Bonnet Transformation: Explaining the Alpha-Helix to Beta Barrel Transition

[akoska]

Hello,

Can anyone explain to me what this is? I can't seem to find any good references on this.

I'm looking into protein transformations from a helix structure to a catenoid structure through the Bonnet transformation (ie, alpha-helix to beta barrel transition)

 

[Chris Hillman]

Well, you probably don't mean the first thing I thought of, the Gauss-Bonnet map.

You might be looking for a local diffeomorphism between two surfaces (as Riemannian two manifolds) in [itex]E^3[/itex], namely the tangent developable surface of a helix and the surface of rotation generated by a catenoid curve. If so, see Lectures on classical differential geometry, by Dirk Struik, available as a Dover reprint.

Are you thinking of proteins as something like two-dimensional ribbons by any chance? If so, you might be looking for a diffeotopy of ribbons, which might be related to the diffeomorphism between the two surfaces I mentioned.
Unfortunately, I don't seem to be familiar with this "barrel", although I've heard of Pauling's alpha helix structure.

(Diffeotopy versus diffeomorphism: see http://planetmath.org/encyclopedia/Diffeotopy.html and create your very "own" [hah!] WP article)

Additional: searching the arXiv, these abstracts suggest that your Bonnet transformation does indeed deform one minimal surface into another, so my guess about the two surfaces (which are both minimal surfaces) is probably about right.

http://arxiv.org/abs/cond-mat/0605617

http://arxiv.org/abs/cond-mat/0102466

http://arxiv.org/abs/cond-mat/0109512

 

[tacman]

and I'm having trouble understanding the mechanics behind it.

The Bonnet transformation is a concept in protein folding that describes the transition from a helical structure to a barrel-like structure, specifically from an alpha-helix to a beta-barrel. This transformation is important in understanding protein folding and how the structure of a protein can change in response to certain conditions or interactions.

To understand this transformation, it's important to first understand the basic structures of an alpha-helix and a beta-barrel. An alpha-helix is a common secondary structure in proteins, where a single polypeptide chain forms a tightly coiled helical shape. On the other hand, a beta-barrel is a type of tertiary structure in proteins where the polypeptide chain folds back and forth, forming a barrel-like structure with multiple beta strands.

The Bonnet transformation occurs when there is a disruption in the hydrogen bonding pattern within the alpha-helix structure. This can be caused by changes in temperature, pH, or interactions with other molecules. When these bonds are disrupted, the alpha-helix begins to unravel and the polypeptide chain starts to adopt a more extended conformation. This extended chain then folds back on itself, forming a beta-barrel structure.

The mechanics behind this transformation are still being studied, but it is believed that the change in hydrogen bonding patterns and the flexibility of the polypeptide chain are key factors in driving this transformation. Additionally, the specific amino acid sequence and side chain interactions within the protein also play a role in determining the stability and likelihood of the Bonnet transformation to occur.

I hope this helps to clarify the Bonnet transformation and its role in protein folding. It is a complex process that is still being researched, but understanding it can provide valuable insights into the structure and function of proteins.