Frog Antibiotics: Statistical Mechanics of Helix-Coil Transitions

c. Michelle M. Francl, 2004

Full module available as PDF from the author at mfrancl@brynmawr.edu

keywords: thermodynamics • biochemistry • statistical mechanics • proteins

Primary Literature Reference: This module is based on J. Mol. Bio. 1999, 294, 785-794. "Thermodynamics of the α-Helix-Coil Transition of Amphipathic Peptides in a Membrane Environment: Implications for the Peptide-Membrane Binding Equlibrium" by T. Wieprecht, O. Apostolov, M. Beyermann, J. Seelig.

Background:

In solution, polypeptides are found as random coils, but when they interact with a membrane, they can adopt α-helical conformations. This change in conformation is important when you consider how proteins might insinuate themselves into a membrane. The details of this transformation are thus of some passing interest to biochemists (and biochemistry students). A simple partition function (based ultimately on the statistics of coin-flipping) to model non-cooperative helix-coil transitions. Using this partition functions, it is straightfoward to compute the entropy. The results can be compared to those of researchers exploring the thermodynamic behavior of the helix-coil transition in magainin, a 23-residue peptide found in the African clawed frog (Xenopus Leavis) [T. Wieprecht, O. Apostolov, M. Beyermann, J. Seelig, J.Mol.Bio. 1999 294 785-794]. These peptides bind to membranes in their helical form. Wiepricht et. al used a more sophisticated partition function based on a cooperative transition model to compute entropy and enthalphy changes.

Sample Critical Reading Questions:

• What is an amphipathic protein?
• The most simple minded model we could think of for modeling this conversion is to think of each residue as being either part of a coil (C) or part of a helix (H). On the simplest level, the probability of any given residue being a type H (i.e. is part of an α-helix) is independent of the type of amino acid and independent of whether either neighbor is a type H or C (non-cooperative). Is this likely to be true? Why or why not?

Sample Problem:

• The authors of the J. Mol. Bio. paper say that the magainin forms a "frayed" helix when bound to the membrane. That is, it's not all helix even when bound; the ends presumably are still in random coil. They find that magainin 2 amide (M2a) is 74% helical at 30^oC. What is S when f_H is 0.74? Compute the change in entropy in going from the partially coiled protein (at 30%) to a more helical form (74% helicity) based on the simple non-cooperative binding partition function. Does your answer make sense? The actual protein is probably about 10% helical in solution, compute the entropy change for going from10% helix to 74% helix. Does this answer make sense?

Culture of Chemistry Feature:

Proteins with antibiotic properties.