Hybrid motility mechanism of sperm at viscoelastic-solid interface

To fertilize eggs, sperm must pass through narrow, complex channels filled with viscoelastic fluids in the female reproductive tract. While it is known that the topography of the surfaces plays a role in guiding sperm movement, sperm have been thought of as swimmers, i.e., their motility comes solely from sperm interaction with the surrounding fluid, and therefore, the surfaces have no direct role in the motility mechanism itself. Here, we examined the role of solid surfaces in the movement of sperm in a highly viscoelastic medium. By visualizing the flagellum interaction with surfaces in a microfluidic device, we found that the flagellum stays close to the surface while the kinetic friction between the flagellum and the surface is in the direction of sperm movement, providing thrust. Additionally, the flow field generated by sperm suggests slippage between the viscoelastic fluid and the solid surface, deviating from the no-slip boundary typically used in standard fluid dynamics models. These observations point to hybrid motility mechanisms in sperm involving direct flagellum-surface interaction in addition to flagellum pushing the fluid. This finding signifies an evolutionary strategy of mammalian sperm crucial for their efficient migration through narrow, mucus-filled passages of the female reproductive tract.


Introduction
For mammalian fertilization to succeed, sperm must pass through complicated and often narrow passageways that could in uence sperm movement 1,2 .The passages are generally lled by a highly viscoelastic uid, such as cervical mucus and oviductal uid 3 .Viscoelastic uid is both viscous and elastic due to the presence of macromolecules, such as mucins, which create a scaffolding structure that provides elasticity while they are not chemically bonded to each other.As a consequence, the structure eventually deforms ( ows).Clinically, however, sperm motility is typically assessed in vitro, commonly in watery media of low viscoelasticity that could alter sperm movement patterns.In this study, we examined the mechanism that thrusts sperm forward in a physical environment that more closely resembles the natural environment to better understand how sperm migrate in vivo; that is, narrow channels lled with highly viscoelastic uid.
It has long been known that sperm typically swim near liquid-solid interfaces 4 , a tendency primarily attributed to the fact that sperm are "pusher" microswimmers, meaning they propel themselves forward by pushing uid backward [5][6][7][8] .This behavior particularly makes sperm tend to travel along the corners formed by the meeting of two surfaces.In the female tract, microgrooves in the walls can act like corners and thereby provide an effective guidance mechanism for sperm migration 9,10 .There is evidence that microgrooves in the walls of the bovine cervical canal not only guide sperm but also protect sperm from being swept away by cleansing uid that ows from the uterus through the cervical canal out to the vagina 11,12 .Hence, sperm interaction with surfaces plays a signi cant role in enhancing their migration through the female tract.
In addition to the effects of surfaces on sperm movement, the mode of sperm locomotion is also highly dependent on the uid environment through which they swim 13 .When not near solid surfaces, sperm tend to swim using a rolling motion 14 .When sperm arrive near a surface, the motility mode depends on the uid properties.In a low-viscosity medium, the same rolling motion continues to be observed as sperm swims along a surface.In a high-viscosity or highly viscoelastic uid, sperm agella are known to beat two-dimensionally on surfaces 13,15 .Sperm swimming in highly viscoelastic uids also tend to form dynamic clusters and swim parallel to their close neighbors 14 .To understand how sperm travel in the female tract to reach the fertilization site, it is essential to know how sperm move at the interface of viscoelastic uid with solid surfaces.Sperm motility through a more complex mechanism beyond merely pushing surrounding uids has been proposed on three occasions.In 1972, it was rst suggested that the sperm agellum exhibits movement similar to a snake crawling on a surface, hinting at a motility mechanism akin to that of a snake 16 .(Note that the exact locomotion mechanism of a snake was not clari ed until 2009 17 .)More recently, total internal re ection uorescence microscopy showed that sperm "slithering" using planar-beating agella were within 1 µm of a solid surface 13 .Although the authors referred to slithering sperm as swimmers, the steric interaction between the sperm and the surface was mentioned as the mechanism that con nes the agella to two-dimensional motion, therefore pointing towards direct agellum-surface interaction.In one of our recent studies, we found that, in a viscoelastic uid, sperm engage in stable, long-range collective dynamics in which thousands of sperm move closely together in the same direction 18 , although this " ocking" behavior is theoretically predicted as unstable when the momentum conservation between the microswimmers and the surrounding uid is taken into account 19 .One possible explanation for the nonconservation of total momentum between the sperm and the uid is the direct transfer of momentum between the sperm and the surface, further supporting the analogy of slithering/crawling behavior.All of these ndings suggest a strong possibility of a direct momentum transfer between the agellum and the solid surface.The role this momentum transfer plays in motility, however, remains to be explored.
Here, using a micro uidic in vitro model, we examined sperm agellum interaction with a solid surface.
We found evidence that kinetic friction between the sperm agellum and the surface plays a role in driving the sperm forward.We found it likely that, in a groove-like structure, the sperm agellum generates thrust through friction from more than one surface simultaneously.At the same time, the part of the agellum that deviates from the surface pushes uid backward.By using tracing beads, we obtained a ow eld generated by the sperm that bears resemblance to a ow eld produced by an idealized pusher swimmer 20,21 , more so when including beads directly pushed by the sperm head or tail.This observation led us to conclude that the polymer solution we used has signi cant slippage at solid surfaces, challenging the conventional 'no-slip' boundary condition typically used in related uid simulations 21,22 .It highlights the potential for re ning existing models to represent sperm movement more accurately in a complex environment.
Overall, our study contributes to a more comprehensive understanding of how sperm can e ciently move within the spatially con ned, viscoelastic uid environments of the female tract.This understanding could lead to improved fertility assessments, novel treatment strategies, and the development of new sperm selection methods.

Results
Flagellar dynamics at the interface reveal that kinetic friction from a solid surface pushes sperm forward.
To study the sperm agellum interaction with a solid surface, we utilized a micro uidic device with a channel that had a clean-cut corner (see Methods) and was lled with a viscoelastic solution of 1% methylcellulose in sperm TALP medium.The channel enabled visualization of sperm interaction with two different surfaces perpendicular to each other (Fig. 1a).The traditional view of sperm moving along a surface is akin to images taken by the objective below in Fig. 1a or imagery seen in Fig. 1d, which will be referred to as the "top view" in the rest of the text; the images represent a view of the broader surface of the paddle-shaped sperm head.The images taken by the objective to the right in Fig. 1a yield imagery of sperm agellum close to the surface and shown in Fig. 1b, referred to as the "side view"; the images represent a view of the narrow surface of the head.In reality, we had only one objective, and the side-view images were taken when sperm traveled on the surface parallel to the objective optical axis.
From the side view in Fig. 1b, it can be seen that a substantial portion of the agellum maintained contact with the surface.The montage of the time-lapse images is shown in Fig. 1c.As the head moved forward (downward in these images), the portion of the agellum that was in contact with the surface was moving backward (upward) (Supplementary Movie 1).It appeared that the agellum slid backward on the surface, therefore incurring kinetic friction in the forward direction and becoming a source of the thrust.
The top view of sperm movement has been reported and analyzed before 5,9 .Here, we note that, even in the top view, the agellum had direct solid contact with the sidewall and with the contact point moving backward, appearing to suggest that kinetic friction in the forward direction is incurred through solid contact (Fig. 1e) (Supplementary Movie 2).This movement pattern was seen on both the upper and lower surfaces of the channel.

Quanti cation of the agellum-surface interaction
To explore the reach and limit of this agellum-surface motility mechanism, we performed several quantitative measurements of sperm agellar beating and the agellum-surface interactions.In Fig. 2a, b, we present our measurements of the agellar beating amplitudes from the top view.This measurement is important because, if a sperm cell is situated in spatial con nement less than this amplitude, the agellum can produce kinetic friction from two parallel surfaces, similar to scenarios encountered in con ned spaces such as in the female tract, rather than with just one surface.
In the top view, we observed that, along the agellum, each bend was sequentially generated at the junction with the head and then propagated down its length, resulting in the consistent formation of three distinct propagating mechanical bends along the agellum (Fig. 2a) (Supplementary Movie 2).Bend 1 is closest to the head and observed around the mid-piece, Bend 2 is around the middle of the principal piece, while Bend 3 is located close to the end of the principal piece or around the end piece.Signi cant amplitude variations between bends in different stages are evident in the box plot (Fig. 2b), a simple re ection of the beating pattern.Note that the largest amplitude was found to be around 10 µm, suggesting that, in a groove-like structure less than 10 µm wide, the agellum could generate thrust from friction on both sidewalls.
The side view, on the other hand, reveals three bends with similar amplitudes, as they were found roughly the same distances from the head (Fig. 2c, d) (Supplementary Movie 1), with amplitudes around 2 µm.This value is slightly higher than the 1 µm distance previously reported between the agellum and the surface 13 , yet not by far.For a narrow slit-like structure with an opening less than 2 µm, such as those found in preovulatory bovine uterotubal junctions 23 , it appears likely that the agellum can touch both surfaces.
Finally, from our detailed analysis of the tracking from videos of sperm movement, it was revealed that as the head moved forward, the portion of the agellum in contact with the surface exhibited backward movement.Further, the speed of the contact point between the agellum and the surface was higher than the speed of the sperm head (Fig. 2e, f), suggesting that the agellum slid backward on the surface, further supporting the hypothesis that the kinetic friction between the agellum and the surface was in the forward direction, thereby providing thrust to the sperm.Moreover, since kinetic friction is solely determined by the force between the two sliding bodies (normal force) and the surface properties (coe cient of friction) and is independent of the relative speed between the sliding objects, this observation seems to imply that the backward traveling of the wave sustained on the agellum has a function other than generating thrust through friction; otherwise, the energy spent on sustaining the mechanical wave would have been wasted.
The ow generated in the surrounding uid by moving sperm does not balance out the forward momentum of the sperm.
We previously reported that the ow generated by sperm in highly viscoelastic uid is less extensive than the ow generated in standard medium 14 .Since the backward propagating wave and the contact point speed both suggest ow generation from the agellum, to better understand the uid's role in sperm motility mechanism, we measured the ow eld around moving sperm in 1% methylcellulose solution containing tracer particles.Figure 3 illustrates how the ow eld was obtained.We rst took raw images of sperm and tracers (Fig. 3a and Supplementary Movie 3).We next tracked the positions of the tracers and the sperm, using these data to determine tracer movement and, consequently, the velocity in real space at different positions relative to the sperm (Fig. 3b).Each tracer movement is represented by a displacement vector and segregated into different bins according to their relative position to the sperm head (Fig. 3c).Velocity vectors from all tracers within the same bin (accumulated throughout the agellum beating cycles) were then averaged into one velocity vector representing the ow velocity of the bin (Fig. 3d, white arrow), and the results of all bins are shown in Fig. 3e, with additional data shown in Supplementary Fig. 1.In Fig. 3e, the measured ow eld roughly resembles an idealized pusher swimmer ow eld 24 20,21 , with forward ow around the head, backward ow around the tail, and inward ow on the left hand side, suggesting that the sperm agellum pushes uid backward, or "swims," simultaneously to pushing the solid surfaces.As observed in Supplementary Movie 4, the bead movement in the side view indicates limited ow toward the sperm in the perpendicular direction, which is another resemblance to the ideal pusher swimmer ow eld.We estimated the net momentum in the y direction to be g-µm/s (for details, see Supplementary Analysis).Although the mean value is positive, indicating net forward momentum combined between the sperm and the uid, the uncertainty is high due to signi cant cancellation between positive and negative values.The uid boundary condition may also reduce the negative uid momentum.
However, we note that the ow eld does not look the same when tracers directly pushed forward by the sperm head, and those hit by the agellum were excluded from the analysis.In this case, the measured ow eld became what is shown in Fig. 3f, with generally much reduced ow.
Since the tracer movements were signi cantly different between those that directly came in contact with the sperm (Supplementary Movie 5) and those without contact (Supplementary Movie 6), we suspect that the no-slip boundary condition was not a good assumption for the interface between the viscoelastic solution and the solid structure of sperm, such as the head and potentially the tail as well.
The ow pro le of the viscoelastic solution reveals a slip boundary at a solid interface.
As our ow eld measurements suggest the existence of a slip boundary of our viscoelastic solution at a solid surface, we decided to explicitly test this possibility.We measured the ow velocity pro le of the two sperm media, standard TALP medium and 1% methylcellulose in TALP, under a pressure-driven ow within a rectangular micro uidic channel approximately 60 µm deep and 2.47 mm wide (see Methods).Figure 4 presents the comparative analysis of uid behavior.
In Fig. 4a, we show the normalized velocity pro les of the standard TALP medium and the 1% methylcellulose solution in TALP.The TALP control pro le is very close to the parabolic Poiseuille pro le of an ideal Newtonian uid, while the MC solution pro le exhibits signi cant attening near the center of the channel, suggesting signi cant shear-thinning of the uid.The slight deviation of the TALP control pro le from the perfect Poiseuille pro le may be attributed to a small shear-thinning property of the bovine serum albumin in TALP 25 .
Regarding the interface boundary conditions, we should focus on the data points close to or 60 µm.In Fig. 4a, we saw that near a surface, in MC solution, the speed of the tracer particles was found to be 51.89% of the peak speed at the middle of the channel.In TALP, the speed of the tracer particles at the surface was 7.31% of the peak speed observed in the middle of the channel.Figure 4b shows the box plot comparison for the measured speeds near the solid surface, demonstrating a statistically signi cant higher speed for MC than in TALP control.Note that the imaging depth of our objective was estimated to (6 ± 9) × 10 −9 z = 0 be 4.375 µm, and therefore, the non-zero mean does not contradict a no-slip boundary.Supplementary Movie 7 shows that some tracer particles did not move with the ow.Overall, the uid slip at the solid boundary was quite prominent in MC solution (Supplementary Movie 8).

Discussion
We investigated how bovine sperm move at the viscoelastic uid-solid interface using a micro uidic model with a 1% methylcellulose solution as the model viscoelastic medium.We present here direct visual evidence of solid-solid interaction between the sperm agellum and solid surfaces.The observed relative motion between sperm and surface suggests that the kinetic friction experienced by the sperm is in the direction of its forward motion, making it part of the hybrid mechanism, besides swimming, that provides thrust to the sperm.
As sperm traveled along a surface, the agellum formed a consistent pattern of bends propagating from the agellar midpiece to the end piece at the tip of the tail.The amplitudes of successive bends demonstrate that when sperm pass through a narrow space (roughly ≤ 2 µm, which is the thickness of the sperm head) lled with highly viscoelastic uid, the thrust generated through friction likely arises from interactions with surfaces on both sides of the sperm.In the case of the bovine uterotubal junction, sperm may simultaneously contact both sidewalls of microgrooves in the mucosal epithelium 11 .In the case of the oviduct, sperm may pass through the narrow spaces between mucosal folds 23 .This is particularly intriguing since kinetic friction dissipates energy.The biological rationale for sperm to adopt this motility mechanism that purposefully dissipates energy remains to be seen.
For friction to occur, one of the necessary conditions is a normal force between the two touching surfaces 26 .In the case of a snake slithering, the normal force balances out the weight of the snake from gravity 17 .In other words, snakes cannot slither on a ceiling.Interestingly, the same agellum-surface interaction was observed on the upper and lower surfaces of the channels in the devices, indicating that the source of the normal force for sperm is NOT from gravity.For all practicality, for a low-Reynolds number swimmer whose inertia is considered negligible 27 , the effects from gravity should not be signi cant.We suspect that the depletion interaction 28 is at work here.When two different sizes of objects are randomly distributed in a small molecule solvent (in this case, our medium, molecularly primarily water), the smaller objects (in this case, the polymer macromolecules) have more freedom to move around, and maximize the entropy of the whole suspension, it is probabilistically more likely that the larger objects (in this case the sperm) get "depleted" from the middle of the uniform distribution of the smaller objects.In the current case, depletion from polymers and the subsequent osmotic force provide the interactions needed to form the normal force between the sperm and the surface.
As the head of the sperm advanced along the walls in the channels of the devices, the agellar contacts with the walls moved backward, interestingly, at a faster rate than the forward motion of the head.While the backward-moving contact points produced kinetic friction with the surface in the direction of the forward movement, this heightened speed of movement seems unnecessary for the generation of the thrust from friction along the wall.This observed phenomenon suggests that the agellum, particularly the parts deviating from the surface, likely pushes the uid while, simultaneously, the portion in contact with the surface pushes against the solid surface 29 .
While the ow eld pattern we observed could be somehow aligned with that generated by the idealized pusher microswimmer, more resemblance was seen when the tracks of tracers directly pushed forward by the sperm head and tail were incorporated into our analysis.If these beads were excluded from the analysis, we could still see backward moving ow, while the forward ow around the sperm head was reduced.From our momentum analysis, the backward momentum of the uid was found to be less than the forward momentum of sperm.Further investigation will be needed to verify the split of the thrust from solid-uid interaction and solid-solid interaction.
Meanwhile, both the ow generated by sperm and our direct measurement of the pressure-driven ow pro le indicated that the viscoelastic polymer solution uid underwent a signi cant amount of slipping along the surface of the solid.We propose that the slippage is related to the depletion interaction between the polymer chains and the imperfections on the surface 30 , although this phenomenon has not been commonly considered in various microswimmer uid models 22,[31][32][33][34][35] .In short, assuming a no-slip boundary is often a good approximation since solvent molecules scatter randomly when colliding into a solid surface that is microscopically rough.When there are random polymer chains (smaller objects) in the solution, due to entropic effects, polymer chains often do not ll in between all the microscopic solid protrusions (larger objects), therefore forming a thin layer of solvent without polymer, allowing the uid with polymer chains entangled in it to slip relative easily to the solid surface.The slip boundary we present here is a direct link to the effects of depletion interaction from the polymer, which further strengthens our argument that the depletion interaction leads sperm toward the surface.
Another implication regarding the slip boundary is the interaction between sperm and the uid.As the viscoelastic polymer solution slips relative to the movement of the sperm, particularly the agellum, the movement of the agellum will not push the uid as e ciently as when pushing a simple saline solution.
This is consistent with our earlier report that passing-by sperm generated more uid movement in the standard medium than in viscoelastic polymeric uid 14 , and further highlights the advantage for sperm agellum to engage in near planar beating that facilitates solid-solid interaction.
In a low-viscosity medium, sperm exhibit a rolling motility, whether near or far away from a solid surface 36 .In a high-viscosity or viscoelasticity uid, the same rolling is seen when sperm are far from a solid surface, yet near planar beating is seen when they are found to be moving along a solid surface.
How and why sperm switch between these different motility modes is not well understood 13 .We note here that, in both high-viscosity (Newtonian) and viscoelastic uids, the uid rheological properties are achieved by the addition of polymer to the solution; therefore, the effect may well come from the dissolved polymer instead of the viscosity.In fact, if the depletion corresponds to the normal force between the sperm and the solid surface, the same forcing toward the solid surface likely also forces the two-dimensional beating of the agellum.Furthermore, when sperm engage in this near planar beating motility between the entangled polymer web and the solid substrate, it is possible that sperm follow a thin layer of solvent, allowing them to move with less resistance from the uid.
In conclusion, we report that, at the interface of a viscoelastic uid and a solid substrate, sperm propel themselves through a combination of direct agella-surface contact and conventional swimming ( agella pushing uid).The solid interaction coincides with the strong tendency of sperm to move near solid boundaries.The natural uids through which the sperm pass in the female reproductive tract are full of macromolecules (mucins in cervical mucus, for example) and highly viscoelastic 37 .Given the narrow con nes of the female reproductive tract, the propulsion from solid-solid interactions may be the predominant force that pushes sperm to reach the fertilization site in mammals.

Media preparation
The medium used in this study, Tyrode's Albumin Lactate Pyruvate (TALP) 38 , was composed of 99 mM NaCl, 3.1 mM KCl, 0.39 mM NaH 2 PO 4 , 25 mM NaHCO 3 , 10 mM HEPES free acid, 2 mM CaCl 2 , 1.1 mM MgCl 2 , 25.4 mM sodium lactate, 1 mM/mL sodium pyruvate, 5 mg/mL gentamicin, and 6 mg/mL bovine serum albumin (BSA), titrated with 1 M HCl to a pH of 7.4.Our viscoelastic uid was made of 1% w/w methyl cellulose (1% MC) in TALP (4,000 cP at 2%) Methylcellulose was added to the medium to add viscoelasticity and closely simulated the conditions of the female reproductive tract, and its weakly elastic nature allows for modeling in numerical simulations 32,39 .The rheological measurements of 1% MC are detailed in Supplementary Fig. 2. 0.35 µm carboxylated polystyrene beads were added to the 1% MC for ow tracing.Carboxylated beads were used because they were found to reduce clumping of plain polystyrene beads in the TALP medium.

Sperm sample preparation
Bull semen frozen in 500 µL plastic straws was obtained from Genex Cooperative, Inc. (Ithaca, NY, United States, prior to its closure in 2021.) and stored in liquid nitrogen.Before use, the straws were thawed in a 37°C water bath for 30 sec.Subsequently, the sample was centrifuged through two layers (40% and 80%) of Bovipure in Bovidilute solution (Spectrum Technologies, Inc., Healdsburg, CA, United States) at 300 x g for 10 min.The supernatant was removed, and the pellet of sperm was suspended in 3 mL TALP, then centrifuged at 300 x g for 3 min.Following supernatant removal, the sperm pellet was re-suspended in 300 µL TALP and placed in an incubator at 38.5°C under 5% CO 2 in humidi ed air.

Construction of micro uidic device
The design of the silicon master mold was adopted from our previous work 12

Flow eld measurement
Using high-speed video microscopy, video sequences capturing both sperm movement and the motion of the tracers (aggregates of polystyrene beads, 0.35 µm, carboxylated) suspended in the 1% MC within a micro uidic device of 120 µm were recorded with a 20× objective at a frame rate of 250 fps.The movement of the tracers was analyzed using ImageJ, viewing the beads highly magni ed so that individual pixels were easily visible.The beads (or the aggregates of the beads) showed up either brighter or darker than the background, and both cases were tracked.A special feature is typically used to reliably identify the same pixel of the bead from frame to frame.No external ow was induced in the device to isolate and analyze the effects of sperm movement on the surrounding uid.The sperm head positions and the tracer bead locations were tracked using the Manual Tracking plugin in ImageJ from around 100 different cells from separate video recordings of sperm.The results from the tracking were analyzed using MATLAB.To map the ow eld, the area surrounding the sperm was segmented into bins based on the relative positions of the tracer particles, and their velocities in each bin were averaged.The overall ow eld was then visualized by assembling these average velocities from all bins, providing a clear map of the uid movement in uenced by sperm (see Fig. 3).

Velocity pro le measurement
Suspensions of 0.35 µm carboxylated polystyrene in 1% methylcellulose dissolved in TALP and 1 µm polystyrene beads in TALP control medium were introduced into a device with a channel depth of about 60 µm at a constant ow rate of 1.5 µl/min using a syringe pump.Videos capturing the movement of each uid were recorded at various Z-positions, using a 20× objective at a capture rate of 20 fps.The video sequences were then analyzed using ImageJ software, which facilitated direct tracking of the respective tracer beads.The software provided instantaneous velocities of each bead by calculating their displacement over time between frames.These velocities were then averaged across several beads in different regions of the channel at different depths to construct the velocity pro le of each uid.   ) from all tracers averaged into one vector (white arrow) representing the bin.e, f These two ow eld plots map the ow velocities surrounding a sperm in two dimensions (x and y).The average velocity is depicted by white arrows, indicating ow magnitude and direction.Note that we obtained the ow eld plot by averaging velocities over time with no externally applied ow, in addition to spatially averaging velocities within a small bin with respect to the sperm's relative positions.The overlaid sperm (red and green dots) depicts sperm head and agellum positions relative to the average ow eld, not a momentby-moment correlation between agellum and ow eld.e The average ow eld generated by sperm when all tracer particles were included in the calculation, including those directly pushed forward by sperm.f The average ow eld generated by sperm that excludes tracers pushed directly by the head and the tail.

Figure 1 Images
Figure 1

Figure 3 Visualizing
Figure 3 . The device contained a channel 4 cm long, 2.47 mm wide, and 60 µm, 120 µm or 250 µm deep.The structure was made by SU-8 negative resist with one layer of photolithography.The usage of SU-8, instead of etching, is crucial in this application in order to have clean, sharp edges.The master mold was treated with (1H,1H,2H,2Hper uorooctyl) trichlorosilane (FOTS) to aid in easily releasing PDMS from the silicon master.Micro uidic devices were cast onto PDMS (10:1 PDMS base to curing agent) (SLYGARD 184 Silicone Elastomer kit, Dow Corning, Midland, MI, United States) on the silicon master.Subsequently, the PDMS mixture underwent 30 min of degassing to remove all air bubbles and was cured at 65°C for 1 hr.Sperm seeding and uid input ports were created by punching holes in PDMS using biopsy punches (Sklar, West Chester, PA, United States).The PDMS components were then securely bonded to glass slides after oxygen plasma treatment (HARRICK PLASMA, PDC-32G, Ithaca, NY, United States) using high RF power for 60 sec.The channels were lled with viscoelastic uid, which was equilibrated at 38.5°C under 5% CO 2 in humidi ed air for at least 2 hr before experiments.For the experiments, the micro uidic devices were placed in an environmentally controlled chamber (operated by OKO-Touch), which was kept at 38.5°C and humidi ed.Sperm were seeded into one end of the micro uidic device to allow them to swim into the channel.Visualization of agellum interaction with a solid surface A Nikon Eclipse inverted phase contrast microscope, equipped with a Hamamatsu ORCA Flash 4.0 V3 camera, was used to capture images.The videos were recorded using NIS Element BR software, with each video lasting 1 min.A micro uidic device featuring a sharp L-shaped corner was lled with 1% MC.No external ow was induced within the device.The experimental setup is illustrated in Supplementary Fig.3.Videos of sperm moving close to one of the upper corners were captured using a 20× objective and a frame rate of > 150 frames per sec (fps).Subsequently, we used ImageJ tracking software (open source, National Institutes of Health) to manually analyze the movement of both the head and the agellum of sperm.