The energetics of rapid cellular mechanotransduction

Cells throughout the human body detect mechanical forces. While it is known that the rapid (millisecond) detection of mechanical forces is mediated by force-gated ion channels, a detailed quantitative understanding of cells as sensors of mechanical energy is still lacking. Here, we combine atomic force microscopy with patch-clamp electrophysiology to determine the physical limits of cells expressing the force-gated ion channels Piezo1, Piezo2, TREK1, and TRAAK. We find that, depending on the ion channel expressed, cells can function either as proportional or nonlinear transducers of mechanical energy, detect mechanical energies as little as ∼100 fJ, and with a resolution of up to ∼1 fJ. These specific energetic values depend on cell size, channel density, and cytoskeletal architecture. We also make the surprising discovery that cells can transduce forces either nearly instantaneously (< 1ms), or with substantial time delay (∼10 ms). Using a chimeric experimental approach and simulations we show how such delays can emerge from channel-intrinsic properties and the slow diffusion of tension in the membrane. Overall, our experiments reveal the capabilities and limits of cellular mechanosensing and provide insights into molecular mechanisms that different cell types may employ to specialize for their distinct physiological roles.


Introduction 49
The ability to detect mechanical forces is essential for a breadth of physiological processes 50 including our sense of light touch, proprioception, blood pressure regulation, bone homeostasis, 51 interoception, and cell differentiation Pathak et al., 2014;Ranade et al., 2014b; 52 Sun et al., 2019;Woo et al., 2014Woo et al., , 2015Zeng et al., 2018). Despite this broad importance, our 53 quantitative understanding of cells as sensors of mechanical energy is extremely limited and 54 even seemingly simple questions about cellular mechanotransduction remain unanswered:

55
What is the smallest mechanical energy a cell can detect? What is the smallest mechanical 56 energy a cell can resolve? And how fast can cells respond?

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The most rapid detection of forces is mediated by force-gated ion channels (FGICs), which 59 respond in as little as 40 µs by gating the flux of ions (Corey and Hudspeth, 1979). FGICs vary 60 in their ion selectivity, single-channel conductance, and gating kinetics, which enables cells to 61 transduce mechanical forces into distinct electrochemical signals. However, how FGICs 62 compare in their most fundamental property, the sensing of mechanical energy, is not well 63 understood (Young et al., 2022). For example, measurements of the gating energy of the well-64 studied ion channel Piezo1 differ substantially (8·10 -21 J and 40·10 -21 J), while for the two-pore 2014a; Sorum et al., 2021;Wu et al., 2016;Ye et al., 2018). In summary, none of these assays 99 can stimulate cells with a precisely quantified indentation, force, and energy, while also 100 measuring the transduction current with the gold-standard of electrophysiology.

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Here, we developed an instrument that combines atomic force microscopy (AFM) with patch-103 clamp electrophysiology to allow for quantitative mechanical stimulation and simultaneous 104 detection of the evoked transduction current. With this tool we set out to explore and precisely 105 quantify how single cells convert the energy of mechanical compression into an electric signal.

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Simultaneous measurements of cell compression and mechanotransduction

109
To quantify the magnitude of energies that cells can sense and respond to we built an 110 instrument that combines an atomic force microscope (AFM) with patch-clamp electrophysiology 111 ( Figure 1A-C). In each experiment, a flexible cantilever compresses a single cultured cell at a 112 speed of 40 µm/s, and then holds its position for 100 ms, before it is retracted at the same 113 speed. The cantilever, whose dimensions are comparable to the size of the cell, is centered on 114 a cell, and displaced for a total of ~6 µm, which altogether results in a large-scale compression 115 of the entire cell. Since the stiffness of each cantilever and the sensitivity of the detector to 116 cantilever bending is calibrated for individual experiments, we can calculate the distance (d), 117 compression force (F), and cumulative work (W) performed on the cell throughout the entire 118 experiment with a relative uncertainty of ≲20% (see Methods). At the same time, we record 119 electrophysiologically from the cell by patching it in the whole-cell configuration, which enables 120 us to measure the evoked transduction current (I) (Figure 1D).

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Initial validation experiments on HEK293T cells overexpressing the force-gated ion channel 123 Piezo1 show that AFM compression evokes rapid transduction currents at -80 mV, which are 124 absent in cells transfected with YFP as control. Peak current amplitudes (1.1±0.5 nA, n=16) are 125 comparable to those from classical poke-indentation experiments and inactivate with a time-126 course of 25±4 ms (n=16), which is expected for Piezo1 at this holding potential (Coste et al., 127 2010;J. Wu et al., 2017). We observed that the cantilever deflection is undergoing a small, but 128 noticeable adaptation during the static phase with a time course of 33±3 ms (n=16) when fit with 129 a single exponential decay, perhaps due to relaxation of the cell. We therefore focused all  power-coefficients of 1.4±0.1 (n=60) and 1.9±0.2 (n=38), respectively, confirming that cells expressing TREK1 and to a lesser extent TRAAK behave approximately as proportional 148 transducers of mechanical energy. However, cells expressing Piezo2, and even more so, cells 149 expressing Piezo1 have substantially larger power coefficients of 2.6±0.2 (n=47), and 6.2±0.4 150 (n=39), respectively, meaning that their responses are indeed highly nonlinear, i.e., their force-151 detection is akin to a switch. More generally, the data demonstrate that the identity of the 152 transduction channel defines this important response property.

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The threshold and resolution for detecting mechanical energy

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To quantify the transduction response further, we next calculated for each individual cell its 156 detection threshold (W threshold ), or the mechanical energy required to elicit a detectable 157 transduction current ( Figure 3A). While measurements vary substantially between individual 158 cells, summary data show that each channel type also confers distinct detection thresholds 159 ( Figure 3B). Cells expressing TREK1 exhibit the lowest thresholds of 68.2±6.3 fJ (n=60),

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in this analysis the current amplitude corresponding to W threshold is equivalent to the activation of 165 only ~2 ion channels (see Methods, (Blin et al., 2016;Coste et al., 2015)). Thus, considering that 166 activating two Piezo1 channels requires an energy of ΔG ~80·10 -8 fJ Lewis 167 and Grandl, 2015) directly implies that >10 7 -times more energy is absorbed by the cell before 168 transduction is initiated. This result shows a considerable capacity of the cell to buffer 169 mechanical energy.

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We next reasoned that once this initial buffering capacity is depleted, the subsequent activation 172 of FGICs may be more efficient. To test this idea, we quantified the work resolution (W resolution ), which we define as the inverse maximum slope of the work-current relationship normalized by 174 the unitary current of the transduction channel (see Methods, Figure 3C) 181 n=60) ( Figure 3D). Analogous to our above estimate, comparing the gating energy of Piezo1 182 yields that even when cellular mechanotransduction is at its most sensitive, >10 5 -times more 183 energy is absorbed by the cell than is required for gating the very next ion channel. Altogether,

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we conclude from this analysis that detection of mechanical energy by cells, despite 185 overexpression of FGICs, is a process that is extremely inefficient.   and is thus a proxy for cell size (Hille, 2001). Indeed, for both Piezo1 and Piezo2 values for 197 W threshold are positively correlated with cell capacitance, supporting this idea ( Figure 4A).

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Surprisingly, K2P channel thresholds as well as W resolution across all channels did not correlate with cell capacitance (data not shown), indicating that cell size is important, but that additional 200 factors may contribute as well. We therefore turned our attention to channel density, which we 201 reasoned might be a more direct predictor of work threshold and work resolution, because it 202 determines the probability of activating multiple channels simultaneously. To test this idea, we 203 performed an additional analysis taking advantage of the polymodal nature of TREK1 and 204 TRAAK, which can be activated by both mechanical force and voltage (Berrier et al., 2013;205 Maingret et al., 1999). Specifically, we measured the membrane capacitance as a proxy for 206 total membrane surface area and the baseline current at 0 mV to calculate channel density, in 207 addition to probing mechanotransduction as described above ( Figure 4B, see Methods). In 208 these measurements, channel density varied ~20-fold for TRAAK and ~50-fold for TREK1, 209 allowing us to sample a wide range. We indeed found that values for W threshold and W resolution 210 correlate negatively with channel density (Figure 4C-F). In summary, we conclude that absolute 211 cell size and, more directly, channel density modulate the detection threshold and resolution of 212 cellular mechanosensing.

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Still, what fraction of all channels are actually activated during a given mechanical stimulus still 214 remains unclear. Mechanotransduction differs from, for example, voltage-sensing, where 215 stimulus intensity is spatially homogenous. In contrast, forces are generally not uniform across 216 the entire cell (Young et al., 2022). To answer this question, we focused on TREK1 for which we 217 designed a new stimulation protocol. We used an internal buffer with Rb + as the dominant ion, 218 which has been shown to left-shift the voltage dependence of TREK1 (Schewe et al., 2016). In 219 this buffer we were able to saturate the conductance-voltage relationship of TREK1 at 160 mV 220 and thus, after normalizing for driving force, calculate the number of channels present in the 221 entire cell (Figure 4G, Figure 4-figure supplement 1). Across all cells we measured, the total 222 number of channels ranged roughly between 1,000 and 2,000. In the same experiment we 223 mechanically stimulated cells, as previously described, and determine the number of channels 224 recruited by the mechanical stimulus relative to the voltage step. Surprisingly, despite an overall 225 large-scale compression, which elicited robust mechanically activated currents (161±22 pA; 226 n=12), only 6.9±1.2% (n=12) of all channels were activated by this mechanical stimulus ( Figure   227 4H). Importantly, the value of 6.9±1.2% may still be an overestimate since the mechanically 228 gated open state of TREK1 has a two-fold higher conductance as compared to the voltage-229 activated state, although this was in standard K + buffer .

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In addition, we hypothesized that the cytoskeleton, which has previously been implicated in 232 mechanoprotection of FGICs, but also in transmitting forces, contributes towards setting cellular 233 detection limits Gottlieb et al., 2012;Jia et al., 2016;Lotshaw, 2007;Shi et al., 234 2018;Verkest et al., 2022;Wang et al., 2022). We therefore decided to disrupt cytoskeletal 235 architecture and measure which of these two opposing effects dominates. Specifically, we 236 treated cells for 1 hour with Cytochalasin D (10 µM), which competes with barbed-end actin-237 binding proteins to affect both polymerization and depolymerization, destabilizing the overall 238 actin architecture (Flanagan and Lin, 1980;MacLean-Fletcher and Pollard, 1980). Any reduction

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We hypothesized that both channel-intrinsic and cellular properties may account for this delay.

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We therefore first repeated our experiments with cells expressing a chimeric channel Piezo1 cap2 , 278 for which previous work from our lab demonstrated that the cap domain of Piezo2 is sufficient to 279 confer the fast inactivation kinetics of Piezo2 onto the normally slowly-inactivating Piezo1 280 ( Figure 6F) (J. . Indeed, cells expressing Piezo1 cap2 responded within ~1 ms

285
Second, we reasoned that the slow diffusion of membrane tension may activate channels near 286 the stimulation site, but with a time delay. We therefore turned to an in silico approach, where 287 we simulated the gating of thousands of individual, spatially randomly distributed (~100 288 channels/µm 2 ), Piezo1 channels with a previously validated four-state Markov model (Lewis and 289 Grandl, 2021) (Lewis and Grandl, 2015;Lewis et al., 2017). We then challenged channels with a 290 spatially confined (2 µm radius) step in membrane tension, which diffused in two dimensions 291 with a speed of either D = 0.024 µm 2 /s, which had been determined experimentally for HeLa 292 cells, or 10 and 100-fold faster speeds (D = 0.24 µm 2 /s and 2.4 µm 2 /s, respectively), which is  (Shi et al., 2022(Shi et al., , 2018. Independent repetitions of this 295 simulation with a diffusion constant of D = 2.4 µm 2 /s consistently showed a time delay in peak 296 current amplitudes (dt = 6.2±0.6 ms) that approximated our experimental findings for Piezo1, 297 while simulations with slower diffusion constants (D = 0 µm 2 /s, D = 0.024 µm 2 /s, and D = 0.24 298 µm 2 /s) produced time delays that were less pronounced or entirely absent ( Figure 7E). Overall,

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we conclude that the time delay we observed experimentally is indeed consistent with being an 300 emergent property of membrane tension diffusion and further that the magnitude of this time delay is determined by the identity of the FGIC and the specific diffusion rate of the cell 302 membrane.

305
In this study, we aimed to explore the capabilities and limitations of cells as transducers of 306 mechanical energy. To this end, we developed an instrument that combines AFM with whole-307 cell patch-clamp electrophysiology. This approach comes with caveats and potential sources for 308 errors that need to be considered: First, we estimate an uncertainty in cantilever calibration of 309 ≲20%, which is consistent with other studies (Song et al., 2015). Second, nonlinearity in the between the cantilever and cell is unknown, which introduces an uncertainty in the spatial 315 distribution of the stimulus as well as variability between measurements. Additionally, the time 316 course of the stimulus (150 ms) is slow relative to the inactivation rates of the channels we 317 studied. As a result, competing activation and inactivation lead to an underestimate of peak 318 channel activity. Finally, by forming a whole-cell configuration the cell is no longer a 319 hydrostatically closed system, and mechanical load may dissipate through the patch pipette, 320 which again may lead to an overestimate of the work performed on the cell. Indeed, this may 321 contribute to the force relaxation we observed during the holding phase of the cantilever. Still, 322 the specific forces we measured at the transduction threshold for Piezo1 (228.2±16.4 nN;n=39) 323 are comparable to those found using calcium imaging (185 nN), where the cell membrane 324 remains intact, giving us confidence in these measuerments (Gaub and Müller, 2017). In any 325 case, the detection threshold and work resolution we obtain for cells expressing different ion 326 channels are clearly distinct, arguing that our instrument has sufficient precision.

328
In addition to experimental uncertainties, our experimental preparation differs from a 329 physiological environment in several aspects: First, we seeded cells at low density and onto 330 glass coverslips, which is necessary to both mechanically and electrically isolate cell properties, 331 but removes contributions from neighboring cells present in tissue, and may alter the 332 mechanical properties of the cell itself. For example, some evidence suggests that cell elasticity 333 may vary with the stiffness of the underlying substrate, although a more recent study challenges 334 this finding (Rheinlaender et al., 2020;Tee et al., 2011). In any case, by using glass, which has 335 a stiffness that is much higher than that of the cantilever, substrate deformation and the related 336 energy loss is minimized and therefore nearly all mechanical work is performed on the cell.

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Second, we overexpress the channel of interest, which does not reflect native expression levels, 338 but is necessary to overcome potential contributions of endogenous FGICs, and allowed us to 339 clearly determine the role that channel identity plays in setting the physical limits (Dubin et al.,

370
Three additional and very surprising findings emerged from our study: First, we found that cells 371 can have pronounced (~10 ms) delays in their transduction response. Our chimeric approach 372 shows that response delay is a channel intrinsic property and that cells can inherently respond 373 rapidly (<1ms). In addition, it was intriguing that this delay is almost absent in cells expressing

374
Piezo2, which are present in DRG neurons, Merkel cells, and hair cells of the inner ear (Ranade 375 et al., 2014b;Woo et al., 2015Woo et al., , 2014Z. Wu et al., 2017). It is therefore interesting to speculate 376 that Piezo2 may have specialized to respond rapidly to fulfill its role in rapid sensory

406
We also identified several factors that influence the response properties of cells. Our data 407 suggest that cell size and channel density may be mechanisms to modulate the response 408 properties of cells. The fact that we only observed a correlation between cell size and response 409 properties in cells expressing Piezos, but not in K2P channels may be due to differences in 410 dynamic range and variability in expression levels we are able to explore. Additionally,     Sader (Chon et al., 2000;Sader, 1998;Sader et al., 1999). Briefly, the dimensions of the cantilever were measured optically (Nikon Ti-E). The quality factor (Q), amplitude (A), and 481 resonant frequency (f 0 ) were determined by fitting the equation for a simple harmonic oscillator 482 to power spectra of the free cantilever vertical displacement signal (P) in air averaged across 483 512 spectra using Welch's method (Welch, 1967) and sampled at > 5-fold the expected 484 resonance frequency using a National Instruments Data Acquisition Board (NI-USB 6361).

485
The resonant frequency (f 0 ), quality factor (Q), cantilever length (L), and width (w) were used to 487 determine the stiffness of the cantilever (k) using the following relationship:

502
All stimuli were applied at 5 s intervals. Prior to initial contact, a coarse step-motor moved the 503 cantilever into contact with the cell in 1-5 µm steps. Contact was determined by a sudden 504 increase in the photodetector signal. Following contact, the step-motor moved the cantilever 505 towards the cell in 0.2-1 µm increments until mechanotransduction currents were observed.

506
Stimuli were applied at a rate of 40 μm/s for a total distance of ~6 μm. The speed was chosen 507 based on initial validation experiments in HEK293T cells overexpressing Piezo1 as it was the 508 slowest speed that was able to elicit robust mechanotransduction currents of the speeds tested

535
The exact probe diameter was measured using an FEI Apreo Scanning Electron Microscope

536
(SEM) and averaged from the major and minor diameter of an overlayed ellipse. The cantilever 537 was calibrated as described above with the exception that only a single invOLS measurement 538 was performed at the start of each measurement. The cantilever was displaced a total distance 539 of ~6 μm at a rate of 1 µm/s before being immediately retracted at the same speed. A linear fit 540 was performed on the first 20% of the data, prior to contact, and subtracted from the trace. The

557
where S denotes the sensitivity and k cant denotes the cantilever stiffness: The distance traveled by the cantilever was corrected to account for cantilever deflection using 560 the following equation: , where α is the calibration factor for the piezoscanner, V command is the command voltage sent to 563 the photodetector, and δ is the deflection of the cantilever.

564
The work was determined by calculating the cumulative integral of the calculated force as a 565 function of the distance traveled by the cantilever.

566
For analyses of the approach phase of each stimulus, only data during the initial ramp of the 568 cantilever was considered.

569
Transduction characteristics were determined as follows:

592
, where g c is the respective single-channel current at the applied voltage and C S is the 594 approximate capacitivity of biological membranes of 1 µF/cm 2 (Gentet et al., 2000).

5)
The total number (N) of TREK1 channels was calculated using the following

598
, where I 160 is the current at 160 mV, I Leak current obtained from a post hoc linear fit to 599 currents evoked by increasing negative steps from -80 mV to -90 mV to -80 to -120 mV, 600 g Trek1 the unitary conductance for TREK1 in K + buffers (Blin et al., 2016), and E R the 601 reversal potential in Rb + buffer determined with a tail-current protocol (Figure 4-figure   602 supplement 1).