Energetics of Proteins in Membranes
Regardless of how a membrane protein finds its way into a membrane, whether constitutive or non-constitutive, once located there it sits in a free energy minimum within the lipid bilayer of the membrane.
One would like to sort out the energetics of protein-protein and protein-bilayer energetics that determine this minimum and hence the structure of the protein. This can be done in principle by unfolding and folding the protein within the bilayer. This is virtually impossible to do with whole membrane proteins: They are insoluble in the bilayer in the unfolded form because of the energetic cost of exposing the peptide bonds to the bilayer hydrocarbon interior. And, they are insoluble in the aqueous phase in both their folded and unfolded forms because of their highly non-polar (hydrophobic) character. How, then, can one approach the problem?
A bootstrap strategy can be adopted in which we surmise the energetics of membrane proteins from the studies of the energetics of small peptides in lipid bilayers.
Bootstrap Strategy
The strategy involves studying the interactions of small peptides (3 - 35 amino acids) with lipid bilayers in order to surmise the thermodynamic principles of the folding and stability of whole membrane proteins. The strategy views membrane proteins at the level of a single secondary structure element, e.g. the alpha-helix.
We divide the assembly process into conceptual thermodynamic steps:
These steps can be used for determining the thermodynamic stability of both constitutive and non-constitutive membrane proteins. The first 3 steps are shown below. For constitutive proteins, one begins with the inserted secondary structure element and proceeds toward the unfolded state (right to left in the figure below). For non-constitutive proteins, one begins with the unfolded state and proceeds toward the inserted state (left to right, below).
1. The Unfolded (Virtual) Reference State. The reference state is taken as the unfolded protein in the interface. However, as far as we know, one cannot actually achieve this state with constitutive membrane proteins because of the solubility problems nor with small non-constitutive membrane-active peptides because binding usually induces secondary structure (partitioning-folding coupling). Thus, as is often the case in solution thermodynamics, the reference state must be a virtual one. We define it by means of an experimental interfacial hydrophobicity scale derived from partitioning studies of pentapeptides that have no secondary structure in the aqueous or interfacial phases. This scale, that includes the peptide bonds as well as the sidechains, can be used to calculate the virtual free energy of transfer of an unfolded chain into the interface. The most important feature of whole-residue partitioning is that the energetics are dominated by the peptide bonds.
2. Partitioning-Folding Coupling and the Energetics of Interfacial Folding. A number of small peptides, such as melittin, are unfolded in the aqueous phase, but are fully structured upon partitioning into the interface. Even though the unfolded state is inaccessible, the energetics of the folding can be estimated from the difference between the virtual free energy of transfer of the unfolded state (calculated using the interfacial hydrophobicity scale) and the measured free energy of transfer of the folded peptide. Secondary structure formation appears to be driven by the reduction in the free energy of partitioning of peptide bonds that accompanies hydrogen bond formation. Experimental measurements indicate that the reduction is about 0.5 kcal/mol per peptide bond for beta-sheet formation by model hexapeptides and 0.4 kcal/mol per peptide bond for alpha-helix formation by melittin. The accumulative effect of this modest reduction can be very large (~5 kcal/mol for melittin).
3. Energetics of Bilayer Insertion. This last step in folding is the crucial one, but the least adequately studied because of the insolubility and aggregation of hydrophobic peptides. Direct measurement of the partitioning of a hydrophobic alpha-helix or beta-barrel across a membrane is absolutely essential because we must know the true cost of partitioning a hydrogen-bonded peptide bond into the bilayer. Estimates for this cost vary from 0 to +1.6 kcal/mol. This means that calculations of insertion free energy based on sidechain free energies could be over-estimated by as much as +30 kcal/mol for a 20-residue helix.
4. Assembly of Secondary Structure Elements. The last important step is to understand the energetics of the association of secondary structure elements within the membrane.
Don Engelman and his colleagues have shown that transmembrane helices from bacteriorhodopsin (bR) helices that have been independently inserted into membranes can subsequently assemble into the native structure of bR. This indicates that the insertion steps are independent of the intra-membrane assembly process. They refer to this insertion-oligomerization process as the 'two-stage' model.