Is there any equivalent to wine for running Mac applications?

It seems that you're looking for an implementation of the Carbon/Cocoa frameworks used in Mac OS X.

I'm pretty sure that there doesn't exist an implementation complete enough to run Mac apps with. The only similar projects of any weight that I can find are Cocotron and GNUstep, both of which seem to implement only portions of the Cocoa API, and even then only for cross-platform development. I would be shocked if you could run any substantial Mac program on Linux with one of these projects.

There is Darling. Here are few quotes from its site:

Darling is a translation layer that allows you to run unmodified MacOS binaries on Linux. In its nature, it is similar to the well-known Wine project.

...

Darling is capable of running many console tools or applications.

In the past running console apps was all it could do. But now it can run some GUI applications too:

Does it support GUI apps?

Almost! This took us a lot of time and effort, but we finally have basic experimental support for running simple graphical applications. It requires some special setup for now though, so do not expect it to work out of the box just yet. We're working on this; stay tuned!