulphated GAG, heparan sulphate and chondroitin-4-sulphate, show no difference in composition during shelf elevation they may have other functions in palate development. Heparan sulphate may contribute to shelf volume and differentiation processes. Chondroitin-4-sulphate may be related to cartilage formation. In non-elevating palatal systems (such as avian) the sulphated GAG are the dominant GAG whereas in mammals, hyaluronic acid is the predominant GAG.

In 1997, Singh et al looked at GAG synthesis in rats with cleft palates induced by 5-fluoro-2-deoxyuridine (FUDR). In rats with FUDR induced cleft palate, shelf elevation fails to occur and this is the cause of the cleft palate. If GAG synthesis is found to be disturbed in the palatal shelves of these FUDR treated rats, this points to GAG synthesis producing the shelf elevating force.

The GAG  found in the normal palate were the same as those found in the FUDR induced cleft palates. The total amount of GAG is significantly decreased by about 32% during cleft development compared with normal palatogenesis. Unlike normal palatogenesis, during cleft formation, the pattern of maximal GAG synthesis in the post-elevation, early histogenesis stage does not occur. There is approximately 50% less GAG at a time equivalent to the crucial stage of pre-elevation in cleft formation. This seems to indicate that GAG is needed for shelf elevation and to maintain elevation if it occurs.
In cleft formation, the presence of hyaluronic acid begins at a lower level compared with normal. It may be that it is a deficiency of hyaluronic acid in particular which impedes the elevating force. The percentage composition of the sulphated GAG was similar to normal palatogenesis showing that they may have less importance in actual shelf elevation.
In conclusion, insufficient GAG synthesis and subsequent deficient extracellular matrix accumulation might lead to inadequate palatal shelf volume which is incompatible with normal shelf elevation.