Fast and Slow Positive Adaptation in Frog Hair Cells
The two models for fast adaptation predict different rates of slow adaptation for small displacements. Because the adaptation motor behaves viscously (Howard and Hudspeth, 1987
; Assad and Corey, 1992
), the rate of slow adaptation should be proportional to the tension applied to the motor. In the channel-reclosure model for fast adaptation, rapid channel closure shortens the mechanical chain connecting the motor to the gating spring, tensing the spring; therefore, elevated tension should increase
the rate of positive adaptation in response to small stimuli (). Moreover, the distance the motor moves—the extent of slow adaptation—also should increase, because the motor must slip farther down the stereociliary actin filaments to reduce tension to its steady-state level.
By contrast, in the release model, fast adaptation lengthens the mechanical chain connected to the gating spring; the resulting reduction in tension should then decrease the rate of slow adaptation (). Fast adaptation thus diminishes the extent of slow adaptation; if the lengthening induced by the release is larger than the stimulus amplitude, no slow adaptation will ensue. In both models, slow adaptation approaches linear viscous behavior with larger-sized stimuli.
We tested these models by measuring fast and slow adaptation for a range of mechanical displacements in 15 bullfrog saccule hair cells. We stimulated hair cells with stiff glass probes, which allowed us to avoid the complications of cooperative transduction-channel gating and time-dependent bundle movements. For each cell, we first measured the current-displacement curve, which describes the activation of transduction channels in response to a stimulus. We follow previous convention (Eatock et al., 1987
) by defining adaptation as the time-dependent shift of the current-displacement curve along the displacement axis, not channel closing per se; for example, for very large bundle displacements, when channels are mostly open, a substantial shift of the current-displacement curve can occur with very little change in open probability.
To measure the progress of adaptation, we used the inferred-shift method (Shepherd and Corey, 1994
). In this method, the transduction current at every point during an adapting stimulus is mapped back onto the current-displacement curve to determine Xe
(t), the adaptive shift or extent of adaptation. The validity of the method rests on the assumption that, during adaptation, neither the size nor shape of the current-displacement curve changes (Shepherd and Corey, 1994
). Similar to previous results in hair cells of the frog (Shepherd and Corey, 1994
; Cheung and Corey, 2005
) and mouse (Holt et al., 1997
; Vollrath and Eatock, 2003
), we found that this assumption holds in our experiments (see Figures S1A and S1B
in the Supplemental Data
available online). The inferred-shift method is described in detail in Figure S1C
We separated fast and slow adaptation by fitting the Xe
(t) data with double-exponential functions (), allowing us to calculate independent fast and slow time constants for each stimulus (see Figure S2
for validation of the fitting routine). The adaptive shift in response to each stimulus size was therefore described by individual values of time constants, τfast
, as well as final amplitudes (adaptation extent) Xe(fast)
. Note that the inferred-shift method gives us the temporal resolution necessary to accurately separate fast and slow adaptation.
Separation of Fast and Slow Adaptation in Frog and Mouse Hair Cells
Fast and slow adaptation were prominent in all cells examined and, as previously noted (Hirono et al., 2004
), their properties were relatively stable over dialysis of 5 min or more. As described previously (Shepherd and Corey, 1994
), the total extent of adaptation—the shifts of the current-displacement curves on fast and slow time scales in response to an adapting stimulus—was linear between 0 and 0.8 µm (); the slope of the displacement-extent curve (X′e(total)
) was 0.85.
By contrast, the extent of fast adaptation saturated. This result is predicted by both models; in the channel-reclosure model, the extent depends on the relative free energies of Ca2+
-free and Ca2+
-bound channels, while in the release model, the extent depends on the length of the release element. Notably, the dependence of fast extent on stimulus size resembled that of the current-displacement curve (). We fit fast-adaptation extent data with a product of Xe(fast) ∞
, the maximum amplitude of the fast shift, and Po
(see Equation S5
in the Supplemental Data
); the data were fit well and gave Xe(fast) ∞
of 0.29 µm. This value is reported in tip coordinates; conversion to the movement at the level of the adaptation motor requires multiplication by the geometrical gain γ (0.12–0.14 in frog; Jacobs and Hudspeth, 1990
). We interpret the observed dependence on Po
as a reflection of fast adaptation’s requirement for Ca2+
entry during transduction (Fettiplace and Ricci, 2003
At the largest stimulus amplitudes, τfast
decreased (). We fit the time constants as a function of displacement with Equation S6
(see the Supplemental Data
), assuming that fast adaptation proceeds with two rates: one independent of stimulus size (and hence independent of force) and the other force dependent. Despite the faster rate for large stimuli, the extent of fast adaptation remained the same; this result suggested that the dependence of extent on Po
and of τfast
on force were different manifestations of a single process that can be triggered by either Ca2+
or force. The decrease in τfast
is consistent with the release model, as force could directly cause the conformational shift producing the release, but is inconsistent with the channel-reclosure model, as larger forces in the gating spring would be unlikely to speed channel closing. The distinct behavior of Xe(fast)
produces a displacement dependence for the initial rate of fast adaptation, Xe(fast)
(), that is more complex than that diagrammed in .
The response of slow adaptation to displacements was markedly different. There was essentially no slow shift of the current-displacement curve (i.e., near-zero extent of slow adaptation) for small Xs, and with larger Xs, the extent of slow adaptation became linear with Xs (). In addition, τslow did not depend on stimulus size ().
The upward-curving slow-adaptation rate curve, in which the rate of slow adaptation is near zero for small displacements (, arrow in inset), is consistent with the release model for fast adaptation (). The slow rate was fit by assuming that the adaptation motor was a linearly viscous element that responds to the difference between total and fast extent (Equation S8
in the Supplemental Data
). We interpret this relationship as indicating that fast and slow adaptation combine linearly to produce the final extent of adaptation: because a release decreases tension, fast adaptation reduces the force that drives slow adaptation. Equation S8
) allowed an excellent fit of the data with a single free parameter, the rate constant for slow adaptation, which was 42 s−1
Fast and Slow Positive Adaptation in Mouse Hair Cells
To determine the generality of these conclusions, we turned to hair cells of the mouse utricle (). Although we initially analyzed data separately from the outbred strain CD-1 and the inbred strain C57BL/6, we found that transduction and adaptation properties were sufficiently similar to pool the two datasets. The rate of fast positive adaptation was significantly lower in mouse than in frog vestibular hair cells (Vollrath and Eatock, 2003
), both because of intrinsic differences between the two species and because mouse data were acquired at a lower extracellular Ca2+
concentration (1.3 mM, versus 4 mM in frog hair cells). All of the features of fast and slow adaptation that we identified in frog hair cells with the inferred-shift analysis were also present in the mouse (), although less prominent; for example, τfast
decreased (from ~12 ms to <8 ms) with our largest stimuli (). Moreover, the extent of fast adaptation was proportional to Po
, yielding an Xe(fast) ∞
of 0.76 µm; that this value is larger than that of frog is not surprising, given the smaller value of γ in mouse (0.05). These results show that fast positive adaptation in mouse vestibular hair cells is mechanistically similar to that in frog saccule hair cells, as shown previously (Vollrath and Eatock, 2003
Moreover, the properties of slow positive adaptation in mouse vestibular hair cells were similar to those in frog vestibular cells. The relation between displacement and slow-adaptation rate in mouse was curved upward and was well fit with Equation S8
, the model used for frog adaptation (, inset); the rate constant for slow adaptation was 22 s−1
. Again, this result is most consistent with the release model for slow adaptation.
As reported previously (Vollrath and Eatock, 2003
), the relationship between the total extent of adaptation and displacement in mouse hair cells was not linear (). Our data were fit well with a second-order polynomial with positive parameter values and were consistent with an extent spring that decreases in stiffness with increasing displacement.
Total Extent Is Constant in Frog and Mouse Hair Cells
Rates and extents of fast and slow adaptation varied substantially from cell to cell, particularly in the mouse utricle. We found no correlation between the rates of fast and slow adaptation in individual frog or mouse hair cells (). By contrast, when we compared slopes of linear fits to displacement-extent plots, we found a strong inverse correlation (R = 0.90 for all mouse cells) between the slopes of the fast and slow adaptation plots in individual vestibular hair cells, even in cells of different genotypes; a cell with a higher extent of fast adaptation had little slow adaptation and vice versa ().
Comparison of the Rate and Extent of Fast and Slow Adaptation
Because the slow and fast extents need not add to a constant value, the presence of the inverse correlation is an important consideration. The release model predicts this relationship because progression of fast adaptation reduces the force that drives slow adaptation, and the adaptation motor need not slip as far to reduce tension. The channel-reclosure model predicts the opposite: the extent of slow adaptation will increase with more fast adaptation. Another explanation for the plateau in slow adaptation rate for small displacements () is that the adaptation motor is deprived of Ca2+ because fast adaptation closes channels. However, this explanation cannot explain the data of , since the adaptation extents were derived from data spanning the entire displacement range, not just over the narrow range in which channel closure might affect Ca2+ levels.
Fast Phase of Negative Adaptation in Frog and Mouse Hair Cells
When bundles are moved in the negative direction, adaptation responds to the reduced gating-spring tension by generating force, thereby restoring sensitivity. We assessed negative adaptation by moving hair bundles sufficiently far in the negative direction that channels stayed closed, despite adaptation; upon return of the bundle to rest, an overshoot current developed whose amplitude reflected the extent of adaptation during the stimulus (). As reported previously (Hirono et al., 2004
), negative adaptation in frog hair cells occurred in two phases, one fast and exponential and the second slower and linear (). In 12 frog cells, the time constant for the fast phase was 10 ± 2 ms, and its amplitude (in tip coordinates) was 0.12 ± 0.02 µm (initial rate of 12 µm/s), while the rate of the slow linear phase was 0.97 ± 0.15 µm/s. We conclude that the fast phase corresponds to reversal of the fast adaptation release (as Ca2+
entry is blocked), and the slow phase results from adaptation-motor myosins cyclically climbing the stereocilia actin cores.
Negative Adaptation in Frog and Mouse Hair Cells
Adaptation to negative steps in mouse vestibular hair cells also showed fast exponential and slow linear phases (). In 12 C57BL/6 control cells, the time constant for the fast phase was 34 ± 13 ms, and its amplitude was 0.27 ± 0.04 µm; averaging rates from individual cells, the initial rate was 18 ± 5 µm/s. The rate of the slow linear phase was 0.38 ± 0.10 µm/s.
We used a chemical-genetic strategy (Holt et al., 2002
) to investigate the mechanism and molecule responsible for fast adaptation. The release model could be satisfied if Myo1c itself dissociates from actin or changes configuration rapidly in response to force and Ca2+
(Hudspeth and Gillespie, 1994
; Bozovic and Hudspeth, 2003
; Batters et al., 2004b
). To allow us to specifically and selectively arrest all Myo1c in stereocilia and prevent its mechanical movements, we generated mice with a targeted gene replacement that introduced the Y61G mutation into both Myo1c
alleles. This mutation sensitizes Myo1c to N6
-modified ADP analogs; for example, N6
(2-methyl butyl) ADP (NMB-ADP) blocked Y61G-Myo1c activity while having little effect on wild-type Myo1c (Gillespie et al., 1999
). Although we previously generated a transgenic mouse expressing Y61G-Myo1c (Holt et al., 2002
), relatively poor expression of the transgene ensured that wild-type Myo1c was the majority of the myosin-1c protein in those mice. In our studies of slow adaptation, the presence of a minority of mutant Myo1c tightly bound to actin was sufficient to arrest the movement of a plaque of Myo1c.
We introduced the Y61G mutation and a loxP-flanked neomycin resistance cassette into a targeting construct (), electroporated the construct into mouse embryonic stem cells, and injected targeted ES cells into blastocysts. We generated one chimeric mouse that transmitted the Y61G mutation to subsequent generations. Mice positive for Y61G were crossed with mice expressing Cre recombinase to remove the neomycin cassette () and backcrossed to C57BL/6 mice.
Generation and Characterization of Myo1cY61G Knockin Mice
Myo1c levels in wild-type and homozygous Y61G mice were nearly identical in all tissues examined (). Moreover, immunoblotting with an antibody that specifically recognizes the Y61G mutant demonstrated directly that Y61G-Myo1c was expressed in the auditory and vestibular systems of Y61G mice ().
Mouse Y61G-Myo1c Is Inhibited by NMB-ADP
We previously used rat Myo1c to characterize the Y61G mutation (Gillespie et al., 1999
). Because mouse Myo1c differs from rat Myo1c at several amino acid residues, including residue 62 (Thr in rat, Ser in mouse), we reinvestigated the inhibition of Myo1c activity by NMB-ADP. After expressing full-length wild-type and Y61G mouse Myo1c using baculoviruses, we purified these proteins and measured their ATPase activities. Y61G-Myo1c hydrolyzed ATP with a slightly lower Km
(9 ± 2 µM; n = 4) than did WT-Myo1c (17 ± 5 µM; n = 4).
NMB-ADP was a potent inhibitor of Y61G-Myo1c ATPase activity. Inhibition of WT-Myo1c required more than 150-fold more NMB-ADP (Ki = 119 ± 10 µM; n = 4) than was required for inhibition of Y61G-Myo1c (0.75 ± 0.10 µM; n = 4) (), indicating that this mutant-inhibitor combination is suitable for examination of the function of mouse Myo1c.
The effect of NMB-ADP on mutant and wild-type Myo1c also was assessed using an in vitro motility assay (). In the presence of 1 mM EGTA, wild-type mouse Myo1c moved actin filaments at 12.4 ± 0.8 nm/s (mean ± SE; n = 323 filaments). As with the rat mutant, mouse Y61G-Myo1c (25.0 ± 0.9 nm/s; n = 317) moved actin filaments faster than wt. In the presence of 2 mM ATP, NMB-ADP (250 µM) had little effect on WT-Myo1c motility (11.0 ± 0.3 nm/s; n = 363) but nearly completely inhibited motility with Y61G-Myo1c (2.7 ± 0.1 nm/s; n = 494).
Ca2+ slowed both wt (6.2 ± 0.3 nm/s; n = 329) and Y61G (12.4 ±1.1 nm/s; n = 243) Myo1c. The relative fraction of immobile filaments was larger in each case; we suggest that motors generate less force in the presence of elevated Ca2+ and cannot overcome the load imparted by ATP-insensitive myosin molecules (“deadheads”) distributed on the surface. Substituting NMB-ATP for ATP also slowed translocation for wt (5.6 ± 0.3 nm/s; n = 394) and Y61G (4.2 ± 0.6 nm/s; n = 87) Myo1c (), perhaps because Myo1c generates less force when NMB-ADP (the hydrolysis product) is bound.
Transduction and Adaptation in Y61G Hair Cells
To determine the role of Myo1c in fast adaptation, we recorded transduction currents from Y61G hair cells (and C57BL/6 cells as a control) with or without 250 µM NMB-ADP in the whole-cell recording pipette. When the pipette contained a control solution, transduction-current amplitudes in Y61G hair cells were similar to those in wild-type cells and were relatively stable during dialysis ().
Adaptation Is Slowed by NMB-ADP in Y61G but Not Wild-Type Hair Cells
Adaptation in the fastest Y61G hair cells was substantially faster than that in the fastest CD-1 or C57BL/6 control hair cells (). We fit rate-displacement data from individual cells with a linear regression and compared the slopes, which correspond to the rate constants (). We found that fast positive adaptation in Y61G hair cells was nearly twice as fast (16 cells; rate constant of 82 ± 19 s−1) than the pooled wild-type hair cells (31 cells; 46 ± 8 s−1) or the geno-typed-matched C57BL/6 hair cells (22 cells; 53 ± 6 s−1). Although this difference reached statistical significance (p < 0.05) for the first comparison, it did not for the second, presumably because of the relatively small Y61G sample size and wide range of adaptation rates. By contrast, the rate constant for slow positive adaptation in Y61G hair cells (8.3 ± 0.8 s−1) was similar to that in all wild-type cells (9.3 ± 1.2 s−1) or in C57BL/6 cells (8.6 ± 0.7 s−1), as shown in . Because they were determined with simple linear fits, these values were smaller than those determined in .
NMB-ADP Reduces Fast and Slow Adaptation Rates in Y61G Hair Cells
The progressive block of adaptation by NMB-ADP in Y61G hair cells was apparent in Xe
(t) plots generated by inferred-shift analysis (). To dissect the effects of NMB-ADP on Y61G hair cells, we averaged the Po
, extent, τ, and rate data from 20 cells for each displacement amplitude to generate average responses (). In Y61G hair cells, NMB-ADP both broadened the current-displacement relation () and reduced the total extent of adaptation (). By fitting individual current-displacement data with a two-state Boltzmann model, we found that broadening of the average curve was due to a large variability in the midpoint (X0
) of the individual curves, rather than a significant change in their slopes (Z) (data not shown). In addition, as noted previously (Holt et al., 2002
), maximum transduction current amplitudes decreased somewhat in Y61G hair cells (but not in C57BL/6 controls; data not shown) when NMB-ADP was included in the pipette (). NMB-ADP had no significant effects on transduction or adaptation in C57BL/6 control hair cells.
Fast and Slow Positive Adaptation Are Slowed by NMB-ADP in Y61G Hair Cells
The rate constant for fast positive adaptation in Y61G hair cells was greatly reduced by 250 µM NMB-ADP ( and ). Averaging linear rate-displacement fits, we found a rate constant for fast positive adaptation of 16 ± 3 s−1
, or one-fifth that of the same cells in the absence of the nucleotide. Fast-adaptation rates were significantly different when NMB-ADP was present (p < 0.01) for the three largest displacement steps (0.8, 1.4, and 2.0 µm). The effect of NMB-ADP on fast positive adaptation arose both from a 50% decrease in final extent of fast adaptation () and a 3-fold increase in τfast
(). Consistent with our previous result (Holt et al., 2002
), NMB-ADP reduced the rate constant for slow positive adaptation (to 3.1 ± 0.5 s−1
; and ). NMB-ADP thus blocks both fast and slow positive adaptation in Y61G hair cells, suggesting that Myo1c underlies both processes.
NMB-ADP Slows Negative Adaptation
As shown in , fast negative adaptation in the nine Y61G hair cells we analyzed was about one-third faster than in C57BL/6 controls (τ of 18 ± 3 ms and extent of 373 ± 81 nm in Y61G). Averaging results from individual cells, the initial rate of fast negative adaptation was 24 ± 6 µm/s in Y61G hair cells. As expected given the faster motility of Y61G-Myo1c (), slow negative adaptation was almost twice as fast in Y61G hair cells (0.62 ± 0.17 µm/s) as in wt ().
Fast and Slow Negative Adaptation Are Slowed by NMB-ADP in Y61G Hair Cells
In seven cells analyzed, NMB-ADP slowed both the fast exponential phase and the slow linear phase of adaptation to negative displacements (). The effect of NMB-ADP on fast negative adaptation was due to slowing of τ (to 68 ± 28 ms) and a decrease in extent (to 164 ± 42 nm); averaging results from individual cells, NMB-ADP reduced the initial rate to one-sixth its control value, or 4 ± 2 µm/s (). At 0.12 ± 0.07 µm/s, slow negative adaptation was reduced by NMB-ADP dialysis to one-fifth its control value (). Both fast and slow negative adaptation are thus inhibited by NMB-ADP in Y61G hair cells, indicating that Myo1c activity is required for both.