Mapping heat exchange in an allosteric protein

The Kinetics and the Permeation Properties of Piezo Channels

Piezo channels are eukaryotic, cation-selective mechanosensitive channels (MSCs), which show rapid activation and voltage-dependent inactivation. The kinetics of these channels are largely consistent across multiple cell types and different stimulation paradigms with some minor variability. No accessory subunits that associate with Piezo channels have been reported. They are homotrimers and each ∼300kD monomer has an N-terminal propeller blade-like mechanosensing module, which can confer mechanosensing capabilities on ASIC-1 (the trimeric non-MSC, acid-sensing ion channel-1) and a C-terminal pore module, which influences conductance, selectivity, and channel inactivation. Repeated stimulation can cause domain fracture and diffusion of these channels leading to synchronous loss of inactivation. The reconstituted channels spontaneously open only in asymmetric bilayers but lack inactivation. Mutations that cause hereditary xerocytosis alter PIEZO1 kinetics. The kinetics of the wild-type PIEZO1 and alterations thereof in mutants (M2225R, R2456K, and DhPIEZO1) are summarized in the form of a quantitative model and hosted online. The pore is permeable to alkali ions although Li⁺ permeates poorly. Divalent cations, notably Ca²⁺, traverse the channel and inhibit the flux of monovalents. The large monovalent organic cations such as tetramethyl ammonium and tetraethyl ammonium can traverse the channel, but slowly, suggesting a pore diameter of ∼8Å, and the estimated in-plane area change upon opening is around 6-20nm². Ruthenium red can enter the channel only from the extracellular side and seems to bind in a pocket close to residue 2496.

Quasithermodynamic contributions to the fluctuations of a protein nanopore

Proteins undergo thermally activated conformational fluctuations among two or more substates, but a quantitative inquiry on their kinetics is persistently challenged by numerous factors, including the complexity and dynamics of various interactions, along with the inability to detect functional substates within a resolvable time scale. Here, we analyzed in detail the current fluctuations of a monomeric β-barrel protein nanopore of known high-resolution X-ray crystal structure. We demonstrated that targeted perturbations of the protein nanopore system, in the form of loop-deletion mutagenesis, accompanying alterations of electrostatic interactions between long extracellular loops, produced modest changes of the differential activation free energies calculated at 25 °C, ΔΔG(⧧), in the range near the thermal energy but substantial and correlated modifications of the differential activation enthalpies, ΔΔH(⧧), and entropies, ΔΔS(⧧). This finding indicates that the local conformational reorganizations of the packing and flexibility of the fluctuating loops lining the central constriction of this protein nanopore were supplemented by changes in the single-channel kinetics. These changes were reflected in the enthalpy-entropy reconversions of the interactions between the loop partners with a compensating temperature, TC, of ∼300 K, and an activation free energy constant of ∼41 kJ/mol. We also determined that temperature has a much greater effect on the energetics of the equilibrium gating fluctuations of a protein nanopore than other environmental parameters, such as the ionic strength of the aqueous phase as well as the applied transmembrane potential, likely due to ample changes in the solvation activation enthalpies. There is no fundamental limitation for applying this approach to other complex, multistate membrane protein systems. Therefore, this methodology has major implications in the area of membrane protein design and dynamics, primarily by revealing a better quantitative assessment on the equilibrium transitions among multiple well-defined and functionally distinct substates of protein channels and pores.

A self-consistent approach for determining pairwise interactions that underlie channel activation

Net free-energy measurements can be combined with mutant cycle analysis to determine interaction energies between specific amino acid pairs during channel activation.

Signaling proteins such as ion channels largely exist in two functional forms, corresponding to the active and resting states, connected by multiple intermediates. Multiparametric kinetic models based on sophisticated electrophysiological experiments have been devised to identify molecular interactions of these conformational transitions. However, this approach is arduous and is not suitable for large-scale perturbation analysis of interaction pathways. Recently, we described a model-free method to obtain the net free energy of activation in voltage- and ligand-activated ion channels. Here we extend this approach to estimate pairwise interaction energies of side chains that contribute to gating transitions. Our approach, which we call generalized interaction-energy analysis (GIA), combines median voltage estimates obtained from charge-voltage curves with mutant cycle analysis to ascertain the strengths of pairwise interactions. We show that, for a system with an arbitrary gating scheme, the nonadditive contributions of amino acid pairs to the net free energy of activation can be computed in a self-consistent manner. Numerical analyses of sequential and allosteric models of channel activation also show that this approach can measure energetic nonadditivities even when perturbations affect multiple transitions. To demonstrate the experimental application of this method, we reevaluated the interaction energies of six previously described long-range interactors in the Shaker potassium channel. Our approach offers the ability to generate detailed interaction energy maps in voltage- and ligand-activated ion channels and can be extended to any force-driven system as long as associated “displacement” can be measured.

SOLVING ION CHANNEL KINETICS WITH THE QuB SOFTWARE

The ability to record the currents from single ion channels led to the need to extract the underlying kinetic model from such data. This inverse hidden Markov problem is difficult but led to the creation of a software suite called QuB utilizing likelihood optimization. This review presents the software. The software is open source and, in addition to solving kinetic models, has many generic database operations including report generation with publishable graphics, function fitting and scripting for new and repeated processing and AD/DA I/O. The core algorithms allow for constraints such as fixed rates or maintaining detailed balance in the model. All rate constants can be driven by a stimulus and the system can analyze nonstationary data. QuB also can analyze the kinetics of multichannel data where individual events cannot be discriminated, but the fitting algorithms utilize the signal variance as well as the mean to fit models. QuB can be applied to any data appropriately modeled with Markov kinetics and has been utilized to solve ion channels but also the movement of motor proteins, the sleep cycles in mice, and physics processes.

[Formula: see text]Special Issue Comment: This is a review about the software QuB that can extract a model from the trajectory. It is connected with the review about treatments when solving single molecules,60 and the reviews about enzymes.61,62

Function of interfacial prolines at the transmitter-binding sites of the neuromuscular acetylcholine receptor

The neuromuscular acetylcholine (ACh) receptor has two conserved prolines in loop D of the complementary subunit at each of its two transmitter-binding sites (α-ε and α-δ). We used single-channel electrophysiology to estimate the energy changes caused by mutations of these prolines with regard to unliganded gating (ΔG0) and the affinity change for ACh that increases the open channel probability (ΔGB). The effects of mutations of ProD2 (εPro-121/δPro-123) were greater than those of its neighbor (εPro-120/δPro-122) and were greater at α-ε versus α-δ. The main consequence of the congenital myasthenic syndrome mutation εProD2-L was to impair the establishment of a high affinity for ACh and thus make ΔGB less favorable. At both binding sites, most ProD2 mutations decreased constitutive activity (increased ΔG0). LRYHQG and RL substitutions reduced substantially the net binding energy (made ΔGB(ACh) less favorable) by ≥2 kcal/mol at α-ε and α-δ, respectively. Mutant cycle analyses were used to estimate energy coupling between the two ProD2 residues and between each ProD2 and glycine residues (αGly-147 and αGly-153) on the primary (α subunit) side of each binding pocket. The distant binding site prolines interact weakly. ProD2 interacts strongly with αGly-147 but only at α-ε and only when ACh is present. The results suggest that in the low to-high affinity change there is a concerted inter-subunit strain in the backbones at εProD2 and αGly-147. It is possible to engineer receptors having a single functional binding site by using a α-ε or α-δ ProD2-R knock-out mutation. In adult-type ACh receptors, the energy from the affinity change for ACh is approximately the same at the two binding sites (approximately -5 kcal/mol).

The energy and work of a ligand-gated ion channel

Ligand-gated ion channels are allosteric membrane proteins that isomerize between C(losed) and O(pen) conformations. A difference in affinity for ligands in the two states influences the C↔O "gating" equilibrium constant. The energies associated with adult-type mouse neuromuscular nicotinic acetylcholine receptor (AChR) channel gating have been measured by using single-channel electrophysiology. Without ligands, the free energy, enthalpy and entropy of gating are ΔG0=+8.4, ΔH0=+10.9 and TΔS0=+2.5kcal/mol (-100mV, 23°C). Many mutations throughout the protein change ΔG0, including natural ones that cause disease. Agonists and most mutations change approximately independently the ground-state energy difference; thus, it is possible to forecast and engineer AChR responses simply by combining perturbations. The free energy of the low↔high affinity change for the neurotransmitter at each of two functionally equivalent binding sites is ΔGB(ACh)=-5.1kcal/mol. ΔGB(ACh) is set mainly by interactions of ACh with just three binding site aromatic groups. For a series of structurally related agonists, there is a correlation between the energies of low- and high-affinity binding, which implies that gating commences with the formation of the low-affinity complex. Brief, intermediate states in binding and gating have been detected. Several proposals for the nature of the gating transition-state energy landscape and the isomerization mechanism are discussed.

Entropy-enthalpy Compensation of Biomolecular Systems in Aqueous Phase: a Dry Perspective

We survey thermodynamic measurements on processes involving biological macromolecules in aqueous solution, which illustrate well the ubiquitous phenomenon of entropy-enthalpy compensation. The processes include protein folding/unfolding and ligand binding/unbinding, with compensation temperatures varying by about 50 K around an average near 293 K. We show that incorporating both near-exact entropy-enthalpy compensation (due to solvent relaxation) and multi-excitation entropy (from vibrational quanta) leads to a compensation temperature in water of about 230 K. We illustrate a general procedure for subtracting solvent and environment-related terms to determine the bare Gibbs free energy changes of chemical processes.

An outer membrane protein undergoes enthalpy- and entropy-driven transitions

β-Barrel membrane proteins often fluctuate among various open substates, yet the nature of these transitions is not fully understood. Using temperature-dependent, single-molecule electrophysiology analysis, along with rational protein design, we show that OccK1, a member of the outer membrane carboxylate channel from Pseudomonas aeruginosa, features a discrete gating dynamics comprising both enthalpy-driven and entropy-driven current transitions. OccK1 was chosen for the analysis of these transitions, because it is a monomeric transmembrane β-barrel of a known high-resolution crystal structure and displays three distinguishable, time-resolvable open substates. Native and loop-deletion OccK1 proteins showed substantial changes in the activation enthalpies and entropies of the channel transitions, but modest alterations in the equilibrium free energies, confirming that the system never departs from equilibrium. Moreover, some current fluctuations of OccK1 indicated a counterintuitive, negative activation enthalpy, which was compensated by a significant decrease in the activation entropy. Temperature scanning of the single-channel properties of OccK1 exhibited a thermally induced switch of the energetically most favorable open substate at the lowest examined temperature of 4 °C. Therefore, such a semiquantitative assessment of the current fluctuation dynamics not only demonstrates the complexity of channel gating but also reveals distinct functional traits of a β-barrel outer membrane protein under different temperature circumstances.

Thinking in cycles: MWC is a good model for acetylcholine receptor-channels

Neuromuscular acetylcholine receptors have long been a model system for understanding the mechanisms of operation of ligand-gated ion channels and fast chemical synapses. These five subunit membrane proteins have two allosteric (transmitter) binding sites and a distant ion channel domain. Occupation of the binding sites by agonist molecules transiently increases the probability that the channel is ion-permeable. Recent experiments show that the Monod, Wyman and Changeux formalism for allosteric proteins, originally developed for haemoglobin, is an excellent model for acetylcholine receptors. By using mutations and single-channel electrophysiology, the gating equilibrium constants for receptors with zero, one or two bound agonist molecules, and the agonist association and dissociation rate constants from both the closed- and open-channel conformations, have been estimated experimentally. The change in affinity for each transmitter molecule between closed and open conformations provides ~-5.1 kcal mol(-1) towards the global gating isomerization of the protein.

Temperature dependence of acetylcholine receptor channels activated by different agonists

The temperature dependence of agonist binding and channel gating were measured for wild-type adult neuromuscular acetylcholine receptors activated by acetylcholine, carbamylcholine, or choline. With acetylcholine, temperature changed the gating rate constants (Q(10) ≈ 3.2) but had almost no effect on the equilibrium constant. The enthalpy change associated with gating was agonist-dependent, but for all three ligands it was approximately equal to the corresponding free-energy change. The equilibrium dissociation constant of the resting conformation (K(d)), the slope of the rate-equilibrium free-energy relationship (Φ), and the acetylcholine association and dissociation rate constants were approximately temperature-independent. In the mutant αG153S, the choline association and dissociation rate constants were temperature-dependent (Q(10) ≈ 7.4) but K(d) was not. By combining two independent mutations, we were able to compensate for the catalytic effect of temperature on the decay time constant of a synaptic current. At mouse body temperature, the channel-opening and -closing rate constants are ∼400 and 16 ms(-1). We hypothesize that the agonist dependence of the gating enthalpy change is associated with differences in ligand binding, specifically to the open-channel conformation of the protein.