Atomic structure of a Na+- and K+-conducting channel

Cryo-EM structures of Kv1.2 potassium channels, conducting and non-conducting

We present near-atomic-resolution cryo-EM structures of the mammalian voltage-gated potassium channel Kv1.2 in open, C-type inactivated, toxin-blocked and sodium-bound states at 3.2 Å, 2.5 Å, 3.2 Å, and 2.9Å. These structures, all obtained at nominally zero membrane potential in detergent micelles, reveal distinct ion-occupancy patterns in the selectivity filter. The first two structures are very similar to those reported in the related Shaker channel and the much-studied Kv1.2-2.1 chimeric channel. On the other hand, two new structures show unexpected patterns of ion occupancy. First, the toxin α-Dendrotoxin, like Charybdotoxin, is seen to attach to the negatively-charged channel outer mouth, and a lysine residue penetrates into the selectivity filter, with the terminal amine coordinated by carbonyls, partially disrupting the outermost ion-binding site. In the remainder of the filter two densities of bound ions are observed, rather than three as observed with other toxin-blocked Kv channels. Second, a structure of Kv1.2 in Na+ solution does not show collapse or destabilization of the selectivity filter, but instead shows an intact selectivity filter with ion density in each binding site. We also attempted to image the C-type inactivated Kv1.2 W366F channel in Na+ solution, but the protein conformation was seen to be highly variable and only a low-resolution structure could be obtained. These findings present new insights into the stability of the selectivity filter and the mechanism of toxin block of this intensively studied, voltage-gated potassium channel.

Coronavirus accessory protein ORF3 biology and its contribution to viral behavior and pathogenesis

Coronavirus porcine epidemic diarrhea virus (PEDV) is classified in the genus Alphacoronavirus, family Coronaviridae that encodes the only accessory protein, ORF3 protein. However, how ORF3 contributes to viral pathogenicity, adaptability, and replication is obscure. In this review, we summarize current knowledge and identify gaps in many aspects of ORF3 protein in PEDV, with emphasis on its unique biological features, including membrane topology, Golgi retention mechanism, potential intrinsic disordered property, functional motifs, protein glycosylation, and codon usage phenotypes related to genetic evolution and gene expression. In addition, we propose intriguing questions related to ORF3 protein that we hope to stimulate further studies and encourage collaboration among virologists worldwide to provide constructive knowledge about the unique characteristics and biological functions of ORF3 protein, by which their potential role in clarifying viral behavior and pathogenesis can be possible.

Asymmetry and Ion Selectivity Properties of Bacterial Channel NaK Mutants Derived from Ionotropic Glutamate Receptors

Ionotropic glutamate receptors are ligand-gated cation channels that play essential roles in the excitatory synaptic transmission throughout the central nervous system. A number of open-pore structures of α-amino-3-hydroxy-5-methyl-4-isoxazolepropionic-acid (AMPA)-type glutamate receptors became available recently by cryo-electron microscopy (cryo-EM). These structures provide valuable insights into the conformation of the selectivity filter (SF), the part of the ion channel that determines the ion selectivity. Nonetheless, due to the moderate resolution of the cryo-EM structures, detailed information such as ion occupancy of monovalent and divalent cations as well as positioning of the side-chains in the SF is still missing. Here, in an attempt to obtain high-resolution information about glutamate receptor SFs, we incorporated partial SF sequences of the AMPA and kainate receptors into the bacterial tetrameric cation channel NaK, which served as a structural scaffold. We determined a series of X-ray structures of NaK-CDI, NaK-SDI and NaK-SELM mutants at 1.42-2.10 Å resolution, showing distinct ion occupation of different monovalent cations. Molecular dynamics (MD) simulations of NaK-CDI indicated the channel to be conductive to monovalent cations, which agrees well with our electrophysiology recordings. Moreover, previously unobserved structural asymmetry of the SF was revealed by the X-ray structures and MD simulations, implying its importance in ion non-selectivity of tetrameric cation channels.

An artificial sodium-selective subnanochannel

Single-ion selectivity with high precision has long been pursued for fundamental bioinspired engineering and applications such as in ion separation and energy conversion. However, it remains a challenge to develop artificial ion channels to achieve single-ion selectivity comparable to their biological analogs, especially for high Na⁺/K⁺ selectivity. Here, we report an artificial sodium channel by subnanoconfinement of 4'-aminobenzo-15-crown-5 ethers (15C5s) into ~6-Å-sized metal-organic framework subnanochannel (MOFSNC). The resulting 15C5-MOFSNC shows an unprecedented Na⁺/K⁺ selectivity of tens to 10² and Na⁺/Li⁺ selectivity of 10³ under multicomponent permeation conditions, comparable to biological sodium channels. A co-ion-responsive single-file transport mechanism in 15C-MOFSNC is proposed for the preferential transport of Na⁺ over K⁺ due to the synergetic effects of size exclusion, charge selectivity, local hydrophobicity, and preferential binding with functional groups. This study provides an alternative strategy for developing potential single-ion selective channels and membranes for many applications.

Conformational plasticity of NaK2K and TREK2 potassium channel selectivity filters

The K+ channel selectivity filter (SF) is defined by TxGYG amino acid sequences that generate four identical K+ binding sites (S1-S4). Only two sites (S3, S4) are present in the non-selective bacterial NaK channel, but a four-site K+-selective SF is obtained by mutating the wild-type TVGDGN SF sequence to a canonical K+ channel TVGYGD sequence (NaK2K mutant). Using single molecule FRET (smFRET), we show that the SF of NaK2K, but not of non-selective NaK, is ion-dependent, with the constricted SF configuration stabilized in high K+ conditions. Patch-clamp electrophysiology and non-canonical fluorescent amino acid incorporation show that NaK2K selectivity is reduced by crosslinking to limit SF conformational movement. Finally, the eukaryotic K+ channel TREK2 SF exhibits essentially identical smFRET-reported ion-dependent conformations as in prokaryotic K+ channels. Our results establish the generality of K+-induced SF conformational stability across the K+ channel superfamily, and introduce an approach to study manipulation of channel selectivity.

Full opening of helix bundle crossing does not lead to NaK channel activation

A critical part of ion channel function is the ability to open and close in response to stimuli and thus conduct ions in a regulated fashion. While x-ray diffraction studies of ion channels suggested a general steric gating mechanism located at the helix bundle crossing (HBC), recent functional studies on several channels indicate that the helix bundle crossing is wide-open even in functionally nonconductive channels. Two NaK channel variants were crystallized in very different open and closed conformations, which served as important models of the HBC gating hypothesis. However, neither of these NaK variants is conductive in liposomes unless phenylalanine 92 is mutated to alanine (F92A). Here, we use NMR to probe distances at near-atomic resolution of the two NaK variants in lipid bicelles. We demonstrate that in contrast to the crystal structures, both NaK variants are in a fully open conformation, akin to Ca2+-bound MthK channel structure where the HBC is widely open. While we were not able to determine what a conductive NaK structure is like, our further inquiry into the gating mechanism suggests that the selectivity filter and pore helix are coupled to the M2 helix below and undergo changes in the structure when F92 is mutated. Overall, our data show that NaK exhibits coupling between the selectivity filter and HBC, similar to K+ channels, and has a more complex gating mechanism than previously thought, where the full opening of HBC does not lead to channel activation.

Interrogating the gating motions of the NaK channel

Previous crystallographic studies depicted a physical gate of the NaK channel localized at a bundle crossing of pore-lining helices, but solution NMR studies in the current issue of JGP suggest otherwise.

Molecular Events behind the Selectivity and Inactivation Properties of Model NaK-Derived Ion Channels

Y55W mutants of non-selective NaK and partly K⁺-selective NaK2K channels have been used to explore the conformational dynamics at the pore region of these channels as they interact with either Na⁺ or K⁺. A major conclusion is that these channels exhibit a remarkable pore conformational flexibility. Homo-FRET measurements reveal a large change in W55–W55 intersubunit distances, enabling the selectivity filter (SF) to admit different species, thus, favoring poor or no selectivity. Depending on the cation, these channels exhibit wide-open conformations of the SF in Na⁺, or tight induced-fit conformations in K⁺, most favored in the four binding sites containing NaK2K channels. Such conformational flexibility seems to arise from an altered pattern of restricting interactions between the SF and the protein scaffold behind it. Additionally, binding experiments provide clues to explain such poor selectivity. Compared to the K⁺-selective KcsA channel, these channels lack a high affinity K⁺ binding component and do not collapse in Na⁺. Thus, they cannot properly select K⁺ over competing cations, nor reject Na⁺ by collapsing, as K⁺-selective channels do. Finally, these channels do not show C-type inactivation, likely because their submillimolar K⁺ binding affinities prevent an efficient K⁺ loss from their SF, thus favoring permanently open channel states.

ION BEHAVIOUR IN THE SELECTIVITY FILTER OF HCN1 CHANNELS

Hyperpolarization-activated cyclic nucleotide-gated channels (HCNs) are responsible for the generation of pacemaker currents (I_f or I_h) in cardiac and neuronal cells. Despite the overall structural similarity to voltage-gated potassium (Kv) channels, HCNs show much lower selectivity for K⁺ over Na⁺ ions. This increased permeability to Na⁺ is critical to their role in membrane depolarization. HCNs can also select between Na⁺ and Li⁺ ions. Here we investigate the unique ion selectivity properties of HCNs using molecular dynamics simulations. Our simulations suggest that the HCN1 pore is flexible and dilated compared to Kv channels with only one stable ion binding site within the selectivity filter. We also observe that ion coordination and hydration differ within the HCN1 selectivity filter compared to those in Kv and CNG channels. Additionally, the C358T mutation further stabilizes the symmetry of the binding site and provides a more fit space for ion coordination, particularly for Li⁺. STATEMENT OF SIGNIFICANCE: Hyperpolarization-activated cyclic-nucleotide gated (HCN) channels represent the molecular correlate of the currents I_f or I_h in cardiomyocytes and neurons. Here we study the unique low conductance and semi-selective properties of HCNs. The conductance and selectivity mechanisms of ion channels are tightly associated with their physiological role and contribute to the specific properties of the excitable cells in which they are expressed.

Studying membrane proteins with MicroED

The structural investigation of biological macromolecules is indispensable in understanding the molecular mechanisms underlying diseases. Several structural biology techniques have been introduced to unravel the structural facets of biomolecules. Among these, the electron cryomicroscopy (cryo-EM) method microcrystal electron diffraction (MicroED) has produced atomic resolution structures of important biological and small molecules. Since its inception in 2013, MicroED established a demonstrated ability for solving structures of difficult samples using vanishingly small crystals. However, membrane proteins remain the next big frontier for MicroED. The intrinsic properties of membrane proteins necessitate improved sample handling and imaging techniques to be developed and optimized for MicroED. Here, we summarize the milestones of electron crystallography of two-dimensional crystals leading to MicroED of three-dimensional crystals. Then, we focus on four different membrane protein families and discuss representatives from each family solved by MicroED.

Angstrom-scale ion channels towards single-ion selectivity

Artificial ion channels with ion permeability and selectivity comparable to their biological counterparts are highly desired for efficient separation, biosensing, and energy conversion technologies. In the past two decades, both nanoscale and sub-nanoscale ion channels have been successfully fabricated to mimic biological ion channels. Although nanoscale ion channels have achieved intelligent gating and rectification properties, they cannot realize high ion selectivity, especially single-ion selectivity. Artificial angstrom-sized ion channels with narrow pore sizes <1 nm and well-defined pore structures mimicking biological channels have accomplished high ion conductivity and single-ion selectivity. This review comprehensively summarizes the research progress in the rational design and synthesis of artificial subnanometer-sized ion channels with zero-dimensional to three-dimensional pore structures. Then we discuss cation/anion, mono-/di-valent cation, mono-/di-valent anion, and single-ion selectivities of the synthetic ion channels and highlight their potential applications in high-efficiency ion separation, energy conversion, and biological therapeutics. The gaps of single-ion selectivity between artificial and natural channels and the connections between ion selectivity and permeability of synthetic ion channels are covered. Finally, the challenges that need to be addressed in this research field and the perspective of angstrom-scale ion channels are discussed.

Direct Detection of Bound Ammonium Ions in the Selectivity Filter of Ion Channels by Solid-State NMR

The flow of ions across cell membranes facilitated by ion channels is an important function for all living cells. Despite the huge amount of structural data provided by crystallography, elucidating the exact interactions between the selectivity filter atoms and bound ions is challenging. Here, we detect bound ¹⁵N-labeled ammonium ions as a mimic for potassium ions in ion channels using solid-state NMR under near-native conditions. The non-selective ion channel NaK showed two ammonium peaks corresponding to its two ion binding sites, while its potassium-selective mutant NaK2K that has a signature potassium-selective selectivity filter with four ion binding sites gave rise to four ammonium peaks. Ions bound in specific ion binding sites were identified based on magnetization transfer between the ions and carbon atoms in the selectivity filters. Magnetization transfer between bound ions and water molecules revealed that only one out of four ions in the selectivity filter of NaK2K is in close contact with water, which is in agreement with the direct knock-on ion conduction mechanism where ions are conducted through the channel by means of direct interactions without water molecules in between. Interestingly, the potassium-selective ion channels investigated here (NaK2K and, additionally, KcsA-Kv1.3) showed remarkably different chemical shifts for their bound ions, despite having identical amino acid sequences and crystal structures of their selectivity filters. Molecular dynamics simulations show similar ion binding and conduction behavior between ammonium and potassium ions and identify the origin of the differences between the investigated potassium channels.

Structural Plasticity of the Selectivity Filter in Cation Channels

Ion channels allow for the passage of ions across biological membranes, which is essential for the functioning of a cell. In pore loop channels the selectivity filter (SF) is a conserved sequence that forms a constriction with multiple ion binding sites. It is becoming increasingly clear that there are several conformations and dynamic states of the SF in cation channels. Here we outline specific modes of structural plasticity observed in the SFs of various pore loop channels: disorder, asymmetry, and collapse. We summarize the multiple atomic structures with varying SF conformations as well as asymmetric and more dynamic states that were discovered recently using structural biology, spectroscopic, and computational methods. Overall, we discuss here that structural plasticity within the SF is a key molecular determinant of ion channel gating behavior.

Preparation of Giant Escherichia coli spheroplasts for Electrophysiological Recordings

Prokaryotic ion channels have been instrumental in furthering our understanding of many fundamental aspects of ion channels' structure and function. However, characterizing the biophysical properties of a prokaryotic ion channel in a native membrane system using patch-clamp electrophysiology is technically challenging. Patch-clamp is regarded as a gold standard technique to study ion channel properties in both native and heterologous expression systems. The presence of a cell wall and the small size of bacterial cells makes it impossible to directly patch clamp using microelectrodes. Here, we describe a method for the preparation of giant E. coli spheroplasts in order to investigate the electrophysiological properties of bacterial cell membranes. Spheroplasts are formed by first inhibiting bacterial cell wall synthesis, followed by enzymatic digestion of the outer cell wall in the presence of a permeabilizing agent. This protocol can be used to characterize the function of any heterologous ion channels or ion transporters expressed in E. coli membranes.

Ion-dependent structure, dynamics, and allosteric coupling in a non-selective cation channel

The selectivity filter (SF) determines which ions are efficiently conducted through ion channel pores. NaK is a non-selective cation channel that conducts Na⁺ and K⁺ with equal efficiency. Crystal structures of NaK suggested a rigid SF structure, but later solid-state NMR and MD simulations questioned this interpretation. Here, we use solution NMR to characterize how bound Na⁺ vs. K⁺ affects NaK SF structure and dynamics. We find that the extracellular end of the SF is flexible on the ps-ns timescale regardless of bound ion. On a slower timescale, we observe a structural change between the Na⁺ and K⁺-bound states, accompanied by increased structural heterogeneity in Na⁺. We also show direct evidence that the SF structure is communicated to the pore via I88 on the M2 helix. These results support a dynamic SF with multiple conformations involved in non-selective conduction. Our data also demonstrate allosteric coupling between the SF and pore-lining helices in a non-selective cation channel that is analogous to the allosteric coupling previously demonstrated for K⁺-selective channels, supporting the generality of this model.

NaK is a bacterial non-selective cation channel. Here, the authors use solution NMR to show that selectivity filter (SF) in NaK is dynamic, with structural differences between the Na+ and K + -bound states. The conformation of the SF is communicated to the pore-lining helices similarly as in the K + -selective channels.

Sodium Ions Do Not Stabilize the Selectivity Filter of a Potassium Channel

Ion conduction is an essential function for electrical activity in all organisms. The non-selective ion channel NaK was previously shown to adopt two stable conformations of the selectivity filter. Here, we present solid-state NMR measurements of NaK demonstrating a population shift between these conformations induced by changing the ions in the sample while the overall structure of NaK is not affected. We show that two K⁺-selective mutants (NaK2K and NaK2K-Y66F) suffer a complete loss of selectivity filter stability under Na⁺ conditions, but do not collapse into a defined structure. Widespread chemical shift perturbations are seen between the Na⁺ and K⁺ states of the K⁺-selective mutants in the region of the pore helix indicating structural changes. We conclude that the stronger link between the selectivity filter and the pore helix in the K⁺-selective mutants, compared to the non-selective wild-type NaK channel, reduces the ion-dependent conformational flexibility of the selectivity filter.

Structural plasticity of the selectivity filter in a nonselective ion channel

The sodium potassium ion channel (NaK) is a nonselective ion channel that conducts both sodium and potassium across the cellular membrane. A new crystallographic structure of NaK reveals conformational differences in the residues that make up the selectivity filter between the four subunits that form the ion channel and the inner helix of the ion channel. The crystallographic structure also identifies a side-entry, ion-conduction pathway for Na+ permeation that is unique to NaK. NMR studies and molecular dynamics simulations confirmed the dynamical nature of the top part of the selectivity filter and the inner helix in NaK as also observed in the crystal structure. Taken together, these results indicate that the structural plasticity of the selectivity filter combined with the dynamics of the inner helix of NaK are vital for the efficient conduction of different ions through the non-selective ion channel of NaK.

Pore-forming transmembrane domains control ion selectivity and selectivity filter conformation in the KirBac1.1 potassium channel

Potassium (K⁺) channels are membrane proteins with the remarkable ability to very selectively conduct K⁺ ions across the membrane. High-resolution structures have revealed that dehydrated K⁺ ions permeate through the narrowest region of the pore, formed by the backbone carbonyls of the signature selectivity filter (SF) sequence TxGYG. However, the existence of nonselective channels with similar SF sequences, as well as effects of mutations in other regions on selectivity, suggest that the SF is not the sole determinant of selectivity. We changed the selectivity of the KirBac1.1 channel by introducing mutations at residue I131 in transmembrane helix 2 (TM2). These mutations increase Na⁺ flux in the absence of K⁺ and introduce significant proton conductance. Consistent with K⁺ channel crystal structures, single-molecule FRET experiments show that the SF is conformationally constrained and stable in high-K⁺ conditions but undergoes transitions to dilated low-FRET states in high-Na⁺/low-K⁺ conditions. Relative to wild-type channels, I131M mutants exhibit marked shifts in the K⁺ and Na⁺ dependence of SF dynamics to higher K⁺ and lower Na⁺ concentrations. These results illuminate the role of I131, and potentially other structural elements outside the SF, in controlling ion selectivity, by suggesting that the physical interaction of these elements with the SF contributes to the relative stability of the constrained K⁺-induced SF configuration versus nonselective dilated conformations.

Structural mechanisms of gating and selectivity of human rod CNGA1 channel

Mammalian cyclic nucleotide-gated (CNG) channels play an essential role in the signal transduction of the visual and olfactory sensory systems. Here we reveal the structural mechanism of ligand gating in human rod CNGA1 channel by determining its cryo-EM structures in both the apo closed and cGMP-bound open states. Distinct from most other members of voltage-gated tetrameric cation channels, CNGA1 forms a central channel gate in the middle of the membrane, occluding the central cavity. Structural analyses of ion binding profiles in the selectivity filters of the wild-type channel and the E365Q filter mutant allow us to unambiguously define the two Ca²⁺ binding sites inside the selectivity filter, providing structural insights into Ca²⁺ blockage and permeation in CNG channels. The structure of the E365Q mutant also reveals two alternative side-chain conformations at Q365, providing a plausible explanation for the voltage-dependent gating of CNG channel acquired upon E365 mutation.

Inferring functional units in ion channel pores via relative entropy

Coarse-grained protein models approximate the first-principle physical potentials. Among those modeling approaches, the relative entropy framework yields promising and physically sound results, in which a mapping from the target protein structure and dynamics to a model is defined and subsequently adjusted by an entropy minimization of the model parameters. Minimization of the relative entropy is equivalent to maximization of the likelihood of reproduction of (configurational ensemble) observations by the model. In this study, we extend the relative entropy minimization procedure beyond parameter fitting by a second optimization level, which identifies the optimal mapping to a (dimension-reduced) topology. We consider anisotropic network models of a diverse set of ion channels and assess our findings by comparison to experimental results.

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.

K2P channel C-type gating involves asymmetric selectivity filter order-disorder transitions

K_2P potassium channels regulate cellular excitability using their selectivity filter (C-type) gate. C-type gating mechanisms, best characterized in homotetrameric potassium channels, remain controversial and are attributed to selectivity filter pinching, dilation, or subtle structural changes. The extent to which such mechanisms control C-type gating of innately heterodimeric K_2Ps is unknown. Here, combining K_2P2.1 (TREK-1) x-ray crystallography in different potassium concentrations, potassium anomalous scattering, molecular dynamics, and electrophysiology, we uncover unprecedented, asymmetric, potassium-dependent conformational changes that underlie K_2P C-type gating. These asymmetric order-disorder transitions, enabled by the K_2P heterodimeric architecture, encompass pinching and dilation, disrupt the S1 and S2 ion binding sites, require the uniquely long K_2P SF2-M4 loop and conserved "M3 glutamate network," and are suppressed by the K_2P C-type gate activator ML335. These findings demonstrate that two distinct C-type gating mechanisms can operate in one channel and underscore the SF2-M4 loop as a target for K_2P channel modulator development.

The structure of a potassium-selective ion channel reveals a hydrophobic gate regulating ion permeation

Protein dynamics are essential to function. One example of this is the various gating mechanisms within ion channels, which are transmembrane proteins that act as gateways into the cell. Typical ion channels switch between an open and closed state via a conformational transition which is often triggered by an external stimulus, such as ligand binding or pH and voltage differences. The atomic resolution structure of a potassium-selective ion channel named NaK2K has allowed us to observe that a hydro-phobic residue at the bottom of the selectivity filter, Phe92, appears in dual conformations. One of the two conformations of Phe92 restricts the diameter of the exit pore around the selectivity filter, limiting ion flow through the channel, while the other conformation of Phe92 provides a larger-diameter exit pore from the selectivity filter. Thus, it can be concluded that Phe92 acts as a hydro-phobic gate, regulating the flow of ions through the selectivity filter.

Ion permeation in potassium ion channels

The study of ion channels dates back to the 1950s and the groundbreaking electrophysiology work of Hodgin and Huxley, who used giant squid axons to probe how action potentials in neurons were initiated and propagated. More recently, several experiments using different structural biology techniques and approaches have been conducted to try to understand how potassium ions permeate through the selectivity filter of potassium ion channels. Two mechanisms of permeation have been proposed, and each of the two mechanisms is supported by different experiments. The key structural biology experiments conducted so far to try to understand how ion permeation takes place in potassium ion channels are reviewed and discussed. Protein crystallography has made, and continues to make, key contributions in this field, often through the use of anomalous scattering. Other structural biology techniques used to study the contents of the selectivity filter include solid-state nuclear magnetic resonance and two-dimensional infrared spectroscopy, both of which make clever use of isotopic labeling techniques, while molecular-dynamics simulations of ion flow through the selectivity filter have been enabled by the growing number of potassium ion channel structures deposited in the Protein Data Bank.

Conformational spread and dynamics in allostery of NMDA receptors

Allostery can be manifested as a combination of repression and activation in multidomain proteins allowing for fine tuning of regulatory mechanisms. Here we have used single molecule fluorescence resonance energy transfer (smFRET) and molecular dynamics simulations to study the mechanism of allostery underlying negative cooperativity between the two agonists glutamate and glycine in the NMDA receptor. These data show that binding of one agonist leads to conformational flexibility and an increase in conformational spread at the second agonist site. Mutational and cross-linking studies show that the dimer-dimer interface at the agonist-binding domain mediates the allostery underlying the negative cooperativity. smFRET on the transmembrane segments shows that they are tightly coupled in the unliganded and single agonist-bound form and only upon binding both agonists the transmembrane domain explores looser packing which would facilitate activation.

Selectivity filter modalities and rapid inactivation of the hERG1 channel

The human ether-á-go-go-related gene (hERG1) channel conducts small outward K⁺ currents that are critical for cardiomyocyte membrane repolarization. The gain-of-function mutation N629D at the outer mouth of the selectivity filter (SF) disrupts inactivation and K⁺-selective transport in hERG1, leading to arrhythmogenic phenotypes associated with long-QT syndrome. Here, we combined computational electrophysiology with Markov state model analysis to investigate how SF-level gating modalities control selective cation transport in wild-type (WT) and mutant (N629D) hERG1 variants. Starting from the recently reported cryogenic electron microscopy (cryo-EM) open-state channel structure, multiple microseconds-long molecular-dynamics (MD) trajectories were generated using different cation configurations at the filter, voltages, electrolyte concentrations, and force-field parameters. Most of the K⁺ permeation events observed in hERG1-WT simulations occurred at microsecond timescales, influenced by the spontaneous dehydration/rehydration dynamics at the filter. The SF region displayed conductive, constricted, occluded, and dilated states, in qualitative agreement with the well-documented flickering conductance of hERG1. In line with mutagenesis studies, these gating modalities resulted from dynamic interaction networks involving residues from the SF, outer-mouth vestibule, P-helices, and S5-P segments. We found that N629D mutation significantly stabilizes the SF in a state that is permeable to both K⁺ and Na⁺, which is reminiscent of the SF in the nonselective bacterial NaK channel. Increasing the external K⁺ concentration induced "WT-like" SF dynamics in N629D, in qualitative agreement with the recovery of flickering currents in experiments. Overall, our findings provide an understanding of the molecular mechanisms controlling selective transport in K⁺ channels with a nonconventional SF sequence.

Structural biology of thermoTRPV channels

Essential for physiology, transient receptor potential (TRP) channels constitute a large and diverse family of cation channels functioning as cellular sensors responding to a vast array of physical and chemical stimuli. Detailed understanding of the inner workings of TRP channels has been hampered by a lack of atomic structures, though structural biology of TRP channels has been an enthusiastic endeavor since their molecular identification two decades ago. These multi-domain integral membrane proteins, exhibiting complex polymodal gating behavior, have been a challenge for traditional X-ray crystallography, which requires formation of well-ordered protein crystals. X-ray structures remain limited to a few TRP channel proteins to date. Fortunately, recent breakthroughs in single-particle cryo-electron microscopy (cryo-EM) have enabled rapid growth of the number of TRP channel structures, providing tremendous insights into channel gating and regulation mechanisms and serving as foundations for further mechanistic investigations. This brief review focuses on recent exciting developments in structural biology of a subset of TRP channels, the calcium-permeable, non-selective and thermosensitive vanilloid subfamily of TRP channels (TRPV1-4), and the permeation and gating mechanisms revealed by structures.

Structure, function, and ion-binding properties of a K+ channel stabilized in the 2,4-ion-bound configuration

Here, we present the atomic resolution crystallographic structure, the function, and the ion-binding properties of the KcsA mutants, G77A and G77C, that stabilize the 2,4-ion-bound configuration (i.e., water, K⁺, water, K⁺-ion-bound configuration) of the K⁺ channel's selectivity filter. A full functional and thermodynamic characterization of the G77A mutant revealed wild-type-like ion selectivity and apparent K⁺-binding affinity, in addition to showing a lack of C-type inactivation gating and a marked reduction in its single-channel conductance. These structures validate, from a structural point of view, the notion that 2 isoenergetic ion-bound configurations coexist within a K⁺ channel's selectivity filter, which fully agrees with the water-K⁺-ion-coupled transport detected by streaming potential measurements.

Crystallization of a potassium ion channel and X-ray and neutron data collection

The mechanism by which potassium ions are transported through ion channels is currently being investigated by several groups using many different techniques. Clarification of the location of water molecules during transport is central to understanding how these integral membrane proteins function. Neutrons have a unique sensitivity to both hydrogen and potassium, rendering neutron crystallography capable of distinguishing waters from K+ ions. Here, the collection of a complete neutron data set from a potassium ion channel to a resolution of 3.55 Å using the Macromolecular Neutron Diffractometer (MaNDi) is reported. A room-temperature X-ray data set was also collected from the same crystal to a resolution of 2.50 Å. Upon further refinement, these results will help to further clarify the ion/water population within the selectivity filter of potassium ion channels.

Effects of Low Intensity Focused Ultrasound on Liposomes Containing Channel proteins

The ability to reversibly and non-invasively modulate region-specific brain activity in vivo suggests Low Intensity Focused Ultrasound (LIFU) as potential therapeutics for neurological dysfunctions such as epilepsy and Parkinson's disease. While in vivo studies provide evidence of the bioeffects of LIFU on neuronal activity, they merely hint at potential mechanisms but do not fully explain how this technology achieves these effects. One potential hypothesis is that LIFU produces local membrane depolarization by mechanically perturbing the neuronal cell membrane, or activating channels or other proteins embedded in the membrane. Proteins that sense mechanical perturbations of the membrane, such as those gated by membrane tension, are prime candidates for activating in response to LIFU and thus leading to the neurological responses that have been measured. Here we use the bacterial mechanosensitive channel MscL, which has been purified and reconstituted in liposomes, to determine how LIFU may affect the activation of this membrane-tension gated channel. Two bacterial voltage-gated channels, KvAP and NaK2K F92A channels were also studied. Surprisingly, the results suggest that ultrasound modulation and membrane perturbation does not induce channel gating, but rather induces pore formation at the membrane protein-lipid interface. However, in vesicles with high MscL mechanosensitive channel concentrations, apparent decreases in pore formation are observed, suggesting that this membrane-tension-sensitive protein may serve to increase the elasticity of the membrane, presumably because of expansion of the channel in the plane of the membrane independent of channel gating.

Anomalous X-ray diffraction studies of ion transport in K+ channels

Potassium ion channels utilize a highly selective filter to rapidly transport K⁺ ions across cellular membranes. This selectivity filter is composed of four binding sites which display almost equal electron density in crystal structures with high potassium ion concentrations. This electron density can be interpreted to reflect a superposition of alternating potassium ion and water occupied states or as adjacent potassium ions. Here, we use single wavelength anomalous dispersion (SAD) X-ray diffraction data collected near the potassium absorption edge to show experimentally that all ion binding sites within the selectivity filter are fully occupied by K⁺ ions. These data support the hypothesis that potassium ion transport occurs by direct Coulomb knock-on, and provide an example of solving the phase problem by K-SAD.

The number of K⁺ occupied binding sites in the selectivity filter of potassium ion channels is still under debate. Here, the authors collect diffraction data on the K⁺ selective NaK channel NaK2K at a wavelength of 3.35 Å, close to the K absorption edge, revealing that all four binding sites in the selectivity filter are fully occupied by K⁺ ions.

Mapping the Conformational Landscape of Glutamate Receptors Using Single Molecule FRET

The ionotropic glutamate receptors mediate excitatory neurotransmission in the mammalian central nervous system. These receptors provide a range of temporally diverse signals which stem from subunit composition and also from the inherent ability of each member to occupy multiple functional states, the distribution of which can be altered by small molecule modulators and binding partners. Hence it becomes essential to characterize the conformational landscape of the receptors under this variety of different conditions. This has recently become possible due to single molecule fluorescence resonance energy transfer measurements, along with the rich foundation of existing structures allowing for direct correlations between conformational and functional diversity.

MicroED structure of the NaK ion channel reveals a Na+ partition process into the selectivity filter

Sodium (Na⁺) is a ubiquitous and important inorganic salt mediating many critical biological processes such as neuronal excitation, signaling, and facilitation of various transporters. The hydration states of Na⁺ are proposed to play critical roles in determining the conductance and the selectivity of Na⁺ channels, yet they are rarely captured by conventional structural biology means. Here we use the emerging cryo-electron microscopy (cryoEM) method micro-electron diffraction (MicroED) to study the structure of a prototypical tetrameric Na⁺-conducting channel, NaK, to 2.5 Å resolution from nano-crystals. Two new conformations at the external site of NaK are identified, allowing us to visualize a partially hydrated Na⁺ ion at the entrance of the channel pore. A process of dilation coupled with Na⁺ movement is identified leading to valuable insights into the mechanism of ion conduction and gating. This study lays the ground work for future studies using MicroED in membrane protein biophysics.

Through a MicroED structure of NaK ion channel, Shian Liu and Tamir Gonen identify a process of dilation coupled with Na⁺ movement, providing mechanistic insights into ion conduction and gating. This study lays the ground work for future studies using MicroED in membrane protein biophysics.

Membrane-spanning α-helical barrels as tractable protein-design targets

The rational (de novo) design of membrane-spanning proteins lags behind that for water-soluble globular proteins. This is due to gaps in our knowledge of membrane-protein structure, and experimental difficulties in studying such proteins compared to water-soluble counterparts. One limiting factor is the small number of experimentally determined three-dimensional structures for transmembrane proteins. By contrast, many tens of thousands of globular protein structures provide a rich source of 'scaffolds' for protein design, and the means to garner sequence-to-structure relationships to guide the design process. The α-helical coiled coil is a protein-structure element found in both globular and membrane proteins, where it cements a variety of helix-helix interactions and helical bundles. Our deep understanding of coiled coils has enabled a large number of successful de novo designs. For one class, the α-helical barrels-that is, symmetric bundles of five or more helices with central accessible channels-there are both water-soluble and membrane-spanning examples. Recent computational designs of water-soluble α-helical barrels with five to seven helices have advanced the design field considerably. Here we identify and classify analogous and more complicated membrane-spanning α-helical barrels from the Protein Data Bank. These provide tantalizing but tractable targets for protein engineering and de novo protein design.This article is part of the themed issue 'Membrane pores: from structure and assembly, to medicine and technology'.

Cryo-EM and X-ray structures of TRPV4 reveal insight into ion permeation and gating mechanisms

The transient receptor potential (TRP) channel TRPV4 participates in multiple biological processes, and numerous TRPV4 mutations underlie several distinct and devastating diseases. Here we present the cryo-EM structure of Xenopus tropicalis TRPV4 at 3.8-Å resolution. The ion-conduction pore contains an intracellular gate formed by the inner helices, but lacks any extracellular gate in the selectivity filter, as observed in other TRPV channels. Anomalous X-ray diffraction analyses identify a single ion-binding site in the selectivity filter, thus explaining TRPV4 nonselectivity. Structural comparisons with other TRP channels and distantly related voltage-gated cation channels reveal an unprecedented, unique packing interface between the voltage-sensor-like domain and the pore domain, suggesting distinct gating mechanisms. Moreover, our structure begins to provide mechanistic insights to the large set of pathogenic mutations, offering potential opportunities for drug development.

Exploring the Viral Channel KcvPBCV-1 Function via Computation

Viral potassium channels (Kcv) are homologous to the pore module of complex \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {K}^+$$\end{document}K+-selective ion channels of cellular organisms. Due to their relative simplicity, they have attracted interest towards understanding the principles of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\hbox {K}^+$$\end{document}K+ conduction and channel gating. In this work, we construct a homology model of the \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {Kcv}}_{\text{PBCV-1}}$$\end{document}KcvPBCV-1 open state, which we validate by studying the binding of known blockers and by monitoring ion conduction through the channel. Molecular dynamics simulations of this model reveal that the re-orientation of selectivity filter carbonyl groups coincides with the transport of potassium ions, suggesting a possible mechanism for fast gating. In addition, we show that the voltage sensitivity of this mechanism can originate from the relocation of potassium ions inside the selectivity filter. We also explore the interaction of \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hbox {Kcv}}_{\text{PBCV-1}}$$\end{document}KcvPBCV-1 with the surrounding bilayer and observe the binding of lipids in the area between two adjacent subunits. The model is available to the scientific community to further explore the structure/function relationship of Kcv channels.

A single NaK channel conformation is not enough for non-selective ion conduction

NaK and other non-selective channels are able to conduct both sodium (Na⁺) and potassium (K⁺) with equally high efficiency. In contrast to previous crystallographic results, we show that the selectivity filter (SF) of NaK in native-like lipid membranes adopts two distinct conformations that are stabilized by either Na⁺ or K⁺ ions. The atomic differences of these conformations are resolved by solid-state NMR (ssNMR) spectroscopy and molecular dynamics (MD) simulations. Besides the canonical K⁺ permeation pathway, we identify a side entry ion-conduction pathway for Na⁺ permeation unique to NaK. Moreover, under otherwise identical conditions ssNMR spectra of the K⁺ selective NaK mutant (NaK2K) reveal only a single conformational state. Therefore, we propose that structural plasticity within the SF and the selection of these conformations by different ions are key molecular determinants for highly efficient conduction of different ions in non-selective cation channels.

The structure-energy landscape of NMDA receptor gating

N-Methyl-D-aspartate (NMDA) receptors are the main calcium-permeable excitatory receptors in the mammalian central nervous system. The NMDA receptor gating is complex, exhibiting multiple closed, open, and desensitized states; however, central questions regarding the conformations and energetics of the transmembrane domains as they relate to the gating states are still unanswered. Here, using single-molecule Förster resonance energy transfer (smFRET), we map the energy landscape of the first transmembrane segment of the Rattus norvegicus NMDA receptor under resting and various liganded conditions. These results show kinetically and structurally distinct changes associated with apo, agonist-bound, and inhibited receptors linked by a linear mechanism of gating at this site. Furthermore, the smFRET data suggest that allosteric inhibition by zinc occurs by an uncoupling of the agonist-induced changes at the extracellular domains from the gating motions leading to an apo-like state, while dizocilpine, a pore blocker, stabilizes multiple closely packed transmembrane states.

The lysosomal potassium channel TMEM175 adopts a novel tetrameric architecture

TMEM175 is a lysosomal K⁺ channel that is important for maintaining the membrane potential and pH stability in lysosomes. It contains two homologous copies of a six-transmembrane-helix (6-TM) domain, which has no sequence homology to the canonical tetrameric K⁺ channels and lacks the TVGYG selectivity filter motif found in these channels. The prokaryotic TMEM175 channel, which is present in a subset of bacteria and archaea, contains only a single 6-TM domain and functions as a tetramer. Here, we present the crystal structure of a prokaryotic TMEM175 channel from Chamaesiphon minutus, CmTMEM175, the architecture of which represents a completely different fold from that of canonical K⁺ channels. All six transmembrane helices of CmTMEM175 are tightly packed within each subunit without undergoing domain swapping. The highly conserved TM1 helix acts as the pore-lining inner helix, creating an hourglass-shaped ion permeation pathway in the channel tetramer. Three layers of hydrophobic residues on the carboxy-terminal half of the TM1 helices form a bottleneck along the ion conduction pathway and serve as the selectivity filter of the channel. Mutagenesis analysis suggests that the first layer of the highly conserved isoleucine residues in the filter is primarily responsible for channel selectivity. Thus, the structure of CmTMEM175 represents a novel architecture of a tetrameric cation channel whose ion selectivity mechanism appears to be distinct from that of the classical K⁺ channel family.

All atom NMDA receptor transmembrane domain model development and simulations in lipid bilayers and water

N-methyl-d-aspartate receptors (NMDARs) are members of the ionotropic glutamate receptor family that mediate excitatory synaptic transmission in the central nervous system. The channels of NMDARs are permeable to Ca²⁺ but blocked by Mg²⁺, distinctive properties that underlie essential brain processes such as induction of synaptic plasticity. However, due to limited structural information about the NMDAR transmembrane ion channel forming domain, the mechanism of divalent cation permeation and block is understood poorly. In this paper we developed an atomistic model of the transmembrane domain (TMD) of NMDARs composed of GluN1 and GluN2A subunits (GluN1/2A receptors). The model was generated using (a) a homology model based on the structure of the NaK channel and a partially resolved structure of an AMPA receptor (AMPAR), and (b) a partially resolved X-ray structure of GluN1/2B NMDARs. Refinement and extensive Molecular Dynamics (MD) simulations of the NMDAR TMD model were performed in explicit lipid bilayer membrane and water. Targeted MD with simulated annealing was introduced to promote structure refinement. Putative positions of the Mg²⁺ and Ca²⁺ ions in the ion channel divalent cation binding site are proposed. Differences in the structural and dynamic behavior of the channel protein in the presence of Mg²⁺ or Ca²⁺ are analyzed. NMDAR protein conformational flexibility was similar with no ion bound to the divalent cation binding site and with Ca²⁺ bound, whereas Mg²⁺ binding reduced protein fluctuations. While bound at the binding site both ions retained their preferred ligand coordination numbers: 6 for Mg²⁺, and 7–8 for Ca²⁺. Four asparagine side chain oxygens, a back-bone oxygen, and a water molecule participated in binding a Mg²⁺ ion. The Ca²⁺ ion first coordination shell ligands typically included four to five side-chain oxygen atoms of the binding site asparagine residues, two water molecules and zero to two backbone oxygens of the GluN2B subunits. These results demonstrate the importance of high-resolution channel structures for elucidation of mechanisms of NMDAR permeation and block.

AnglerFish: a webserver for defining the geometry of α-helices in membrane proteins

Summary

Integral membrane proteins that form helical pores and bundles constitute major drug targets, and many of their structures have been defined by crystallography and cryo-electron microscopy. The gating of channels and ligand binding of transporters generally involve changes in orientation of one or more the constituent helices in the structures. At present there is no standard easily accessible means for defining the orientation of a helix in a membrane protein structure. AnglerFish is a web-based tool for parameterising the angles of transmembrane helices based on PDB coordinates, with the helical orientations defined by the angles ‘tilt’ and ‘swing’. AnglerFish is particularly useful for defining changes in structure between different states, including both symmetric and asymmetric transitions, and can be used to quantitate differences between related structures or different subunits within the same structure.

Availability and Implementation

AnglerFish is freely available at http://anglerfish.cryst.bbk.ac.uk. The website is implemented in Perl-cgi and Apache and operation in all major browsers is supported. The source code is available at GitHub.

Supplementary information

Supplementary data are available at Bioinformatics online.

Structures of the Human HCN1 Hyperpolarization-Activated Channel

Hyperpolarization-activated cyclic nucleotide-gated (HCN) channels underlie the control of rhythmic activity in cardiac and neuronal pacemaker cells. In HCN, the polarity of voltage dependence is uniquely reversed. Intracellular cyclic adenosine monophosphate (cAMP) levels tune the voltage response, enabling sympathetic nerve stimulation to increase the heart rate. We present cryo-electron microscopy structures of the human HCN channel in the absence and presence of cAMP at 3.5 Å resolution. HCN channels contain a K⁺ channel selectivity filter-forming sequence from which the amino acids create a unique structure that explains Na⁺ and K⁺ permeability. The voltage sensor adopts a depolarized conformation, and the pore is closed. An S4 helix of unprecedented length extends into the cytoplasm, contacts the C-linker, and twists the inner helical gate shut. cAMP binding rotates cytoplasmic domains to favor opening of the inner helical gate. These structures advance understanding of ion selectivity, reversed polarity gating, and cAMP regulation in HCN channels.

A reduced mechanical model for cAMP-modulated gating in HCN channels

We developed an in silico mechanical model to analyze the process of cAMP-induced conformational modulations in hyperpolarization-activated cyclic nucleotide-gated (HCN) channels, which conduct cations across the membrane of mammalian heart and brain cells. The structural analysis reveals a quaternary twist in the cytosolic parts of the four subunits in the channel tetramer. This motion augments the intrinsic dynamics of the very same protein structure. The pronounced differences between the cAMP bound and unbound form include a mutual interaction between the C-linker of the cyclic nucleotide binding domain (CNBD) and the linker between the S4 and S5 transmembrane domain of the channel. This allows a mechanistic annotation of the twisting motion in relation to the allosteric modulation of voltage-dependent gating of this channel by cAMP.

Divalent ions are potential permeating blockers of the non-selective NaK ion channel: combined QM and MD based investigations

The interplay between the hydration energy barrier and optimum site-selectivity controls the permeation and blocking features of divalent metal ions.

The Outer Pore and Selectivity Filter of TRPA1

TRPA1 (transient-receptor-potential-related ion channel with ankyrin domains) is a direct receptor or indirect effector for a wide variety of nociceptive signals, and thus is a compelling target for development of analgesic pharmaceuticals such as channel blockers. Recently, the structure of TRPA1 was reported, providing insights into channel assembly and pore architecture. Here we report whole-cell and single-channel current recordings of wild-type human TRPA1 as well as TRPA1 bearing point mutations of key charged residues in the outer pore. These measurements demonstrate that the glutamate at position 920 plays an important role in collecting cations into the mouth of the pore, by changing the effective surface potential by ~16 mV, while acidic residues further out have little effect on permeation. Electrophysiology experiments also confirm that the aspartate residue at position 915 represents a constriction site of the TRPA1 pore and is critical in controlling ion permeation.

Structural and functional characterization of a calcium-activated cation channel from Tsukamurella paurometabola

The selectivity filter is an essential functional element of K⁺ channels that is highly conserved both in terms of its primary sequence and its three-dimensional structure. Here, we investigate the properties of an ion channel from the Gram-positive bacterium Tsukamurella paurometabola with a selectivity filter formed by an uncommon proline-rich sequence. Electrophysiological recordings show that it is a non-selective cation channel and that its activity depends on Ca²⁺ concentration. In the crystal structure, the selectivity filter adopts a novel conformation with Ca²⁺ ions bound within the filter near the pore helix where they are coordinated by backbone oxygen atoms, a recurrent motif found in multiple proteins. The binding of Ca²⁺ ion in the selectivity filter controls the widening of the pore as shown in crystal structures and in molecular dynamics simulations. The structural, functional and computational data provide a characterization of this calcium-gated cationic channel.

Tetrameric cationic channels specificity is determined by the sequence and structural conformation of their selectivity filter. Here, the authors show that a cationic channel from Tsukamurella paurometabola is non-selective due to a Ca²⁺-binding motif within its unusual proline-rich filter.

Can I solve my structure by SAD phasing? Planning an experiment, scaling data and evaluating the useful anomalous correlation and anomalous signal

A key challenge in the SAD phasing method is solving a structure when the anomalous signal-to-noise ratio is low. Here, algorithms and tools for evaluating and optimizing the useful anomalous correlation and the anomalous signal in a SAD experiment are described. A simple theoretical framework [Terwilliger et al. (2016), Acta Cryst. D72, 346-358] is used to develop methods for planning a SAD experiment, scaling SAD data sets and estimating the useful anomalous correlation and anomalous signal in a SAD data set. The phenix.plan_sad_experiment tool uses a database of solved and unsolved SAD data sets and the expected characteristics of a SAD data set to estimate the probability that the anomalous substructure will be found in the SAD experiment and the expected map quality that would be obtained if the substructure were found. The phenix.scale_and_merge tool scales unmerged SAD data from one or more crystals using local scaling and optimizes the anomalous signal by identifying the systematic differences among data sets, and the phenix.anomalous_signal tool estimates the useful anomalous correlation and anomalous signal after collecting SAD data and estimates the probability that the data set can be solved and the likely figure of merit of phasing.