From shut to open: what can we learn from linear free energy relationships?

Energetic contributions to channel gating of residues in the muscle nicotinic receptor β1 subunit

In the pentameric ligand-gated ion channel family, transmitter binds in the extracellular domain and conformational changes result in channel opening in the transmembrane domain. In the muscle nicotinic receptor and other heteromeric members of the family one subunit does not contribute to the canonical agonist binding site for transmitter. A fundamental question is whether conformational changes occur in this subunit. We used records of single channel activity and rate-equilibrium free energy relationships to examine the β1 (non-ACh-binding) subunit of the muscle nicotinic receptor. Mutations to residues in the extracellular domain have minimal effects on the gating equilibrium constant. Positions in the channel lining (M2 transmembrane) domain contribute strongly and relatively late during gating. Positions thought to be important in other subunits in coupling the transmitter-binding to the channel domains have minimal effects on gating. We conclude that the conformational changes involved in channel gating propagate from the binding-site to the channel in the ACh-binding subunits and subsequently spread to the non-binding subunit.

Linear rate-equilibrium relations arising from ion channel-bilayer energetic coupling

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.

Relationships between structural dynamics and functional kinetics in oligomeric membrane receptors

Recent efforts to broaden understanding of the molecular mechanisms of membrane receptors in signal transduction make use of rate-equilibrium free-energy relationships (REFERs), previously applied to chemical reactions, enzyme kinetics, and protein folding. For oligomeric membrane receptors, we distinguish between a), the Leffler parameter α_L, to characterize the global transition state for the interconversion between conformations; and b), the Fersht parameter, ϕ_F, to assign the degree of progression of individual residue positions at the transition state. For both α_L and ϕ_F, insights are achieved by using harmonic energy profiles to reflect the dynamic nature of proteins, as illustrated with single-channel results reported for normal and mutant nicotinic receptors. We also describe new applications of α_L based on published results. For large-conductance calcium-activated potassium channels, data are satisfactorily fit with an α_L value of 0.65, in accord with REFERs. In contrast, results reported for the flip conformational state of glycine and nicotinic receptors are in disaccord with REFERs, since they yield α_L values outside the usual limits of 0–1. Concerning published ϕ_F values underlying the conformational wave hypothesis for nicotinic receptors, we note that interpretations may be complicated by variations in the width of harmonic energy profiles.

Relationship between nucleotide binding and ion channel gating in cystic fibrosis transmembrane conductance regulator

We have employed rate-equilibrium free energy relationship (REFER) analysis to characterize the dynamic events involved in the allosteric regulation of cystic fibrosis transmembrane conductance regulator (CFTR) function. A wide range of different hydrolysable and poorly hydrolysable nucleoside triphosphates were used to elucidate the role of ATP hydrolysis in CFTR function. The linearity of the REFER plots and Phi values near unity for all ligands tested implies that CFTR channel gating is a reversible thermally driven process with all structural reorganization in the binding site(s) completed prior to channel opening. This is consistent with the requirement for nucleotide binding for channel opening. However, the channel structural transition from the open to the closed state occurs independently of any events in the binding sites. Similar results were obtained on substitution of amino acids at coupling joints between both nucleotide binding domains (NBD) and cytoplasmic loops (CL) in opposite halves of the protein, indicating that any structural reorganization there also had occurred in the channel closed state. The fact that fractional Phi values were not observed in either of these distant sites suggests that there may not be a deterministic 'lever-arm' mechanism acting between nucleotide binding sites and the channel gate. These findings favour a stochastic coupling between binding and gating in which all structural transitions are thermally driven processes. We speculate that increase of channel open state probability is due to reduction of the number of the closed state configurations available after physical interaction between ligand bound NBDs and the channel.

Unliganded gating of acetylcholine receptor channels

We estimated the unliganded opening and closing rate constants of neuromuscular acetylcholine receptor-channels (AChRs) having mutations that increased the gating equilibrium constant. For some mutant combinations, spontaneous openings occurred in clusters. For 25 different constructs, the unliganded gating equilibrium constant (E(0)) was correlated with the product of the predicted fold-increase in the diliganded gating equilibrium constant caused by each mutation alone. We estimate that (i) E(0) for mouse, wild-type alpha(2)beta delta epsilon AChRs is approximately 1.15 x 10(-7); (ii) unliganded AChRs open for approximately 80 micros, once every approximately 15 min; (iii) the affinity for ACh of the O(pen) conformation is approximately 10 nM, or approximately 15,600 times greater than for the C(losed) conformation; (iv) the ACh-monoliganded gating equilibrium constant is approximately 1.7 x 10(-3); (v) the C-->O isomerization reduces substantially ACh dissociation, but only slightly increases association; and (vi) ACh provides only approximately 0.9 k(B)T more binding energy per site than carbamylcholine but approximately 3.1 k(B)T more than choline, mainly because of a low O conformation affinity. Most mutations of binding site residue alphaW149 increase E(0). We estimate that the mutation alphaW149F reduces the ACh affinity of C only by 13-fold, but of O by 190-fold. Rate-equilibrium free-energy relationships for different regions of the protein show similar slopes (Phi values) for un- vs. diliganded gating, which suggests that the conformational pathway of the gating structural change is fundamentally the same with and without agonists. Agonist binding is a perturbation that (like most mutations) changes the energy, but not the mechanism, of the gating conformational change.

Structural answers and persistent questions about how nicotinic receptors work

The electron diffraction structure of nicotinic acetylcholine receptor (nAChR) from Torpedo marmorata and the X-ray crystallographic structure of acetylcholine binding protein (AChBP) are providing new answers to persistent questions about how nAChRs function as biophysical machines and as participants in cellular and systems physiology. New high-resolution information about nAChR structures might come from advances in crystallography and NMR, from extracellular domain nAChRs as high fidelity models, and from prokaryotic nicotinoid proteins. At the level of biophysics, structures of different nAChRs with different pharmacological profiles and kinetics will help describe how agonists and antagonists bind to orthosteric binding sites, how allosteric modulators affect function by binding outside these sites, how nAChRs control ion flow, and how large cytoplasmic domains affect function. At the level of cellular and systems physiology, structures of nAChRs will help characterize interactions with other cellular components, including lipids and trafficking and signaling proteins, and contribute to understanding the roles of nAChRs in addiction, neurodegeneration, and mental illness. Understanding nAChRs at an atomic level will be important for designing interventions for these pathologies.

Agonist-activated ion channels

This paper looks at ion channels as an example of the pharmacologist's stock in trade, the action of an agonist on a receptor to produce a response. Looked at in this way, ion channels have been helpful because they are still the only system which is simple enough for quantitative investigation of transduction mechanisms. A short history is given of attempts to elucidate what happens between the time when agonist first binds, and the time when the channel opens.

The quantitative analysis of drug–receptor interactions: a short history

Pharmacology started to develop into a real quantitative science in 1909, when A.V. Hill derived the Langmuir equation in the course of his studies on nicotine and curare. A history of the developments since then shows both brilliant insights and missed opportunities. It also shows that much remains to be done. There is still no mathematical description that can describe quantitatively the actions of agonists on G-protein-coupled receptors, although progress has been greater with agonist-activated ion channels, which are much simpler.