That depends on the enzyme. Multi-subunit enzymes like, for example, the ATP-synthase have several binding sites that cooperate in the catalytic cycle (doi:10.1146/annurev.biochem.66.1.717). But there are also monomeric enzymes with multiple binding sites, for example, the Mdr1 multiple drug resistance transporter. It has two binding sites for ATP (doi:10.1046/j.1432-1327.1999.00643.x), which also cooperate. The number of binding sites for transported substrate may be even higher (doi:10.1046/j.1432-1327.1999.00644.x). The only (asymmetric!) protein I know of that has multiple binding sites apparently without co-operativity is transferrin (doi:10.1073/pnas.81.14.4326, not an enzyme, but a transport protein for Fe3+ in our blood).
Enzymes have multiple active sites. The allosteric enzymes possess a catalytic site and one or more regulatory sites (also known as allosteric sites). The activity of allosteric enzymes is regulated by non-covalent binding of certain substances (known as allosteric modulators or effectors or modifiers) to the regulatory sites.
All enzymes that use two substrates in a reaction have two sites, one for each substrate. An example is hexokinase, which catalyzes the phosphorylation of glucose:
Yes, transferrin is a single-chain monomeric protein with two (structurally and energetically) different binding sites for iron, but exhibiting small positive cooperativity.
See: Article Isothermal Titration Calorimetry. General Formalism Using Bi...
The reply from Sourbh Garg is misleading. Allosteric enzymes usually have more than one active site which are identical but interact i.e. there is cooperativity. Separate sites that are specific for activators or inhibitors may also be present but these are not catalytic sites.
Also, enzymes that act on two substrates possess a site that can bind each substate in a manner that is appropriate for the chemical reaction between the substrates. For hydrolases where the reaction can involve the formation of an enzyme-substrate covalent intermediate, the second substate is water and this becomes bound in a location in the active site that permits attack on the covalent bond.
Another category of enzymes with multiple catalytic sites consists of enzymes that are homo-oligomeric, which is very common. The whole enzyme molecule may consist of 2 or more identical subunits in a noncovalent complex, each subunit containing one active site. The active sites may or may not interact with each other. Sometimes, the active site is located at the interface between adjacent subunits. A further extension of this type of enzyme is the hetero-oligomer, in which two or more different subunits are present in 2 or more copies each. This is also common. The most abundant enzyme on Earth, RuBisCO, is such an enzyme. It contains 8 large and 8 small subunits.
When dealing with such enzymes, you have to decide on what you consider the concentration to be: the concentration of enzyme molecules or the concentration of active sites. You should be careful to specify which you use when reporting experiments for which this fact is relevant.
As for example of enzymes with two or more different kinds of active sites, an example is GlmU of bacteria. This enzyme is a homotrimer that catalyzes two sequential reactions in a biosynthetic pathway using two completely separate active sites, each of which binds 2 substrates.
DNA polymerase I from prokaryotes have three different activities 3’-5’ Exonuclease Activity, 5’-3’ Exonuclease Activity and 5’-3’ Polymerase activity on a single polypeptide chain in different domains.
There are hence enzymes that show more than one activity.
Each subunit (monomer) has an active site; for example, hemoglobin has 4 subunits, which means it has 4 active sites, but myoglobin has one subunit, and it has one active site.