Also, you should know that your claims about driving 3840x2160 are a bit misleading. You may be able to do it over a single HDMI link, but you're not getting full 60 Hz progressive refresh. HDMI doesn't have enough bandwidth to support that. You're probably dropping down to ~30 or even ~15 Hz refresh.
That's what I suspected too. Usually there is an on-screen display which shows you the refresh rate you're using.
Cool. I have monitors with a similar resolution but only 22 inches - so I have to set the font size to extra large in every application. I imagine that you can keep fonts at 'normal' size and just have a super huge desktop. Here's a photo of my setup: http://farm8.staticflickr.com/7145/6851350945_e582af1ed5_o.jpg (it's a big image but I guess you will have no problem displaying it!) Do you have a photo of yours?
The DVI specification mandates a maximum pixel clock frequency of 165 MHz when running in single-link mode. With a single DVI link, the highest supported standard resolution is 2.75 megapixels (including blanking interval) at 60 Hz refresh.
Dual-link DVI is twice the bandwidth but that is still not nearly enough for a 4k*4k display at 60Hz.
I have first-hand experience of this driving T221 monitors (which are less than ten megapixels). Over a dual-link DVI connection only about 30Hz refresh is possible, even if you overclock the DVI link beyond the spec.
As for analogue VGA connectors, there is no defined limit, but basic signal processing laws limit the pixels you can push down the wire. In practice, even with a very short 0.5 metre cable of the highest quality I could find, the picture quality at a mere 1920x1080 resolution is noticeably worse with analogue cabling than with DVI. That might be due to the A-to-D converter in the monitor rather than to a limitation of the cable or graphics card, but making A-to-D converters capable of handling this large bandwidth, together with the higher-spec cabling required, would be very expensive. Much more so than using a digital interface such as Displayport 2.0.
Disc space -- the final frontier!