One metaphor that I have found to explain how proteins fold so quickly to a native shape is that of the blind golfer.

I have made a video to illustrate this metaphor. This shows how the shape of a slope can determine precisely where individual elements will end up.

The video represents many zero-dimensional points each following its own one-dimensional path down a three-dimensional slope to end up in a two-dimensional arrangement. Or almost: the one-dimensional paths are curves in three-dimensional space, the final resting surface is not flat, and one marble sits on top of three others.) The movement takes place through the fourth dimension of time.

Proteins form three-dimensional shapes, so the "slope" that their components slide down must be in an extra dimension.

Atoms have been observed to jump through a crystal lattice, without any indication that, in travelling from their start point to their end point, they pass through the three-dimensional space that we can observe. Is it conceivable that the component parts of a protein move through an extra dimension as the protein "folds"?

There are very simple protein chains whose native folded shape is well known. Is there any data available to suggest what path the different molecules in the protein follow during the folding process? Or do they appear to "jump"?

I imagine that it would be possible to create a mathematical model in n-dimensions to describe the simplest "slope" that the protein molecules could follow as the protein collapses into its native state.

What mathematical work is currently being done in this area?

  • $\begingroup$ What are you asking about precisely - like now it looks too broad - there's like 100 thousand know structures. You also don't get that PES is mathematical construct - these slopes simply describe energy and there's one dimension on degree of freedom $\endgroup$
    – Mithoron
    Aug 10 '15 at 19:19
  • $\begingroup$ PES = "protein expression signatures"? Sure, there are lots of things I don't get. I do understand that that "the map is not the terrain", however closely a mathematical construct appears to model reality. Precisely, I'm asking if there have been attempts to generate n-dimensional shapes which can describe the movement of individual molecules in a protein as it folds, in the same way that my video shows a 3D shape that defines the movement of a set of virtual marbles so that the end up always in the same position. $\endgroup$ Aug 10 '15 at 19:35
  • $\begingroup$ There are really two question nuclei in here. One about quantum tunneling in protein folding, and another one about free energy surfaces and trajectories on them. They're related and both interesting, but definitely distinct. $\endgroup$
    – Resonating
    Aug 11 '15 at 14:05

Short Answer

What mathematical work is currently being done in this area?

A... lot?

Longer Answer

The "n-dimensional slope" thing that you're talking about shows up in the modern theory of protein dynamics as the "landscapes" 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.


Oh, and also the current consensus is that the "quantum leap"-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 "collapse" phase of protein folding has finished).

  • $\begingroup$ Thanks for your rapid answer. From skimming the first articles that come on a Google search for folding funnel protein, it looks as if the mathematics that is used is mostly concerned with describing the release of energy, not with the topology of the "funnel" itself. The diagrams I see look more like artist's impressions than calculated projections onto a 2D screen. Are their names of people you can suggest, who are dealing specifically with the topology of these funnels? $\endgroup$ Aug 10 '15 at 19:25

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