Two-dimensional kinetic analysis suggests nonsequential gating of mechanosensitive channels in Xenopus oocytes

Microscopic mechanism of PIEZO1 activation by pressure-induced membrane stretch

Mechanosensitive PIEZO1 ion channels open in response to membrane stretch. Yet, the underlying microscopic mechanism of this activation remains unknown. To probe this mechanism, we used cell-attached pressure-clamp recordings to measure single channel currents at different steady-state negative pipette pressures, spanning the full range of the channel's pressure sensitivity. Pressure-dependent activation occurs through a sharp reduction of the mean shut duration and through a moderate increase of the mean open duration. Across all tested pressures, the distribution of open and shut dwell times best follows sums of two and three exponential components, respectively. As the magnitude of the pressure stimulus increases, the time constants of most of these exponential components gradually change, in opposite directions for open and shut dwell times, and to a similar extent. In addition, while the relative amplitudes of fast and slow components remain unchanged for open intervals, they fully reverse for shut intervals, further reducing the mean shut duration. Using two-dimensional dwell time analysis, Markov-chain modeling, and simulations, we identified a minimal five-states model which recapitulates essential characteristics of single channel data, including microscopic reversibility, correlations between adjacent open and shut intervals, and asymmetric modulation of dwell times by pressure. This study identifies a microscopic mechanism for the activation of PIEZO1 channels by pressure-induced membrane stretch and deepens our fundamental understanding of mechanotransduction by a vertebrate member of the PIEZO channel family.

Single-channel kinetics of BK (Slo1) channels

Single-channel kinetics has proven a powerful tool to reveal information about the gating mechanisms that control the opening and closing of ion channels. This introductory review focuses on the gating of large conductance Ca²⁺- and voltage-activated K⁺ (BK or Slo1) channels at the single-channel level. It starts with single-channel current records and progresses to presentation and analysis of single-channel data and the development of gating mechanisms in terms of discrete state Markov (DSM) models. The DSM models are formulated in terms of the tetrameric modular structure of BK channels, consisting of a central transmembrane pore-gate domain (PGD) attached to four surrounding transmembrane voltage sensing domains (VSD) and a large intracellular cytosolic domain (CTD), also referred to as the gating ring. The modular structure and data analysis shows that the Ca²⁺ and voltage dependent gating considered separately can each be approximated by 10-state two-tiered models with five closed states on the upper tier and five open states on the lower tier. The modular structure and joint Ca²⁺ and voltage dependent gating are consistent with a 50 state two-tiered model with 25 closed states on the upper tier and 25 open states on the lower tier. Adding an additional tier of brief closed (flicker states) to the 10-state or 50-state models improved the description of the gating. For fixed experimental conditions a channel would gate in only a subset of the potential number of states. The detected number of states and the correlations between adjacent interval durations are consistent with the tiered models. The examined models can account for the single-channel kinetics and the bursting behavior of gating. Ca²⁺ and voltage activate BK channels by predominantly increasing the effective opening rate of the channel with a smaller decrease in the effective closing rate. Ca²⁺ and depolarization thus activate by mainly destabilizing the closed states.

Utrophin regulates modal gating of mechanosensitive ion channels in dystrophic skeletal muscle

Dystrophin is a large, submembrane cytoskeletal protein, absence of which causes Duchenne muscular dystrophy. Utrophin is a dystrophin homologue found in both muscle and brain whose physiological function is unknown. Recordings of single-channel activity were made from membrane patches on skeletal muscle from mdx, mdx/utrn(+/-) heterozygotes and mdx/utrn(-/-) double knockout mice to investigate the role of these cytoskeletal proteins in mechanosensitive (MS) channel gating. We find complex, gene dose-dependent effects of utrophin depletion in dystrophin-deficient mdx muscle: (1) increased MS channel open probability, (2) a shift of MS channel gating to larger pressures, (3) appearance of modal gating of MS channels and small conductance channels and (4) expression of large conductance MS channels. We suggest a physical model in which utrophin acts as a scaffolding protein that stabilizes lipid microdomains and clusters MS channel subunits. Depletion of utrophin disrupts domain composition in a manner that favours open channel area expansion, as well as allowing diffusion and aggregation of additional MS channel subunits.

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

Partial opening and subconductance gating of mechanosensitive ion channels in dystrophic skeletal muscle

We recorded the activity of single mechanosensitive (MS) ion channels in skeletal muscle from the mdx mouse, a deletion mutant that lacks the cytoskeletal protein, dystrophin. Experiments were designed to examine the influence of dystrophin, a major component of skeletal muscle costameres, on the behaviour of single MS channels. In the majority of recordings from cell-attached patches, MS channels have a conductance of ∼23 pS. Recordings from some patches, however, showed a smaller conductance channel of ∼7-14 pS. Large and small conductance channels were detected in a single patch and showed serial, non-random gating, suggesting different opening levels of a single channel. Analysis of the distribution of current amplitudes within the open channel showed MS channels fluctuate between subconductance levels. MS channels in dystrophic muscle spend ∼60% of the time at smaller subconductance levels, often failing to reach the fully open level. Applying pressure to the membrane of mdx fibres increases in a graded manner occupancy of the fully open state, while reducing occupancy of subconductance levels. Recordings also show partial openings of MS channels in both wild-type and mdx muscle that fail to reach the fully open state. Partial openings occur at a higher frequency in mdx muscle and reflect occupancy of subconductance levels seen during complete activations. In muscle from mdx/utrn(-/-) double knockout mice, MS channels also spend more time at subconductance levels than the fully open state. Conductance variability of MS channels may represent gating of a heteromeric protein composed of different channel subunits. The results also show that partial opening and prolonged burst duration are distinct mechanisms that contribute to excess Ca(2+) entry in dystrophic muscle.

Voltage- and cold-dependent gating of single TRPM8 ion channels

Transient receptor potential (TRP) channels play critical roles in cell signaling by coupling various environmental factors to changes in membrane potential that modulate calcium influx. TRP channels are typically activated in a polymodal manner, thus integrating multiple stimuli. Although much progress has been made, the underlying mechanisms of TRP channel activation are largely unknown. The TRPM8 cation channel has been extensively investigated as a major neuronal cold sensor but is also activated by voltage, calcium store depletion, and some lipids as well as by compounds that produce cooling sensations, such as menthol or icilin. Several models of TRPM8 activation have been proposed to explain the interaction between these diverse stimuli. However, a kinetic scheme is not yet available that can describe the detailed single-channel kinetics to gain further insight into the underlying gating mechanism. To work toward this goal, we investigated voltage-dependent single-channel gating in cell-attached patches at two different temperatures (20 and 30°C) using HEK293 cells stably expressing TRPM8. Both membrane depolarization and cooling increased channel open probability (P_o) mainly by decreasing the duration of closed intervals, with a smaller increase in the duration of open intervals. Maximum likelihood analysis of dwell times at both temperatures indicated gating in a minimum of five closed and two open states, and global fitting over a wide range of voltages identified a seven-state model that described the voltage dependence of P_o, the single-channel kinetics, and the response of whole-cell currents to voltage ramps and steps. The major action of depolarization and cooling was to accelerate forward transitions between the same two sets of adjacent closed states. The seven-state model provides a general mechanism to account for TRPM8 activation by membrane depolarization at two temperatures and can serve as a starting point for further investigations of multimodal TRP activation.

Coupling and cooperativity in voltage activation of a limited-state BK channel gating in saturating Ca2+

Voltage-dependent gating mechanisms of large conductance Ca²⁺ and voltage-activated (BK) channels were investigated using two-dimensional maximum likelihood analysis of single-channel open and closed intervals. To obtain sufficient data at negative as well as positive voltages, single-channel currents were recorded at saturating Ca²⁺ from BK channels mutated to remove the RCK1 Ca²⁺ and Mg²⁺ sensors. The saturating Ca²⁺ acting on the Ca²⁺ bowl sensors of the resulting BK_B channels increased channel activity while driving the gating into a reduced number of states, simplifying the model. Five highly constrained idealized gating mechanisms based on extensions of the Monod-Wyman-Changeux model for allosteric proteins were examined. A 10-state model without coupling between the voltage sensors and the opening/closing transitions partially described the voltage dependence of Po but not the single-channel kinetics. With allowed coupling, the model gave improved descriptions of Po and approximated the single-channel kinetics; each activated voltage sensor increased the opening rate approximately an additional 23-fold while having little effect on the closing rate. Allowing cooperativity among voltage sensors further improved the description of the data: each activated voltage sensor increased the activation rate of the remaining voltage sensors approximately fourfold, with little effect on the deactivation rate. The coupling factor was decreased in models with cooperativity from ∼23 to ∼18. Whether the apparent cooperativity among voltage sensors arises from imposing highly idealized models or from actual cooperativity will require additional studies to resolve. For both cooperative and noncooperative models, allowing transitions to five additional brief (flicker) closed states further improved the description of the data. These observations show that the voltage-dependent single-channel kinetics of BK_B channels can be approximated by highly idealized allosteric models in which voltage sensor movement increases Po mainly through an increase in channel opening rates, with limited effects on closing rates.

Linking exponential components to kinetic states in Markov models for single-channel gating

Discrete state Markov models have proven useful for describing the gating of single ion channels. Such models predict that the dwell-time distributions of open and closed interval durations are described by mixtures of exponential components, with the number of exponential components equal to the number of states in the kinetic gating mechanism. Although the exponential components are readily calculated (Colquhoun and Hawkes, 1982, Phil. Trans. R. Soc. Lond. B. 300:1-59), there is little practical understanding of the relationship between components and states, as every rate constant in the gating mechanism contributes to each exponential component. We now resolve this problem for simple models. As a tutorial we first illustrate how the dwell-time distribution of all closed intervals arises from the sum of constituent distributions, each arising from a specific gating sequence. The contribution of constituent distributions to the exponential components is then determined, giving the relationship between components and states. Finally, the relationship between components and states is quantified by defining and calculating the linkage of components to states. The relationship between components and states is found to be both intuitive and paradoxical, depending on the ratios of the state lifetimes. Nevertheless, both the intuitive and paradoxical observations can be described within a consistent framework. The approach used here allows the exponential components to be interpreted in terms of underlying states for all possible values of the rate constants, something not previously possible.

Twenty odd years of stretch-sensitive channels

After formation of the giga-seal, the membrane patch can be stimulated by hydrostatic or osmotic pressure gradients applied across the patch. This feature led to the discovery of stretch-sensitive or mechanosensitive (MS) channels, which are now known to be ubiquitously expressed in cells representative of all the living kingdoms. In addition to mechanosensation, MS channels have been implicated in many basic cell functions, including regulation of cell volume, shape, and motility. The successful cloning, overexpression, and crystallization of bacterial MS channel proteins combined with patch clamp and modeling studies have provided atomic insight into the working of these nanomachines. In particular, studies of MS channels have revealed new understanding of how the lipid bilayer modulates membrane protein function. Three major membrane protein families, transient receptor potential, 2 pore domain K(+), and the epithelial Na(+) channels, have been shown to form MS channels in animal cells, and their polymodal activation embrace fields far beyond mechanosensitivity. The discovery of new drugs highly selective for MS channels ("mechanopharmaceutics") and the demonstration of MS channel involvement in several major human diseases ("mechanochannelopathies") provide added motivation for devising new techniques and approaches for studying MS channels.

Estimating binding affinities of the nicotinic receptor for low-efficacy ligands using mixtures of agonists and two-dimensional concentration-response relationships

The phenomenon of ligand-induced ion channel gating hinges upon the ability of a receptor channel to bind ligand molecules with conformation-specific affinities. However, our understanding of this fundamental phenomenon is notably limited, not only because the changes in binding site structure and ligand conformation that occur upon gating are largely unknown but, also, because the strength of these ligand–receptor interactions are experimentally elusive. Both high- and low-efficacy ligands pose a number of analytical and experimental challenges that can render the estimation of their conformation-specific binding affinities impossible. In this paper, we present a novel assay that overcomes some of the hurdles presented by weak agonists of the muscle nicotinic receptor and allows the estimation of their closed-state affinities. The method, which we have termed the “activation-competition” assay, consists of a single-channel concentration–response assay performed in the presence of a binary mixture of ligands of widely different efficacies. By plotting the channel response (i.e., the open probability) as a function of the concentration of each agonist in the mixture, interpreting the observed response in the framework of a plausible kinetic scheme, and fitting the open probability surface with the corresponding function, the affinities of the closed receptor for the two agonists can be simultaneously extracted as free parameters. Here, we applied this methodology to estimate the closed-state affinity of the muscle nicotinic receptor for choline (a very weak agonist) using acetylcholine (ACh) as the partner in the mixture. We estimated the dissociation equilibrium constant of choline (K_D) from the wild type's closed state to be 4.1 ± 0.5 mM (and that of ACh to be 106 ± 6 μM). We also discuss the use of accurate estimates of affinities for low-efficacy agonists as a tool to discriminate between binding and gating effects of mutations, and in the context of the rational design of therapeutic drugs.

Gating reaction mechanisms for NMDA receptor channels

NMDA receptors (NMDARs) mediate the slow component of excitatory transmission in the CNS and play key roles in synaptic plasticity and excitotoxicity. We investigated the gating reaction mechanism of fully liganded NR1/NR2A recombinant NMDARs (expressed in Xenopus oocytes) by fitting all possible three-closed/two-open-state, noncyclic kinetic schemes to currents elicited by saturating concentrations of glutamate plus glycine. The adequacy of each scheme was assessed by maximum likelihood values and autocorrelation coefficients of single-channel currents, as well as by the predicted time courses of transient macroscopic currents. Two schemes provided the best description for NMDAR gating at both the single-channel and macroscopic levels. These two schemes had coupled open states, only one gateway between the closed and open aggregates, and at least two preopening closed states. These two models could be condensed into a cyclic reaction mechanism. Using a linear reaction scheme, the overall "gating" rates (from the initial stable closed state to the final stable open state) are 177 and 4.4 s(-1).

Dynamic regulation of mechanosensitive channels: capacitance used to monitor patch tension in real time

All cells, from bacteria to human, are mechanically sensitive. The most rapid of these membrane protein transducers are mechanosensitive ion channels, ionic pores in the membrane that open and close in response to membrane tension. In specific sensory organs, these channels serve the senses of touch and hearing, and inform the central nervous system about the filling of hollow organs such as the bladder. Non-specialized cells use these channels to report on changes in cell volume and local strain. To preserve dynamic sensitivity, sensory receptors adapt to steady-state stimuli. Here we show that in rat astrocytes, the most abundant cells in the brain, this apparent adaptation to the stimulus is actually an inactivation. We have been able to track the time course of local strain by measuring attofarad changes in membrane capacitance and show that it is not correlated with loss of channel activity. The reduction in current with time is caused by an increased occupancy of low conductance states, and a reduction in the probability of opening, not a relaxation of local stress. The occupancy of these substates depends on the integrity of the cell's cytoplasm. However, while disruption of the cytoskeleton leads to a loss of inactivation, it leaves activation unaffected. The activation process is voltage-insensitive, closely correlated with changes in capacitance, and seems to arise solely from stress in the bilayer. The inactivation rate decreases with depolarization, and kinetic analysis suggests that the process involves multiple cytoplasmic ligands. Surprisingly, multivalent ions such as Gd(+3) and Ca(+2) that bind to the lipids and affect channel gating, do not affect the strain-induced increase in membrane capacitance; contrary to expectations, membrane elasticity is unchanged.

Model-based fitting of single-channel dwell-time distributions

Single-channel recordings provide unprecedented resolutions on kinetics of conformational changes of ion channels. Several approaches exist for analysis of the data, including the dwell-time histogram fittings and the full maximal-likelihood approaches that fit either the idealized dwell-time sequence or more ambitiously the noisy data directly using hidden Markov modeling. Although the full maximum likelihood approaches are statistically advantageous, they can be time-consuming especially for large datasets and/or complex models. We present here an alternative approach for model-based fitting of one-dimensional and two-dimensional dwell-time histograms. To improve performance, we derived analytical expressions for the derivatives of one-dimensional and two-dimensional dwell-time distribution functions and employed the gradient-based variable metric method for fast search of optimal rate constants in a model. The algorithm also has the ability to allow for a first-order correction for the effects of missed events, global fitting across different experimental conditions, and imposition of typical constraints on rate constants including microscopic reversibility. Numerical examples are presented to illustrate the performance of the algorithm, and comparisons with the full maximum likelihood fitting are discussed.