Integrity constraints should be defined in the model classes of an MVC app since they are part of the business semantics of a model class (representing a business object type). However, a more difficult question is where to perform data validation? In the database? In the model classes? In the controller? Or in the user interface ("view")? Or in all of them?
A relational database management system (DBMS) performs data validation whenever there is an attempt to change data in the database, provided that all relevant integrity constraints have been defined in the database. This is essential since we want to avoid, under all circumstances, that invalid data enters the database. However, it requires that we somehow duplicate the code of each integrity constraint, because we want to have it also in the model class to which the constraint belongs.
Also, if the DBMS would be the only application component that validates the data, this would create a latency, and hence usability, problem in distributed applications because the user would not get immediate feedback on invalid input data. Consequently, data validation needs to start in the user interface (UI).
However, it is not sufficient to perform data validation in the UI. We also need to do it in the model classes, and in the database, for making sure that no flawed data enters the application's persistent data store. This creates the problem of how to maintain the constraint definitions in one place (the model), but use them in two or three other places (at least in the model classes and in the UI code, and possibly also in the database).We call this the multiple validation problem. This problem can be solved in different ways. For instance:
Define the constraints in a declarative language (such as Java Persistency and Bean Validation Annotations or ASP.NET Data Annotations) and generate the back-end/model and front-end/UI validation code both in a back-end application programming language such as Java or C#, and in JavaScript.
Keep your validation functions in the (PHP, Java, C# etc.) model classes on the back-end, and invoke them from the JavaScript UI code via XHR. This approach can only be used for specific validations, since it implies the penalty of an additional HTTP communication latency for each validation invoked in this way.
Use JavaScript as your back-end application programming language (such as with NodeJS), then you can encode your validation functions in your JavaScript model classes on the back-end and execute them both before committing changes on the back-end and on user input and form submission in the UI on the front-end side.
The simplest, and most responsive, solution is the third one, using only JavaScript both in the back-end and front-end components.