Determining the correct stoichiometry of Kv2.1/Kv6.4 heterotetramers, functional in multiple stoichiometrical configurations.

The electrically silent (KvS) members of the voltage-gated potassium (Kv) subfamilies Kv5, Kv6, Kv8, and Kv9 selectively modulate Kv2 subunits by forming heterotetrameric Kv2/KvS channels. Based on the reported 3:1 stoichiometry of Kv2.1/Kv9.3 channels, we tested the hypothesis that Kv2.1/Kv6.4 channels express, in contrast to the assumed 3:1, in a 2:2 stoichiometry. We investigate the Kv2.1/Kv6.4 stoichiometry using single subunit counting and functional characterization of tetrameric concatemers. For selecting the most probable stoichiometry, we introduce a model-selection method that is applicable for any multimeric complex by investigating the stoichiometry of Kv2.1/Kv6.4 channels. Weighted likelihood calculations bring rigor to a powerful technique. Using the weighted-likelihood model-selection method and analysis of electrophysiological data, we show that Kv2.1/Kv6.4 channels express, in contrast to the assumed 3:1, in a 2:2 stoichiometry. Within this stoichiometry, the Kv6.4 subunits have to be positioned alternating with Kv2.1 to express functional channels. The variability in Kv2/KvS assembly increases the diversity of heterotetrameric configurations and extends the regulatory possibilities of KvS by allowing the presence of more than one silent subunit.

Inverted allosteric coupling between activation and inactivation gates in K+ channels.

The selectivity filter and the activation gate in potassium channels are functionally and structurally coupled. An allosteric coupling underlies C-type inactivation coupled to activation gating in this ion-channel family (i.e., opening of the activation gate triggers the collapse of the channel's selectivity filter). We have identified the second Threonine residue within the TTVGYGD signature sequence of K+ channels as a crucial residue for this allosteric communication. A Threonine to Alanine substitution at this position was studied in three representative members of the K+-channel family. Interestingly, all of the mutant channels exhibited lack of C-type inactivation gating and an inversion of their allosteric coupling (i.e., closing of the activation gate collapses the channel's selectivity filter). A state-dependent crystallographic study of KcsA-T75A proves that, on activation, the selectivity filter transitions from a nonconductive and deep C-type inactivated conformation to a conductive one. Finally, we provide a crystallographic demonstration that closed-state inactivation can be achieved by the structural collapse of the channel's selectivity filter.

iPSC-Cardiomyocyte Models of Brugada Syndrome-Achievements, Challenges and Future Perspectives.

Brugada syndrome (BrS) is an inherited cardiac arrhythmia that predisposes to ventricular fibrillation and sudden cardiac death. It originates from oligogenic alterations that affect cardiac ion channels or their accessory proteins. The main hurdle for the study of the functional effects of those variants is the need for a specific model that mimics the complex environment of human cardiomyocytes. Traditionally, animal models or transient heterologous expression systems are applied for electrophysiological investigations, each of these models having their limitations. The ability to create induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs), providing a source of human patient-specific cells, offers new opportunities in the field of cardiac disease modelling. Contemporary iPSC-CMs constitute the best possible in vitro model to study complex cardiac arrhythmia syndromes such as BrS. To date, thirteen reports on iPSC-CM models for BrS have been published and with this review we provide an overview of the current findings, with a focus on the electrophysiological parameters. We also discuss the methods that are used for cell derivation and data acquisition. In the end, we critically evaluate the knowledge gained by the use of these iPSC-CM models and discuss challenges and future perspectives for iPSC-CMs in the study of BrS and other arrhythmias.

Constitutive, Basal, and ß-Alanine-Mediated Activation of the Human Mas-Related G Protein-Coupled Receptor D Induces Release of the Inflammatory Cytokine IL-6 and Is Dependent on NF-κB Signaling.

G protein-coupled receptors (GPCRs) have emerged as key players in regulating (patho)physiological processes, including inflammation. Members of the Mas-related G protein coupled receptors (MRGPRs), a subfamily of GPCRs, are largely expressed by sensory neurons and known to modulate itch and pain. Several members of MRGPRs are also expressed in mast cells, macrophages, and in cardiovascular tissue, linking them to pseudo-allergic drug reactions and suggesting a pivotal role in the cardiovascular system. However, involvement of the human Mas-related G-protein coupled receptor D (MRGPRD) in the regulation of the inflammatory mediator interleukin 6 (IL-6) has not been demonstrated to date. By stimulating human MRGPRD-expressing HeLa cells with the agonist ß-alanine, we observed a release of IL-6. ß-alanine-induced signaling through MRGPRD was investigated further by probing downstream signaling effectors along the Gαq/Phospholipase C (PLC) pathway, which results in an IkB kinases (IKK)-mediated canonical activation of nuclear factor kappa-B (NF-κB) and stimulation of IL-6 release. This IL-6 release could be blocked by a Gαq inhibitor (YM-254890), an IKK complex inhibitor (IKK-16), and partly by a PLC inhibitor (U-73122). Additionally, we investigated the constitutive (ligand-independent) and basal activity of MRGPRD and concluded that the observed basal activity of MRGPRD is dependent on the presence of fetal bovine serum (FBS) in the culture medium. Consequently, the dynamic range for IL-6 detection as an assay for ß-alanine-mediated activation of MRGPRD is substantially increased by culturing the cells in FBS free medium before treatment. Overall, the observation that MRGPRD mediates the release of IL-6 in an in vitro system, hints at a role as an inflammatory mediator and supports the notion that IL-6 can be used as a marker for MRGPRD activation in an in vitro drug screening assay.

Developmental Toxicity and Biotransformation of Two Anti-Epileptics in Zebrafish Embryos and Early Larvae.

The zebrafish (Danio rerio) embryo is gaining interest as a bridging tool between in-vitro and in-vivo developmental toxicity studies. However, cytochrome P450 (CYP)-mediated drug metabolism in this model is still under debate. Therefore, we investigated the potential of zebrafish embryos and larvae to bioactivate two known anti-epileptics, carbamazepine (CBZ) and phenytoin (PHE), to carbamazepine-10,11-epoxide (E-CBZ) and 5-(4-hydroxyphenyl)-5-phenylhydantoin (HPPH), respectively. First, zebrafish were exposed to CBZ, PHE, E-CBZ and HPPH from 5»- to 120-h post fertilization (hpf) and morphologically evaluated. Second, the formations of E-CBZ and HPPH were assessed in culture medium and in whole-embryo extracts at different time points by targeted LC-MS. Finally, E-CBZ and HPPH formation was also assessed in adult zebrafish liver microsomes and compared with those of human, rat, and rabbit. The present study showed teratogenic effects for CBZ and PHE, but not for E-CBZ and HPPH. No HPPH was detected during organogenesis and E-CBZ was only formed at the end of organogenesis. E-CBZ and HPPH formation was also very low-to-negligible in adult zebrafish compared with the mammalian species. As such, other metabolic pathways than those of mammals are involved in the bioactivation of CBZ and PHE, or, these anti-epileptics are teratogens and do not require bioactivation in the zebrafish.

The Selectivity Filter Is Involved in the U-Type Inactivation Process of Kv2.1 and Kv3.1 Channels.

Voltage-gated potassium (Kv) channels display several types of inactivation processes, including N-, C-, and U-types. C-type inactivation is attributed to a nonconductive conformation of the selectivity filter (SF). It has been proposed that the activation gate and the channel's SF are allosterically coupled because the conformational changes of the former affect the structure of the latter and vice versa. The second threonine of the SF signature sequence (e.g., TTVGYG) has been proven to be essential for this allosteric coupling. To further study the role of the SF in U-type inactivation, we substituted the second threonine of the TTVGYG sequence by an alanine in the hKv2.1 and hKv3.1 channels, which are known to display U-type inactivation. Both hKv2.1-T377A and hKv3.1-T400A yielded channels that were resistant to inactivation, and as a result, they displayed noninactivating currents upon channel opening; i.e., hKv2.1-T377A and hKv3.1-T400A remained fully conductive upon prolonged moderate depolarizations, whereas in wild-type hKv2.1 and hKv3.1, the current amplitude typically reduces because of U-type inactivation. Interestingly, increasing the extracellular K+ concentration increased the macroscopic current amplitude of both hKv2.1-T377A and hKv3.1-T400A, which is similar to the response of the homologous T to A mutation in Shaker and hKv1.5 channels that display C-type inactivation. Our data support an important role for the second threonine of the SF signature sequence in the U-type inactivation gating of hKv2.1 and hKv3.1.

Mutations in the S6 gate isolate a late step in the activation pathway and reduce 4-AP sensitivity in shaker K(v) channel.

Kv channels detect changes in the membrane potential via their voltage-sensing domains (VSDs) that control the status of the S6 bundle crossing (BC) gate. The movement of the VSDs results in a transfer of the S4 gating charges across the cell membrane but only the last 10-20% of the total gating charge movement is associated with BC gate opening, which involves cooperative transition(s) in the subunits. Substituting the proline residue P475 in the S6 of the Shaker channel by a glycine or alanine causes a considerable shift in the voltage-dependence of the cooperative transition(s) of BC gate opening, effectively isolating the late gating charge component from the other gating charge that originates from earlier VSD movements. Interestingly, both mutations also abolished Shaker's sensitivity to 4-aminopyridine, which is a pharmacological tool to isolate the late gating charge component. The alanine substitution (that would promote a α-helical configuration compared to proline) resulted in the largest separation of both gating charge components; therefore, BC gate flexibility appears to be important for enabling the late cooperative step of channel opening.

Dual effect of phosphatidylinositol (4,5)-bisphosphate PIP(2) on Shaker K(+) [corrected] channels.

Phosphatidylinositol (4,5)-bisphosphate (PIP(2)) is a phospholipid of the plasma membrane that has been shown to be a key regulator of several ion channels. Functional studies and more recently structural studies of Kir channels have revealed the major impact of PIP(2) on the open state stabilization. A similar effect of PIP(2) on the delayed rectifiers Kv7.1 and Kv11.1, two voltage-gated K(+) channels, has been suggested, but the molecular mechanism remains elusive and nothing is known on PIP(2) effect on other Kv such as those of the Shaker family. By combining giant-patch ionic and gating current recordings in COS-7 cells, and voltage-clamp fluorimetry in Xenopus oocytes, both heterologously expressing the voltage-dependent Shaker channel, we show that PIP(2) exerts 1) a gain-of-function effect on the maximal current amplitude, consistent with a stabilization of the open state and 2) a loss-of-function effect by positive-shifting the activation voltage dependence, most likely through a direct effect on the voltage sensor movement, as illustrated by molecular dynamics simulations.

Correction: Gubic et al. Design of New Potent and Selective Thiophene-Based KV1.3 Inhibitors and Their Potential for Anticancer Activity. Cancers 2022, 14, 2595.

In the original publication [...].

Clinical and functional characterisation of a recurrent KCNQ1 variant in the Belgian population.

BACKGROUND: The c.1124_1127delTTCA p.(Ile375Argfs*43) pathogenic variant is the most frequently identified molecular defect in the KCNQ1 gene in the cardiogenetics clinic of the Antwerp University Hospital. This variant was observed in nine families presenting with either Jervell-Lange-Nielsen syndrome or long QT syndrome (LQTS). Here, we report on the molecular, clinical and functional characterization of the KCNQ1 c.1124_1127delTTCA variant. RESULTS: Forty-one heterozygous variant harboring individuals demonstrated a predominantly mild clinical and electrophysiological phenotype, compared to individuals harboring other KCNQ1 pathogenic variants (5% symptomatic before 40 years of age, compared to 24% and 29% in p.(Tyr111Cys) and p.(Ala341Val) variant carriers, respectively, 33% with QTc ≤ 440 ms compared to 10% in p.(Tyr111Cys) and p.(Ala341Val) variant carriers). The LQTS phenotype was most comparable to that observed for the Swedish p.(Arg518*) founder mutation (7% symptomatic at any age, compared to 17% in p.(Arg518*) variant carriers, 33% with QTc ≤ 440 ms compared to 16% in p.(Arg518*) variant carriers). Surprisingly, short tandem repeat analysis did not reveal a common haplotype for all families. One KCNQ1 c.1124_1127delTTCA harboring patient was diagnosed with Brugada syndrome (BrS). The hypothesis of a LQTS/BrS overlap syndrome was supported by electrophysiological evidence for both loss-of-function and gain-of-function (acceleration of channel kinetics) in a heterologous expression system. However, BrS phenotypes were not identified in other affected individuals and allelic KCNQ1 expression testing in patient-specific induced pluripotent stem cell-derived cardiomyocytes (iPSC-CMs) showed nonsense mediated decay of the c.1124_1127delTTCA allele. CONCLUSIONS: The c.1124_1127delTTCA frameshift variant shows a high prevalence in our region, despite not being confirmed as a founder mutation. This variant leads to a mild LQTS phenotype in the heterozygous state. Despite initial evidence for a gain-of-function effect based on in vitro electrophysiological assessment in CHO cells and expression of the KCNQ1 c.1124_1127delTTCA allele in patient blood cells, additional testing in iPSC-CMs showed lack of expression of the mutant allele. This suggests haploinsufficiency as the pathogenic mechanism. Nonetheless, as inter-individual differences in allele expression in (iPSC-) cardiomyocytes have not been assessed, a modifying effect on the BrS phenotype through potassium current modulation cannot be excluded.

Immunosuppressive effects of new thiophene-based KV1.3 inhibitors.

Voltage-gated potassium channel KV1.3 inhibitors have been shown to be effective in preventing T-cell proliferation and activation by affecting intracellular Ca2+ homeostasis. Here, we present the structure-activity relationship, KV1.3 inhibition, and immunosuppressive effects of new thiophene-based KV1.3 inhibitors with nanomolar potency on K+ current in T-lymphocytes and KV1.3 inhibition on Ltk- cells. The new KV1.3 inhibitor trans-18 inhibited KV1.3 -mediated current in phytohemagglutinin (PHA)-activated T-lymphocytes with an IC50 value of 26.1 nM and in mammalian Ltk- cells with an IC50 value of 230 nM. The KV1.3 inhibitor trans-18 also had nanomolar potency against KV1.3 in Xenopus laevis oocytes (IC50 = 136 nM). The novel thiophene-based KV1.3 inhibitors impaired intracellular Ca2+ signaling as well as T-cell activation, proliferation, and colony formation.

The S4-S5 linker of KCNQ1 channels forms a structural scaffold with the S6 segment controlling gate closure.

In vivo, KCNQ1 α-subunits associate with the ß-subunit KCNE1 to generate the slowly activating cardiac potassium current (I(Ks)). Structurally, they share their topology with other Kv channels and consist out of six transmembrane helices (S1-S6) with the S1-S4 segments forming the voltage-sensing domain (VSD). The opening or closure of the intracellular channel gate, which localizes at the bottom of the S6 segment, is directly controlled by the movement of the VSD via an electromechanical coupling. In other Kv channels, this electromechanical coupling is realized by an interaction between the S4-S5 linker (S4S5(L)) and the C-terminal end of S6 (S6(T)). Previously we reported that substitutions for Leu(353) in S6(T) resulted in channels that failed to close completely. Closure could be incomplete because Leu(353) itself is the pore-occluding residue of the channel gate or because of a distorted electromechanical coupling. To resolve this and to address the role of S4S5(L) in KCNQ1 channel gating, we performed an alanine/tryptophan substitution scan of S4S5(L). The residues with a "high impact" on channel gating (when mutated) clustered on one side of the S4S5(L) α-helix. Hence, this side of S4S5(L) most likely contributes to the electromechanical coupling and finds its residue counterparts in S6(T). Accordingly, substitutions for Val(254) resulted in channels that were partially constitutively open and the ability to close completely was rescued by combination with substitutions for Leu(353) in S6(T). Double mutant cycle analysis supported this cross-talk indicating that both residues come in close contact and stabilize the closed state of the channel.

KCNQ1 channels voltage dependence through a voltage-dependent binding of the S4-S5 linker to the pore domain.

Voltage-dependent potassium (Kv) channels are tetramers of six transmembrane domain (S1-S6) proteins. Crystallographic data demonstrate that the tetrameric pore (S5-S6) is surrounded by four voltage sensor domains (S1-S4). One key question remains: how do voltage sensors (S4) regulate pore gating? Previous mutagenesis data obtained on the Kv channel KCNQ1 highlighted the critical role of specific residues in both the S4-S5 linker (S4S5(L)) and S6 C terminus (S6(T)). From these data, we hypothesized that S4S5(L) behaves like a ligand specifically interacting with S6(T) and stabilizing the closed state. To test this hypothesis, we designed plasmid-encoded peptides corresponding to portions of S4S5(L) and S6(T) of the voltage-gated potassium channel KCNQ1 and evaluated their effects on the channel activity in the presence and absence of the ancillary subunit KCNE1. We showed that S4S5(L) peptides inhibit KCNQ1, in a reversible and state-dependent manner. S4S5(L) peptides also inhibited a voltage-independent KCNQ1 mutant. This inhibition was competitively prevented by a peptide mimicking S6(T), consistent with S4S5(L) binding to S6(T). Val(254) in S4S5(L) is known to contact Leu(353) in S6(T) when the channel is closed, and mutations of these residues alter the coupling between the two regions. The same mutations introduced in peptides altered their effects, further confirming S4S5(L) binding to S6(T). Our results suggest a mechanistic model in which S4S5(L) acts as a voltage-dependent ligand bound to its receptor on S6 at rest. This interaction locks the channel in a closed state. Upon plasma membrane depolarization, S4 pulls S4S5(L) away from S6(T), allowing channel opening.

A polyether biotoxin binding site on the lipid-exposed face of the pore domain of Kv channels revealed by the marine toxin gambierol.

Gambierol is a marine polycyclic ether toxin belonging to the group of ciguatera toxins. It does not activate voltage-gated sodium channels (VGSCs) but inhibits Kv1 potassium channels by an unknown mechanism. While testing whether Kv2, Kv3, and Kv4 channels also serve as targets, we found that Kv3.1 was inhibited with an IC(50) of 1.2 +/- 0.2 nM, whereas Kv2 and Kv4 channels were insensitive to 1 microM gambierol. Onset of block was similar from either side of the membrane, and gambierol did not compete with internal cavity blockers. The inhibition did not require channel opening and could not be reversed by strong depolarization. Using chimeric Kv3.1-Kv2.1 constructs, the toxin sensitivity was traced to S6, in which T427 was identified as a key determinant. In Kv3.1 homology models, T427 and other molecular determinants (L348, F351) reside in a space between S5 and S6 outside the permeation pathway. In conclusion, we propose that gambierol acts as a gating modifier that binds to the lipid-exposed surface of the pore domain, thereby stabilizing the closed state. This site may be the topological equivalent of the neurotoxin site 5 of VGSCs. Further elucidation of this previously undescribed binding site may explain why most ciguatoxins activate VGSCs, whereas others inhibit voltage-dependent potassium (Kv) channels. This previously undescribed Kv neurotoxin site may have wide implications not only for our understanding of channel function at the molecular level but for future development of drugs to alleviate ciguatera poisoning or to modulate electrical excitability in general.

The nonconducting W434F mutant adopts upon membrane depolarization an inactivated-like state that differs from wild-type Shaker-IR potassium channels.

Voltage-gated K+ (Kv) channels mediate the flow of K+ across the cell membrane by regulating the conductive state of their activation gate (AG). Several Kv channels display slow C-type inactivation, a process whereby their selectivity filter (SF) becomes less or nonconductive. It has been proposed that, in the fast inactivation-removed Shaker-IR channel, the W434F mutation epitomizes the C-type inactivated state because it functionally accelerates this process. By introducing another pore mutation that prevents AG closure, P475D, we found a way to record ionic currents of the Shaker-IR-W434F-P475D mutant at hyperpolarized membrane potentials as the W434F-mutant SF recovers from its inactivated state. This W434F conductive state lost its high K+ over Na+ selectivity, and even NMDG+ can permeate, features not observed in a wild-type SF. This indicates that, at least during recovery from inactivation, the W434F-mutant SF transitions to a widened and noncationic specific conformation.

A Possible Explanation for the Low Penetrance of Pathogenic KCNE1 Variants in Long QT Syndrome Type 5.

Long QT syndrome (LQTS) is an inherited cardiac rhythm disorder associated with increased incidence of cardiac arrhythmias and sudden death. LQTS type 5 (LQT5) is caused by dominant mutant variants of KCNE1, a regulatory subunit of the voltage-gated ion channels generating the cardiac potassium current IKs. While mutant LQT5 KCNE1 variants are known to inhibit IKs amplitudes in heterologous expression systems, cardiomyocytes from a transgenic rabbit LQT5 model displayed unchanged IKs amplitudes, pointing towards the critical role of additional factors in the development of the LQT5 phenotype in vivo. In this study, we demonstrate that KCNE3, a candidate regulatory subunit of IKs channels minimizes the inhibitory effects of LQT5 KCNE1 variants on IKs amplitudes, while current deactivation is accelerated. Such changes recapitulate IKs properties observed in LQT5 transgenic rabbits. We show that KCNE3 accomplishes this by displacing the KCNE1 subunit within the IKs ion channel complex, as evidenced by a dedicated biophysical assay. These findings depict KCNE3 as an integral part of the IKs channel complex that regulates IKs function in cardiomyocytes and modifies the development of the LQT5 phenotype.

Design of New Potent and Selective Thiophene-Based KV1.3 Inhibitors and Their Potential for Anticancer Activity.

The voltage-gated potassium channel KV1.3 has been recognized as a tumor marker and represents a promising new target for the discovery of new anticancer drugs. We designed a novel structural class of KV1.3 inhibitors through structural optimization of benzamide-based hit compounds and structure-activity relationship studies. The potency and selectivity of the new KV1.3 inhibitors were investigated using whole-cell patch- and voltage-clamp experiments. 2D and 3D cell models were used to determine antiproliferative activity. Structural optimization resulted in the most potent and selective KV1.3 inhibitor 44 in the series with an IC50 value of 470 nM in oocytes and 950 nM in Ltk- cells. KV1.3 inhibitor 4 induced significant apoptosis in Colo-357 spheroids, while 14, 37, 43, and 44 significantly inhibited Panc-1 proliferation.

Morpho-functional comparison of differentiation protocols to create iPSC-derived cardiomyocytes.

Cardiomyocytes derived from induced pluripotent stem cells (iPSC-CMs) offer an attractive platform for cardiovascular research. Patient-specific iPSC-CMs are very useful for studying disease development, and bear potential for disease diagnostics, prognosis evaluation and development of personalized treatment. Several monolayer-based serum-free protocols have been described for the differentiation of iPSCs into cardiomyocytes, but data on their performance are scarce. In this study, we evaluated two protocols that are based on temporal modulation of the Wnt/ß-catenin pathway for iPSC-CM differentiation from four iPSC lines, including two control individuals and two patients carrying an SCN5A mutation. The SCN5A gene encodes the cardiac voltage-gated sodium channel (Nav1.5) and loss-of-function mutations can cause the cardiac arrhythmia Brugada syndrome. We performed molecular characterization of the obtained iPSC-CMs by immunostaining for cardiac specific markers and by expression analysis of selected cardiac structural and ionic channel protein-encoding genes with qPCR. We also investigated cell growth morphology, contractility and survival of the iPSC-CMs after dissociation. Finally, we performed electrophysiological characterization of the cells, focusing on the action potential (AP) and calcium transient (CT) characteristics using patch-clamping and optical imaging, respectively. Based on our comprehensive morpho-functional analysis, we concluded that both tested protocols result in a high percentage of contracting CMs. Moreover, they showed acceptable survival and cell quality after dissociation (>50% of cells with a smooth cell membrane, possible to seal during patch-clamping). Both protocols generated cells presenting with typical iPSC-CM AP and CT characteristics, although one protocol (that involves sequential addition of CHIR99021 and Wnt-C59) rendered iPSC-CMs, which were more accessible for patch-clamp and calcium transient experiments and showed an expression pattern of cardiac-specific markers more similar to this observed in human heart left ventricle samples.

Properties of deactivation gating currents in Shaker channels.

The charge versus voltage relation of voltage-sensor domains shifts in the voltage axis depending on the initial voltage. Here we show that in nonconducting W434F Shaker K(+) channels, a large portion of this charge-voltage shift is apparent due to a dramatic slowing of the deactivation gating currents, Ig(D) (with τ up to 80 ms), which develops with a time course of ∼1.8 s. This slowing in Ig(D) adds up to the slowing due to pore opening and is absent in the presence of 4-aminopyridine, a compound that prevents the last gating step that leads to pore opening. A remaining 10-15 mV negative shift in the voltage dependence of both the kinetics and the charge movement persists independently of the depolarizing prepulse duration and remains in the presence of 4-aminopyridine, suggesting the existence of an intrinsic offset in the local electric field seen by activated channels. We propose a new (to our knowledge) kinetic model that accounts for these observations.