We first tested if prokaryotic sodium channels are mechanically sensitive, as previously shown for eukaryotic Na_Vs (Beyder et al., 2010; Morris and Juranka, 2007; Strege et al., 2003; Figure 1). In a side-by-side comparison with the eukaryotic Na_V1.5, we examined two prokaryotic channels: the wild-type (WT) NaChBac and a mutant (T220A) NaChBac with inactivation removed (Lee et al., 2012a; Lee et al., 2012b; Figure 1A). We expressed each channel in HEK293 cells and assayed its mechanosensitivity via whole-cell electrophysiology, with fluid shear stress (~1.1 dyn/cm²) applied as mechanical stimulation. Under control conditions, the wild-type NaChBac responded to depolarizing voltage pulses with steep activation followed by complete inactivation, like Na_V1.5 but with slower kinetics (Figure 1B, Figure 1—figure supplement 1A-D). The T220A mutant activated and stayed open with minimal inactivation (Figure 1B; Figure 1—figure supplement 1B).

Shear stress increased the whole-cell currents of both prokaryotic channels, comparably to Na_V1.5 (Figure 1B, ‘control’ vs. ‘shear’; Figure 1—figure supplement 1B, E; I_Peak in Table 1). Both activation and inactivation responded to shear stress, as demonstrated by the difference currents (I_Shear – I_Control) from both wild-type NaChBac and Na_V1.5 (Figure 1C). Removal of inactivation in NaChBac T220A allowed us to separate these responses and focus on activation. Shear forces also increased T220A NaChBac currents, albeit slightly less than for wild-type (Figure 1C), suggesting that mechanical forces act predominantly on the mechanistic steps associated with the channel’s activation and/or opening. Overall, shear stress increased maximum conductance (G_Max) by 47% for WT NaChBac and 34% for T220A NaChBac, compared to 26% for Na_V1.5 (Figure 1D, G_Max in Table 1).

Although the steady-state conductance curves obtained under shear stress mostly appear as vertically stretched versions of the control curves, accounting for the higher maximum current, they exhibit a slight negative shift of the half-activation voltage (Figure 1D; V_1/2a in Table 1). This effect is more easily visualized when each conductance curve is normalized to its maximum (Figure 1—figure supplement 1F). Shear stress also increased the conductance slope (δV_a in Table 1). Interestingly, the half-inactivation voltage also exhibits a negative shift (Figure 1—figure supplement 1G ; V_1/2i in Table 1). Kinetically, shear stress accelerates the time course of both activation (Figure 1—figure supplement 1C ; τ_a in Table 1) and inactivation (Figure 1—figure supplement 1D ; τ_i in Table 1).

The whole-cell shear stress experiments demonstrate that mechanical forces affect NaChBac macroscopic currents. These results are likely to have mechanistic implications, but ambiguities inherent to macroscopic currents limit the information that can be extracted from data about individual state transitions. We addressed these ambiguities via single-channel recordings, followed by a mechanistic analysis to determine how force interacts with voltage to gate the channel. To simplify experiments and interpretations, we focused on NaChBac T220A, which lacks inactivation (Lee et al., 2012a; Lee et al., 2012b). We expressed NaChBac T220A in Piezo1-knockout (P1KO) HEK293 cells, free of mechanosensitive channel activity (Dubin et al., 2017; Figure 2A, Figure 2—figure supplement 1A-F). We assayed mechanosensitivity via cell-attached patch-clamp electrophysiology, using a high-speed pressure clamp (Besch et al., 2002) to apply controlled suction to patches.

The single-channel amplitude of voltage-gated sodium channels is tiny (~1 pA at –80 mV and ~0.5 pA at –20 mV), and pressure-clamping introduces additional noise and transient artifacts. Together with rapid channel kinetics, these limitations have traditionally prevented single-channel studies on mechanosensitivity in VGICs. After careful mechanical and electrical optimization, despite the low signal-to-noise ratio typical for sodium channels (Vandenberg and Bezanilla, 1991), and the noise introduced by the pressure clamp (Figure 2—figure supplement 1G), we were able to resolve single-channel events across a physiologically relevant voltage range, and with enough bandwidth (~1 kHz) to capture sufficiently fast kinetics (Figure 2A).

Suction on the membrane patch exerts a mechanical force on the channel (Coste et al., 2010). Because patches have non-zero resting tension (Suchyna et al., 2009), we designed stimulation protocols to test voltage- and mechano-sensitivity in a pairwise fashion (Figure 2A), enabling us to assess mechanosensitivity from the difference between the suction-induced currents and the no-suction baseline, for all channels and traces. Under these conditions, a non-zero patch tension is expected to slightly bias the kinetic properties at rest but not obscure the magnitude and location of mechanosensitive steps within the gating mechanism. Within each 400ms voltage step from –100 to –20 mV, the suction pressure alternated between 0 and −10, –30, or –50 mmHg. Thus, we could obtain and compare control and pressure data in the same cell, using test pressures relevant to mechanosensitive channel function (Coste et al., 2010; Gottlieb et al., 2012). As indicated by the current amplitude histograms (Figure 2B), the single-channel current is less than 0.5 pA at –20 mV, but we could still separate the closed and open levels. Above –20 mV, the unitary current became too small for reliable analysis. Using a half-amplitude threshold method, we measured open-state occupancy between –100 and –20 mV (Figure 2C). We cross-checked this approach against fitting all-point amplitude histograms with sums of two Gaussian distributions, one for each current level (Figure 2B), where the relative weight of the open-level Gaussian indicates the open-state occupancy probability (P_O). The two methods produced similar results.

Under control conditions (zero applied patch pressure), P_O was strongly voltage-dependent (Figure 2A–C), as predicted by the whole-cell activation curve (Figure 1D). P_O was nominally zero at –80 mV and below, and P_O increased as the voltage became more positive, reaching 0.525 at –20 mV. Relative to whole-cell activation, the P_O curve is shallower and ~20 mV more positive. This discrepancy is likely an artifact of a scattered and non-zero resting potential, unmeasurable in cell-attached recordings (averaging sigmoid curves with a scattered and shifted midpoint results in a shallower and shifted sigmoid).

Patch suction altered the voltage-dependent P_O (Figure 2A–C; Table 2). At extremely negative voltages (–100 and –80 mV), where the channel is closed under control conditions, P_O remained zero under suction. However, pressure significantly increased P_O at more positive voltages. Responses were dependent on suction strength (Figure 2C and D), but even at high negative pressures (–30 and –50 mmHg), the induced changes were confined to the voltage activation range (−80 to –20 mV) (Figure 2C and D). These results agree with the whole-cell experiments, where shear stress stretched the curve vertically. As single-channel data yield the actual P_O values under different pressures and voltages, we could establish that the increase in whole-cell conductance results from an increase in P_O and not in single-channel conductance, which remained constant under pressure (Figure 2A and B).

Because some previous studies have shown that shear stress and patch pressure can create irreversible changes (Beyder et al., 2010; Schmidt et al., 2012; Wang et al., 2009), we tested specifically for reversibility in our preparations. In whole-cell experiments, we found that the increase in peak Na_V1.5 and NaChBac T220A current density induced by shear stress are fully reversible (Figure 3A–B, Figure 3—figure supplement 2), although in some cells the acceleration in Na_V1.5 kinetics or shift in half-activation voltage was not reversible and led to a non-zero difference current (Strege et al., 2003; Figure 3—figure supplement 2B). With single channels, to test the reversibility of P_O increase by patch pressure, we lengthened the time before pressure application to 2 s, applied –30 mmHg pressure for 500ms, and compared the pre- and post-pressure P_O values (Figure 3C, Figure 3—figure supplement 1A). Pressure increased P_O throughout the –80 to –20 mV activation range (Figure 3—figure supplement 1B), with 20 out of 21 cells responding at –60 mV (Figure 3D–E). Once pressure returned to 0 mmHg, P_O returned to its baseline value (Figure 3F, Figure 3—figure supplement 1C-D). As expected, this change was not instantaneous, because the channel must transition back into a different set of state occupancies, which takes time (Figure 3—figure supplement 1B).

An intuitive interpretation of the whole-cell and single-channel results is that force alone does not open the channel. If it did, we would see openings at voltages where the channel is typically closed, provided that we applied enough membrane tension. Instead, we see that force enhances openings (increases P_O) that are already driven by membrane depolarization. A simple interpretation is that force does not create additional conformational states but modifies the energetics of the existing transitions. If this is true, then force will interact with at least one mechanistic component: (1) voltage sensor activation, (2) pore opening, or (3) inactivation. It seems to us that inactivation is unlikely to play a significant role. First, NaChBac T220A responds to patch pressure like the wild type does, even though the mutant virtually lacks inactivation (Figure 1B and C). Second, eukaryotic Na_V and wild-type NaChBac have similar responses to shear stress (Figure 1B and C), even though they inactivate via different mechanisms (Gamal El-Din et al., 2019). Thus, the effects of force on inactivation could simply be due to the coupling of inactivation to activation (Aldrich et al., 1983). For these reasons, we focus here on the NaChBac T220A channels, which show minimal inactivation.

The remaining possibilities are that force interacts with (1) the voltage sensors or (2) the pore. While not necessarily mutually exclusive, the two extreme models corresponding to these interactions are easier to formulate and discriminate than mixed models. Hence, we examined the specific changes in kinetic properties driven by force and compared them against model predictions. We first formulated a kinetic model (Figure 4A) that encapsulates the homo-tetrameric nature of NaChBac T220A, its voltage-dependent activation, and its lack of inactivation. We made the rates along the activation pathway (closed states C₁ to C₅) strongly voltage-dependent to agree with the whole-cell and single-channel activation curves (Figures 1D and 2C). In contrast, we made the concerted opening transition (C₅ to open state O₆) voltage-independent, as previously shown for eukaryotic Na_Vs (Kuo and Bean, 1994) and based on our observation that the whole-cell activation curve reaches a steady maximum (Figure 1D), which, according to the single-channel data, corresponds to a maximum P_O of ~0.6 (Figure 2C). If the concerted opening were significantly voltage-dependent, the maximum P_O would approach unity at strongly depolarizing voltages. The model parameters were manually adjusted to match the experimental data under control conditions (see Methods).

The first scenario, where mechanical force interacts only with the voltage sensors, is captured by a mechanosensitive activation (MSA) model (Figure 4A). In this case, we expect to see force-induced changes in the mechanosensitive rate constants along the C₁ to C₅ pathway. Experimentally, we observed increased whole-cell current by shear stress (Figure 4B), matched by an increase in P_O when membrane tension is raised via patch suction (Figure 4C). With the MSA model, we can explain this result by ascribing positive tension sensitivity (i.e. negative pressure sensitivity) to the activation (forward) rates and/or negative tension sensitivity to the deactivation (backward) rates. A situation where both activation and deactivation rates have positive or negative tension sensitivities is also acceptable, as long as the forward sensitivities are more positive than the backward ones.

The MSA model predicts that the activation curve shifts toward more negative voltages when tension increases, but its slope and maximum value remain precisely the same (Figure 4B, MSA). The activation midpoint would change because tension shifts the equilibrium of each activation step (C₁ to C₅) toward C₅ at any given voltage. In contrast, the slope and maximum P_O would be unchanged by tension because they are determined by the voltage sensitivity of activation and by the voltage- and force-independent opening transition (C₅ to O₆), respectively. In other words, extreme tension would push the channel to reside in the C₅ and O₆ states, but the equilibrium between these two states – and hence maximum P_O – would remain the same. However, we did not observe this behavior experimentally. Instead, when membrane tension increased, both the whole-cell activation curve (Figure 4B) and the P_O curve (Figure 4C) exhibited increased steepness and greater maximum value. The experimental activation data are thus in stark contrast with the predictions of the MSA model.

The alternative scenario, where mechanical force interacts only with the channel pore, is captured by a mechanosensitive opening (MSO) model (Figure 4A). In this case, we expect to see force-induced changes in the mechanosensitive C₅ to O₆ rate constants. With the MSO model, the observed increase in P_O by tension can be explained by ascribing positive tension sensitivity to the opening (forward) rate, and/or negative tension sensitivity to the closing (backward) rate, or any combination where the forward sensitivity is more positive than the backward one.

The MSO model predicts that the activation curve reaches a larger value and becomes steeper when tension increases and shifts slightly toward more negative voltages (Figure 4B, MSO). The maximum P_O would change because it is determined by the tension-dependent pore opening rates, but why would the voltage activation curve shift and steepen under tension, when the tension-dependent rates are voltage-insensitive? The reason is that voltage acts through the voltage-dependent activation/deactivation rates to increase the joint occupancy of the final two states, C₅ and O₆, while tension acts through the tension-dependent opening rates to increase the occupancy of the open state O₆. Thus, under tension, an increase in voltage will lead to a proportionately larger increase in P_O, compared to zero-tension conditions, and cause a shift in the activation curve, increased steepness, and a greater maximum value. Indeed, the MSO model supports the mechanically-induced changes in the whole-cell and single-channel activation curves (Figure 4B and C, MSO).

Having examined the changes in P_O vs. voltage under different pressure values, we conversely examined P_O vs. tension under different voltages (Figure 4D). Reversing voltage and tension as independent variables does not create new information, as we are using the same data points as in Figure 4C, but it makes it easier to judge the fitness of each model. Thus, the MSA model predicts a significant shift in the P_O vs. tension curve when the voltage increases but no change in the maximum value and the slope of the curve (Figure 4D, MSA). In contrast, the MSO model predicts a significant change in the maximum value and the slope but only a small shift in the curve (Figure 4D, MSO). The experimental P_O data points align well with either the MSA or the MSO model at zero pressure. However, the MSO model becomes a significantly better match to the data as the pressure increases (Figure 4C).

The analysis so far clearly favors the MSO model. However, we used only the steady-state information in the data, and we do not know if the MSO model can also explain the observed kinetics. The MSO model assumes tension-dependent opening and closing rates (at least one, if not both), whereas the MSA model assumes these rates to be tension-independent. If the pore opening transition were tension-dependent, then the pore opening (C₅ to O₆) and/or the closing (O₆ to C₅) rate would be affected by force, which would be reflected in the single-channel closed and open lifetimes. In our simple NaChBac kinetic model, the open state lifetime distribution has only one component, with the time constant equal to the inverse of the closing rate constant (O₆ to C₅). In contrast, the closed-state lifetime distribution has five components, without an easy way to isolate the opening rate constant. However, the deactivation rates are likely so small at extremely depolarizing voltages (e.g. ≥–20 mV) that the channel essentially flickers between the last two states (C₅ and O₆). Hence, as an approximation, the closed lifetime distribution has only one component at these extreme voltages, with a time constant that approaches the inverse of the opening rate constant (C₅ to O₆). Consequently, a truncated model with only the final two states would approximate the channel at –20 mV (Figure 4E).

Because NaChBac T220A has some residual inactivation (Figure 1—figure supplement 1E, J), we used relatively short (200–500 ms) voltage/pressure stimulation episodes, so many recorded traces contained no events. To fit the single-channel data with the MIL algorithm (Qin et al., 1996), we had to discard the first and last dwells in each trace because they are by necessity truncated and cannot be used for analysis, which means that all the eventless traces were also discarded. Under these conditions, the remaining traces that are suitable for analysis would slightly bias the estimated rates because of the inherently higher P_O. Nevertheless, the mechanosensitivity of the opening and closing rates should emerge clearly from this analysis. As a verification, we also performed the analysis with the model parameters constrained (Navarro et al., 2018; Salari et al., 2018) to enforce a ratio between the opening and closing rate constants corresponding to the P_O measured under control (zero added tension) conditions, and also to enforce the total pressure sensitivity, which can be reliably estimated from the P_O data. The results obtained with these parameter constraints were similar to those obtained in the constraint-free analysis.

The closed state lifetime distribution shifts toward shorter dwell times by 15% under –10 mmHg pressure (k_O: 124.9 ± 5.7 s^–1 at 0 mmHg to 144.4 ± 6.6 s^–1 at –10 mmHg; n=124 traces from 10 patches) and by 21% under –50 mmHg pressure (k_O: 178.2 ± 11.9 s^–1 at 0 mmHg to 217.0 ± 14.7 s^–1 at –50 mmHg; n=23 traces from three patches) (Figure 4E). The average closed lifetime approaches the bandwidth limit (~1 ms) and, even though the fitting algorithm partially compensates for the missed events, it’s possible that the increase in the opening rate with pressure is underestimated. In contrast, the open state distribution remained virtually unchanged by tension under –10 mmHg pressure (k_C: 48.1 ± 2.2 s^–1 to –48.2 ± 2.3 s^–1), although it shifts toward longer dwell times under –50 mmHg (k_C: 101.4 ± 6.8 s^–1 to –87.5 ± 6.1 s^–1).

The observed shift in the closed state lifetimes further confirms that the channel is better represented by the MSO model, as the competing MSA model would exhibit no such shift at saturating voltages. Moreover, it suggests that force destabilizes the closed state, as the opening rate changes the most with tension. As we now have an idea about the magnitude of opening and closing dwell times, we can also examine activation kinetics. In principle, we can extract this information by fitting the single-channel data recorded at intermediate voltages (e.g. –60 mV), where the channel visits all states. However, the changes in voltage and pressure stimuli make these data non-stationary, and a more straightforward approach is to examine the macroscopic data created by averaging the single-channel recordings. As shown in Figure 4F, the MSO model captures well the time course of the average current and gives us an idea about the magnitude of the activation rates. In all, our modeling of the whole-cell and single channel results suggest that the MSO model, which assigns tension sensitivity to the voltage-insensitive pore opening step, best fits the experimental data and associates the NaChBac mechanosensor with the pore structure.

According to the ‘force-from-lipid’ model (Martinac et al., 1990), ion channels gain mechanosensitivity when their cross-section expands or shrinks upon a conformational change (Perozo et al., 2002a; Sachs and Morris, 1998). Based on our kinetic analysis, the site of mechanosensitivity in NaChBac is most likely the pore opening, the final gating transition (C₅ to O₆ in the MSO model in Figure 4A). Interestingly, previous structural modeling studies have predicted that when voltage sensors are suitably activated, mechanical energy is required to open the gate (Fowler and Sansom, 2013), which implies that negative membrane tension (i.e. patch suction) would facilitate opening. If our hypothesis were true, we would predict a change in the cross-section between the final two states in the MSO model: the activated but still closed C₅ and the open O₆. To test this hypothesis, we examined the two existing prokaryotic voltage-gated sodium channel structural models: Na_VAb, capturing the channel in the closed conformation (Boiteux et al., 2014), and Na_VMs, representing the open state (McCusker et al., 2012).

By contrasting closed and open models, we searched for the channel substructures undergoing the largest movements within the membrane plane and found that the intracellular portion of the pore-forming S6 segment is displaced laterally around a ‘gating hinge’ (Figure 5A and B). Interestingly, this type of movement has been previously proposed in functional studies (Beyder and Sachs, 2009; Webster et al., 2004; Zhao et al., 2004) and confirmed by structural experiments (Lenaeus et al., 2017), including an example where the intracellular side of a VGIC pore was found to expand the area of the bilayer’s inner leaflet upon S6 lateral movement (Beyder and Sachs, 2009; Iwasa et al., 1980).

According to our structural analysis, the ‘force-from-lipid’ model applies to NaChBac. Because S6 helices move and open the pore only after voltage sensors activate, it follows that mechanosensitivity, which is associated with S6 movement, resides with the pore opening (C₅ to O₆ in the MSO model) and not with the voltage sensor activation (C₁ to C₅ in the MSA model). This interpretation agrees with the MSO model, with one potential caveat being that Na_VAb as a closed channel could represent other closed states along the activation pathway, rather than the fully activated closed conformation (C₅ in the MSO model). As a result, a mechanosensitive transition could still occur before the pore opening. In other words, although the pore opening is likely mechanosensitive, it might not be the only mechanosensitive transition, based solely on these structural models.

If mechanosensitivity were built into the pore opening, altering S6 lateral movement via mutagenesis would alter the effects of patch suction on P_O. However, if voltage sensor activation were additionally mechanosensitive, then voltage sensor mutagenesis would only change the response to suction but not eliminate it. We tested these ideas via site-directed mutagenesis within the S6 hinge and the voltage sensor, using NaChBac T220A as background. Most mutations we tried within the pore resulted in non-expressing or non-functional channels, but we eventually settled on I228G in the S6 hinge region (Figure 5B). Within the voltage sensor, we chose D93A to stabilize the sensor in the resting position (DeCaen et al., 2009; Figure 5B). We applied the same single-channel experimental paradigms to directly compare the double mutants (NaChBac T220A plus I228G or D93A) with the T220A results described above (Figure 5C).

The voltage sensor NaChBac T220A+D93A double mutant shifted its voltage sensitivity relative to T220A (Figure 5D; Figure 5—figure supplement 1C). However, its mechanosensitivity remained intact and followed the negative shift of voltage-dependent gating (Figure 5D and E). The pore NaChBac T220A+I228G double mutant channel exhibits some interesting properties. First, the channel could gate normally with voltage, like the single mutant controls (Figure 5D). Second, the effect of membrane tension on P_O was nearly eliminated at all pressures (Figure 5E). Thus, at –60 mV, membrane tension increased P_O by 0.096 for the NaChBac T220A mutant but only by 0.014 for NaChBac T220A+I228G, corresponding to an approximate sevenfold difference in effects between the two mutants. At –40 mV, the difference was similar (~sevenfold): 0.090 with NaChBac T220A and only 0.012 with NaChBac T220A+I228G. We could explain the small remaining effect of tension on P_O in the double mutant in two ways: either there is a partial displacement of S6 during pore opening and a resulting (smaller) cross-section expansion, or there is another (weakly) mechanosensitive transition in the gating mechanism. The first possibility seems more plausible, because some degree of S6 displacement is probably necessary for channel opening, and also because NaChBac T220A+D93A maintained a tension sensitivity similar to NaChBac T220A, even though its voltage sensitivity shifted by more than –30 mV (Figure 5D). Overall, these mutagenesis results provide experimental evidence that strengthens our conclusion that mechanical forces interact primarily with the pore opening transition.

Human embryonic kidney cells (HEK293; American Type Culture Collection, Manassas, VA) were cultured in minimum essential medium (MEM, 11095–080) supplemented with 10% fetal bovine serum (FBS, 10082147) and 1% penicillin-streptomycin (15140–122, Life Technologies, Co., Grand Island, NY). Regular or Piezo1 knockout (P1KO) HEK293 cells (a kind gift from Dr. Ardem Patapoutian, Scripps Research Institute Dubin et al., 2017) were transfected with DNA plasmids encoding wild-type Na_V1.5 (variant H558/Q1077del) or wild-type or T220A NaChBac, along with GFP as a reporter, by Lipofectamine 3000 reagent (L3000-008) in OPTI-MEM medium (31985–070; Life Technologies, Co., Grand Island, NY). P1KO cells submitted to American Type Culture Collection (ATCC, Manassas, VA) for STR profiling were an exact match (eight core loci plus Amelogenin) for the Piezo1 knockout HEK293T cell line, CRL-3519. PCR testing on P1KO cells was negative for mycoplasma. Transfected cells were incubated at 37 °C for 24 hr (Na_V1.5) or 32 °C for 24–48 hr (WT or T220A NaChBac). Then, cells were lifted by trypsin and resuspended in NaCl Ringer’s extracellular solution (composition below) before electrophysiology.

Site-directed mutagenesis was performed in the T220A NaChBac background to introduce an additional mutation, I228G or D93A, by using the QuikChange Lightning Site-Directed Mutagenesis Kit (Agilent Technologies, Santa Clara, CA). Upon verification of construct integrity and successful mutagenesis by DNA sequencing, either plasmid was transfected into P1KO cells for electrophysiology (Table 3, Figure 5).

Data were analyzed in pClamp version 10.6 or 11.0.3 (Molecular Devices, Sunnyvale, CA), Excel 2010 (Microsoft, Redmond, WA), and SigmaPlot 12.5 (Systat Software, San Jose, CA). To estimate whole-cell conductance and the voltage of half-activation, the peak current evoked by voltage step 1 in the protocol described above was fit with a Boltzmann equation, IV=V-ERev×GMax/1+eV-V1/2a/δVa , where I_V is the peak current (pA/pF) at the test voltage V (mV), E_Rev is the reversal potential (mV), G_Max is maximum conductance (nS), V_1/2a is the half-activation voltage (mV), and δV_a is the voltage sensitivity of activation (mV). To estimate the voltage of half-inactivation, the peak current I_V evoked by voltage step 2 in the protocol was first normalized as a percentage to its maximum across all sweeps and then was fit with a Boltzmann equation, IV=1/1+eV-V1/2i/δVi , where V_1/2i is the half-inactivation voltage and δV_i is the voltage sensitivity of inactivation. For kinetic analysis, whole-cell currents were fit to an exponential equation, It=A1×e-t/τa+A2×e-t/τi+C, where τ_a and τ_i are activation and inactivation time constants (ms), respectively, and A₁, A₂, and C are constants.

To characterize single-channel conductance properties, all-point histograms of T220A NaChBac single-channel activity were fit with a sum of two Gaussian functions, fx=A1×e-0.5×x-μ12/σ12/σ1×2π+A2×e-0.5×x-μ22/σ22/σ2×2π+C, where x is current (pA), µ and σ represent the mean and standard deviation of the closed and open state current (pA), A₁ and A₂ are the weights of the closed and open state Gaussian components, respectively, and C is baseline current. Open probability was calculated as P_O = A₂/(A₂ +A₁). The response to pressure, P_O(x)–P_O(0), where x stands for –10 or –30 mmHg, was obtained as the difference in P_O values within the same trace. The single-channel closed and open times were calculated in QuB. Single channel time constants are expressed as means ± standard deviation (SD). Change from shear stress or pressure was considered statistically significant when p<0.05 for mechano-stimulus vs. control, as determined by a two-way ANOVA with Dunnett’s post-test.

The analysis and simulations were done with the QuB program, the MLab edition (http://milesculabs.org/QuB.html). QuB was used to digitally low-pass filter the data at 0.5 kHz to eliminate a periodic artifact induced by the pressure clamp system (Figure 2—figure supplement 1G) and to extract (‘idealize’) the signal from the noisy data. QuB was further used to simulate the behavior of the tested NaChBac model and to calculate its properties: the voltage-activation curve at different pressures, the pressure-activation curve at different voltages, and the probability density function for closed and open dwell times, and to extract rate constants from single channel data, using the MIL algorithm that features a first-order approximation to correct for missed events (Qin et al., 1996).

To capture the basic properties of the NaChBac channel (homotetramer, inactivation removed), we used the simple linear kinetic scheme C₁-C₂-C₃-C₄-C₅-O₆. Each rate constant had the general expression k = k₀ × exp(k_v ×V+ k_p×P), where V is membrane potential, P is patch pressure, k₀ is a pre-exponential factor representing the value of the rate constant at zero voltage and pressure, and k_v and k_p are sensitivity factors for voltage and pressure, respectively. Lack of voltage or pressure dependence was encoded by setting k_v or k_p to zero. The rates along the activation pathway were in the expected 4:3:2:1 ratio (e.g. k₂₃=2 × k₄₅). The parameters of the model were tweaked by hand to match the macroscopic and single-channel data, collected within our unique experimental configuration defined above by the pipette geometry. First, we chose a set of k₀ preexponential parameters for the C₅-O₆ transition, to match the observed P_O at saturating voltages (at –20 mV). Then, we adjusted the k_v exponential parameters that describe the voltage sensitivity of the C₁ through C₅ transitions, to match the normalized macroscopic activation curve under no-shear conditions. Next, we determined the statistical distribution (average and standard deviation) of the resting potential of the single-channel patched cells—to match the voltage-dependent P_O curve—which is voltage-shifted and shallower relative to the macroscopic activation curve. To generate a P_O curve that takes into account the scattered and non-zero resting potential, the P_O value at each voltage point was obtained by numerically integrating over the Gaussian distribution describing the resting potential. Next, we adjusted the k₀ preexponential parameters for the C₁ through C₅ transitions to approximately match the observed single-channel lifetimes. Finally, for the MSO model, we adjusted the k_p exponential parameters describing the pressure sensitivity of the C₅ to C₆ transition, to match the P_O curve under negative patch pressure. The same k_p values were also used for the MSA model. The kinetic parameters used for the simulations shown in Figure 4B–D were the following: k_0,activation = 800 s^–1, k_{0,deactivation} = 0.1 s^–1, k_0,opening = 70 s^–1, k_0,closing = 55 s^–1, k_v,activation = 0.055 V^–1, k_{v,deactivation} = -0.055 V^–1, k_{p,activation/opening} = -0.05 mmHg^–1, and k_{p,deactivation/closing} = -0.005 mmHg^–1.