Maximum likelihood estimation of aggregated Markov processes

Increasing the accuracy of single-molecule data analysis using tMAVEN

Time-dependent single-molecule experiments contain rich kinetic information about the functional dynamics of biomolecules. A key step in extracting this information is the application of kinetic models, such as hidden Markov models (HMMs), which characterize the molecular mechanism governing the experimental system. Unfortunately, researchers rarely know the physicochemical details of this molecular mechanism a priori, which raises questions about how to select the most appropriate kinetic model for a given single-molecule data set and what consequences arise if the wrong model is chosen. To address these questions, we have developed and used time-series modeling, analysis, and visualization environment (tMAVEN), a comprehensive, open-source, and extensible software platform. tMAVEN can perform each step of the single-molecule analysis pipeline, from preprocessing to kinetic modeling to plotting, and has been designed to enable the analysis of a single-molecule data set with multiple types of kinetic models. Using tMAVEN, we have systematically investigated mismatches between kinetic models and molecular mechanisms by analyzing simulated examples of prototypical single-molecule data sets exhibiting common experimental complications, such as molecular heterogeneity, with a series of different types of HMMs. Our results show that no single kinetic modeling strategy is mathematically appropriate for all experimental contexts. Indeed, HMMs only correctly capture the underlying molecular mechanism in the simplest of cases. As such, researchers must modify HMMs using physicochemical principles to avoid the risk of missing the significant biological and biophysical insights into molecular heterogeneity that their experiments provide. By enabling the facile, side-by-side application of multiple types of kinetic models to individual single-molecule data sets, tMAVEN allows researchers to carefully tailor their modeling approach to match the complexity of the underlying biomolecular dynamics and increase the accuracy of their single-molecule data analyses.

Mechanism of hydrophobic gating in the acetylcholine receptor channel pore

Neuromuscular acetylcholine receptors (AChRs) are hetero-pentameric, ligand-gated ion channels. The binding of the neurotransmitter acetylcholine (ACh) to two target sites promotes a global conformational change of the receptor that opens the channel and allows ion conduction through the channel pore. Here, by measuring free-energy changes from single-channel current recordings and using molecular dynamics simulations, we elucidate how a constricted hydrophobic region acts as a "gate" to regulate the channel opening in the pore of AChRs. Mutations of gate residues, including those implicated in congenital myasthenia syndrome, lower the permeation barrier of the channel substantially and increase the unliganded gating equilibrium constant (constitutive channel openings). Correlations between hydrophobicity and the observed free-energy changes, supported by calculations of water densities in the wild-type versus mutant channel pores, provide evidence for hydrophobic wetting-dewetting transition at the gate. The analysis of a coupled interaction network provides insight into the molecular mechanism of closed- versus open-state conformational changes at the gate. Studies of the transition state by "phi"(φ)-value analysis indicate that agonist binding serves to stabilize both the transition and the open state. Intersubunit interaction energy measurements and molecular dynamics simulations suggest that channel opening involves tilting of the pore-lining M2 helices, asymmetric outward rotation of amino acid side chains, and wetting transition of the gate region that lowers the barrier to ion permeation and stabilizes the channel open conformation. Our work provides new insight into the hydrophobic gate opening and shows why the gate mutations result in constitutive AChR channel activity.

Increasing the accuracy of single-molecule data analysis using tMAVEN

Time-dependent single-molecule experiments contain rich kinetic information about the functional dynamics of biomolecules. A key step in extracting this information is the application of kinetic models, such as hidden Markov models (HMMs), which characterize the molecular mechanism governing the experimental system. Unfortunately, researchers rarely know the physico-chemical details of this molecular mechanism a priori, which raises questions about how to select the most appropriate kinetic model for a given single-molecule dataset and what consequences arise if the wrong model is chosen. To address these questions, we have developed and used time-series Modeling, Analysis, and Visualization ENvironment (tMAVEN), a comprehensive, open-source, and extensible software platform. tMAVEN can perform each step of the single-molecule analysis pipeline, from pre-processing to kinetic modeling to plotting, and has been designed to enable the analysis of a single-molecule dataset with multiple types of kinetic models. Using tMAVEN, we have systematically investigated mismatches between kinetic models and molecular mechanisms by analyzing simulated examples of prototypical single-molecule datasets exhibiting common experimental complications, such as molecular heterogeneity, with a series of different types of HMMs. Our results show that no single kinetic modeling strategy is mathematically appropriate for all experimental contexts. Indeed, HMMs only correctly capture the underlying molecular mechanism in the simplest of cases. As such, researchers must modify HMMs using physico-chemical principles to avoid the risk of missing the significant biological and biophysical insights into molecular heterogeneity that their experiments provide. By enabling the facile, side-by-side application of multiple types of kinetic models to individual single-molecule datasets, tMAVEN allows researchers to carefully tailor their modeling approach to match the complexity of the underlying biomolecular dynamics and increase the accuracy of their single-molecule data analyses.

Agonist efficiency links binding and gating in a nicotinic receptor

Receptors signal by switching between resting (C) and active (O) shapes ('gating') under the influence of agonists. The receptor's maximum response depends on the difference in agonist binding energy, O minus C. In nicotinic receptors, efficiency (η) represents the fraction of agonist binding energy applied to a local rearrangement (an induced fit) that initiates gating. In this receptor, free energy changes in gating and binding can be interchanged by the conversion factor η. Efficiencies estimated from concentration-response curves (23 agonists, 53 mutations) sort into five discrete classes (%): 0.56 (17), 0.51(32), 0.45(13), 0.41(26), and 0.31(12), implying that there are 5 C versus O binding site structural pairs. Within each class efficacy and affinity are corelated linearly, but multiple classes hide this relationship. η unites agonist binding with receptor gating and calibrates one link in a chain of coupled domain rearrangements that comprises the allosteric transition of the protein.

Impaired gating of γ- and ε-AChR respectively causes Escobar syndrome and fast-channel myasthenia

OBJECTIVE

To dissect the kinetic defects of acetylcholine receptor (AChR) γ subunit variant in an incomplete form of the Escobar syndrome without pterygium and compare it with those of a variant of corresponding residue in the AChR ε subunit in a congenital myasthenic syndrome (CMS).

METHODS

Whole exome sequencing, α-bungarotoxin binding assay, single channel patch-clamp recordings, and maximum likelihood analysis of channel kinetics.

RESULTS

We identified compound heterozygous variants in AChR γ and ε subunits in three Escobar syndrome (1-3) and three CMS patients (4-6), respectively. Each Escobar syndrome patient carries γP121R along with γV221Afs*44 in patients 1 and 2, and γY63* in patient 3. Three CMS patients share εP121T along with εR20W, εG-8R, and εY15H in patients 4, 5, and 6, respectively. Surface expressions of γP121R- and εP121T-AChR were 80% and 138% of the corresponding wild-type AChR, whereas εR20W, εG-8R, and εY15H reduced receptor expression to 27%, 35%, and 30% of wild-type εAChR, respectively. γV221Afs*44 and γY63* are null variants. Thus, γP121R and εP121T determine the phenotype. γP121R and εP121T shorten channel opening burst duration to 28% and 18% of corresponding wild-type AChR by reducing the channel gating equilibrium constant 44- and 63-fold, respectively.

INTERPRETATION

Similar impairment of channel gating efficiency of a corresponding P121 residue in the acetylcholine-binding site of the AChR γ and ε subunits causes Escobar syndrome without pterygium and fast-channel CMS, respectively, suggesting that therapy for the fast-channel CMS will benefit Escobar syndrome.

2D-dwell-time analysis with simulations of ion-channel gating using high-performance computing

Single-channel patch-clamp recordings allow observing the action of a single protein complex in real time and hence the deduction of the underlying conformational changes in the ion-channel protein. Commonly, recordings are modeled using hidden Markov chains, connecting open and closed states in the experimental data with protein conformations. The rates between states denote transition probabilities that could be modified by membrane voltage or ligand binding. Modeling algorithms have to deal with limited recording bandwidth and a very noisy background. It was previously shown that the fit of two-dimensional (2D)-dwell-time histograms with simulations is very robust in that regard. Errors introduced by the low-pass filter or noise cancel out to a certain degree when comparing experimental and simulated data. In addition, the topology of models (that is, the chain of open and closed states) could be inferred from 2D-histograms. However, the 2D-fit was never applied to its full potential. A major reason may be the extremely time-consuming and often unreliable fitting process, due to the stochastic variability in the simulations. We have now solved these issues by introducing a message-passing interface (MPI) allowing massive parallel computing on a high-performance computing (HPC) cluster and obtaining ensemble solutions. With ensembles, we have demonstrated how important ranked solutions are for difficult tasks related to a noisy background, fast gating events beyond the corner frequency of the low-pass filter, and topology estimation of the underlying Markov model. Finally, we have shown that, by combining the objective function of the 2D-fit with the deviation of the current amplitude distributions, automatic determination of the current level of the conducting state is possible, even with an apparent current reduction due to low-pass filtering. Making use of an HPC cluster, the power of 2D-dwell-time analysis can be used to its fullest with minor input of the experimenter.

The pathogenic N650K variant in the GluN1 subunit regulates the trafficking, conductance, and pharmacological properties of NMDA receptors

N-methyl-D-aspartate receptors (NMDARs) play an essential role in excitatory neurotransmission in the mammalian brain, and their physiological importance is underscored by the large number of pathogenic mutations that have been identified in the receptor's GluN subunits and associated with a wide range of diseases and disorders. Here, we characterized the functional and pharmacological effects of the pathogenic N650K variant in the GluN1 subunit, which is associated with developmental delay and seizures. Our microscopy experiments showed that when expressed in HEK293 cells (from ATCC®), the GluN1-N650K subunit increases the surface expression of both GluN1/GluN2A and GluN1/GluN2B receptors, but not GluN1/GluN3A receptors, consistent with increased surface expression of the GluN1-N650K subunit expressed in hippocampal neurons (from embryonic day 18 of Wistar rats of both sexes). Using electrophysiology, we found that the GluN1-N650K variant increases the potency of GluN1/GluN2A receptors to both glutamate and glycine but decreases the receptor's conductance and open probability. In addition, the GluN1-N650K subunit does not form functional GluN1/GluN2B receptors but does form fully functional GluN1/GluN3A receptors. Moreover, in the presence of extracellular Mg²⁺, GluN1-N650K/GluN2A receptors have a similar and increased response to ketamine and memantine, respectively, while the effect of both drugs had markedly slower onset and offset compared to wild-type GluN1/GluN2A receptors. Finally, we found that expressing the GluN1-N650K subunit in hippocampal neurons reduces excitotoxicity, and memantine shows promising neuroprotective effects in neurons expressing either wild-type GluN1 or the GluN1-N650K subunit. This study provides the functional and pharmacological characterization of NMDARs containing the GluN1-N650K variant.

Complex functional phenotypes of NMDA receptor disease variants

NMDA receptors have essential roles in the physiology of central excitatory synapses and their dysfunction causes severe neuropsychiatric symptoms. Recently, a series of genetic variants have been identified in patients, however, functional information about these variants is sparse and their role in pathogenesis insufficiently known. Here we investigate the mechanism by which two GluN2A variants may be pathogenic. We use molecular dynamics simulation and single-molecule electrophysiology to examine the contribution of GluN2A subunit-residues, P552 and F652, and their pathogenic substitutions, P552R and F652V, affect receptor functions. We found that P552 and F652 interact during the receptors' normal activity cycle; the interaction stabilizes receptors in open conformations and is required for a normal electrical response. Engineering shorter side-chains at these positions (P552A and/or F652V) caused a loss of interaction energy and produced receptors with severe gating, conductance, and permeability deficits. In contrast, the P552R side chain resulted in stronger interaction and produced a distinct, yet still drastically abnormal electrical response. These results identify the dynamic contact between P552 and F652 as a critical step in the NMDA receptor activation, and show that both increased and reduced communication through this interaction cause dysfunction. Results show that subtle differences in NMDA receptor primary structure can generate complex phenotypic alterations whose binary classification is too simplistic to serve as a therapeutic guide.

GPCR-mediated β-arrestin activation deconvoluted with single-molecule precision

β-arrestins bind G protein-coupled receptors to terminate G protein signaling and to facilitate other downstream signaling pathways. Using single-molecule fluorescence resonance energy transfer imaging, we show that β-arrestin is strongly autoinhibited in its basal state. Its engagement with a phosphopeptide mimicking phosphorylated receptor tail efficiently releases the β-arrestin tail from its N domain to assume distinct conformations. Unexpectedly, we find that β-arrestin binding to phosphorylated receptor, with a phosphorylation barcode identical to the isolated phosphopeptide, is highly inefficient and that agonist-promoted receptor activation is required for β-arrestin activation, consistent with the release of a sequestered receptor C tail. These findings, together with focused cellular investigations, reveal that agonism and receptor C-tail release are specific determinants of the rate and efficiency of β-arrestin activation by phosphorylated receptor. We infer that receptor phosphorylation patterns, in combination with receptor agonism, synergistically establish the strength and specificity with which diverse, downstream β-arrestin-mediated events are directed.

NMDA receptor channel gating control by the pre-M1 helix

The NMDA receptor (NMDAR) is an ionotropic glutamate receptor formed from the tetrameric assembly of GluN1 and GluN2 subunits. Within the flexible linker between the agonist binding domain (ABD) and the M1 helix of the pore-forming transmembrane helical bundle lies a two-turn, extracellular pre-M1 helix positioned parallel to the plasma membrane and in van der Waals contact with the M3 helix thought to constitute the channel gate. The pre-M1 helix is tethered to the bilobed ABD, where agonist-induced conformational changes initiate activation. Additionally, it is a locus for de novo mutations associated with neurological disorders, is near other disease-associated de novo sites within the transmembrane domain, and is a structural determinant of subunit-selective modulators. To investigate the role of the pre-M1 helix in channel gating, we performed scanning mutagenesis across the GluN2A pre-M1 helix and recorded whole-cell macroscopic and single channel currents from HEK293 cell-attached patches. We identified two residues at which mutations perturb channel open probability, the mean open time, and the glutamate deactivation time course. We identified a subunit-specific network of aromatic amino acids located in and around the GluN2A pre-M1 helix to be important for gating. Based on these results, we are able to hypothesize about the role of the pre-M1 helix in other NMDAR subunits based on sequence and structure homology. Our results emphasize the role of the pre-M1 helix in channel gating, implicate the surrounding amino acid environment in this mechanism, and suggest unique subunit-specific contributions of pre-M1 helices to GluN1 and GluN2 gating.

Sleep-related hypermotor epilepsy associated mutations uncover important kinetic roles of α4β2- nicotinic acetylcholine receptor intracellular structures

Sleep-related hypermotor epilepsy (SHE) is a group of seizure disorders prominently associated with mutations in nicotinic acetylcholine receptors (nAChR). The most prevalent central nervous system nAChR subtype contains α4 and β2 subunits, in two ratios. (α4β2)₂β2-nAChR have high agonist sensitivity (HS-isoform), whereas (α4β2)₂α4-nAChR agonist responses exhibit a small high-sensitivity, and a predominant low-sensitivity, phase of function (LS-isoform). Multiple non-synonymous mutations in the second and third transmembrane domains of α4 and β2 subunits are associated with SHE. We recently demonstrated that two additional, SHE-associated, missense mutations in the major cytoplasmic loops of these subunits [α4(R336H) and β2(V337G)] cause increased macroscopic function-per receptor. Here, we use single-channel patch-clamp electrophysiology to show that these mutations influence single-channel amplitudes and open- and closed-state kinetics. Pure populations of HS- or LS-isoform α4β2-nAChR were expressed by injecting either 1:10 or 30:1 α4:β2 cRNA ratios, respectively, into Xenopus laevis oocytes. Functional properties of the resulting mutant α4β2-nAChR isoforms were compared to their wildtype counterparts. α4(R336H) subunit incorporation minimally affected single-channel amplitudes, whereas β2(V337G) subunit incorporation reduced them significantly in both isoforms. However, for both mutant subunits, increased function-per-receptor was predominantly caused by altered single channel kinetics. The α4(R336H) mutation primarily destabilizes desensitized states between openings. By contrast, the β2(V337G) mutation principally stabilizes receptor open states. The use of naturally-occurring and physiologically-impactful mutations has allowed us to define valuable new insights regarding the functional roles of nAChR intracellular domains. Further mechanistic context is provided by intracellular-domain structures recently published for other members of the Cys-loop receptor superfamily (α3β4-nAChR and 5-HT_3AR).

Agonist efficiency from concentration-response curves: Structural implications and applications

Agonists are evaluated by a concentration-response curve (CRC), with a midpoint (EC₅₀) that indicates potency, a high-concentration asymptote that indicates efficacy, and a low-concentration asymptote that indicates constitutive activity. A third agonist attribute, efficiency (η), is the fraction of binding energy that is applied to the conformational change that activates the receptor. We show that η can be calculated from EC₅₀ and the asymptotes of a CRC derived from either single-channel or whole-cell responses. For 20 agonists of skeletal muscle nicotinic receptors, the distribution of η-values is bimodal with population means at 51% (including acetylcholine, nornicotine, and dimethylphenylpiperazinium) and 40% (including epibatidine, varenicline, and cytisine). The value of η is related inversely to the size of the agonist's headgroup, with high- versus low-efficiency ligands having an average volume of 70 vs. 102 Å³. Most binding site mutations have only a small effect on acetylcholine efficiency, except for αY190A (35%), αW149A (60%), and those at αG153 (42%). If η is known, the EC₅₀ and high-concentration asymptote can be calculated from each other. Hence, an entire CRC can be estimated from the response to a single agonist concentration, and efficacy can be estimated from EC₅₀ of a CRC that has been normalized to 1. Given η, the level of constitutive activity can be estimated from a single CRC.

Evolution of mathematical models of cardiomyocyte electrophysiology

Advanced computational techniques and mathematical modeling have become more and more important to the study of cardiac electrophysiology. In this review, we provide a brief history of the evolution of cardiomyocyte electrophysiology models and highlight some of the most important ones that had a major impact on our understanding of the electrical activity of the myocardium and associated transmembrane ion fluxes in normal and pathological states. We also present the use of these models in the study of various arrhythmogenesis mechanisms, particularly the integration of experimental pharmacology data into advanced humanized models for in silico proarrhythmogenic risk prediction as an essential component of the Comprehensive in vitro Proarrhythmia Assay (CiPA) drug safety paradigm.

Palmitoylation Controls NMDA Receptor Function and Steroid Sensitivity

NMDARs are ligand-gated ion channels that cause an influx of Na⁺ and Ca²⁺ into postsynaptic neurons. The resulting intracellular Ca²⁺ transient triggers synaptic plasticity. When prolonged, it may induce excitotoxicity, but it may also activate negative feedback to control the activity of NMDARs. Here, we report that a transient rise in intracellular Ca²⁺ (Ca²⁺ challenge) increases the sensitivity of NMDARs but not AMPARs/kainate receptors to the endogenous inhibitory neurosteroid 20-oxo-5β-pregnan-3α-yl 3-sulfate and to its synthetic analogs, such as 20-oxo-5β-pregnan-3α-yl 3-hemipimelate (PAhPim). In cultured hippocampal neurons, 30 μm PAhPim had virtually no effect on NMDAR responses; however, following the Ca²⁺ challenge, it inhibited the responses by 62%; similarly, the Ca²⁺ challenge induced a 3.7-fold decrease in the steroid IC₅₀ on recombinant GluN1/GluN2B receptors. The increase in the NMDAR sensitivity to PAhPim was dependent on three cysteines (C849, C854, and C871) located in the carboxy-terminal domain of the GluN2B subunit, previously identified to be palmitoylated (Hayashi et al., 2009). Our experiments suggested that the Ca²⁺ challenge induced receptor depalmitoylation, and single-channel analysis revealed that this was accompanied by a 55% reduction in the probability of channel opening. Results of in silico modeling indicate that receptor palmitoylation promotes anchoring of the GluN2B subunit carboxy-terminal domain to the plasma membrane and facilitates channel opening. Depalmitoylation-induced changes in the NMDAR pharmacology explain the neuroprotective effect of PAhPim on NMDA-induced excitotoxicity. We propose that palmitoylation-dependent changes in the NMDAR sensitivity to steroids serve as an acute endogenous mechanism that controls NMDAR activity.SIGNIFICANCE STATEMENT There is considerable interest in negative allosteric modulators of NMDARs that could compensate for receptor overactivation by glutamate or de novo gain-of-function mutations in neurodevelopmental disorders. By a combination of electrophysiological, pharmacological, and computational techniques we describe a novel feedback mechanism regulating NMDAR activity. We find that a transient rise in intracellular Ca²⁺ increases NMDAR sensitivity to inhibitory neurosteroids in a process dependent on GluN2B subunit depalmitoylation. These results improve our understanding of the molecular mechanisms of steroid action at the NMDAR and indeed of the basic properties of this important glutamate-gated ion channel and may aid in the development of therapeutics for treating neurologic and psychiatric diseases related to overactivation of NMDARs without affecting normal physiological functions.

Orthosteric and Allosteric Activation of Human 5-HT3A Receptors

The serotonin type 3 receptor (5-HT₃) is a ligand-gated ion channel that converts the binding of the neurotransmitter serotonin (5-HT) into a transient cation current that mediates fast excitatory responses in peripheral and central nervous systems. Information regarding the activation and modulation of the human 5-HT₃ type A receptor has been based only on macroscopic current measurements because of its low ion conductance. By constructing a high-conductance human 5-HT₃A receptor, we here revealed mechanistic information regarding the orthosteric activation by 5-HT and by the partial agonist tryptamine, and the allosteric activation by the terpenoids, carvacrol, and thymol. Terpenoids potentiated macroscopic currents elicited by the orthosteric agonist and directly elicited currents with slow-rising phases and submaximal amplitudes. At the single-channel level, activation by orthosteric and allosteric agonists appeared as openings in quick succession (bursts) that showed no ligand concentration dependence. Bursts were grouped into long-duration clusters in the presence of 5-HT and even longer in the presence of terpenoids, whereas they remained isolated in the presence of tryptamine. Kinetic analysis revealed that allosteric and orthosteric activation mechanisms can be described by the same scheme that includes transitions of the agonist-bound receptor to closed intermediate states before opening (priming). Reduced priming explained the partial agonism of tryptamine; however, equilibrium constants for gating and priming were similar for 5-HT and terpenoid activation. Thus, our kinetic analysis revealed that terpenoids are efficacious agonists for 5-HT₃A receptors. These findings not only extend our knowledge about the human 5-HT₃A molecular function but also provide novel insights into the mechanisms of action of allosteric ligands, which are of increasing interest as therapeutic drugs in all the superfamily.

Direct Measurement of Single-Molecule Ligand-Receptor Interactions

Measuring the kinetics that govern ligand-receptor interactions is fundamental to our understanding of pharmacology. For ligand-gated ion channels, binding of an agonist triggers allosteric motions that open an integral ion-permeable pore. By mathematically modeling stochastic electrophysiological responses with high temporal resolution (ms), previous single channel studies have been able to infer the rate constants of ligands binding to these receptors. However, there are no reports of the direct measurement of the single-molecule binding events that are vital to how agonists exert their functional effects. For the first time, we report these direct measurements, the rate constants, and corresponding free energy changes, which describe the transitions between the different binding states. To achieve this, we use the super resolution technique: points accumulation for imaging in nanoscale topography (PAINT) to observe binding of ATP to orthosteric binding sites on the P2X1 receptor. Furthermore, an analysis of time-resolved single-molecule interactions is used to measure elementary rate constants and thermodynamic forces that drive the allosteric motions. These single-molecule measurements unequivocally establish the location of each binding states of the P2X1 receptor and the stochastic nature of the interaction with its native ligand. The analysis leads to the measurement of the forward and reverse rates from a weak ligand-binding state to a strong ligand binding state that is linked to allosteric motion and ion pore formation. These rates (k_α = 1.41 sec^-1 and k_β = 0.32 sec^-1) were then used to determine the free energy associated with this critical mechanistic step (3.7 kJ/mol). Importantly, the described methods can be readily applied to all ligand-gated ion channels, and more broadly to the molecular interactions of other classes of membrane proteins.

Transmembrane Epitope Delivery by Passive Protein Threading through the Pores of the OmpF Porin Trimer

Trimeric porins in the outer membrane (OM) of Gram-negative bacteria are the conduits by which nutrients and antibiotics diffuse passively into cells. The narrow gateways that porins form in the OM are also exploited by bacteriocins to translocate into cells by a poorly understood process. Here, using single-channel electrical recording in planar lipid bilayers in conjunction with protein engineering, we explicate the mechanism by which the intrinsically unstructured N-terminal translocation domain (IUTD) of the endonuclease bacteriocin ColE9 is imported passively across the Escherichia coli OM through OmpF. We show that the import is dominated by weak interactions of OmpF pores with binding epitopes within the IUTD that are orientationally biased and result in the threading of over 60 amino acids through 2 subunits of OmpF. Single-molecule kinetic analysis demonstrates that the IUTD enters from the extracellular side of OmpF and translocates to the periplasm where the polypeptide chain does an about turn in order to enter a neighboring subunit, only for some of these molecules to pop out of this second subunit before finally re-entering to form a stable complex. These intimately linked transport/binding processes generate an essentially irreversible, hook-like assembly that constrains an import activating peptide epitope between two subunits of the OmpF trimer.

A novel fast-channel myasthenia caused by mutation in β subunit of AChR reveals subunit-specific contribution of the intracellular M1-M2 linker to channel gating

Genetic variants causing the fast-channel congenital myasthenic syndrome (CMS) have been identified in the α, δ, and ε but not the β subunit of acetylcholine receptor (AChR). A 16-year-old girl with severe myasthenia had low-amplitude and fast-decaying miniature endplate potentials. Mutation analysis revealed two heteroallelic variants in CHRNB1 encoding the AChR β subunit: a novel c.812C>T (p.P248L) variant in M1-M2 linker (p.P271L in HGVS nomenclature), and a ~430 bp deletion causing loss of exon 8 leading to frame-shift and a premature stop codon (p.G251Dfs*21). P248 is conserved in all β subunits of different species, but not in other AChR subunits. Measurements of radio-labeled α-bungarotoxin binding show that βP248L reduces AChR expression to 60% of wild-type. Patch clamp recordings of ACh-elicited single channel currents demonstrate that βP248L shortens channel opening bursts from 3.3 ms to 1.2 ms, and kinetic analyses predict that the decay of the synaptic response is accelerated 2.4-fold due to reduced probability of channel reopening. Substituting βP248 with threonine, alanine or glycine reduces the burst duration to 2.3, 1.7, and 1.5 ms, respectively. In non-β subunits, substituting leucine for residues corresponding to βP248 prolongs the burst duration to 4.5 ms in the α subunit, shortens it to 2.2 ms in the δ subunit, and has no effect in the ε subunit. Conversely, substituting proline for residues corresponding to βP248 prolongs the burst duration to 8.7 ms in the α subunit, to 4.6 ms in the δ subunit, but has no effect in the ε subunit. Thus, this fast channel CMS is caused by the dual defects of βP248L in reducing expression of the mutant receptor and accelerating the decay of the synaptic response. The results also reveal subunit-specific contributions of the M1-M2 linker to the durations of channel opening bursts.

Ca2+-Dependent Inactivation of GluN2A and GluN2B NMDA Receptors Occurs by a Common Kinetic Mechanism

N-Methyl-d-aspartate (NMDA) receptors are Ca2+-permeable channels gated by glutamate and glycine that are essential for central excitatory transmission. Ca2+-dependent inactivation (CDI) is a regulatory feedback mechanism that reduces GluN2A-type NMDA receptor responses in an activity-dependent manner. Although CDI is mediated by calmodulin binding to the constitutive GluN1 subunit, prior studies suggest that GluN2B-type receptors are insensitive to CDI. We examined the mechanism of CDI subtype dependence using electrophysiological recordings of recombinant NMDA receptors expressed in HEK-293 cells. In physiological external Ca2+, we observed robust CDI of whole-cell GluN2A currents (0.42 ± 0.05) but no CDI in GluN2B currents (0.08 ± 0.07). In contrast, when Ca2+ was supplied intracellularly, robust CDI occurred for both GluN2A and GluN2B currents (0.75 ± 0.03 and 0.67 ± 0.02, respectively). To examine how the source of Ca2+ affects CDI, we recorded one-channel Na+ currents to quantify the receptor gating mechanism while simultaneously monitoring ionomycin-induced intracellular Ca2+ elevations with fluorometry. We found that CDI of both GluN2A and GluN2B receptors reflects receptor accumulation in long-lived closed (desensitized) states, suggesting that the observed subtype-dependent differences in macroscopic CDI reflect intrinsic differences in equilibrium open probabilities (Po). We tested this hypothesis by measuring substantial macroscopic CDI, in physiologic conditions, for high Po GluN2B receptors (GluN1A652Y/GluN2B). Together, these results show that Ca2+ flux produces activity-dependent inactivation for both GluN2A and GluN2B receptors and that the extent of CDI varies with channel Po. These results are consistent with CDI as an autoinhibitory feedback mechanism against excessive Ca2+ load during high Po activation.

X-ray structure of LeuT in an inward-facing occluded conformation reveals mechanism of substrate release

Neurotransmitter:sodium symporters (NSS) are conserved from bacteria to man and serve as targets for drugs, including antidepressants and psychostimulants. Here we report the X-ray structure of the prokaryotic NSS member, LeuT, in a Na⁺/substrate-bound, inward-facing occluded conformation. To obtain this structure, we were guided by findings from single-molecule fluorescence spectroscopy and molecular dynamics simulations indicating that L-Phe binding and mutation of the conserved N-terminal Trp8 to Ala both promote an inward-facing state. Compared to the outward-facing occluded conformation, our structure reveals a major tilting of the cytoplasmic end of transmembrane segment (TM) 5, which, together with release of the N-terminus but without coupled movement of TM1, opens a wide cavity towards the second Na⁺ binding site. The structure of this key intermediate in the LeuT transport cycle, in the context of other NSS structures, leads to the proposal of an intracellular release mechanism of substrate and ions in NSS proteins.

Projecting demands for renal replacement therapy in the Northern Territory: a stochastic Markov model

Objective The aim of the present study was to evaluate the potential effects of different health intervention strategies on demand for renal replacement therapy (RRT) services in the Northern Territory (NT). Methods A Markov chain simulation model was developed to estimate demand for haemodialysis (HD) and kidney transplantation (Tx) over the next 10 years, based on RRT registry data between 2002 and 2013. Four policy-relevant scenarios were evaluated: (1) increased Tx; (2) increased self-care dialysis; (3) reduced incidence of end-stage kidney disease (ESKD); and (4) reduced mortality. Results There were 957 new cases of ESKD during the study period, with most patients being Indigenous people (85%). The median age was 50 years at onset and 57 years at death, 12 and 13 years younger respectively than Australian medians. The prevalence of RRT increased 5.6% annually, 20% higher than the national rate (4.7%). If current trends continue (baseline scenario), the demand for facility-based HD (FHD) would approach 100000 treatments (95% confidence interval 75000-121000) in 2023, a 5% annual increase. Increasing Tx (0.3%), increasing self-care (5%) and reducing incidence (5%) each attenuate demand for FHD to ~70000 annually by 2023. Conclusions The present study demonstrates the effects of changing service patterns to increase Tx, self-care and prevention, all of which will substantially attenuate the growth in FHD requirements in the NT. What is known about the topic? The burden of ESKD is projected to increase in the NT, with demand for FHD doubling every 15 years. Little is known about the potential effect of changes in health policy and clinical practice on demand. What does this paper add? This study assessed the usefulness of a stochastic Markov model to evaluate the effects of potential policy changes on FHD demand. What are the implications for practitioners? The scenarios simulated by the stochastic Markov models suggest that changes in current ESKD management practices would have a large effect on future demand for FHD.

Modulation of the potassium channel KcsA by anionic phospholipids: Role of arginines at the non-annular lipid binding sites

The role of arginines R64 and R89 at non-annular lipid binding sites of KcsA, on the modulation of channel activity by anionic lipids has been investigated. In wild-type (WT) KcsA reconstituted into asolectin lipid membranes, addition of phosphatidic acid (PA) drastically reduces inactivation in macroscopic current recordings. Consistent to this, PA increases current amplitude, mean open time and open probability at the single channel level. Moreover, kinetic analysis reveals that addition of PA causes longer open channel lifetimes and decreased closing rate constants. Effects akin to those of PA on WT-KcsA are observed when R64 and/or R89 are mutated to alanine, regardless of the added anionic lipids. We interpret these results as a consequence of interactions between the arginines and the anionic PA bound to the non-annular sites. NMR data shows indeed that at least R64 is involved in binding PA. Moreover, molecular dynamics (MD) simulations predict that R64, R89 and surrounding residues such as T61, mediate persistent binding of PA to the non-annular sites. Channel inactivation depends on interactions within the inactivation triad (E71-D80-W67) behind the selectivity filter. Therefore, it is expected that such interactions are affected when PA binds the arginines at the non-annular sites. In support of this, MD simulations reveal that PA binding prevents interaction between R89 and D80, which seems critical to the effectiveness of the inactivation triad. This mechanism depends on the stability of the bound lipid, favoring anionic headgroups such as that of PA, which thrive on the positive charge of the arginines.

Bayesian-Estimated Hierarchical HMMs Enable Robust Analysis of Single-Molecule Kinetic Heterogeneity

Single-molecule kinetic experiments allow the reaction trajectories of individual biomolecules to be directly observed, eliminating the effects of population averaging and providing a powerful approach for elucidating the kinetic mechanisms of biomolecular processes. A major challenge to the analysis and interpretation of these experiments, however, is the kinetic heterogeneity that almost universally complicates the recorded single-molecule signal versus time trajectories (i.e., signal trajectories). Such heterogeneity manifests as changes and/or differences in the transition rates that are observed within individual signal trajectories or across a population of signal trajectories. Because characterizing kinetic heterogeneity can provide critical mechanistic information, we have developed a computational method that effectively and comprehensively enables such analysis. To this end, we have developed a computational algorithm and software program, hFRET, that uses the variational approximation for Bayesian inference to estimate the parameters of a hierarchical hidden Markov model, thereby enabling robust identification and characterization of kinetic heterogeneity. Using simulated signal trajectories, we demonstrate the ability of hFRET to accurately and precisely characterize kinetic heterogeneity. In addition, we use hFRET to analyze experimentally recorded signal trajectories reporting on the conformational dynamics of ribosomal pre-translocation (PRE) complexes. The results of our analyses demonstrate that PRE complexes exhibit kinetic heterogeneity, reveal the physical origins of this heterogeneity, and allow us to expand the current model of PRE complex dynamics. The methods described here can be applied to signal trajectories generated using any type of signal and can be easily extended to the analysis of signal trajectories exhibiting more complex kinetic behaviors. Moreover, variations of our approach can be easily developed to integrate kinetic data obtained from different experimental constructs and/or from molecular dynamics simulations of a biomolecule of interest.

Distinctive single-channel properties of α4β2-nicotinic acetylcholine receptor isoforms

Central nervous system nicotinic acetylcholine receptors (nAChR) are predominantly of the α4β2 subtype. Two isoforms exist, with high or low agonist sensitivity (HS-(α4β2)2β2- and LS-(α4β2)2α4-nAChR). Both isoforms exhibit similar macroscopic potency and efficacy values at low acetylcholine (ACh) concentrations, mediated by a common pair of high-affinity α4(+)/(-)β2 subunit binding interfaces. However LS-(α4β2)2α4-nAChR also respond to higher concentrations of ACh, acting at a third α4(+)/(-)α4 subunit interface. To probe isoform functional differences further, HS- and LS-α4β2-nAChR were expressed in Xenopus laevis oocytes and single-channel responses were assessed using cell-attached patch-clamp. In the presence of a low ACh concentration, both isoforms produce low-bursting function. HS-(α4β2)2β2-nAChR exhibit a single conductance state, whereas LS-(α4β2)2α4-nAChR display two distinctive conductance states. A higher ACh concentration did not preferentially recruit either conductance state, but did result in increased LS-(α4β2)2α4-nAChR bursting and reduced closed times. Introduction of an α4(+)/(-)α4-interface loss-of-function α4W182A mutation abolished these changes, confirming this site's role in mediating LS-(α4β2)2α4-nAChR responses. Small or large amplitude openings are highly-correlated within individual LS-(α4β2)2α4-nAChR bursts, suggesting that they arise from distinct intermediate states, each of which is stabilized by α4(+)/(-)α4 site ACh binding. These findings are consistent with α4(+)/(-)α4 subunit interface occupation resulting in allosteric potentiation of agonist actions at α4(+)/(-)β2 subunit interfaces, rather than independent induction of high conductance channel openings.

Molecular Modulation of Human α7 Nicotinic Receptor by Amyloid-β Peptides

Amyloid β peptide (Aβ) is a key player in the development of Alzheimer's disease (AD). It is the primary component of senile plaques in AD patients and is also found in soluble forms. Cholinergic activity mediated by α7 nicotinic receptors has been shown to be affected by Aβ soluble forms. To shed light into the molecular mechanism of this effect, we explored the direct actions of oligomeric Aβ_1-40 and Aβ_1-42 on human α7 by fluorescence spectroscopy and single-channel recordings. Fluorescence measurements using the conformational sensitive probe crystal violet (CrV) revealed that in the presence of Aβ α7 undergoes concentration-dependent conformational changes. Exposure of α7 to 100 pM Aβ changes CrV K_D towards that of the desensitized state. However, α7 is still reactive to high carbamylcholine (Carb) concentrations. These observations are compatible with the induction of active/desensitized states as well as of a novel conformational state in the presence of both Aβ and Carb. At 100 nM Aβ, α7 adopts a resting-state-like structure which does not respond to Carb, suggesting stabilization of α7 in a blocked state. In real time, we found that Aβ is capable of eliciting α7 channel activity either in the absence or presence of the positive allosteric modulator (PAM) PNU-120596. Activation by Aβ is favored at picomolar or low nanomolar concentrations and is not detected at micromolar concentrations. At high Aβ concentrations, the mean duration of activation episodes elicited by ACh in the presence of PNU-120596 is significantly reduced, an effect compatible with slow open-channel block. We conclude that Aβ directly affects α7 function by acting as an agonist and a negative modulator. Whereas the capability of low concentrations of Aβ to activate α7 could be beneficial, the reduced α7 activity in the presence of higher Aβ concentrations or its long exposure may contribute to the cholinergic signaling deficit and may be involved in the initiation and development of AD.

Efficiency measures the conversion of agonist binding energy into receptor conformational change

Receptors alternate between resting↔active conformations that bind agonists with low↔high affinity. Here, we define a new agonist attribute, energy efficiency (η), as the fraction of ligand-binding energy converted into the mechanical work of the activation conformational change. η depends only on the resting/active agonist-binding energy ratio. In a plot of activation energy versus binding energy (an "efficiency" plot), the slope gives η and the y intercept gives the receptor's intrinsic activation energy (without agonists; ΔG₀). We used single-channel electrophysiology to estimate η for eight different agonists and ΔG₀ in human endplate acetylcholine receptors (AChRs). From published equilibrium constants, we also estimated η for agonists of K_Ca1.1 (BK channels) and muscarinic, γ-aminobutyric acid, glutamate, glycine, and aryl-hydrocarbon receptors, and ΔG₀ for all of these except K_Ca1.1. Regarding AChRs, η is 48-56% for agonists related structurally to acetylcholine but is only ∼39% for agonists related to epibatidine; ΔG₀ is 8.4 kcal/mol in adult and 9.6 kcal/mol in fetal receptors. Efficiency plots for all of the above receptors are approximately linear, with η values between 12% and 57% and ΔG₀ values between 2 and 12 kcal/mol. Efficiency appears to be a general attribute of agonist action at receptor binding sites that is useful for understanding binding mechanisms, categorizing agonists, and estimating concentration-response relationships.

A structurally derived model of subunit-dependent NMDA receptor function

Key points

The kinetics of NMDA receptor (NMDAR) signalling are a critical aspect of the physiology of excitatory synaptic transmission in the brain.

Here we develop a mechanistic description of NMDAR function based on the receptor tetrameric structure and the principle that each agonist‐bound subunit must undergo some rate‐limiting conformational change after agonist binding, prior to channel opening.

By fitting this mechanism to single channel data using a new MATLAB‐based software implementation of maximum likelihood fitting with correction for limited time resolution, rate constants were derived for this mechanism that reflect distinct structural changes and predict the properties of macroscopic and synaptic NMDAR currents.

The principles applied here to develop a mechanistic description of the heterotetrameric NMDAR, and the software used in this analysis, can be equally applied to other heterotetrameric glutamate receptors, providing a unifying mechanistic framework to understanding the physiology of glutamate receptor signalling in the brain.

Abstract

NMDA receptors (NMDARs) are tetrameric complexes comprising two glycine‐binding GluN1 and two glutamate‐binding GluN2 subunits. Four GluN2 subunits encoded by different genes can produce up to 10 different di‐ and triheteromeric receptors. In addition, some neurological patients contain a de novo mutation or inherited rare variant in only one subunit. There is currently no mechanistic framework to describe tetrameric receptor function that can be extended to receptors with two different GluN1 or GluN2 subunits. Here we use the structural features of glutamate receptors to develop a mechanism describing both single channel and macroscopic NMDAR currents. We propose that each agonist‐bound subunit undergoes some rate‐limiting conformational change after agonist binding, prior to channel opening. We hypothesize that this conformational change occurs within a triad of interactions between a short helix preceding the M1 transmembrane helix, the highly conserved M3 motif encoded by the residues SYTANLAAF, and the linker preceding the M4 transmembrane helix of the adjacent subunit. Molecular dynamics simulations suggest that pre‐M1 helix motion is uncorrelated between subunits, which we interpret to suggest independent subunit‐specific conformational changes may influence these pre‐gating steps. According to this interpretation, these conformational changes are the main determinants of the key kinetic properties of NMDA receptor activation following agonist binding, and so these steps sculpt their physiological role. We show that this structurally derived tetrameric model describes both single channel and macroscopic data, giving a new approach to interpreting functional properties of synaptic NMDARs that provides a logical framework to understanding receptors with non‐identical subunits.

The kinetics of NMDA receptor (NMDAR) signalling are a critical aspect of the physiology of excitatory synaptic transmission in the brain.

Here we develop a mechanistic description of NMDAR function based on the receptor tetrameric structure and the principle that each agonist‐bound subunit must undergo some rate‐limiting conformational change after agonist binding, prior to channel opening.

By fitting this mechanism to single channel data using a new MATLAB‐based software implementation of maximum likelihood fitting with correction for limited time resolution, rate constants were derived for this mechanism that reflect distinct structural changes and predict the properties of macroscopic and synaptic NMDAR currents.

The principles applied here to develop a mechanistic description of the heterotetrameric NMDAR, and the software used in this analysis, can be equally applied to other heterotetrameric glutamate receptors, providing a unifying mechanistic framework to understanding the physiology of glutamate receptor signalling in the brain.

Stochastic shielding and edge importance for Markov chains with timescale separation

Nerve cells produce electrical impulses (“spikes”) through the coordinated opening and closing of ion channels. Markov processes with voltage-dependent transition rates capture the stochasticity of spike generation at the cost of complex, time-consuming simulations. Schmandt and Galán introduced a novel method, based on the stochastic shielding approximation, as a fast, accurate method for generating approximate sample paths with excellent first and second moment agreement to exact stochastic simulations. We previously analyzed the mathematical basis for the method’s remarkable accuracy, and showed that for models with a Gaussian noise approximation, the stationary variance of the occupancy at each vertex in the ion channel state graph could be written as a sum of distinct contributions from each edge in the graph. We extend this analysis to arbitrary discrete population models with first-order kinetics. The resulting decomposition allows us to rank the “importance” of each edge’s contribution to the variance of the current under stationary conditions. In most cases, transitions between open (conducting) and closed (non-conducting) states make the greatest contributions to the variance, but there are exceptions. In a 5-state model of the nicotinic acetylcholine receptor, at low agonist concentration, a pair of “hidden” transitions (between two closed states) makes a greater contribution to the variance than any of the open-closed transitions. We exhaustively investigate this “edge importance reversal” phenomenon in simplified 3-state models, and obtain an exact formula for the contribution of each edge to the variance of the open state. Two conditions contribute to reversals: the opening rate should be faster than all other rates in the system, and the closed state leading to the opening rate should be sparsely occupied. When edge importance reversal occurs, current fluctuations are dominated by a slow noise component arising from the hidden transitions.

Discrete state, continuous time Markov processes occur throughout cell biology, neuroscience, and ecology, representing the random dynamics of processes transitioning among multiple locations or states. Complexity reduction for such models aims to capture the essential dynamics and stochastic properties via a simpler representation, with minimal loss of accuracy. Classical approaches, such as aggregation of nodes and elimination of fast variables, lead to reduced models that are no longer Markovian. Stochastic shielding provides an alternative approach by simplifying the description of the noise driving the process, while preserving the Markov property, by removing from the model those fluctuations that are not directly observable. We previously applied the stochastic shielding approximation to several Markov processes arising in neuroscience and processes on random graphs. Here we explore the range of validity of stochastic shielding for processes with nonuniform stationary probabilities and multiple timescales, including ion channels with “bursty” dynamics. We show that stochastic shielding is robust to the introduction of timescale separation, for a class of simple networks, but it can break down for more complex systems with three distinct timescales. We also show that our related edge importance measure remains valid for arbitrary networks regardless of multiple timescales.

A human-specific, truncated α7 nicotinic receptor subunit assembles with full-length α7 and forms functional receptors with different stoichiometries

The cholinergic α7 nicotinic receptor gene, CHRNA7, encodes a subunit that forms the homopentameric α7 receptor, involved in learning and memory. In humans, exons 5-10 in CHRNA7 are duplicated and fused to the FAM7A genetic element, giving rise to the hybrid gene CHRFAM7A Its product, dupα7, is a truncated subunit lacking part of the N-terminal extracellular ligand-binding domain and is associated with neurological disorders, including schizophrenia, and immunomodulation. We combined dupα7 expression on mammalian cells with patch clamp recordings to understand its functional role. Transfected cells expressed dupα7 protein, but they exhibited neither surface binding of the α7 antagonist α-bungarotoxin nor responses to acetylcholine (ACh) or to an allosteric agonist that binds to the conserved transmembrane region. To determine whether dupα7 assembles with α7, we generated receptors comprising α7 and dupα7 subunits, one of which was tagged with conductance substitutions that report subunit stoichiometry and monitored ACh-elicited channel openings in the presence of a positive allosteric α7 modulator. We found that α7 and dupα7 subunits co-assemble into functional heteromeric receptors, which require at least two α7 subunits for channel opening, and that dupα7's presence in the pentameric arrangement does not affect the duration of the potentiated events compared with that of α7. Using an α7 subunit mutant, we found that activation of (α7)₂(dupα7)₃ receptors occurs through ACh binding at the α7/α7 interfacial binding site. Our study contributes to the understanding of the modulation of α7 function by the human specific, duplicated subunit, associated with human disorders.

The LILI Motif of M3-S2 Linkers Is a Component of the NMDA Receptor Channel Gate

N-methyl-D-aspartate receptors (NMDARs) mediate excitatory synaptic transmission in the central nervous system, underlie the induction of synaptic plasticity, and their malfunction is associated with human diseases. Native NMDARs are tetramers composed of two obligatory GluN1 subunits and various combinations of GluN2A-D or, more rarely, GluN3A-B subunits. Each subunit consists of an amino-terminal, ligand-binding, transmembrane and carboxyl-terminal domain. The ligand-binding and transmembrane domains are interconnected via polypeptide chains (linkers). Upon glutamate and glycine binding, these receptors undergo a series of conformational changes leading to the opening of the Ca²⁺-permeable ion channel. Here we report that different deletions and mutations of amino acids in the M3-S2 linkers of the GluN1 and GluN2B subunits lead to constitutively open channels. Irrespective of whether alterations were introduced in the GluN1 or the GluN2B subunit, application of glutamate or glycine promoted receptor channel activity; however, responses induced by the GluN1 agonist glycine were larger, on average, than those induced by glutamate. We observed the most prominent effect when residues GluN1(L657) and GluN2B(I655) were deleted or altered to glycine. In parallel, molecular modeling revealed that two interacting pairs of residues, the LILI motif (GluN1(L657) and GluN2B(I655)), form a functional unit with the TTTT ring (GluN1(T648) and GluN2B(T647)), described earlier to control NMDAR channel gating. These results provide new insight into the structural organization and functional interplay of the LILI and the TTTT ring during the course of NMDAR channel opening and closing.

Computational Neuroscience: Mathematical and Statistical Perspectives

Mathematical and statistical models have played important roles in neuroscience, especially by describing the electrical activity of neurons recorded individually, or collectively across large networks. As the field moves forward rapidly, new challenges are emerging. For maximal effectiveness, those working to advance computational neuroscience will need to appreciate and exploit the complementary strengths of mechanistic theory and the statistical paradigm.

Mutations causing congenital myasthenia reveal principal coupling pathway in the acetylcholine receptor ε-subunit

We identify 2 homozygous mutations in the ε-subunit of the muscle acetylcholine receptor (AChR) in 3 patients with severe congenital myasthenia: εR218W in the pre-M1 region in 2 patients and εE184K in the β8-β9 linker in 1 patient. Arg218 is conserved in all eukaryotic members of the Cys-loop receptor superfamily, while Glu184 is conserved in the α-, δ-, and ε-subunits of AChRs from all species. εR218W reduces channel gating efficiency 338-fold and AChR expression on the cell surface 5-fold, whereas εE184K reduces channel gating efficiency 11-fold but does not alter AChR cell surface expression. Determinations of the effective channel gating rate constants, combined with mutant cycle analyses, demonstrate strong energetic coupling between εR218 and εE184, and between εR218 and εE45 from the β1-β2 linker, as also observed for equivalent residues in the principal coupling pathway of the α-subunit. Thus, efficient and rapid gating of the AChR channel is achieved not only by coupling between conserved residues within the principal coupling pathway of the α-subunit, but also between corresponding residues in the ε-subunit.

Bayesian Statistical Inference in Ion-Channel Models with Exact Missed Event Correction

The stochastic behavior of single ion channels is most often described as an aggregated continuous-time Markov process with discrete states. For ligand-gated channels each state can represent a different conformation of the channel protein or a different number of bound ligands. Single-channel recordings show only whether the channel is open or shut: states of equal conductance are aggregated, so transitions between them have to be inferred indirectly. The requirement to filter noise from the raw signal further complicates the modeling process, as it limits the time resolution of the data. The consequence of the reduced bandwidth is that openings or shuttings that are shorter than the resolution cannot be observed; these are known as missed events. Postulated models fitted using filtered data must therefore explicitly account for missed events to avoid bias in the estimation of rate parameters and therefore assess parameter identifiability accurately. In this article, we present the first, to our knowledge, Bayesian modeling of ion-channels with exact missed events correction. Bayesian analysis represents uncertain knowledge of the true value of model parameters by considering these parameters as random variables. This allows us to gain a full appreciation of parameter identifiability and uncertainty when estimating values for model parameters. However, Bayesian inference is particularly challenging in this context as the correction for missed events increases the computational complexity of the model likelihood. Nonetheless, we successfully implemented a two-step Markov chain Monte Carlo method that we called "BICME", which performs Bayesian inference in models of realistic complexity. The method is demonstrated on synthetic and real single-channel data from muscle nicotinic acetylcholine channels. We show that parameter uncertainty can be characterized more accurately than with maximum-likelihood methods. Our code for performing inference in these ion channel models is publicly available.

Unraveling the Thousand Word Picture: An Introduction to Super-Resolution Data Analysis

Super-resolution microscopy provides direct insight into fundamental biological processes occurring at length scales smaller than light's diffraction limit. The analysis of data at such scales has brought statistical and machine learning methods into the mainstream. Here we provide a survey of data analysis methods starting from an overview of basic statistical techniques underlying the analysis of super-resolution and, more broadly, imaging data. We subsequently break down the analysis of super-resolution data into four problems: the localization problem, the counting problem, the linking problem, and what we've termed the interpretation problem.

Unsupervised Idealization of Ion Channel Recordings by Minimum Description Length: Application to Human PIEZO1-Channels

Researchers can investigate the mechanistic and molecular basis of many physiological phenomena in cells by analyzing the fundamental properties of single ion channels. These analyses entail recording single channel currents and measuring current amplitudes and transition rates between conductance states. Since most electrophysiological recordings contain noise, the data analysis can proceed by idealizing the recordings to isolate the true currents from the noise. This de-noising can be accomplished with threshold crossing algorithms and Hidden Markov Models, but such procedures generally depend on inputs and supervision by the user, thus requiring some prior knowledge of underlying processes. Channels with unknown gating and/or functional sub-states and the presence in the recording of currents from uncorrelated background channels present substantial challenges to such analyses. Here we describe and characterize an idealization algorithm based on Rissanen's Minimum Description Length (MDL) Principle. This method uses minimal assumptions and idealizes ion channel recordings without requiring a detailed user input or a priori assumptions about channel conductance and kinetics. Furthermore, we demonstrate that correlation analysis of conductance steps can resolve properties of single ion channels in recordings contaminated by signals from multiple channels. We first validated our methods on simulated data defined with a range of different signal-to-noise levels, and then showed that our algorithm can recover channel currents and their substates from recordings with multiple channels, even under conditions of high noise. We then tested the MDL algorithm on real experimental data from human PIEZO1 channels and found that our method revealed the presence of substates with alternate conductances.

Conformational changes at cytoplasmic intersubunit interactions control Kir channel gating

The defining structural feature of inward-rectifier potassium (Kir) channels is the unique Kir cytoplasmic domain. Recently we showed that salt bridges located at the cytoplasmic domain subunit interfaces (CD-Is) of eukaryotic Kir channels control channel gating via stability of a novel inactivated closed state. The cytoplasmic domains of prokaryotic and eukaryotic Kir channels show similar conformational rearrangements to the common gating ligand, phosphatidylinositol bisphosphate (PIP₂), although these exhibit opposite coupling to opening and closing transitions. In Kir2.1, mutation of one of these CD-I salt bridge residues (R204A) reduces apparent PIP₂ sensitivity of channel activity, and here we show that Ala or Cys substitutions of the functionally equivalent residue (Arg-165) in the prokaryotic Kir channel KirBac1.1 also significantly decrease sensitivity of the channel to PIP₂ (by 5-30-fold). To further understand the structural basis of CD-I control of Kir channel gating, we examined the effect of the R165A mutation on PIP₂-induced changes in channel function and conformation. Single-channel analyses indicated that the R165A mutation disrupts the characteristic long interburst closed state of reconstituted KirBac1.1 in giant liposomes, resulting in a higher open probability due to more frequent opening bursts. Intramolecular FRET measurements indicate that, relative to wild-type channels, the R165A mutation results in splaying of the cytoplasmic domains away from the central axis and that PIP₂ essentially induces opposite motions of the major β-sheet in this channel mutant. We conclude that the removal of stabilizing CD-I salt bridges results in a collapsed state of the Kir domain.

Control of Kir channel gating by cytoplasmic domain interface interactions

The pore-forming unit of ATP-sensitive K channels is composed of four Kir6.2 subunits. Borschel et al. show that salt bridges between the cytoplasmic domain of adjacent Kir6.2 subunits determine the degree to which channels inactivate after removal of ATP.

Inward rectifier potassium (Kir) channels are expressed in almost all mammalian tissues and play critical roles in the control of excitability. Pancreatic ATP-sensitive K (K_ATP) channels are key regulators of insulin secretion and comprise Kir6.2 subunits coupled to sulfonylurea receptors. Because these channels are reversibly inhibited by cytoplasmic ATP, they link cellular metabolism with membrane excitability. Loss-of-function mutations in the pore-forming Kir6.2 subunit cause congenital hyperinsulinism as a result of diminished channel activity. Here, we show that several disease mutations, which disrupt intersubunit salt bridges at the interface of the cytoplasmic domains (CD-I) of adjacent subunits, induce loss of channel activity via a novel channel behavior: after ATP removal, channels open but then rapidly inactivate. Re-exposure to inhibitory ATP causes recovery from this inactivation. Inactivation can be abolished by application of phosphatidylinositol-4,5-bisphosphate (PIP₂) to the cytoplasmic face of the membrane, an effect that can be explained by a simple kinetic model in which PIP₂ binding competes with the inactivation process. Kir2.1 channels contain homologous salt bridges, and we find that mutations that disrupt CD-I interactions in Kir2.1 also reduce channel activity and PIP₂ sensitivity. Kir2.1 channels also contain an additional CD-I salt bridge that is not present in Kir6.2 channels. Introduction of this salt bridge into Kir6.2 partially rescues inactivating mutants from the phenotype. These results indicate that the stability of the intersubunit CD-I is a major determinant of the inactivation process in Kir6.2 and may control gating in other Kir channels.

Molecular Mechanism of Disease-Associated Mutations in the Pre-M1 Helix of NMDA Receptors and Potential Rescue Pharmacology

N-methyl-D-aspartate receptors (NMDARs), ligand-gated ionotropic glutamate receptors, play key roles in normal brain development and various neurological disorders. Here we use standing variation data from the human population to assess which protein domains within NMDAR GluN1, GluN2A and GluN2B subunits show the strongest signal for being depleted of missense variants. We find that this includes the GluN2 pre-M1 helix and linker between the agonist-binding domain (ABD) and first transmembrane domain (M1). We then evaluate the functional changes of multiple missense mutations in the NMDAR pre-M1 helix found in children with epilepsy and developmental delay. We find mutant GluN1/GluN2A receptors exhibit prolonged glutamate response time course for channels containing 1 or 2 GluN2A-P552R subunits, and a slow rise time only for receptors with 2 mutant subunits, suggesting rearrangement of one GluN2A pre-M1 helix is sufficient for rapid activation. GluN2A-P552R and analogous mutations in other GluN subunits increased the agonist potency and slowed response time course, suggesting a functionally conserved role for this residue. Although there is no detectable change in surface expression or open probability for GluN2A-P552R, the prolonged response time course for receptors that contained GluN2A-P552R increased charge transfer for synaptic-like activation, which should promote excitotoxic damage. Transfection of cultured neurons with GluN2A-P552R prolonged EPSPs, and triggered pronounced dendritic swelling in addition to excitotoxicity, which were both attenuated by memantine. These data implicate the pre-M1 region in gating, provide insight into how different subunits contribute to gating, and suggest that mutations in the pre-M1 helix can compromise neuronal health. Evaluation of FDA-approved NMDAR inhibitors on the mutant NMDAR-mediated current response and neuronal damage provides a potential clinical path to treat individuals harboring similar mutations in NMDARs.

The Kinetics and the Permeation Properties of Piezo Channels

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

Altering intracellular pH reveals the kinetic basis of intraburst gating in the CFTR Cl- channel

KEY POINTS

The cystic fibrosis transmembrane conductance regulator (CFTR), which is defective in the genetic disease cystic fibrosis (CF), forms a gated pathway for chloride movement regulated by intracellular ATP. To understand better CFTR function, we investigated the regulation of channel openings by intracellular pH. We found that short-lived channel closures during channel openings represent subtle changes in the structure of CFTR that are regulated by intracellular pH, in part, at ATP-binding site 1 formed by the nucleotide-binding domains. Our results provide a framework for future studies to understand better the regulation of channel openings, the dysfunction of CFTR in CF and the action of drugs that repair CFTR gating defects.

ABSTRACT

Cystic fibrosis transmembrane conductance regulator (CFTR) is an ATP-gated Cl^- channel defective in the genetic disease cystic fibrosis (CF). The gating behaviour of CFTR is characterized by bursts of channel openings interrupted by brief, flickery closures, separated by long closures between bursts. Entry to and exit from an open burst is controlled by the interaction of ATP with two ATP-binding sites, sites 1 and 2, in CFTR. To understand better the kinetic basis of CFTR intraburst gating, we investigated the single-channel activity of human CFTR at different intracellular pH (pH_i ) values. When compared with the control (pH_i 7.3), acidifying pH_i to 6.3 or alkalinizing pH_i to 8.3 and 8.8 caused small reductions in the open-time constant (τ_o ) of wild-type CFTR. By contrast, the fast closed-time constant (τ_cf ), which describes the short-lived closures that interrupt open bursts, was greatly increased at pH_i 5.8 and 6.3. To analyse intraburst kinetics, we used linear three-state gating schemes. All data were satisfactorily modelled by the C₁ ↔ O ↔ C₂ kinetic scheme. Changing the intracellular ATP concentration was without effect on τ_o , τ_cf and their responses to pH_i changes. However, mutations that disrupt the interaction of ATP with ATP-binding site 1, including K464A, D572N and the CF-associated mutation G1349D all abolished the prolongation of τ_cf at pH_i 6.3. Taken together, our data suggest that the regulation of CFTR intraburst gating is distinct from the ATP-dependent mechanism that controls channel opening and closing. However, our data also suggest that ATP-binding site 1 modulates intraburst gating.

Decoding Single Molecule Time Traces with Dynamic Disorder

Single molecule time trajectories of biomolecules provide glimpses into complex folding landscapes that are difficult to visualize using conventional ensemble measurements. Recent experiments and theoretical analyses have highlighted dynamic disorder in certain classes of biomolecules, whose dynamic pattern of conformational transitions is affected by slower transition dynamics of internal state hidden in a low dimensional projection. A systematic means to analyze such data is, however, currently not well developed. Here we report a new algorithm—Variational Bayes-double chain Markov model (VB-DCMM)—to analyze single molecule time trajectories that display dynamic disorder. The proposed analysis employing VB-DCMM allows us to detect the presence of dynamic disorder, if any, in each trajectory, identify the number of internal states, and estimate transition rates between the internal states as well as the rates of conformational transition within each internal state. Applying VB-DCMM algorithm to single molecule FRET data of H-DNA in 100 mM-Na⁺ solution, followed by data clustering, we show that at least 6 kinetic paths linking 4 distinct internal states are required to correctly interpret the duplex-triplex transitions of H-DNA.

We have developed a new algorithm to better decode single molecule data with dynamic disorder. Our new algorithm, which represents a substantial improvement over other methodologies, can detect the presence of dynamic disorder in each trajectory and quantify the kinetic characteristics of underlying energy landscape. As a model system, we applied our algorithm to the single molecule FRET time traces of H-DNA. While duplex-triplex transitions of H-DNA are conventionally interpreted in terms of two-state kinetics, slowly varying dynamic patterns corresponding to hidden internal states can also be identified from the individual time traces. Our algorithm reveals that at least 4 distinct internal states are required to correctly interpret the data.

Molecular recognition at cholinergic synapses: acetylcholine versus choline

KEY POINTS

Neuromuscular acetylcholine (ACh) receptors have a high affinity for the neurotransmitter ACh and a low affinity for its metabolic product choline. At each transmitter binding site three aromatic groups determine affinity, and together provide ∼50% more binding energy for ACh than for choline. Deprotonation of αY190 by a nearby lysine strengthens the interaction between this aromatic ring and both ACh and choline. H-bonds position ACh and choline differently in the aromatic cage to generate the different affinities.

ABSTRACT

Acetylcholine (ACh) released at the vertebrate nerve-muscle synapse is hydrolysed rapidly to choline (Cho), so endplate receptors (AChRs) are exposed to high concentrations of both of these structurally related ligands. To understand how these receptors distinguish ACh and Cho, we used single-channel electrophysiology to measure resting affinities (binding free energies) of these and other agonists in adult-type mouse AChRs having a mutation(s) at the transmitter-binding sites. The aromatic rings of αY190, αW149 and αY198 each provide ∼50% less binding energy for Cho compared to ACh. At αY198 a phenylalanine substitution had no effect, but at αY190 this substitution caused a large, agonist-independent loss in binding energy that depended on the presence of αK145. The results suggest that (1) αY190 is deprotonated by αK145 to strengthen the interaction between this benzene ring and the agonist's quaternary ammonium (QA) and (2) AChRs respond strongly to ACh because an H-bond positions the QA to interact optimally with the rings, and weakly to Cho because a different H-bond tethers the ligand to misalign the QA and form weaker interactions with the aromatic groups. The results suggest that the difference in ACh versus Cho binding energies is determined by different ligand positions within a fixed protein structure.

Precisely and Accurately Inferring Single-Molecule Rate Constants

The kinetics of biomolecular systems can be quantified by calculating the stochastic rate constants that govern the biomolecular state vs time trajectories (i.e., state trajectories) of individual biomolecules. To do so, the experimental signal vs time trajectories (i.e., signal trajectories) obtained from observing individual biomolecules are often idealized to generate state trajectories by methods such as thresholding or hidden Markov modeling. Here, we discuss approaches for idealizing signal trajectories and calculating stochastic rate constants from the resulting state trajectories. Importantly, we provide an analysis of how the finite length of signal trajectories restricts the precision of these approaches and demonstrate how Bayesian inference-based versions of these approaches allow rigorous determination of this precision. Similarly, we provide an analysis of how the finite lengths and limited time resolutions of signal trajectories restrict the accuracy of these approaches, and describe methods that, by accounting for the effects of the finite length and limited time resolution of signal trajectories, substantially improve this accuracy. Collectively, therefore, the methods we consider here enable a rigorous assessment of the precision, and a significant enhancement of the accuracy, with which stochastic rate constants can be calculated from single-molecule signal trajectories.

Mutations Causing Slow-Channel Myasthenia Reveal That a Valine Ring in the Channel Pore of Muscle AChR is Optimized for Stabilizing Channel Gating

We identify two novel mutations in acetylcholine receptor (AChR) causing a slow-channel congenital myasthenia syndrome (CMS) in three unrelated patients (Pts). Pt 1 harbors a heterozygous βV266A mutation (p.Val289Ala) in the second transmembrane domain (M2) of the AChR β subunit (CHRNB1). Pts 2 and 3 carry the same mutation at an equivalent site in the ε subunit (CHRNE), εV265A (p.Val285Ala). The mutant residues are conserved across all AChR subunits of all species and are components of a valine ring in the channel pore, which is positioned four residues above the leucine ring. Both βV266A and εV265A reduce the amino acid size and lengthen the channel opening bursts by fourfold by enhancing gating efficiency by approximately 30-fold. Substitution of alanine for valine at the corresponding position in the δ and α subunit prolongs the burst duration four- and eightfold, respectively. Replacing valine at ε codon 265 either by a still smaller glycine or by a larger leucine also lengthens the burst duration. Our analysis reveals that each valine in the valine ring contributes to channel kinetics equally, and the valine ring has been optimized in the course of evolution to govern channel gating.

Subconductance gating and voltage sensitivity of sarcoplasmic reticulum K(+) channels: a modeling approach

Sarcoplasmic reticulum (SR) K⁺ channels are voltage-regulated channels that are thought to be actively gating when the membrane potential across the SR is close to zero as is expected physiologically. A characteristic of SR K⁺ channels is that they gate to subconductance open states but the relevance of the subconductance events and their contribution to the overall current flowing through the channels at physiological membrane potentials is not known. We have investigated the relationship between subconductance and full conductance openings and developed kinetic models to describe the voltage sensitivity of channel gating. Because there may be two subtypes of SR K⁺ channels (TRIC-A and TRIC-B) present in most tissues, to conduct our study on a homogeneous population of SR K⁺ channels, we incorporated SR vesicles derived from Tric-a knockout mice into artificial membranes to examine the remaining SR K⁺ channel (TRIC-B) function. The channels displayed very low open probability (Po) at negative potentials (≤0 mV) and opened predominantly to subconductance open states. Positive holding potentials primarily increased the frequency of subconductance state openings and thereby increased the number of subsequent transitions into the full open state, although a slowing of transitions back to the sublevels was also important. We investigated whether the subconductance gating could arise as an artifact of incomplete resolution of rapid transitions between full open and closed states; however, we were not able to produce a model that could fit the data as well as one that included multiple distinct current amplitudes. Our results suggest that the apparent subconductance openings will provide most of the K⁺ flux when the SR membrane potential is close to zero. The relative contribution played by openings to the full open state would increase if negative charge developed within the SR thus increasing the capacity of the channel to compensate for ionic imbalances.