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Progressive recruitment of distal MEC-4 channels determines touch response strength in C. elegans

Through experiment and simulation, Katta et al. reveal that pushing faster and deeper recruits more and more distant mechano-electrical transduction channels during touch. The net result is a dynamic receptive field whose size and shape depends on tissue mechanics, stimulus parameters, and channel distribution within sensory neurons.


30
Touch deforms, or strains, the skin beyond the immediate point of contact. The spatiotemporal 31 nature of the touch-induced strain fields depend on the mechanical properties of the skin and the 32 tissues below. Somatosensory neurons that sense touch branch out within the skin and rely on a 33 set of mechano-electrical transduction channels distributed within their dendrites to detect 34 mechanical stimuli. Here, we sought to understand how tissue mechanics shape touch-induced 35 mechanical strain across the skin over time and how individual channels located in different 36 regions of the strain field contribute to the overall touch response. We leveraged C. elegans' 37 touch receptor neurons (TRNs) as a simple model amenable to in vivo whole-cell patch clamp 38 recording and an integrated experimental-computational approach to dissect the mechanisms 39 underlying the spatial and temporal dynamics that we observed. Consistent with the idea that 40 strain is produced at a distance, we show that delivering strong stimuli outside the anatomical 41 extent of the neuron is sufficient to evoke MRCs. The amplitude and kinetics of the MRCs

Introduction
Electrophysiology 121 We recorded from the ALMR and ALML touch receptor neurons in TU2769 worms. Due to the 122 geometric constraints of this stimulator system, we recorded from ALMR when stimulating 123 anterior to the cell body and from ALML when stimulating posterior to the cell body. These two 124 neurons are bilaterally symmetric and exhibit no detectable variation in voltage-or touch-evoked 125 currents (not shown). The extracellular solution contained (in mM): NaCl (145), KCl (5), MgCl 2 126 (5), CaCl 2 (1), and Na-HEPES (10), adjusted to a pH of 7.2 with NaOH. Before using the 127 solution, we added 20mM of D-glucose, which brought the osmolarity to ~325mOsm. The 128 intracellular solution contained (in mM): K-gluconate (125), KCl (18), NaCl (4), MgCl 2 (1), 129 CaCl 2 (0.6), K-HEPES (10), and K 2 EGTA (10), adjusted to a pH of 7.2 with KOH. Before use, 130 we added 1mM of sulforhodamine 101 (Invitrogen) to help visualize whether the neuron was 131 being successfully recorded. 132 We used an EPC-10 USB amplifier controlled by Patchmaster software (version 2x90.1, 133 HEKA/Harvard Biosciences) to set the membrane voltage and control the mechanical stimulator. 134 We corrected the membrane voltage for the liquid-junction potential (-14 mV) between the 135 extracellular and intracellular solutions; we also corrected for errors that may have resulted from 136 an imperfect space clamp based on stimulus distance, as described previously (Goodman et al.,137 1998; O' Hagan et al., 2005). We filtered the analog data at 2.9 kHz and digitized it at 10 kHz. stack with no independent measurement of stimulator motion (Kang et al., 2010). We previously 144 employed a slow closed-loop system driven by a piezoelectric stack with a piezoresistive 145 cantilever for force detection (Eastwood et al., 2015). Here, we used an open-loop system 146 adapted from the piezoelectric stack system with a photodiode motion detector described by 147 Peng and Ricci (2016) in their study on hair cells. This system enables faster stimulation than the 148 force-clamp system and allows us to measure the time course of stimulation. Patchmaster software. We filtered this analog signal at 2.5 kHz for steps or 5 kHz for ramps and 154 sines on an eight-pole Bessel filter (LPF-8, Warner Instruments) and used a high-voltage, high-155 current amplifier (Peng and Ricci, 2016) to achieve a signal between 0-75 V. The stack was 156 biased with a starting offset of 3-4 μm, and the largest displacement we used was 3-4 μm short of the 20 μm total travel limit. This protocol ensured that stack motion was linearly related to the 158 analog voltage signal. 159 Beads glued to force-clamp cantilevers create a defined and reproducible contact surface that is 160 easy to model (Eastwood et al., 2015;Petzold et al., 2013). We adapted this technique for a 161 system relying on stiff glass, rather than silicon probes and for axial stimulus motion. We pulled 162 and polished borosilicate glass pipettes (Sutter, BF150-86-10) to a tip diameter that was half or 163 three-fourths of the diameter of the bead that we intended to use. We attached black polyethylene 164 beads (20-24 μm diameter; BKPMS-1.2, Cospheric) to the glass pipettes using UV-curable glue 165 (Loctite 352, Henkel). The bead-attached pipettes were then waxed in place to a 3D-printed 166 acrylic pipette holder (custom design available from https://3dprint.nih.gov as Model ID 3DPX-167 010770) and epoxied to a steel tip (PAA001, ThorLabs) that was mounted on the piezo stack. 168 Step protocols had a 250 ms or 300 ms hold at the commanded indentation, and used an inter- To monitor the motion of the stimulus probe, we modified the system reported by Peng and Ricci 175 (2016) to detect larger movements by using the SPOT-2D segmented photodiode (OSI 176 Optoelectronics) and a higher resistance in the differential amplifier circuit. The photodiode was 177 mounted in an XY translator on top of a rotation stage (ST1XY-D, LCP02R, ThorLabs) such that 178 the photodiode gap was aligned perpendicular to the direction of the probe motion. This 179 apparatus was fixed above a secondary camera port on the microscope (Eclipse E600FN, Nikon) 180 with no additional magnification.

181
Before obtaining an on-cell, high resistance seal for patch clamp, we aligned the front edge of the 182 bead under the 60X objective with the highest clearly visible edge of the worm's cuticle. After 183 achieving whole-cell access, we moved the microscope to visually align the image of the bead 184 with the outer edge of the photodiode. As the bead moved, the output from the photodiode circuit 185 was read directly by Patchmaster, and we used this signal to check that resonance during steps 186 and relative attenuation of sine amplitude at high frequencies were small.

187
At the end of each recording, we calibrated the image motion to actual motion. We drove the XY 188 translator in steps of known distances in a direction that was opposite to the probe motion using a 189 stepper motor actuator (ZFS-06, ThorLabs) controlled by Kinesis software (ThorLabs). We took 190 these steps once with the probe at the edge of the worm and once with only the worm. Distances Data Analysis 198 We measured whole-cell capacitance and series resistance as previously described (Goodman et 199 al., 1998). We conducted data analysis using MATLAB from Mathworks (data import and 200 analysis functions are available online at: https://github.com/wormsenseLab/Matlab-201 PatchMaster/tree/vDynamicsJGP) and Igor Pro 6.37 (Wavemetrics).

202
Our analysis only included recordings with a holding current less than -10 pA at -60 mV and a 203 series resistance less than 250 MΩ. As these experiments were conducted at constant voltage, the 204 voltage errors due to uncompensated series resistance were negligible, and we did not correct the 205 reported data for these errors. Where noted, we corrected for voltage attenuation due to space-206 clamp errors as previously described (O'Hagan et al., 2005). Briefly, we computed the 207 theoretical capacitance for each neuron based on body size and compared it to the measured 208 capacitance to estimate the ratio of membrane resistance to axial resistance for ALM. This 209 allowed us to calculate the length constant for each neuron and estimate the actual voltage at the 210 center of the stimulus, which we used as the average channel location for the purpose of 211 accounting for space-clamp error. We calculated total charge, or the area under the MRC curve, 212 from stimulus start to 150-ms after stimulus end, and subtracted the charge at baseline for an  216 We mounted young adult GN753 pgSi116 mNeonGreen::3xFLAG::MEC-4 transgenic animals 217 on grooved 5% agarose pads dissolved in M9 buffer. Grooved pads were prepared by casting 218 agarose on the surface of an LP vinyl record (Rivera Gomez and Schvarzstein, 2018). Animals 219 were immobilized using levamisole (5 mM) dissolved in M9 buffer. Micrographs were acquired 220 with an automated inverted epifluorescence microscope (Keyence BZ-X800) equipped with 221 software and hardware to generate stitched images of entire ALM neurons with a 40x objective 222 (Nikon plan apo 40x/1.0 oil).

223
The stitched images were pre-processed using ImageJ, where we manually traced a line along the 224 neurite from the cell body to the distal tip to create a 20-pixel wide straightened image of the 225 neurite. We then used these straightened neurite images to analyze MEC-4 puncta distribution 226 using a custom Python script (https://github.com/wormsenseLab/Puncta_analysis/tree/vJGP).

227
Briefly, we averaged the pixel intensities in the middle rows to calculate the raw neurite  Table 1). We took this approach for the following reasons.

239
First, the previous dataset directly linked force, indentation, and current, enabling the inference 240 of model parameters. By contrast, the current data set was collected using a mechanical    The Strain Energy Density (SED) needed to activate a single channel was estimated as follows. 262 We considered a single channel located 1μm below the cuticle surface and 1μm from the  (Fig. 1A). Similarly, we expect that stimulus speed influences the evolution of the strain 282 field, thereby introducing an additional factor that affects the synchrony or phase of MeT 283 channel activation. As such, the spatial distribution of these MeT channels can affect how they 284 respond to stimuli that vary across space and time. diameter) polyethylene bead into living, wild-type worms ( Fig. 1B and 1C). We applied 292 displacements up to 12 µm, which is about 30% of the average body width (39 ± 4 µm, 293 mean ± SD, N = 53). Unexpectedly, the peak MRCs we report here are about five-fold larger 294 than those previously reported by us (Fig. 1E). Here, we recorded from ALM, rather than PLM. 295 We pushed the bead perpendicularly, rather than tangentially into the worm (Árnadóttir et al.,  Table 1 and an internal pressure of 4 kPa, which reflects an intermediate stiffness.

363
To test the effect of body stiffness in vivo, we obtained two high-quality recordings under the 364 minimally dissected ('stiff') regime described in Eastwood et al. (2015). While these currents 365 were larger than the average, they fell within the observed range for dissected preps in this study 366 ( Fig. 3A-B, dark grey). This may be due to inadvertent selection wherein we were only able to 367 successfully isolate cell bodies from the least pressurized animals, but we cannot distinguish 368 between these possibilities in the present data set. Alternately, the factors that we believe led to  (Table 1). We found that the peak 376 current decreased slightly with the inter-punctum interval (Fig. 3C, left), but that the shape of the 377 relationship between displacement and normalized peak current was unaffected (Fig. 3C, right).

378
These simulations show that, while the quantitative aspect of our results depend on the inter-379 punctum interval chosen, the scaling relations found are robust to the specific choice. In the 380 following plots, we report simulations performed with an inter-punctum interval of 1.4µm; by 381 using the smallest value within the physiologically reported range, we avoided position-related 382 artifacts in the responses to small displacements.

383
In all prior studies of MRCs in C. elegans touch receptor neurons, current-indentation curves for 384 MeT channels have been treated as a saturating function of stimulus size. These experimental   We estimated activation rates by measuring the time required for the current to rise to half the 456 peak value from the start of the stimulus, and decay rates from the time to peak to when the 457 current dropped to half the peak value. Activation rate increased with stimulus size and was 458 similar for anterior and posterior stimulation (Fig. 5C, left). We failed to detect any difference in 459 latency. The decay rate for anterior-but not posterior-stimulation increased slowly with 460 displacement (Fig. 5D, left). This observation is consistent with space-clamp error for channels In contrast to displacement sensitivity, measured current and charge saturate at high speed and 498 simulated current and charge clearly saturate at speeds above 1,000 μm/s (Fig. 7A, 7B left). This 499 finding suggests that indentation depth governs the number of channels eligible for recruitment.

500
To estimate the relative contributions of channel recruitment and gating to speed dependence, we 501 turned to simulations, which predicted a similar dependence on speed as with displacement ( Fig.   502 7A-D right). We found that both peak channel current and the number of open channels saturate 503 at high speeds (Fig. 7E, 7F) and that the number of open channels increases with stimulus speed 504 (Fig. 7F). and 7A and 7B, left), but to different extents. At low speeds, 'off' MRCs have a larger peak 516 current than 'on' MRCs, but the ratio reverses at high speeds (Fig. 6D). This observation was not 517 recapitulated in simulations, suggesting that its origin lies in an element that is absent from the 518 present computational model or an assumption that may not hold. For instance, the model 519 assumes that tissue indentation follows the stimulator speed precisely. It is possible, however, 520 that the stimulator bead detaches from the body during fast 'off' stimuli creating asymmetries in 521 the mechanical loads delivered at high speed. Above, we argued that synchrony or phase 522 differences in channel activation do not fully account for speed-dependence generally. When we 523 explored the possibility that phase differences contributed to the 'on'/'off' asymmetry observed 524 in peak current amplitudes by plotting the ratio of 'off' to 'on' charge against stimulus speed, we 525 found that 'off' responses consistently carried less charge than 'on' responses. This ratio was not 526 obviously speed dependent (Fig. 6E).

527
'On' currents activate slowly at slow speeds, while 'off' currents activate rapidly and vary less 528 with stimulus speed in both experimental and simulated data (Fig. 7C). The simulation predicts 529 that recruiting more channels by decreasing 0 would increase the asymmetry in activation rate 530 (Fig. 7C, right). This is not true for the decay rate, however. Both 'on' and 'off' MRCs seem to 531 decay at a relatively constant rate regardless of stimulus speed (Fig. 7D). This suggests that 532 activation depends on stimulus speed, while decay depends on tissue relaxation. Intuitively, we 533 might expect channels to be more likely to be opened in-phase during 'off' stimuli because all 534 channels affected by the deformation will start moving once the stimulator moves. In contrast, 535 during slow 'on' stimuli, channels closer to the stimulator will be affected before the 536 deformation reaches further channels, resulting in out-of-phase opening and slower MRC 537 activation. This is supported by the observation that activation of 'on' MRCs appears to be faster alternation between 'on' and 'off' responses. We next examined the power spectral density of the 559 stimulus and the MRC response. We found that MRCs have roughly equal power at 1x and 2x 560 the stimulus frequency (Fig. 8C), whereas the spectrum of the stimulator shows a larger peak at 561 the stimulus frequency and a smaller one at its second harmonic. The relative power of the 562 second harmonic peak in the MRC response decreases slightly at higher frequencies, which is 563 reflected in the decreasing asymmetry between subsequent ('on' vs. 'off') peaks (Fig. 8B). This 564 finding demonstrates that the neuron's response to stimulation is non-linear.

565
The average steady-state current continues to increase with frequency (Fig. 8A, 8D). Although high-pass filter (Fig. 8D). This is consistent with TRNs being relatively insensitive to slowly 569 varying stimuli and thus ignoring self-motion. By contrast, the variance in the current, as 570 measured by the root mean square (RMS) of the response at steady state, shows band-pass 571 behavior (Fig. 8E). Again, the peak of the experimental curve is shifted to higher frequencies 572 than the model predicts with the previous parameters (dashed line). The band-pass behavior in 573 Fig. 8E can be understood as being due to the fact that channels do not have time to transition to 574 lower-conductance states during high-frequency stimulation. Because the channels are held in an 575 open or sub-conducting state, their contribution to the RMS noise declines with frequency. 576 We hypothesized that the simulated results were shifted to the left because channels were not 577 able to close in phase with the sinusoidal stimulus. To test this possibility, we shortened the time 578 required for the elastic filament to relax to baseline (τ = 0.6), which allowed us to better match 579 the peak RMS (Fig. 8E, dotted line). However, this change also shifted the steady-state current to 580 the right. Collectively, these observations suggest that additional modifications to model 581 parameters will be needed to fine-tune the mechanical filter that links touch sensation to MeT 582 channel activation. current predicted by the simulation (Fig. 9A, left panel) is smaller than what we observed at high 600 speeds. This discrepancy could be due to uncertainty in some assumptions used in the model. For 601 instance, channels in the model were distributed at regular 1.4 μm spacing, which is shorter than 602 the average 2.95 μm spacing we observed in the region we were stimulating (Fig. 2). However,  (Table 1). Our estimates of SED were two to three orders of magnitude larger than that 635 those reported by Elmi et al. (2017). There are two main factors contributing to this difference.

636
First, SED is proportional to the Young's modulus, which is 40 times larger in our simulations.

637
Although the origin of this discrepancy is not clear, it may arise from differences in the finite 638 element models used to infer the Young's modulus. Second, different assumptions were used to 639 deduce the minimum SED for single channel activation. Rather than assuming that maximal conducting state (Fig. S1).

643
Because the SED estimate applies only to the responses to displacement steps and involves 644 several uncertainties, we turned to our model linking body indentation to activation of single 645 channels via elongation of a hypothetical gating filament. In our model (Sanzeni et al., 2018), 646 the filament extension need to activate a single channel is of the order 0 / 1 ; such an elongation 647 is generated by a deformation of constant rate 0 / 1 / if it is applied for a time of order, .

648
Using values reported in Table 1, the model predicts that a single channel is able to sense a 649 deformation on the order of 0.003 times the length of the linker generated over a time of 3 ms.  justifiably assume that is independent of stimulus intensity. We can also assume that while the stimulus posterior to all channels, the current-displacement curve was shifted to the right 684 (larger displacements) because we began to observe responses only once the displacement was 685 large enough for the mechanical strain to reach the nearest channels (Figs. 4, 5, and 9). Our 686 model also shows that both larger displacements and faster speeds increase the number of 687 channels that fall within the indentation-induced strain field (Figs. 3D and 7F). Increasing either 688 displacement or speed increases the probability that a channel will be in a sub-conducting or 689 open state in a manner that depends on the channel's distance from the stimulus (Fig. 9). The ). This initial rapid, but modest stimulation may be followed by a slower but more complete 712 closure of the constricting ring (Barron, 1979). Thus, the initial indentation would be expected to  suggest that the high 'off'/'on' ratio at slow speeds is due to a change in synchrony (Fig. 7).              Figure S1