Time and power dependence of laser-induced photodamage on human sperm revealed by longitudinal rolling measurement using optical tweezers

Lasers are widely applied in assisted reproductive technologies, including sperm fixation, sperm selection and intracytoplasmic sperm injections, to reduce procedure time and improve consistency and reproducibility. However, quantitative studies on laser-induced photodamage of sperm are lacking. In this study, we demonstrated that, by using optical tweezers, the kinematic parameters of freely swimming sperm are correlated with the frequency as well as the percentage of pausing duration of longitudinal rolling of the same sperm head in the optical trap. Furthermore, by trapping individual sperm cells using 1064-nm optical tweezers, we quantitatively characterized the time-dependence of longitudinal rolling frequency and percentage of pausing duration of sperm under different laser powers. Our study revealed that, as trapping time and the laser power time increase, the longitudinal rolling frequency of the optically trapped sperm decreases with an increasing percentage of pausing duration, which characterizes the effect of laser power and duration on the photodamage of individual sperm cells. Our study provides experimental basis for the optimization of laser application in assisted reproductive technology, which may reduce the photodamage-induced biosafety risk in the future.


Introduction
With the development of assisted reproductive techniques (ART), the use of laser technology in intracytoplasmic sperm injection (ICSI), preimplantation genetic testing (PGT), and in vitro manipulation of gametes and embryos has seen significant advancements over the past few decades [1].Numerous studies have been conducted to explore the application of various laser technologies in the in vitro manipulation of human sperm, which involves sperm selection, sorting, immobilization, and quality assessment [1,2].However, despite the extensive application of laser in ART, fewer studies focused on the effect of laser on human spermatozoa.The lack of systematic understanding of photobiological responses of laser in sperm manipulation, as well as safety considerations in ART, prevent accurate decisions on the clinical value of these laser technologies.Therefore, it is necessary to quantitatively characterize the photodamage effect of laser on human sperm under different laser powers and irradiation times.
Low-level light therapy has been shown to be effective in improving sperm motility in patients with asthenozoospermia [3][4][5].On the contrary, a previous study focused on the biological effects of near infrared radiation (NIR) on sperm, revealing a significant damage on sperm function after exposure to 1305 lux/min of NIR for 15 minutes [6].In order to achieve optical manipulation of sperm, highly focused laser beam is needed to optically trap sperm cells, which undergo high power density of laser exposure in a short period of time during this process.Thus, to evaluate the time-and power-dependent biological effects of laser on sperm in ART applications, it is necessary to monitor the function of the irradiated sperm in real time.
Motility is clinically applied to estimate the quality and function of sperm [3,7].Due to the high swimming speed of sperm, standard sperm motility analysis methods, such as computer-assisted sperm analysis, are difficult to measure the same sperm multiple times.On the other hand, several studies on optical trapping of sperm have proposed different methods for measurement of sperm motility.Tadir et al. quantified sperm motility by measuring sperm swimming force [8], and demonstrated a positive correlation between sperm swimming force and sperm motility [9].Nevertheless, accurate measurement of sperm swimming force requires complex calibration methods and several assumptions to determine the trapping efficiency and escape power, which limits its application [8].Standalone escape power was also applied to characterize sperm motility [10], and a linear relationship was found between swimming force and escape power with R 2 ≈ 0.9 [11].However, the escape power measurement process requires dynamic adjustment of laser power, and sperm needs to escape from the laser trap during the measurement, making it difficult to achieve long-term and real-time recording of sperm motility status, and to measure the effects of a definite power of laser beam on the sperm.Chow et al proposed that the swimming force can be estimated using the mean squared displacement of the trapped sperm and the trap stiffness of an optical pseudo-potential [12].The calculation of the pseudo-potential, however, requires the assumption that the particle undergoes rotational Brownian motion near its equilibrium orientation, which averages out the effects of orientation on the time-averaged forces [13].This assumption may not be valid in the case of optically trapped sperm, as sperm can propel themselves forward and rotate.Therefore, a simple method is needed to continuously evaluate the motility of optically trapped sperm with a certain power of laser in real time.
Recently, it has been confirmed that the head of human spermatozoa displayed 360°longitudinal rolling [14,15].According to our theoretical analysis, the longest axis of a triaxial ellipsoid in the optical trap tends to automatically adjusted to parallel to the optic axis by the torque generated by the optical field [16,17].The sperm head can be considered as a triaxial ellipsoid, and its longest axis is parallel to the longitudinal axis of the sperm.As a result, sperm cell tends to be vertically oriented when it is in the optical trap, which the longitudinal rolling behavior can be easily analyzed according to the trajectory of its head projection, allowing for real-time measurement over a long period of time.Schiffer et al revealed that the rolling frequency is relative to many factors including sperm motility, viscosity and viscoelasticity of the solvent, and carbonate concentration [14,18].In highly viscous or viscoelastic solutions, the rolling of mammal sperm head is suppressed with increasement of asymmetry flagellar beating, suggesting a critical role of the longitudinal rolling in sperm navigation in reproductive-tract microenvironments with different rheological properties [18].In a previous study, we developed a method to measure both the chirality and frequency of longitudinal rolling of human sperm using optical trap, and discovered that all the sperm we observed have the same right-hand longitudinal rolling chirality, as well as pausing events may occur during the longitudinal rolling [19].The unidirectional longitudinal rolling of sperm head may associated with the asymmetric structure of dynamic basal complex of the sperm flagellum, which couples the tail beating with asymmetric head kinking motion [20].These studies suggest that, measurement of the longitudinal rolling behavior of sperm is a suitable method to evaluate the cumulative photodamage effect of laser.
In this study, by using 1064-nm optical tweezers, we demonstrated that the frequency and percentage of pausing duration of longitudinal rolling of an optically trapped sperm are correlated with its pre-trap kinematic parameters.We also confirmed that the distance between the optically trapped sperm and the bottom surface of the chamber does not affect longitudinal rolling frequency.As a result, we proved that longitudinal rolling parameters of the sperm head are able to characterize the motility of optically trapped sperm in real time.Then we captured individual sperm cells under different laser powers and different trapping durations, and measured the longitudinal rolling parameters in real time.The experimental results clearly show that as the laser power and trapping time increase, the longitudinal rolling of sperm head decreases, and the pausing duration ratio increases, which indicates the time and power dependence of the photodamage effect of 1064-nm laser on human sperm.

Sperm sample preparation
This study was performed in accordance with the standards set by the Declaration of Helsinki.The human semen samples were collected from individual patients seeking in vitro fertilization treatment at the Reproductive Medicine Center of Hefei BOE Hospital.All patients gave their informed consents prior to their inclusion in this study.Ejaculates were incubated at 37°C for 30 minutes to allow liquefaction.The semen samples were then purified using density gradient centrifugation method.Briefly, 1.0 mL of 90% sperm gradient separation solution (10138, SpermGrad, Vitrolife, Sweden) was pipetted into a 15 mL centrifuge tube, and then 1.0 mL of 45% solution (10139, SpermGrad) was added slowly, followed by adding ≤3 mL of liquefied semen on the top gently.After 600×g centrifugation for 20 minutes, the supernatant of the tube was discarded, and the pellet was transferred and resuspended in 2 mL of sperm sample diluent (BEION AR7-10, Shanghai Beion, China), followed by 300×g centrifugation for 8 minutes.The supernatant of the tube was discarded, and the pellet was resuspended in 0.5 mL of sperm sample diluent.30 µL of the purified sperm sample was loaded into a coverslip-made chamber with internal height of about 140 µm.The two ends of the chamber were then sealed with silicone grease (1597418, Dow Corning, USA) to minimize water evaporation.

Optical tweezers setup
The home-built optical tweezers device was described in previous studies [19,[21][22][23].Briefly, a 1064-nm fiber laser (Amonics Ltd.AFL-1064-37-R-CL, Hong Kong, China) was expanded by two lenses and focused by a water immersion objective (×60, NA 1.20, Olympus, Japan) in an inverted microscope (IX73, Olympus, Japan), generating an optical trap.The chamber position was controlled by a three-dimensional piezoelectric stage (P-563.3CD,Physik Instrumente, Karlsruhe, Germany).A CMOS camera (MVSUA231GM-T, MindVision, China) was applied to recorded the greyscale images of sperm at a rate of 200 frames per second.The experiments were conducted in a temperature-controlled laboratory (25 ± 1 °C).Each sperm cell was captured by the optical tweezers only once.

Data analysis method
A MATLAB-based program was applied to the extraction of longitudinal rolling parameters from videos of optically trap sperm.Briefly, the gradient of greyscale image of vertically trapped sperm cell per frame was calculated, followed by steps of image dilation, hole filling, image erosion and binarization, and then fit with an ellipse [24], and the time dependent orientation angle θ(t) of the sperm head can be calculated according to the orientation of the ellipse (Fig. 1(a)).Note that θ(t) varies from −90°to 90°, and the period of θ(t) is equal to half of that of the longitudinal rolling of sperm.Consequently, the longitudinal rolling frequency distribution can be obtained from the power spectrum of cosθ(t) according to Eq. ( 1), determination of moments that the sperm are pausing rolling (Fig. 1d).Specifically, the |dθ/dt| was calculated for sperm cells trapped at different laser powers that did not exhibit apparent rolling behavior (Visualization 1 and Fig. S1), and more than 99.7% of the |dθ/dt| values were smaller than 23 rad/s.Then we regarded 23 rad/s as a threshold, and durations in which the |dθ/dt| values of at least five consecutive points are less than the threshold are considered to be durations of sperm in the pausing state (Fig. 1e).The percentage of pausing duration was then calculated as the ratio of the total time the sperm spent in a non-rolling state to the total video duration.

Longitudinal rolling frequency of sperm is not affected by trap height.
First, we investigated whether the longitudinal rolling frequency and pausing duration ratio of the optically trapped sperm are affected by trap height, namely the distance between the trapped sperm and the bottom surface of the chamber.The position of the bottom surface of the sample chamber was regarded as the zero point of trap height.Then the optical trap was lifted up using the piezoelectric stage to catch a freely swimming sperm, and immediately adjusted to various heights for a period of 14 seconds, followed by recording the 5-second video of sperm rolling in the trap (Fig. 2a).In this experiment the laser power was 144 mW incident on the objective.Here ω is longitudinal rolling frequency of sperm, i.e., rotation frequency of projection of the vertically-trapped sperm head, P denotes the power spectrum of cosθ(t), F denotes Fourier transformation, R(τ) denotes the autocorrelation function of cosθ(t), and τ is the lag time.The averaged longitudinal rolling frequency can be obtained from the peak value of P(ω) (Fig. 1(c)).The absolute value of derivative of θ with respect to time, |dθ/dt|, was calculated for determination of moments that the sperm are pausing rolling (Fig. 1(d)).Specifically, the |dθ/dt| was calculated for sperm cells trapped at different laser powers that did not exhibit apparent rolling behavior (Visualization 1 and Fig. S1), and more than 99.7% of the |dθ/dt| values were smaller than 23 rad/s.Then we regarded 23 rad/s as a threshold, and durations in which the |dθ/dt| values of at least five consecutive points are less than the threshold are considered to be durations of sperm in the pausing state (Fig. 1(e)).The percentage of pausing duration was then calculated as the ratio of the total time the sperm spent in a non-rolling state to the total video duration.

Longitudinal rolling frequency of sperm is not affected by trap height
First, we investigated whether the longitudinal rolling frequency and pausing duration ratio of the optically trapped sperm are affected by trap height, namely the distance between the trapped sperm and the bottom surface of the chamber.The position of the bottom surface of the sample chamber was regarded as the zero point of trap height.Then the optical trap was lifted up using the piezoelectric stage to catch a freely swimming sperm, and immediately adjusted to various heights for a period of 14 seconds, followed by recording the 5-second video of sperm rolling in the trap (Fig. 2(a)).In this experiment the laser power was 144 mW incident on the objective.As described in our previous study, head orientations of the trapped sperm can be horizontal or vertical after they were trapped and lifted [19].The trapped sperm cells were counted according to head orientations, revealing that with the trap height increasing, the proportion of horizontally trapped sperm decreased and proportion of vertically trapped sperm increased, until the ratio of vertically trapped sperm reaches almost 100% at a distance of 50 µm (Fig. 2(b) and Table S1).Such trend is in accordance with our previous study of smaller sample size [19].Interestingly, the longitudinal rolling frequencies of vertically trapped sperm at different trap height varies from 8.4 ± 1.8 to 10.7 ± 1.7 Hz (mean ± S.E.M.), which did not show statistically significant difference (Fig. 2(c)).Such result indicates that the trap height did not affect the longitudinal rolling frequency, and the longitudinal rolling frequency may present an intrinsic feature of sperm motility.On the other hand, percentages of pausing duration slightly increase with the trap height increasing (Fig. 2(d)).As the head of a vertically trapped sperm can orient downward or upward, the sperm cells were classified according to their head orientations (Fig. S2 and Table S1).This revealed that as the trap height increased, the proportion of sperms with downward heads decreased from 35% at a trap height of 10 µm to 1.5% at 80 µm, while the proportion of sperms with upward heads increased from 0% to 98.5% (Fig. S2).This result suggests that the change in percentages of pausing duration with increasing trap height may be due to the change in the proportion of head orientations.Using the two-sample Kolmogorov-Smirnov test, we compared the distributions of longitudinal rolling frequencies and percentages of pausing duration for sperm cells with downward and upward heads, respectively.The longitudinal rolling frequencies of sperm cells with downward and upward heads are 8.2 ± 0.4 Hz and 9.0 ± 0.2 Hz, respectively, showing no statistically significant difference (P > 0.05).On the other hand, the percentages of pausing duration for sperm cells with downward and upward heads are 4.4 ± 0.9% and 6.2 ± 0.9%, respectively, which indicates a slight but statistically significant difference (P < 0.05).These results imply that the differences in percentages of pausing duration are due to varying distributions of sperm orientations at different trap heights.As the height of the optical trap increases, the proportion of sperm with upward heads also increases, resulting in a slight increase in the percentages of pausing duration.

Kinematic parameters of freely swimming sperm are correlated with longitudinal rolling parameters of the same sperm in the optical trap
Next, we also revealed the correlation between kinematic parameters of freely swimming sperm and longitudinal rolling parameters of the same sperm in the optical trap (Fig. 3).First, a 4-second video of a freely swimming sperm was shot with a frame rate of 40 fps with 60× amplification in bright field (Visualization 2), then the sperm was optically trapped and lifted to a trap height of 70 µm in 14 seconds, followed by recording a 2-second video at 200 fps (Visualization 3).In this experiment the laser power was 224 mW incident on the objective.The centroid trajectories of freely swimming sperm were extracted using TrackMate [25], followed by calculations of kinematic parameters, including curvilinear velocity (VCL), straightline velocity (VSL), average path velocity (VAP), linearity (LIN), wobble (WOB), straightness (STR), beat-cross frequency (BCF), mean angular displacement (MAD) and mean amplitude of lateral head displacement (mean ALH) [7,26].The longitudinal rolling parameters were obtained according to the data analysis method described in section 2.3.The kinematic parameters and the longitudinal rolling parameters were compared (Fig. 4).Revealing by Spearman correlation analysis (Table 1), longitudinal rolling frequency is positively correlated to VSL, VAP, LIN, and WOB, and the correlation coefficients are 0.511, 0.526, 0.400 and 0.402 (all with P < 0.005), respectively.Moreover, percentage of pausing duration is negatively correlated to VSL and VAP, and the correlation coefficients are −0.408(P < 0.005) and −0.390 (P < 0.01), Smirnov test, we compared the distributions of longitudinal rolling frequencies and percentages of pausing duration for sperm cells with downward and upward heads, respectively.The longitudinal rolling frequencies of sperm cells with downward and upward heads are 8.2 ± 0.4 Hz and 9.0 ± 0.2 Hz, respectively, showing no statistically significant difference (P > 0.05).On the other hand, the percentages of pausing duration for sperm cells with downward and upward heads are 4.4 ± 0.9 % and 6.2 ± 0.9 %, respectively, which indicates a slight but statistically significant difference (P < 0.05).These results imply that the differences in percentages of pausing duration are due to varying distributions of sperm orientations at different trap heights.
As the height of the optical trap increases, the proportion of sperm with upward heads also increases, resulting in a slight increase in the percentages of pausing duration.

The kinematic parameters of freely swimming sperm are correlated with longitudinal rolling parameters of the same sperm in the optical trap.
Next, we also revealed the correlation between kinematic parameters of freely swimming sperm and longitudinal rolling parameters of the same sperm in the optical trap (Fig. 3).First, a 4second video of a freely swimming sperm was shot with a frame rate of 40 fps with 60× amplification in bright field (Visualization 2), then the sperm was optically trapped and lifted to a trap height of 70 μm in 14 seconds, followed by recording a 2-second video at 200 fps (Visualization 3).In this experiment the laser power was 224 mW incident on the objective.The centroid trajectories of freely swimming sperm were extracted using TrackMate [25], followed by calculations of kinematic parameters, including curvilinear velocity (VCL), straight-line velocity (VSL), average path velocity (VAP), linearity (LIN), wobble (WOB), straightness (STR), beat-cross frequency (BCF), mean angular displacement (MAD) and mean amplitude of lateral head displacement (mean ALH) [7,26].The longitudinal rolling parameters were obtained according to the data analysis method described in section 2.3.The kinematic parameters and the longitudinal rolling parameters were compared (Fig. 4).Revealing by Spearman correlation analysis (Table 1), longitudinal rolling frequency is positively correlated to VSL, VAP, LIN, and WOB, and the correlation coefficients are 0.511, 0.526, 0.400 and respectively.Interestingly, MAD is negatively correlated to longitudinal rolling frequency and positively correlated to percentage of pausing duration, and the correlation coefficients are −0.502(P < 0.005) and 0.344 (P < 0.05), respectively.These correlations indicate that sperm motility can be characterized by longitudinal rolling frequency and percentage of pausing duration.

Longitudinal rolling parameters are dependent on trapping time and laser power
Finally, we evaluated the time-and power-dependent photodamage effects of sperm by measuring the longitudinal rolling parameters.First, a sperm was optically trapped at a certain power and lifted to a trap height of 70 µm during 14 seconds, then the sperm was held for 245 seconds, and 5-second videos were recorded repeatedly with intervals of 10 seconds.The laser power incident on the objective ranged from 224 mW to 447 mW in increments of 28 mW, and at least 40 sperm cells were trapped and measured for each power (Table S2).As revealed by our experiment (Fig. 5 and Fig. S3), when the laser power was 224 mW, the averaged longitudinal rolling frequency decreased from 9.0 ± 0.6 Hz to 1.1 ± 0.3 Hz in 4 minutes, with a percentage of pausing duration increasing from 8.1 ± 1.9% to 72.1 ± 5.9%.Such tendency that the average longitudinal rolling frequency decreases and the percentage of pausing duration increases with increasing trapping time is consistent for all laser powers.Furthermore, at a constant trapping time, it also roughly shows a trend that with the increase of laser power, the longitudinal rolling frequency decreases and the percentage of pausing duration increases (Fig. S3).These results suggest that the decrease in motility of sperm captured by optical tweezers is positively correlated with cumulative irradiation dose of 1064-nm laser.

Discussion and conclusion
In this study, regardless of the experimental conditions, the longitudinal rolling of each vertically trapped sperm was in a clockwise direction as seen from tail to head, that is, with right-hand longitudinal rolling chirality (Fig. 1a, Fig. 3c and Visualization 3), which is consistent with our previous report [19], as well as a recent study on freely swimming sperm by Gabriel Corkidi et al [27].Such unidirectional rolling may be associated with the special mechanical transmission structure in the sperm neck, i.e., the dynamic basal complex of the sperm flagellum [20], as the basal complex bends in response to the beating force of flagellum [28].The coupling of the tail beating and asymmetric head kinking indicates a correlation between BCF and longitudinal rolling frequency.However, such correlation was not observed in our study, which may be due to the fact that the calculation of BCF is based on the 2D projection of the sperm head, which lacks the information of displacement of the z-axis.
Moreover, values of BCF can be significantly affected by the fitting of average path during the calculation.Consequently, considerable significant uncertainty may be introduced to the BCF calculation.
It has been found that NIR exposure reduces sperm viability, increases lipid peroxidation, and impairs membrane function, which is accompanied by a decrease in superoxide dismutase activity in spermatozoa, indicating an increase in the damaging effects of free radicals [6].
Additionally, NIR exposure causes disruption of protamine-DNA toroids, making the DNA more susceptible to fragmentation and ultimately leading to apoptosis [6].It is worth noting that 1064-nm optical tweezers can induce oxidative damage on DNA in vitro by generating singlet oxygen when a sensitizer exists in the optical trap [29].Longitudinal rolling of sperm may be affected by laser-induced photodamage through two possible ways: 1) damage to ATP synthesis mechanisms, as absorption bands of mitochondrial cytochromes, porphyrins and flavoproteins are possessed in NIR region [3]; 2) interference or disruption of mechanical transmission structures of the sperm, which may be induced by laser-generated reactive free radicals.Combining fluorescence imaging with optical tweezers technology [30], the mechanism of sperm photodamage on sperm motility is expected to be clarified in the future.
On the other hand, laser-induced photodamage effect may be reduced by carefully selection of wavelength of laser used in ART [31], or by adding photodamage-preventing agents, such as mitochondria-targeted antioxidants including melatonin [32], spermine and spermidine [33,34].
In summary, we proved that the motility of sperm can be characterized by longitudinal rolling parameters.Moreover, the changes in longitudinal rolling parameters at different times and with varying power of a 1064-nm laser were investigated in this study.Our results clearly

Discussion and conclusion
In this study, regardless of the experimental conditions, the longitudinal rolling of each vertically trapped sperm was in a clockwise direction as seen from tail to head, that is, with right-hand longitudinal rolling chirality (Fig. 1(a), Fig. 3(c) and Visualization 3), which is consistent with our previous report [19], as well as a recent study on freely swimming sperm by Gabriel Corkidi et al [27].Such unidirectional rolling may be associated with the special mechanical transmission structure in the sperm neck, i.e., the dynamic basal complex of the sperm flagellum [20], as the basal complex bends in response to the beating force of flagellum [28].The coupling of the tail beating and asymmetric head kinking indicates a correlation between BCF and longitudinal rolling frequency.However, such correlation was not observed in our study, which may be due to the fact that the calculation of BCF is based on the 2D projection of the sperm head, which lacks the information of displacement of the z-axis.Moreover, values of BCF can be significantly affected by the fitting of average path during the calculation.Consequently, considerable significant uncertainty may be introduced to the BCF calculation.It has been found that NIR exposure reduces sperm viability, increases lipid peroxidation, and impairs membrane function, which is accompanied by a decrease in superoxide dismutase activity in spermatozoa, indicating an increase in the damaging effects of free radicals [6].Additionally, NIR exposure causes disruption of protamine-DNA toroids, making the DNA more susceptible to fragmentation and ultimately leading to apoptosis [6].It is worth noting that 1064-nm optical tweezers can induce oxidative damage on DNA in vitro by generating singlet oxygen when a sensitizer exists in the optical trap [29].Longitudinal rolling of sperm may be affected by laser-induced photodamage through two possible ways: 1) damage to ATP synthesis mechanisms, as absorption bands of mitochondrial cytochromes, porphyrins and flavoproteins are possessed in NIR region [3]; 2) interference or disruption of mechanical transmission structures of the sperm, which may be induced by laser-generated reactive free radicals.Combining fluorescence imaging with optical tweezers technology [30], the mechanism of sperm photodamage on sperm motility is expected to be clarified in the future.On the other hand, laser-induced photodamage effect may be reduced by carefully selection of wavelength of laser used in ART [31], or by adding photodamage-preventing agents, such as mitochondria-targeted antioxidants including melatonin [32], spermine and spermidine [33,34].
In summary, we proved that the motility of sperm can be characterized by longitudinal rolling parameters.Moreover, the changes in longitudinal rolling parameters at different times and with varying power of a 1064-nm laser were investigated in this study.Our results clearly showed that the laser induced motility reduction of sperm is positively correlated to the laser power and irradiation time, providing a reference for the study on photodamage-preventing agents for laser-based sperm manipulation in the future.

Fig. 1 .
Fig.1.Longitudinal rolling parameter measurement.(a) Measurement of the time-dependent orientation angle θ(t) of a sperm head by ellipse fitting.Grayscale image of sperm head was fitted by an ellipse, and the angle between the long axis of the ellipse and the positive half of xaxis is defined as orientation angle θ, which is indicated in red color.(b) Representative temporal changes in the cosine of orientation angle.(c) Distribution of longitudinal rolling frequencies revealing by the power spectrum of cosθ(t) corresponding to Fig. 1(b).(d) Temporal changes in the absolute value of derivative of θ with respect to time (|dθ/dt|), which is corresponding to the 1-2 s interval of Fig. 1(b).Data points where the |dθ/dt| values of at least five consecutive points are less than a threshold of 23 rad/s are labeled by red circles.(e) The zoom-in of 1-2 s interval of Fig. 1(b).The data points considered to be durations in the pausing state are labeled with red circles.

Fig. 1 .
Fig. 1.Longitudinal rolling parameter measurement.(a) Measurement of the timedependent orientation angle θ(t) of a sperm head by ellipse fitting.Grayscale image of sperm head was fitted by an ellipse, and the angle between the long axis of the ellipse and the positive half of x-axis is defined as orientation angle θ, which is indicated in red color.(b) Representative temporal changes in the cosine of orientation angle.(c) Distribution of longitudinal rolling frequencies revealing by the power spectrum of cosθ(t) corresponding to Fig. 1(b).(d) Temporal changes in the absolute value of derivative of θ with respect to time (|dθ/dt|), which is corresponding to the 1-2 s interval of Fig. 1(b).Data points where the |dθ/dt| values of at least five consecutive points are less than a threshold of 23 rad/s are labeled by red circles.(e) The zoom-in of 1-2 s interval of Fig. 1(b).The data points considered to be durations in the pausing state are labeled with red circles.

Fig. 2 .Fig. 2 .
Fig.2.Dependence of longitudinal rolling parameters on trap height.(a)Schematic representation of trapping sperm cells at different trap heights.(b) Percentages of vertically trapped sperm at trap heights ranging from 10 to 80 μm.(c) Longitudinal rolling frequencies of vertically trapped sperm at trap heights ranging from 10 to 80 μm.The longitudinal rolling frequency distributions at different trap heights were analyzed using the two-sample Kolmogorov-Smirnov test, resulting in no statistically significant difference.P value of 0.05 Fig. 2. Dependence of longitudinal rolling parameters on trap height.(a)Schematic representation of trapping sperm cells at different trap heights.(b) Percentages of vertically trapped sperm at trap heights ranging from 10 to 80 µm.(c) Longitudinal rolling frequencies of vertically trapped sperm at trap heights ranging from 10 to 80 µm.The longitudinal rolling frequency distributions at different trap heights were analyzed using the two-sample Kolmogorov-Smirnov test, resulting in no statistically significant difference.P value of 0.05 was considered statistically significant.(d) Percentages of pausing duration at the trap height of 10 to 80 µm.was considered statistically significant.(d) Percentages of pausing duration at the trap height of 10 to 80 μm.

Fig. 3 .
Fig.3.Measurements of kinematic parameters of freely swimming sperm and longitudinal rolling parameters of the same sperm in the optical trap.(a) Schematic representation of the experiment.(b) Trace of a freely swimming sperm (See Visualization 2).Scale bar = 5 μm.(c) The projection of the same sperm in the optical trap (See Visualization 3).Yellow triangles highlight the orientations of the rolling sperm head.Scale bar = 5 μm.

Fig. 3 .
Fig. 3. Measurements of kinematic parameters of freely swimming sperm and longitudinal rolling parameters of the same sperm in the optical trap.(a) Schematic representation of the experiment.(b) Trace of a freely swimming sperm (See Visualization 2).Scale bar = 5 µm.(c) The projection of the same sperm in the optical trap (See Visualization 3).Yellow triangles highlight the orientations of the rolling sperm head.Scale bar = 5 µm.

Fig. 4 .
Fig.4.Correlation between kinematic parameters of freely swimming sperm and longitudinal rolling parameters of the same sperm in the optical trap.(a) Scattered plots of kinematic parameters versus longitudinal rolling frequency.(b) Scattered plots of kinematic parameters versus percentage of pausing duration.N=50.

Fig. 4 .
Fig. 4. Correlation between kinematic parameters of freely swimming sperm and longitudinal rolling parameters of the same sperm in the optical trap.(a) Scattered plots of kinematic parameters versus longitudinal rolling frequency.(b) Scattered plots of kinematic parameters versus percentage of pausing duration.N = 50.

Fig. 5 .
Fig.5.The trapping time and laser power dependence of longitudinal rolling parameters.The abscissa is the starting time of the 5-second video after optically trapping the sperm.Error bars are standard errors.(a) The longitudinal rolling frequency versus trapping time at different laser powers incident on the objective.(b) The percentage of pausing duration versus trapping time at different laser powers incident on the objective.

Fig. 5 .
Fig. 5.The trapping time and laser power dependence of longitudinal rolling parameters.The abscissa is the starting time of the 5-second video after optically trapping the sperm.Error bars are standard errors.(a) The longitudinal rolling frequency versus trapping time at different laser powers incident on the objective.(b) The percentage of pausing duration versus trapping time at different laser powers incident on the objective.

Table 1 . Spearman Correlation Analysis Between Kinematic Parameters of Freely Swimming Sperm and Longitudinal Rolling Parameters of the Same Sperm in the Optical Trap. N = 50 a
a Note: *** denotes p < 0.001, ** denotes p < 0.01, and * denotes p < 0.05.