Why should it be unique among proteins? Bags of water and proteins famously behave in extremely statistically predictable ways on a cellular level ... and are conscious. Animals and humans are nothing but a lot of those bags. Ok ... a very large number. I also have a Msc in statitstics, which tells me a combination of a large number of statistically predictable variables is itself a statistically predictable variable.

So why couldn't a large collection of statistical variables be conscious? Mathematically, it's the same thing.