From the point of view of understanding I think it is better to talk about the constant and variable regions of antibodies, rather than Fab and Fc, as these are historical designations for fragments of the molecules that were useful in research, but do not exist as separate entities.
It is possible to represent the immunoglobulin molecule diagrammatically as shown below. In the left-hand diagram V = variable and C = constant, and the suffixes H and L refer to the heavy and light chains. The right-hand diagram, which purports to be more three-dimensional, shows how the variable regions are responsible for binding the antigen — different manifestations of the variable region have different antigen-specificity.
The different iotypes for an immunoglobulin with a particular antigen-specificity are shown next, with a pre-colour scheme that focuses on the difference between the constant regions of each isotype.
Functions of the constant region of different isotypes
The variable region of an immunoglobulin does the exciting stuff — it binds an antigen, but that is not sufficient for its action. As well as the specific discriminatory action of the variable region, there are roles in presentation and disposal that are the same for all antibodies of a class, but may differ between classes. That is what the constant regions do.
I am not an immunologist (although had to teach the biochemistry at one time in my life — hence the diagrams) so the examples I present are simplistic and incomplete. However here are a few:
- IgM is made early in the immune response and hence is not very abundant. In order to enhance its response it forms pentamers in which the constant region of the heavy chain interacts with an additional J chain.
- IgA is involved in immune protection in mucous regions of the body exposed to the exterior. It is directed there by interaction with a receptor on the appropriate epithelial cells, which binds the constant regions of an IgA dimer attached to a J chain.
- IgE stimulates mast cells to produce histamine. These mast cells have receptors for the constant region of the heavy chains of IgE.
There are many sources on line dealing with this topic, including a section in Berg et al. that has a similar structural approach to that presented here.