Durability of GH2 shutter

I know how shutters worked on cameras with film with the shutter curtain in front of the film.

I must admit that I have no idea how it works on digital cameras. On my different micro43 cameras I have owned there of course no shutter curtain in front of the sensor and I expect that the shutter is just some all digital readings of the sensor data with no mekanical parts at all. If this is the case I have difficult to understand why there is a upper limit to how many shots you can take with these cameras since there are no mekanical parts the will degrade at least in mirror less digital cameras.

I am sure there are people here that can explain these things properly.