Protein folding, extra dimensions and bio-mathematics
Short Answer

What mathematical work is currently being done in this area?

A... lot?
Longer Answer
The &quot;n-dimensional slope&quot; thing that you're talking about shows up in the modern theory of protein dynamics as the &quot;landscapes&quot; concept. There's no truly standardized form for the theory, so it goes by many names. Try googling folding funnel, energy landscape, probability landscape, free energy surface, etc.
adendum
Oh, and also the current consensus is that the &quot;quantum leap&quot;-style effects that you were talking a little bit about don't play a large role in folding, at least in the initial stages. The current thinking is that most (not all!) of the dynamics of protein folding can be modeled using classical physics. Quantum effects can't come into play until the atoms of a protein are closely smooshed together (ie after the initial &quot;collapse&quot; phase of protein folding has finished).