A linkage analysis toolkit for studying allosteric networks in ion channels

Charge-voltage curves of Shaker potassium channel are not hysteretic at steady state

Charge-voltage curves of many voltage-gated ion channels exhibit hysteresis but such curves are also a direct measure of free energy of channel gating and, hence, should be path-independent. Here, we identify conditions to measure steady-state charge-voltage curves and show that these are curves are not hysteretic. Charged residues in transmembrane segments of voltage-gated ion channels (VGICs) sense and respond to changes in the electric field. The movement of these gating charges underpins voltage-dependent activation and is also a direct metric of the net free-energy of channel activation. However, for most voltage-gated ion channels, the charge-voltage (Q-V) curves appear to be dependent on initial conditions. For instance, Q-V curves of Shaker potassium channel obtained by hyperpolarizing from 0 mV is left-shifted compared to those obtained by depolarizing from a holding potential of -80 mV. This hysteresis in Q-V curves is a common feature of channels in the VGIC superfamily and raises profound questions about channel energetics because the net free-energy of channel gating is a state function and should be path independent. Due to technical limitations, conventional gating current protocols are limited to test pulse durations of <500 ms, which raises the possibility that the dependence of Q-V on initial conditions reflects a lack of equilibration. Others have suggested that the hysteresis is fundamental thermodynamic property of voltage-gated ion channels and reflects energy dissipation due to measurements under non-equilibrium conditions inherent to rapid voltage jumps (Villalba-Galea. 2017. Channels. https://doi.org/10.1080/19336950.2016.1243190). Using an improved gating current and voltage-clamp fluorometry protocols, we show that the gating hysteresis arising from different initial conditions in Shaker potassium channel is eliminated with ultra-long (18-25 s) test pulses. Our study identifies a modified gating current recording protocol to obtain steady-state Q-V curves of a voltage-gated ion channel. Above all, these findings demonstrate that the gating hysteresis in Shaker channel is a kinetic phenomenon rather than a true thermodynamic property of the channel and the charge-voltage curve is a true measure of the net-free energy of channel gating.

A gating lever and molecular logic gate that couple voltage and calcium sensor activation to opening in BK potassium channels

BK channels uniquely integrate voltage and calcium signaling in diverse cell types through allosteric activation of their K+-conducting pore by structurally distinct V and Ca2+ sensor domains. Here, we define mechanisms and interaction pathways that link V sensors to the pore by analyzing effects on allosteric coupling of point mutations in the context of Slo1 BK channel structure. A gating lever, mediated by S4/S5 segment interaction within the transmembrane domain, rotates to engage and stabilize the open conformation of the S6 inner pore helix upon V sensor activation. In addition, an indirect pathway, mediated by the carboxyl-terminal cytosolic domain (CTD) and C-linker that connects the CTD to S6, stabilizes the closed conformation when V sensors are at rest. Unexpectedly, this mechanism, which bypasses the covalent connections of C-linker to CTD and pore, also transduces Ca2+-dependent coupling in a manner that is completely nonadditive with voltage, analogous to the function of a digital logic (OR) gate.

The distinct role of the four voltage sensors of the skeletal CaV1.1 channel in voltage-dependent activation

Initiation of skeletal muscle contraction is triggered by rapid activation of RYR1 channels in response to sarcolemmal depolarization. RYR1 is intracellular and has no voltage-sensing structures, but it is coupled with the voltage-sensing apparatus of Ca_V1.1 channels to inherit voltage sensitivity. Using an opto-electrophysiological approach, we resolved the excitation-driven molecular events controlling both Ca_V1.1 and RYR1 activations, reported as fluorescence changes. We discovered that each of the four human Ca_V1.1 voltage-sensing domains (VSDs) exhibits unique biophysical properties: VSD-I time-dependent properties were similar to ionic current activation kinetics, suggesting a critical role of this voltage sensor in Ca_V1.1 activation; VSD-II, VSD-III, and VSD-IV displayed faster activation, compatible with kinetics of sarcoplasmic reticulum Ca²⁺ release. The prominent role of VSD-I in governing Ca_V1.1 activation was also confirmed using a naturally occurring, charge-neutralizing mutation in VSD-I (R174W). This mutation abolished Ca_V1.1 current at physiological membrane potentials by impairing VSD-I activation without affecting the other VSDs. Using a structurally relevant allosteric model of Ca_V activation, which accounted for both time- and voltage-dependent properties of Ca_V1.1, to predict VSD-pore coupling energies, we found that VSD-I contributed the most energy (~75 meV or ∼3 kT) toward the stabilization of the open states of the channel, with smaller (VSD-IV) or negligible (VSDs II and III) energetic contribution from the other voltage sensors (<25 meV or ∼1 kT). This study settles the longstanding question of how Ca_V1.1, a slowly activating channel, can trigger RYR1 rapid activation, and reveals a new mechanism for voltage-dependent activation in ion channels, whereby pore opening of human Ca_V1.1 channels is primarily driven by the activation of one voltage sensor, a mechanism distinct from that of all other voltage-gated channels.

cAMP binding to closed pacemaker ion channels is non-cooperative

Electrical activity in the brain and heart depends on rhythmic generation of action potentials by pacemaker ion channels (HCN) whose activity is regulated by cAMP binding1. Previous work has uncovered evidence for both positive and negative cooperativity in cAMP binding2,3, but such bulk measurements suffer from limited parameter resolution. Efforts to eliminate this ambiguity using single-molecule techniques have been hampered by the inability to directly monitor binding of individual ligand molecules to membrane receptors at physiological concentrations. Here we overcome these challenges using nanophotonic zero-mode waveguides4 to directly resolve binding dynamics of individual ligands to multimeric HCN1 and HCN2 ion channels. We show that cAMP binds independently to all four subunits when the pore is closed, despite a subsequent conformational isomerization to a flip state at each site. The different dynamics in binding and isomerization are likely to underlie physiologically distinct responses of each isoform to cAMP5 and provide direct validation of the ligand-induced flip-state model6-9. This approach for observing stepwise binding in multimeric proteins at physiologically relevant concentrations can directly probe binding allostery at single-molecule resolution in other intact membrane proteins and receptors.

Mapping Electromechanical Coupling Pathways in Voltage-Gated Ion Channels: Challenges and the Way Forward

Inter- and intra-molecular allosteric interactions underpin regulation of activity in a variety of biological macromolecules. In the voltage-gated ion channel superfamily, the conformational state of the voltage-sensing domain regulates the activity of the pore domain via such long-range allosteric interactions. Although the overall structure of these channels is conserved, allosteric interactions between voltage-sensor and pore varies quite dramatically between the members of this superfamily. Despite the progress in identifying key residues and structural interfaces involved in mediating electromechanical coupling, our understanding of the biophysical mechanisms remains limited. Emerging new structures of voltage-gated ion channels in various conformational states will provide a better three-dimensional view of the process but to conclusively establish a mechanism, we will also need to quantitate the energetic contribution of various structural elements to this process. Using rigorous unbiased metrics, we want to compare the efficiency of electromechanical coupling between various sub-families in order to gain a comprehensive understanding. Furthermore, quantitative understanding of the process will enable us to correctly parameterize computational approaches which will ultimately enable us to predict allosteric activation mechanisms from structures. In this review, we will outline the challenges and limitations of various experimental approaches to measure electromechanical coupling and highlight the best practices in the field.

Activation of the archaeal ion channel MthK is exquisitely regulated by temperature

Physiological response to thermal stimuli in mammals is mediated by a structurally diverse class of ion channels, many of which exhibit polymodal behavior. To probe the diversity of biophysical mechanisms of temperature-sensitivity, we characterized the temperature-dependent activation of MthK, a two transmembrane calcium-activated potassium channel from thermophilic archaebacteria. Our functional complementation studies show that these channels are more efficient at rescuing K+ transport at 37°C than at 24°C. Electrophysiological activity of the purified MthK is extremely sensitive (Q10 >100) to heating particularly at low-calcium concentrations whereas channels lacking the calcium-sensing RCK domain are practically insensitive. By analyzing single-channel activities at limiting calcium concentrations, we find that temperature alters the coupling between the cytoplasmic RCK domains and the pore domain. These findings reveal a hitherto unexplored mechanism of temperature-dependent regulation of ion channel gating and shed light on ancient origins of temperature-sensitivity.

Microcanonical coarse-graining of the kinetic Ising model

We propose a scheme for coarse-graining the dynamics of the 2-D kinetic Ising model onto the microcanonical ensemble. At subcritical temperatures, 2-D and higher-dimensional Ising lattices possess two basins of attraction separated by a free energy barrier. Projecting onto the microcanonical ensemble has the advantage that the dependence of the crossing rate constant on environmental conditions can be obtained from a single Monte Carlo trajectory. Using various numerical methods, we computed the forward rate constants of coarse-grained representations of the Ising model and compared them with the true value obtained from brute force simulation. While coarse-graining preserves detailed balance, the computed rate constants for barrier heights between 5 kT and 9 kT were consistently 50% larger than the true value. Markovianity testing revealed loss of dynamical memory, which we propose accounts for coarse-graining error. Committor analysis did not support the alternative hypothesis that microcanonical projection is incompatible with an optimal reaction coordinate. The correct crossing rate constant was obtained by spectrally decomposing the diffusion coefficient near the free energy barrier and selecting the slowest (reactive) component. The spectral method also yielded the correct rate constant in the 3-D Ising lattice, where coarse-graining error was 6% and memory effects were diminished. We conclude that microcanonical coarse-graining supplemented by spectral analysis of short-term barrier fluctuations provides a comprehensive kinetic description of barrier crossing in a non-inertial continuous-time jump process.

Linkage analysis reveals allosteric coupling in Kir2.1 channels

Inwardly rectifying potassium (Kir) channels experience strong (blocking) and weak (intrinsic) rectification. Linkage analysis in the form of a conductance Hill plot is a sensitive method of resolving allosteric interactions between the pore and mediators of the Kir gating process.

Potassium-selective inward rectifier (Kir) channels are a class of membrane proteins necessary for maintaining stable resting membrane potentials, controlling excitability, and shaping the final repolarization of action potentials in excitable cells. In addition to the strong inward rectification of the ionic current caused by intracellular blockers, Kir2.1 channels possess “weak” inward rectification observed in inside-out patches after prolonged washout of intracellular blockers. The mechanisms underlying strong inward rectification have been attributed to voltage-dependent block by intracellular Mg²⁺ and polyamines; however, the mechanism responsible for weak rectification remains elusive. Hypotheses include weak voltage-dependent block and intrinsic voltage-dependent gating. Here, we performed a conductance Hill analysis of currents recorded with a double-ramp protocol to evaluate different mechanisms proposed for weak inward rectification of Kir2.1 channels. Linkage analysis in the form of a Hill plot revealed that the ramp currents could be best explained by allosteric coupling between a mildly voltage-dependent pore gate (gating charge ∼0.18 e_o) and a voltage sensor (gating charge ∼1.7 e_o). The proposed voltage sensor stabilized the closing of the pore gate (coupling factor ∼31). We anticipate that the use of linkage analysis will broaden understanding of functional coupling in ion channels and proteins in general.

Gating currents

A voltage change across a membrane protein moves charges or dipoles producing a gating current that is an electrical expression of a conformational change.

Many membrane proteins sense the voltage across the membrane where they are inserted, and their function is affected by voltage changes. The voltage sensor consists of charges or dipoles that move in response to changes in the electric field, and their movement produces an electric current that has been called gating current. In the case of voltage-gated ion channels, the kinetic and steady-state properties of the gating charges provide information of conformational changes between closed states that are not visible when observing ionic currents only. In this Journal of General Physiology Milestone, the basic principles of voltage sensing and gating currents are presented, followed by a historical description of the recording of gating currents. The results of gating current recordings are then discussed in the context of structural changes in voltage-dependent membrane proteins and how these studies have provided new insights on gating mechanisms.

A nonequilibrium binary elements-based kinetic model for benzodiazepine regulation of GABAA receptors

A nonequilibrium kinetic model that explicitly treats the energetics of interactions between structural domains is used to describe positive modulation of the GABA_A receptor by benzodiazepines.

Ion channels, like many other proteins, are composed of multiple structural domains. A stimulus that impinges on one domain, such as binding of a ligand to its recognition site, can influence the activity of another domain, such as a transmembrane channel gate, through interdomain interactions. Kinetic schemes that describe the function of interacting domains typically incorporate a minimal number of states and transitions, and do not explicitly model interactions between domains. Here, we develop a kinetic model of the GABA_A receptor, a ligand-gated ion channel modulated by numerous compounds including benzodiazepines, a class of drugs used clinically as sedatives and anxiolytics. Our model explicitly treats both the kinetics of distinct functional domains within the receptor and the interactions between these domains. The model describes not only how benzodiazepines that potentiate GABA_A receptor activity, such as diazepam, affect peak current dose–response relationships in the presence of desensitization, but also their effect on the detailed kinetics of current activation, desensitization, and deactivation in response to various stimulation protocols. Finally, our model explains positive modulation by benzodiazepines of receptor currents elicited by either full or partial agonists, and can resolve conflicting observations arguing for benzodiazepine modulation of agonist binding versus channel gating.

Functional heterogeneity of the four voltage sensors of a human L-type calcium channel

Excitation-evoked Ca(2+) influx is the fastest and most ubiquitous chemical trigger for cellular processes, including neurotransmitter release, muscle contraction, and gene expression. The voltage dependence and timing of Ca(2+) entry are thought to be functions of voltage-gated calcium (CaV) channels composed of a central pore regulated by four nonidentical voltage-sensing domains (VSDs I-IV). Currently, the individual voltage dependence and the contribution to pore opening of each VSD remain largely unknown. Using an optical approach (voltage-clamp fluorometry) to track the movement of the individual voltage sensors, we discovered that the four VSDs of CaV1.2 channels undergo voltage-evoked conformational rearrangements, each exhibiting distinct voltage- and time-dependent properties over a wide range of potentials and kinetics. The voltage dependence and fast kinetic components in the activation of VSDs II and III were compatible with the ionic current properties, suggesting that these voltage sensors are involved in CaV1.2 activation. This view is supported by an obligatory model, in which activation of VSDs II and III is necessary to open the pore. When these data were interpreted in view of an allosteric model, where pore opening is intrinsically independent but biased by VSD activation, VSDs II and III were each found to supply ∼50 meV (∼2 kT), amounting to ∼85% of the total energy, toward stabilizing the open state, with a smaller contribution from VSD I (∼16 meV). VSD IV did not appear to participate in channel opening.

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.

Modeling ion channels: past, present, and future

Ion channels are membrane-bound enzymes whose catalytic sites are ion-conducting pores that open and close (gate) in response to specific environmental stimuli. Ion channels are important contributors to cell signaling and homeostasis. Our current understanding of gating is the product of 60 plus years of voltage-clamp recording augmented by intervention in the form of environmental, chemical, and mutational perturbations. The need for good phenomenological models of gating has evolved in parallel with the sophistication of experimental technique. The goal of modeling is to develop realistic schemes that not only describe data, but also accurately reflect mechanisms of action. This review covers three areas that have contributed to the understanding of ion channels: traditional Eyring kinetic theory, molecular dynamics analysis, and statistical thermodynamics. Although the primary emphasis is on voltage-dependent channels, the methods discussed here are easily generalized to other stimuli and could be applied to any ion channel and indeed any macromolecule.

Transduction of voltage and Ca2+ signals by Slo1 BK channels

Large-conductance Ca2+ -and voltage-gated K+ channels are activated by an increase in intracellular Ca2+ concentration and/or depolarization. The channel activation mechanism is well described by an allosteric model encompassing the gate, voltage sensors, and Ca2+ sensors, and the model is an excellent framework to understand the influences of auxiliary β and γ subunits and regulatory factors such as Mg2+. Recent advances permit elucidation of structural correlates of the biophysical mechanism.

The gating charge should not be estimated by fitting a two-state model to a Q-V curve

The voltage dependence of charges in voltage-sensitive proteins, typically displayed as charge versus voltage (Q-V) curves, is often quantified by fitting it to a simple two-state Boltzmann function. This procedure overlooks the fact that the fitted parameters, including the total charge, may be incorrect if the charge is moving in multiple steps. We present here the derivation of a general formulation for Q-V curves from multistate sequential models, including the case of infinite number of states. We demonstrate that the commonly used method to estimate the charge per molecule using a simple Boltzmann fit is not only inadequate, but in most cases, it underestimates the moving charge times the fraction of the field.