Significantly more complex V-ATPase

From PLOS One.  Discussed in more detail here. 

Two very distinct mechanisms, which most likely evolved independently, are employed for ATP-driven H⁺ pumps: the rotary mechanism of the V-ATPase and the alternating access mechanism used by the P-ATPases (Fig 1). The significantly more complex V-ATPase consists of 25–39 protein chains compared to a monomeric or homodimeric polypeptide for the P-ATPase. The operating mechanism for the V-ATPase is also more elaborate consisting of an electric motor-like rotary mechanism. In contrast, the P-ATPase operates by switching between two (E1 and E2) conformations similar to most allosteric mechanisms.

How do we measure "significantly more complex" in terms of bits? 
Mechanism is discussed in more detail here. 

It's complicated.

Some people equate complexity with randomness/disorder because of algorithmic information is also called complexity.

Small probabilities tend to represent a highly select, unusual chain of contingencies.  In the bean machine, the lefts vs. rights taken by the beans will have a more ordered structure at the tail ends.   This low algorithmic information in tail-end result represents a path whose description has low algorithmic information.

How many things must go just right (or just wrong) to get the unusual result?  It is highly contingent.  Maybe specified contingency is a better phrase?

"Entanglement."