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Linear rate-equilibrium (RE) relations, also known as linear free energy relations, are widely observed in chemical reactions, including protein folding, enzymatic catalysis, and channel gating. Despite the widespread occurrence of linear RE relations, the principles underlying the linear relation between changes in activation and equilibrium energy in macromolecular reactions remain enigmatic. When examining amphiphile regulation of gramicidin channel gating in lipid bilayers, we noted that the gating process could be described by a linear RE relation with a simple geometric interpretation. This description is possible because the gating process provides a well-understood reaction, in which structural changes in a bilayer-embedded model protein can be studied at the single-molecule level. It is thus possible to obtain quantitative information about the energetics of the reaction transition state and its position on a spatial coordinate. It turns out that the linear RE relation for the gramicidin monomer-dimer reaction can be understood, and the quantitative relation between changes in activation energy and equilibrium energy can be interpreted, by considering the effects of amphiphiles on the changes in bilayer elastic energy associated with channel gating. We are not aware that a similar simple mechanistic explanation of a linear RE relation has been provided for a chemical reaction in a macromolecule. RE relations generally should be useful for examining how amphiphile-induced changes in bilayer properties modulate membrane protein folding and function, and for distinguishing between direct (e.g., due to binding) and indirect (bilayer-mediated) effects.

To explore the consequences of burying polar, hydrogen-bonding hydroxyl groups within the hydrocarbon core of lipid bilayer membranes, we examined the structural and functional effects of alanine-to-serine substitutions in bilayer-spanning gramicidin channels. A native Ala was replaced by Ser at position 3 or 5 in the gramicidin A (gA) sequence: formyl-VG(2)A(3)LA(5)VVVWLWLWLW-ethanolamide (d-residues underlined). In the head-to-head dimers that form the conducting, membrane-spanning gA channels, these sequence positions are located near the lipid bilayer center (and subunit interface). The sequence substitutions at positions 3 and 5 were tested within the context of having either Gly or d-Ala at position 2, because d-Ala(2) causes the channel lifetimes to increase 3-fold relative to Gly(2) [Mattice et al. (1995) Biochemistry 34, 6827]. Size-exclusion chromatograms and circular dichroism spectra show that the Ala --> Ser replacements are well tolerated and have little effect on channel structure. In planar bilayers, the Ser-substituted gramicidins form well-defined channels, with cation conductances that are approximately 60% of those of the reference channels. The Ser-substituted channels are structurally equivalent to native gramicidin channels, as demonstrated by the formation of heterodimeric channels between a Ser-containing subunit and a native gramicidin subunit. These hybrid channels exhibit rectification, attributable to asymmetric placement of the single Ser hydroxyl group with respect to the bilayer center. Compared to the corresponding Ala-containing reference channels, the polar Ser residues decrease the analogues' channel-forming potency by 3 orders of magnitude, indicating a substantial energetic penalty ( approximately 15 kJ/mol) for burying the polar Ser side chain in the bilayer hydrophobic core.

To better understand the structural and functional roles of tryptophan at the membrane/water interface in membrane proteins, we examined the structural and functional consequences of Trp --> 1-methyl-tryptophan substitutions in membrane-spanning gramicidin A channels. Gramicidin A channels are miniproteins that are anchored to the interface by four Trps near the C terminus of each subunit in a membrane-spanning dimer. We masked the hydrogen bonding ability of individual or multiple Trps by 1-methylation of the indole ring and examined the structural and functional changes using circular dichroism spectroscopy, size exclusion chromatography, solid state (2)H NMR spectroscopy, and single channel analysis. N-Methylation causes distinct changes in the subunit conformational preference, channel-forming propensity, single channel conductance and lifetime, and average indole ring orientations within the membrane-spanning channels. The extent of the local ring dynamic wobble does not increase, and may decrease slightly, when the indole NH is replaced by the non-hydrogen-bonding and more bulky and hydrophobic N-CH(3) group. The changes in conformational preference, which are associated with a shift in the distribution of the aromatic residues across the bilayer, are similar to those observed previously with Trp --> Phe substitutions. We conclude that indole N-H hydrogen bonding is of major importance for the folding of gramicidin channels. The changes in ion permeability, however, are quite different for Trp --> Phe and Trp --> 1-methyl-tryptophan substitutions, indicating that the indole dipole moment and perhaps also ring size and are important for ion permeation through these channels.

The hydrophobic coupling between membrane-spanning proteins and the lipid bilayer core causes the bilayer thickness to vary locally as proteins and other "defects" are embedded in the bilayer. These bilayer deformations incur an energetic cost that, in principle, could couple membrane proteins to each other, causing them to associate in the plane of the membrane and thereby coupling them functionally. We demonstrate the existence of such bilayer-mediated coupling at the single-molecule level using single-barreled as well as double-barreled gramicidin channels in which two gramicidin subunits are covalently linked by a water-soluble, flexible linker. When a covalently attached pair of gramicidin subunits associates with a second attached pair to form a double-barreled channel, the lifetime of both channels in the assembly increases from hundreds of milliseconds to a hundred seconds--and the conductance of each channel in the side-by-side pair is almost 10% higher than the conductance of the corresponding single-barreled channels. The double-barreled channels are stabilized some 100,000-fold relative to their single-barreled counterparts. This stabilization arises from: first, the local increase in monomer concentration around a single-barreled channel formed by two covalently linked gramicidins, which increases the rate of double-barreled channel formation; and second, from the increased lifetime of the double-barreled channels. The latter result suggests that the two barrels of the construct associate laterally. The underlying cause for this lateral association most likely is the bilayer deformation energy associated with channel formation. More generally, the results suggest that the mechanical properties of the host bilayer may cause the kinetics of membrane protein conformational transitions to depend on the conformational states of the neighboring proteins.

Negatively charged side chains are important for the function of particular ion channels and certain other membrane proteins. To investigate the influence of single glutamic acid side chains on helices that span lipid-bilayer membranes, we have employed GWALP23 (acetyl-GGALW 5 LALALALALALALW 19 LAGA-amide) as a favorable host peptide framework. We substituted individual Leu residues with Glu residues (L12E or L14E or L16E) and incorporated specific 2 H-labeled alanine residues within the core helical region or near the ends of the sequence. Solid-state 2 H NMR spectra reveal little change for the core labels in GWALP23-E12, –E14 and –E16 over a pH range of 4 to 12.5, with the spectra being broader for samples in DOPC compared to DLPC bilayers. The spectra for samples with deuterium labels near the helix ends on alanines 3 and 21 show modest pH-dependent changes in the extent of unwinding of the helix terminals in DLPC and DOPC bilayers. The combined results indicate minor overall responses of these transmembrane helices to changes in pH, with the most buried residue E12 showing no pH dependence. While the Glu residues E14 and E16 may have high pK a values in the lipid bilayer environment, it is also possible that a paucity of helix response is masking the pK a values. Interestingly, when E16 is present, spectral changes at high pH report significant local unwinding of the core helix. Our results are consistent with the expectation that buried carboxyl groups aggressively hold their protons and/or waters of hydration. [ABSTRACT FROM AUTHOR]