Transport proteins can become saturated with solute, have specificity for certain substances, undergo conformational (shape) changes, and are regulated by the cell. What other type of cellular proteins have these four general characteristics?

Enzymes are substances, mostly proteins, that helps in increasing the speed or rate of a biochemical reaction (conversion of substrate to product) by reducing the activation energy barrier of the reaction.
The enzymes which are made up of proteins have an specific location or region inside them which is called the Active Site.
The biochemical reaction occurs at this active site.
The specific substrate molecule(s) comes and associated with the active site of the enzyme, mostly by means of non-covalent interactions.
By means of amino acid side chains (which have a definite pKa) the exact environment (oxidising or reducing) required for the chemical reaction to occur is maintained by the enzyme at its active site.
After associating with its substrate(s) the enzyme undergoes certain conformational changes in order to position the substrate(s) in the correct orientation such the biochemical reaction can occur.
After the products are formed, the enzyme further undergoes some conformational changes to release them.
Enzymes are similar to transport proteins because:

When the concentration of substrates is far more than that of the available enzymes molecules, then the enzymes would get saturated with substrates, like the transport proteins.
The enzymes are highly specific for their substrates like the transport proteins.
The enzymes undergo conformational changes during the biochemical reaction like the transport proteins.
Both the rate of enzymatic reaction and membrane transport is regulated by the cell.