State-dependent block of BK channels by synthesized shaker ball peptides

Crystal structures of potassium channels have strongly corroborated an earlier hypothetical picture based on functional studies, in which the channel gate was located on the cytoplasmic side of the pore. However, accessibility studies on several types of ligand-sensitive K(+) channels have suggested that their activation gates may be located near or within the selectivity filter instead. It remains to be determined to what extent the physical location of the gate is conserved across the large K(+) channel family. Direct evidence about the location of the gate in large conductance calcium-activated K(+) (BK) channels, which are gated by both voltage and ligand (calcium), has been scarce. Our earlier kinetic measurements of the block of BK channels by internal quaternary ammonium ions have raised the possibility that they may lack a cytoplasmic gate. We show in this study that a synthesized Shaker ball peptide (ShBP) homologue acts as a state-dependent blocker for BK channels when applied internally, suggesting a widening at the intracellular end of the channel pore upon gating. This is consistent with a gating-related conformational change at the cytoplasmic end of the pore-lining helices, as suggested by previous functional and structural studies on other K(+) channels. Furthermore, our results from two BK channel mutations demonstrate that similar types of interactions between ball peptides and channels are shared by BK and other K(+) channel types.     

State-dependent inhibition of sodium channels by local anesthetics: A 40-year evolution

Knowledge about the mechanism of impulse blockade by local anesthetics has evolved over the past four decades, from the realization that Na⁺ channels were inhibited to affect the impulse blockade to an identification of the amino acid residues within the Na⁺ channel that bind the local anesthetic molecule. Within this period appreciation has grown of the state-dependent nature of channel inhibition, with rapid binding and unbinding at relatively high affinity to the open state, and weaker binding to the closed resting state. Slow binding of high affinity for the inactivated state accounts for the salutary therapeutic as well as the toxic actions of diverse class I anti-arrhythmic agents, but may have little importance for impulse blockade, which requires concentrations high enough to block the resting state. At the molecular level, residues on the S6 transmembrane segments in three of the homologous domains of the channel appear to contribute to the binding of local anesthetics, with some contribution also from parts of the selectivity filter. Binding to the inactivated state, and perhaps the open state, involves some residues that are not identical to those that bind these drugs in the resting state, suggesting spatial flexibility in the “binding site”. Questions remaining include the mechanism that links local anesthetic binding with the inhibition of gating charge movements, and the molecular nature of the theoretical “hydrophobic pathway” that may be critical for determining the recovery rates from blockade of closed channels, and thus account for both therapeutic and cardiotoxic actions.     

State-dependent block of CNG channels by dequalinium

Cyclic nucleotide-gated (CNG) ion channels are nonselective cation channels with a high permeability for Ca(2+). Not surprisingly, they are blocked by a number of Ca(2+) channel blockers including tetracaine, pimozide, and diltiazem. We studied the effects of dequalinium, an extracellular blocker of the small conductance Ca(2+)-activated K(+) channel. We previously noted that dequalinium is a high-affinity blocker of CNGA1 channels from the intracellular side, with little or no state dependence at 0 mV. Here we examined block by dequalinium at a broad range of voltages in both CNGA1 and CNGA2 channels. We found that dequalinium block was mildly state dependent for both channels, with the affinity for closed channels 3-5 times higher than that for open channels. Mutations in the S4-S5 linker did not alter the affinity of open channels for dequalinium, but increased the affinity of closed channels by 10-20-fold. The state-specific effect of these mutations raises the question of whether/how the S4-S5 linker alters the binding of a blocker within the ion permeation pathway.     

State-dependent inhibition of cystic fibrosis transmembrane conductance regulator chloride channels by a novel peptide toxin

Peptide toxins from animal venom have been used for many years for the identification and study of cation-permeable ion channels. However, no peptide toxins have been identified that interact with known anion-selective channels, including cystic fibrosis transmembrane conductance regulator (CFTR), the protein defective in cystic fibrosis and a member of the ABC transporter superfamily. Here, we describe the identification and initial characterization of a novel 3.7-kDa peptide toxin, GaTx1, which is a potent and reversible inhibitor of CFTR, acting from the cytoplasmic side of the membrane. Thus, GaTx1 is the first peptide toxin identified that inhibits a chloride channel of known molecular identity. GaTx1 exhibited high specificity, showing no effect on a panel of nine transport proteins, including Cl(-) and K(+) channels, and ABC transporters. GaTx1-mediated inhibition of CFTR channel activity is strongly state-dependent; both potency and efficacy are reduced under conditions of elevated [ATP], suggesting that GaTx1 may function as a non-competitive inhibitor of ATP-dependent channel gating. This tool will allow the application of new quantitative approaches to study CFTR structure and function, particularly with respect to the conformational changes that underlie transitions between open and closed states.     

State-dependent inhibition of L-type calcium channels: cell-based assay in high-throughput format

The current studies describe a new, robust cell-based functional assay useful to characterize L-type voltage-dependent calcium channels and their antagonists. The basis of this assay is measurement in plate format of Ca2+ influx through the L-type Ca2+ channel complex (alpha1C, alpha2delta, and beta2a subunits) in response to potassium-mediated depolarization; EC(50)=11 mM [K+](o). The Ca2+ influx was inhibited by the L-type Ca2+ channel antagonist, nimodipine; IC(50)=59 nM. These cells were also transfected with the Kir2.3 inward rectifier K(+) channel, which allows for changing the cell membrane potential by modulation of extracellular [K](o); -65 mV in physiological [K](o) and -28 mV in 30 mM [K](o) containing buffer. The conformational state of the voltage-sensitive Ca2+ channel is altered under these different conditions. Under the depolarized condition, nimodipine was a more potent antagonist, inhibiting Ca2+ influx with an IC(50) value of 3 nM. The results demonstrate that the interaction of nimodipine and other antagonists with the channel is modulated by changes in membrane potential and thus the state of the channel. Overall, this novel assay can be used to identify state-dependent calcium channel antagonists and should be useful for evaluating state-dependent inhibitory potency of a large number of samples.     

BK channels mediate cholinergic inhibition of high frequency cochlear hair cells

Background

Outer hair cells are the specialized sensory cells that empower the mammalian hearing organ, the cochlea, with its remarkable sensitivity and frequency selectivity. Sound-evoked receptor potentials in outer hair cells are shaped by both voltage-gated K⁺ channels that control the membrane potential and also ligand-gated K⁺ channels involved in the cholinergic efferent modulation of the membrane potential. The objectives of this study were to investigate the tonotopic contribution of BK channels to voltage- and ligand-gated currents in mature outer hair cells from the rat cochlea.

Methodology/Principal

Findings In this work we used patch clamp electrophysiology and immunofluorescence in tonotopically defined segments of the rat cochlea to determine the contribution of BK channels to voltage- and ligand-gated currents in outer hair cells. Although voltage and ligand-gated currents have been investigated previously in hair cells from the rat cochlea, little is known about their tonotopic distribution or potential contribution to efferent inhibition. We found that apical (low frequency) outer hair cells had no BK channel immunoreactivity and little or no BK current. In marked contrast, basal (high frequency) outer hair cells had abundant BK channel immunoreactivity and BK currents contributed significantly to both voltage-gated and ACh-evoked K⁺ currents.

Conclusions/Significance

Our findings suggest that basal (high frequency) outer hair cells may employ an alternative mechanism of efferent inhibition mediated by BK channels instead of SK2 channels. Thus, efferent synapses may use different mechanisms of action both developmentally and tonotopically to support high frequency audition. High frequency audition has required various functional specializations of the mammalian cochlea, and as shown in our work, may include the utilization of BK channels at efferent synapses. This mechanism of efferent inhibition may be related to the unique acetylcholine receptors that have evolved in mammalian hair cells compared to those of other vertebrates.     

Tuning magnesium sensitivity of BK channels by mutations

Intracellular Mg(2+) at physiological concentrations activates mSlo1 BK channels by binding to a metal-binding site in the cytosolic domain. Previous studies suggest that residues E374, Q397, and E399 are important in Mg(2+) binding. In the present study, we show that mutations of E374 or E399 to other amino acids, except for Asp, abolish Mg(2+) sensitivity. These results further support that the side chains of E374 and E399 are essential for Mg(2+) coordination. To the contrary, none of the Q397 mutations abolishes Mg(2+) sensitivity, suggesting that its side chain may not coordinate to Mg(2+). However, because Q397 is spatially close to E374 and E399, its mutations affect the Mg(2+) sensitivity of channel gating by either reducing or increasing the Mg(2+) binding affinity. The pattern of mutational effects and the effect of chemical modification of Q397C indicate that Q397 is involved in the Mg(2+)-dependent activation of BK channels and that mutations of Q397 alter Mg(2+) sensitivity by affecting the conformation of the Mg(2+) binding site as well as by electrostatic interactions with the bound Mg(2+) ion.     

State-dependent modification of ATP-sensitive K+ channels by phosphatidylinositol 4,5-bisphosphate

With inside-out patchrecordings in ventricular myocytes from the hearts of guinea pigs, westudied ATP-sensitive K⁺ (K_ATP) channelsactivated by phosphatidylinositol 4,5-bisphosphate (PIP₂)with respect to sensitivity to ATP when in either a rundown state (RS)or a non-rundown state (NRS). Rundown of K_ATP channels wasinduced by exposure either to ATP-free solution or to ATP-free solutioncontaining 19 µM Ca²⁺. Exposure of membrane patches to 10 µM PIP₂ reactivated channels with both types of rundown.The reactivation by PIP₂ did not require ATP in the bath.The IC₅₀ of channels recovered from RS and before therundown was 37.1 and 31.1 µM, respectively. PIP₂irreversibly increased the mean current when the channel was in theNRS. This was associated with a shift of IC₅₀ to 250.6 µMafter PIP₂ exposure. PIP₂ activates NRSK_ATP channels by decreasing their sensitivity to ATP,whereas PIP₂ reactivates RS-K_ATP channelsindependently of ATP without changing ATP sensitivity.

     

State-dependent block of wild-type and inactivation-deficient Na+ channels by flecainide

The antiarrhythmic agent flecainide appears beneficial for painful congenital myotonia and LQT-3/DeltaKPQ syndrome. Both diseases manifest small but persistent late Na+ currents in skeletal or cardiac myocytes. Flecainide may therefore block late Na+ currents for its efficacy. To investigate this possibility, we characterized state-dependent block of flecainide in wild-type and inactivation-deficient rNav1.4 muscle Na+ channels (L435W/L437C/A438W) expressed with beta1 subunits in Hek293t cells. The flecainide-resting block at -140 mV was weak for wild-type Na+ channels, with an estimated 50% inhibitory concentration (IC50) of 365 micro M when the cell was not stimulated for 1,000 s. At 100 micro M flecainide, brief monitoring pulses of +30 mV applied at frequencies as low as 1 per 60 s, however, produced an approximately 70% use-dependent block of peak Na+ currents. Recovery from this use-dependent block followed an exponential function, with a time constant over 225 s at -140 mV. Inactivated wild-type Na+ channels interacted with flecainide also slowly at -50 mV, with a time constant of 7.9 s. In contrast, flecainide blocked the open state of inactivation-deficient Na+ channels potently as revealed by its rapid time-dependent block of late Na+ currents. The IC50 for flecainide open-channel block at +30 mV was 0.61 micro M, right within the therapeutic plasma concentration range; on-rate and off-rate constants were 14.9 micro M-1s-1 and 12.2 s-1, respectively. Upon repolarization to -140 mV, flecainide block of inactivation-deficient Na+ channels recovered, with a time constant of 11.2 s, which was approximately 20-fold faster than that of wild-type counterparts. We conclude that flecainide directly blocks persistent late Na+ currents with a high affinity. The fast-inactivation gate, probably via its S6 docking site, may further stabilize the flecainide-receptor complex in wild-type Na+ channels.     

Acid sensing ion channels regulate neuronal excitability by inhibiting BK potassium channels

Acid sensing ion channels (ASICs), Ca²⁺ and voltage-activated potassium channels (BK) are widely present throughout the central nervous system. Previous studies have shown that when expressed together in heterologous cells, ASICs inhibit BK channels, and this inhibition is relieved by acidic extracellular pH. We hypothesized that ASIC and BK channels might interact in neurons, and that ASICs may regulate BK channel activity. We found that ASICs inhibited BK currents in cultured wild-type cortical neurons, but not in ASIC1a/2/3 triple knockout neurons. The inhibition in the wild-type was partially relieved by a drop in extracellular pH to 6. To test the consequences of ASIC-BK interaction for neuronal excitability, we compared action potential firing in cultured cortical neurons from wild-type and ASIC1a/2/3 null mice. We found that in the knockout, action potentials were narrow and exhibited increased after-hyperpolarization. Moreover, the excitability of these neurons was significantly increased. These findings are consistent with increased BK channel activity in the neurons from ASIC1a/2/3 null mice. Our data suggest that ASICs can act as endogenous pH-dependent inhibitors of BK channels, and thereby can reduce neuronal excitability.     

State-dependent cAMP binding to functioning HCN channels studied by patch-clamp fluorometry

One major goal of ion channel research is to delineate the molecular events from the detection of the stimuli to the movement of channel gates. For ligand-gated channels, it is challenging to separate ligand binding from channel gating. Here we studied the cyclic adenosine monophosphate (cAMP)-dependent gating in hyperpolarization-activated cAMP-regulated (HCN) channel by simultaneously recording channel opening and ligand binding, using the patch-clamp fluorometry technique with a unique fluorescent cAMP analog that fluoresces strongly in the hydrophobic binding pocket and exerts regulatory effects on HCN channels similar to those imposed by cAMP. Corresponding to voltage-dependent channel activation, we observed a robust, close-to-threefold increase in ligand binding, which was more pronounced at subsaturating ligand concentrations than higher concentrations. This observation supported the cyclic allosteric models and indicated that protein allostery can be implemented through differentiating ligand binding affinities between resting and active states. The kinetics of ligand binding largely matched channel activation. However, during channel deactivation, ligand unbinding was slower than channel closing, suggesting a delayed response to membrane potential by the ligand binding machinery. Our results provide what we believe to be new insights into the cAMP-dependent gating in HCN channel and the interpretation of protein allostery for general ligand-gated channels and receptors.     

State-independent block of BK channels by an intracellular quaternary ammonium

Intracellular blockade by quaternary ammonium (QA) molecules of many potassium channels is state dependent, where the requirement for channel opening is evidenced by a time-dependent component of block in the macroscopic record. Whether this is the case for Ca(2+)- and voltage-activated potassium (BK) channels, however, remains unclear. Previous work (Li, W., and R.W. Aldrich. 2004. J. Gen. Physiol. 124:43-57) tentatively proposed a state-dependent, trapping model, but left open the possibility of state-independent block. Here, we found BK channel blockade by a novel QA derivative, bbTBA, was time dependent, raising the possibility of state-dependent, open channel block. Alternatively, the observed voltage dependence of block could be sufficient to explain time-dependent block. We have used steady-state and kinetic measurements of bbTBA blockade in order to discriminate between these two possibilities. bbTBA did not significantly slow deactivation kinetics at potentials between -200 and -100 mV, suggesting that channels can close unhindered by bound bbTBA. We further find no evidence that bbTBA is trapped inside BK channels after closing. Measurements of steady state fractional block at +40 mV revealed a 1.3-fold change in apparent affinity for a 33-fold change in P(o), in striking contrast to the 31-fold change predicted by state-dependent block. Finally, the appearance of a third kinetic component of bbTBA blockade at high concentrations is incompatible with state-dependent block. Our results suggest that access of intracellular bbTBA to the BK channel cavity is not strictly gated by channel opening and closing, and imply that the permeation gate for BK channels may not be intracellular.     

Protons block BK channels by competitive inhibition with K+ and contribute to the limits of unitary currents at high voltages

Proton block of unitary currents through BK channels was investigated with single-channel recording. Increasing intracellular proton concentration decreased unitary current amplitudes with an apparent pKa of 5.1 without discrete blocking events, indicating fast proton block. Unitary currents recorded at pH(i) 8.0 and 9.0 had the same amplitudes, indicating that 10(-8) M H(+) had little blocking effect. Increasing H(+) by recording at pH(i) 7.0, 6.0, and 5.0 then reduced the unitary currents by 13%, 25%, and 53%, respectively, at +200 mV. Increasing K(+)(i) relieved the proton block in a manner consistent with competitive inhibition of K(+)(i) action by H(+)(i). Proton block was voltage dependent, increasing with depolarization, indicating that block was coupled to the electric field of the membrane. Proton block was not described by the Woodhull equation for noncompetitive voltage-dependent block, but was described by an equation for cooperative competitive inhibition that included voltage-dependent block from the Woodhull equation. Proton block was still present after replacing the eight negative charges in the ring of charge at the entrance to the intracellular vestibule by uncharged amino acids. Thus, the ring of charge is not the site of proton block or of competitive inhibition of K(+)(i) action by H(+)(i). With 150 mM symmetrical KCl, unitary current amplitudes increased with depolarization, reaching 66 pA at +350 mV (pH(i) 7.0). The increase in amplitude with voltage became sublinear for voltages >100 mV. The sublinearity was unaffected by removing from the intracellular solutions Ca(2+) and Ba(2+) ions, the Ca(2+) buffers EGTA and HEDTA, the pH buffer TES, or by replacing Cl(-) with MeSO(3)(-). Proton block accounted for approximately 40% of the sublinearity at +200 mV and pH 7.0, indicating that factors in addition to proton block contribute to the sublinearity of the unitary currents through BK channels.     

Recognition of opioid agonist and antagonist in the opioid receptor binding site

By treating the rat crude synaptosomal fraction with 5,5'-dithio-bis-(2-nitrobenzoic acid), DTNB, a marked decrease of stereo-specific binding of opioid agonist (dihydromorphine or D-Ala-D-Leu-enkephalin) was observed, but there was no effect in the case of the binding of opioid antagonist (naloxone or diprenorphine). The decrease of the agonist binding in the presence of 500 microM of DTNB was nearly equal to that of 100 mM of NaCl. The ability of opioids to inhibit 3H-naloxone binding in the absence of DTNB was compared to their inhibitory potency in the presence of 500 microM of DTNB to obtain DTNB response ratio. This ratio closely correlated with sodium index of each opioid. Potency of the inactivation of the agonist binding by congeners of DTNB changed with net charge of the reagents, and 2,2'-dithiobis-(5-nitropyridine), bearing a positive charge, was most effective. These results suggest that an aliphatic sulfhydryl group, being sensitive to DTNB is located to the active center of an anionic binding site for the agonist, and controls opioid agonist binding through a proton transfer mechanism.     

Renovascular BK(Ca) channels are not activated in vivo under resting conditions and during agonist stimulation

We investigated the role of large-conductance Ca(2+)-activated K(+) (BK(Ca)) channels for the basal renal vascular tone in vivo. Furthermore, the possible buffering by BK(Ca) of the vasoconstriction elicited by angiotensin II (ANG II) or norepinephrine (NE) was investigated. The possible activation of renal vascular BK(Ca) channels by cAMP was investigated by infusing forskolin. Renal blood flow (RBF) was measured in vivo using electromagnetic flowmetry or ultrasonic Doppler. Renal preinfusion of tetraethylammonium (TEA; 3.0 mumol/min) caused a small reduction of baseline RBF, but iberiotoxin (IBT; 0.3 nmol/min) did not have any effect. Renal injection of ANG II (1-4 ng) or NE (10-40 ng) produced a transient decrease in RBF. These responses were not affected by preinfusion of TEA or IBT. Renal infusion of the BK(Ca) opener NS-1619 (90.0 nmol/min) did not affect basal RBF or the response to NE, but it attenuated the response to ANG II. Coadministration of NS-1619 with TEA or IBT abolished this effect. Forskolin caused renal vasodilation that was not inhibited by IBT. The presence of BK(Ca) channels in the preglomerular vessels was confirmed by immunohistochemistry. Despite their presence, there is no indication for a major role for BK(Ca) channels in the control of basal renal tone in vivo. Furthermore, BK(Ca) channels do not have a buffering effect on the rat renal vascular responses to ANG II and NE. The fact that NS-1619 attenuates the ANG II response indicates that the renal vascular BK(Ca) channels can be activated under certain conditions.     

Closed-channel block of BK potassium channels by bbTBA requires partial activation

Blockade of large-conductance Ca²⁺-activated K⁺ (BK) channels by the bulky quaternary ammonium compound, N-(4-[benzoyl]benzyl)-N,N,N-tributylammonium (bbTBA), exhibits features consistent with blockade of both closed and open states. Here, we examine block of closed BK channels by bbTBA and how it may differ from block of open channels. Although our observations generally confirm earlier results, we describe three observations that are inconsistent with a model in which closed and open channels are equally accessible to blockade by bbTBA. First, block by bbTBA exhibits Ca²⁺-dependent features that are inconsistent with strictly state-independent block. Second, the steady-state voltage dependence of bbTBA block at negative potentials shows that any block of completely closed states either does not occur or is completely voltage independent. Third, determination of the fractional unblock by bbTBA at either low or high Ca²⁺ reveals deviations from a model in which open- and closed-state block is identical. The results support the view that bbTBA blockade of fully closed channels does not occur. We imagine two general types of explanation. First, a stronger voltage dependence of closed-channel block may minimize the contribution of closed-channel block at negative potentials. Second, voltage-dependent conformational changes among closed-channel states may permit block by bbTBA. The analysis supports the latter view, suggesting that bbTBA blockade of fully closed channels does not occur, but the ability of bbTBA to block a closed channel requires movement of one or more voltage sensors. Models in which block is coupled to voltage sensor movement can qualitatively account for (1) the ability of open-channel block to better fit block of conductance–voltage curves at high Ca²⁺; (2) the voltage dependence of fractional availability; and (3) the fractional unblock at different open probabilities. BK channels appear to undergo voltage-dependent conformational changes among closed states that are permissive for bbTBA block.     

Paxilline inhibits BK channels by an almost exclusively closed-channel block mechanism

Paxilline, a tremorogenic fungal alkaloid, potently inhibits large conductance Ca²⁺- and voltage-activated K⁺ (BK)-type channels, but little is known about the mechanism underlying this inhibition. Here we show that inhibition is inversely dependent on BK channel open probability (Po), and is fully relieved by conditions that increase Po, even in the constant presence of paxilline. Manipulations that shift BK gating to more negative potentials reduce inhibition by paxilline in accordance with the increase in channel Po. Measurements of Po times the number of channels at negative potentials support the idea that paxilline increases occupancy of closed states, effectively reducing the closed–open equilibrium constant, L(0). Gating current measurements exclude an effect of paxilline on voltage sensors. Steady-state inhibition by multiple paxilline concentrations was determined for four distinct equilibration conditions, each with a distinct Po. The IC₅₀ for paxilline shifted from around 10 nM when channels were largely closed to near 10 µM as maximal Po was approached. Model-dependent analysis suggests a mechanism of inhibition in which binding of a single paxilline molecule allosterically alters the intrinsic L(0) favoring occupancy of closed states, with affinity for the closed conformation being >500-fold greater than affinity for the open conformation. The rate of inhibition of closed channels was linear up through 2 µM paxilline, with a slope of 2 × 10⁶ M⁻¹s⁻¹. Paxilline inhibition was hindered by either the bulky cytosolic blocker, bbTBA, or by concentrations of cytosolic sucrose that hinder ion permeation. However, paxilline does not hinder MTSET modification of the inner cavity residue, A313C. We conclude that paxilline binds more tightly to the closed conformation, favoring occupancy of closed-channel conformations, and propose that it binds to a superficial position near the entrance to the central cavity, but does not hinder access of smaller molecules to this cavity.     

Generation of functional fluorescent BK channels by random insertion of GFP variants

The yellow and cyan variants of green fluorescent protein (GFP) constitute an excellent pair for fluorescence resonance energy transfer (FRET) and can be used to study conformational rearrangements of proteins. Our aim was to develop a library of fluorescent large conductance voltage- and Ca2+-gated channels (BK or slo channels) for future use in FRET studies. We report the results of a random insertion of YFP and CFP into multiple sites of the alpha subunit of the hslo channel using a Tn5 transposon-based technique. 55 unique fluorescent fusion proteins were obtained and tested for cell surface expression and channel function. 19 constructs are expressed at the plasma membrane and show voltage and Ca2+-dependent currents. In 16 of them the voltage and Ca2+ dependence is very similar to the wild-type channel. Two insertions in the Ca2+ bowl and one in the RCK2 domain showed a strong shift in the G-V curve. The remaining 36 constructs were retained intracellularly; a solubility assay suggests that these proteins are not forming intracellular aggregates. The "success rate" of 19 out of 55 hslo insertion constructs compares very favorably with other studies of random GFP fusions.     

BK channels: the spring between sensor and gate

K+ channels contain two main functional domains, an ion-selective pore and a sensor that determines whether the cytoplasmic pore gate is open or closed. In this issue of Neuron, Niu et al. provide compelling evidence that the link between sensor and gate is a remarkably simple mechanical spring.