1. Cell Biology
  2. Physics of Living Systems
Download icon

Flagellar energetics from high-resolution imaging of beating patterns in tethered mouse sperm

  1. Ashwin Nandagiri
  2. Avinash Satish Gaikwad
  3. David L Potter
  4. Reza Nosrati
  5. Julio Soria
  6. Moira K O'Bryan
  7. Sameer Jadhav
  8. Ranganathan Prabhakar  Is a corresponding author
  1. IITB-Monash Research Academy, India
  2. Department of Chemical Engineering, Indian Institute of Technology Bombay, India
  3. Department of Mechanical and Aerospace Engineering, Monash University, Australia
  4. School of BioSciences, University of Melbourne, Australia
  5. Monash Micro-Imaging, Monash University, Australia
Research Article
Cite this article as: eLife 2021;10:e62524 doi: 10.7554/eLife.62524
11 figures, 4 tables and 1 additional file

Figures

Schematic representations for the Soft, Internally driven Kirchhoff rod model.

(A) Geometric variables defined along the centerline. (B) An arbitrary control volume used for deriving the equations of the model: the volume consists of the passive flagellar material; hydrodynamic forces act on the external surface while axonemal motors act on the internal surfaces. The passive material adjacent to the cross-sectional faces at either end exerts stresses on those faces.

Key variables of the Chebyshev polynomial-based proper orthogonal decomposition (C-POD) of experimental tangent-angle data.

(A) Time-averaged tangent-angle profiles for five wildtype (WT) (continuous curves) and five knockout (KO) (dashed curves) samples. (B) First (top) and second (bottom) C-POD shape modes for WT (continuous curves) and KO (dashed curves) samples; the colors are as in (A). (C) Cumulative accuracy of the C-POD representation for WT and KO samples; the colors are as in (A). A representation using the first four modes captures 95% or more of the observed centerline shapes for all samples. (D) Five shape cycles for a single WT sample in the parameter space defined by the time-dependent coefficients of the first two C-POD shape modes. The zero-crossing of the second modal coefficient marks the start of a new cycle. (E) Contributions of the first four modes to the tangent angle at the midpoint of the sperm body in the five tangent-angle cycles in (D): the horizontal line in the top plot is the time-averaged tangent angle for this WT sample. The starting time of the i th cycle is denoted as ti0, and its duration (i.e., cycle time) is Ti.

Spatiotemporal distributions of the rates of (A) hydrodynamic dissipation, (B) elastic storage, and (C) internal dissipation, and (D) the active power along the flagellum of a wildtype sperm over several beat cycles: red indicates positive rates, while blue indicates negative rates.

The data in (C) and (D) have been obtained using the scaling value of 103 Pa s μm4 for the internal friction coefficient.

Mean cycles of beat patterns and energetics.

(A) Each colored curve shows the mean shape at a particular phase of the mean cycle for the five wildtype (WT) (top row) and knockout (KO) (bottom row) samples. The color bands around each curve indicate the standard error in the mean component. (B) Mean cycles for the magnitudes of the net elastic storage (yellow), hydrodynamic dissipation (black), internal frictional dissipation (magenta), and active power (red) in WT (top panel) and KO (bottom panel) sperm samples corresponding to those in (A). Bands show standard errors in means. (C) Statistical distributions of cycle times and dissipation rates in each of the WT (top panel) and KO (bottom panel) samples. The box-plots present the median (red line), the first and third quartile (bottom and top box edges), and minimum and maximum (lower and upper whiskers) values for 40–60 cycles. Outliers that are more than 1.5 times the interquartile range away from the top or bottom of the box are indicated by red crosses. The notch extremes correspond to q2±1.57(q3q1)/n, where q1, q2, and q3 are the first, second (median), and third quartiles, respectively, and n is the number of observations (McGill et al., 1978).

Figure 5 with 3 supplements
External versus internal dissipation in flagella.

(A) Effect of the value of internal friction coefficient, ηN, on the minimum value of the net active power required to overcome dissipation for wildtype (WT) (blue) and knockout (KO) (red) samples. At each ηN, and for each sample, the minimum in the mean cycle of the net active power, Pmin, is normalized by the time average of the motor input, P¯¯mi, over all cycles. The vertical line is the scaling value of 103 Pa s μm4. (B) Correlation of time averages of the hydrodynamic dissipation and net active power for ηN=103 Pa s μm(top) and 0 (bottom). The lines are linear fits through data for both species. (C) Comparison of the external hydrodynamic dissipation (black) with the motor (blue) and passive internal frictional (magenta) dissipations obtained with ηN=103 Pa s μm(left) and 0 (right). The bars represent the averages of the cycle-means of dissipations pooled from all the five sperm samples in each genotype; the error bars represent 1 standard deviation in each direction in the set of pooled cycle-means. (D) Statistical distributions of the cycle-means of powers from the WT (dark color boxes) and KO (light color boxes) samples pooled together over the entire tail (left), mid-piece (middle), and principal piece (right). The top and bottom panels are for ηN=103 Pa s μm4 and 0, respectively. In (C) and (D), unpaired two-tailed t-tests are used to compare population means; **** refers to a significance level of p10-4 , *** p10-3, ** p10-3, *p0.05. Differences are not significant (n.s.) when p>0.05.

Figure 5—figure supplement 1
Comparison of population means of time-averaged dissipations obtained with the five wildtype and Crisp2 knockout mice sperm samples obtained with (AηN=10 Pa.s.m4 and (BηN = 0 Pa.s.m.

Error bars shown correspond to 1 standard deviation in the set of samples. Unpaired two-tailed t-tests are used to compare population means; ** p103, *p0.05. Differences are not significant (n.s.) when p>0.05.

Figure 5—figure supplement 2
Comparison across genotypes of population means of time-averaged powers obtained with the five wildtype and Crisp2 knockout mice sperm samples o ηn=10 Pa.s.m4 is shown in A and ηn = 0 Pa.s.m4 in B.

Error bars shown correspond to 1 standard deviation in the set of samples. Unpaired two-tailed t-tests are used to compare population means; **p10-3, *p0.05. Differences are not significant (n.s.) when p>0.05.

Figure 5—figure supplement 3
Comparison of pooled averages of the cycle-means of hydrodynamic dissipation in the tail (black) and dissipation at head due to hydrodynamic and tethering resistances (purple): p10-3, *p0.05ηn=10 Pa.s.m4 is shown in A and ηn = 0 Pa.s.m4 in B.

Differences are not significant (n.s.) when p>0.05.

Out-of-phase mean beat cycles of active moment density and angular rotation rate at s=0.5 in (A) wildtype (WT)-1 and (B) knockout (KO)-1 samples.
Main steps in the image-processing algorithm shown for a single frame.

A. The original frame B. Enhanced and filtered C. Thresholded frame D. Segmented E. Skeletonized frame F. Smoothed centreline.

Appendix 2—figure 1
Orientation of the sperm cell with respect to the glass slide.

(a) Image from Woolley, 2003 showing the left side (L) of a mouse sperm head facing the viewer with the ventral (V) and dorsal (D) sides of the head indicated. The concave side of the hook is towards the dorsal side. Also shown is the neck (N) at the proximal end of the flagellum. (b) Schematic showing the mouse sperm body as viewed from its dorsal side when the left side of its head is against the wall. The intrinsic angle made by the head with the flagellum at the neck enables planar beating when the left side of the head is against the wall. The red and green lines indicate the axes of the head and the tail. In this orientation, the flagellum beats in a plane parallel to the wall and its centerline is at a distance equal to the neck radius ,an, from the wall. If there had been no angle at the neck, the tip of the tail would be at a height of ht=hmax. (c) The angle (in radians) of the head axis to the wall, θan/h.

Author response image 1
(a) Schematic showing the mouse sperm body as viewed from its dorsal side when the left side of its head is against the wall. The intrinsic angle made by the head with the flagellum at the neck enables planar beating when the left side of the head is against the wall. The red and green lines indicate the axes of the head and the tail. In this orientation, the flagellum beats in a plane parallel to the wall and its centreline is at a distance equal to the neck radius ,an, from the wall. If there had been no angle at the neck, the tip of the tail would be at a height of hT = hmax. (b) The angle (in radians) of the head axis to the wall, θan/ ℓh.
Author response image 2
Ratio of the Wall-RFT coefficients in revised manuscript to the bulk coefficients in the original submission.
Author response image 3
Comparison of revised values of the cycle-means of (i) hydrodynamic dissipation, (ii) motor dissipation, (iii) active power input, and (iv) the proportion of hydrodynamic dissipation out of the total dissipation against their values in the original manuscript for WT (green symbols) and KO (yellow symbols) samples, with ηn = 0 (top panel) and 103 Pa s µm4(bottom panel): the values in the original submission are along the horizontal axes and the revised values are along the vertical axes.

Tables

Key resources table
Reagent type (species) or resourceDesignationSource or referenceIdentifiersAdditional information
Gene (Mus musculus)Crisp2Lim et al., 2019--
Strain, strain background (Mus musculus)C57BL/6NLim et al., 2019PMID:30759213Mice produced through the Australian Phenomics Network
Biological sample (Mus musculus)SpermLim et al., 2019-Collected from the cauda epididymis and vas deferens using the backflushing method
Chemical compound, drugTYH medium with 0.3 mg/ml BSALim et al., 2019-Buffer media for sperm
Software, algorithmMATLAB, MATLAB Image Processing Toolbox, FijiSCR 001622,SCR 002285Code (Nandagiri, 2021) and original videos (Nandagiri et al., 2020) available for public access
Appendix 3—table 1
One-way ANOVA data for establishing that sample means of cycle variables are significantly different from population means in the wildtype (WT) and knockout (KO) genotypes; F denotes the F-test statistic and p denotes probability of the null hypothesis.
GenotypeFlagellar regionPowerTreatments DOFError DOFFp
WTFullCycle time430650.31<10-16
WTFullInput power4306833.19<10-16
WTFullHyd. dissn.43061441.37<10-16
WTFullInternal dissn.4306730.68<10-16
WTFull tailMotor dissn.4306246.17<10-16
WTMid-pieceInput power4306483.02<10-16
WTMid-pieceHyd. dissn.4306186.86<10-16
WTMid-pieceInternal dissn.4306436.92<10-16
WTMid-pieceMotor dissn.4306421.04<10-16
WTPrincipal pieceInput power4306786.93<10-16
WTPrincipal pieceHyd. disspn.43061716.31<10-16
WTPrincipal pieceInternal dissn.4306520.19<10-16
WTPrincipal pieceMotor dissn.4306140.96<10-16
KOFull tailCycle time4270235.45<10-16
KOFull tailInput power4270110.04<10-16
KOFull tailHyd. dissn.4270198.37<10-16
KOFull tailInternal dissn.427090.02<10-16
KOFull tailMotor dissn.4270120.31<10-16
KOMid-pieceInput power4270528.12<10-16
KOMid-pieceHyd. dissn.4270216.51<10-16
KOMid-pieceInternal dissn.4270247.53<10-16
KOMid-pieceMotor dissn.4270374.02<10-16
KOPrincipal pieceInput power4270125.73<10-16
KOPrincipal pieceHyd. dissn.4270206.07<10-16
KOPrincipal pieceInternal dissn.4270109.09<10-16
KOPrincipal pieceMotor dissn.427020.3<10-16
Appendix 3—table 2
Comparison of the external hydrodynamic dissipation with the internal frictional and motor dissipations: t denotes the Student's t-test statistic in an unpaired, two-tailed test; p is the probability of the null hypothesis.
GenotypeFlagellar regionηn (Pa s μm4)Hyd. dissn. (fW)Int. dissn. (fW)tp
WTFull tail10389.07240.0522.71<10-16
WTMid-piece1036.69108.4336.39<10-16
WTPrincipal piece10382.21131.119.82<10-16
KOFull tail10366.39200.9121.44<10-16
KOMid-piece1034.8032.4029.16<10-16
KOPrincipal piece10361.48168.2816.73<10-16
GenotypeFlagellar regionηn (Pa s μm4)Hyd. dissn. (fW)Motor dissn. (fW)tp
WTFull tail10389.07135.0611.48<10-16
WTMid-piece1036.69109.7536.21<10-16
WTPrincipal piece10382.2125.0920.71<10-16
KOFull tail10366.3948.729.74<10-16
KOMid-piece1034.8029.1424.87<10-16
KOPrincipal piece10361.4819.4928.4<10-16
WTFull tail089.07155.5811.48<10-16
WTMid-piece06.69112.5636.21<10-16
WTPrincipal piece082.2142.7120.71<10-16
KOFull tail066.3977.619.74<10-16
KOFull tail04.8035.2324.87<10-16
KOPrincipal piece061.4842.2828.4<10-16
Appendix 3—table 3
Comparison of wildtype (WT) and knockout (KO) samples.

The values in in columns 2 and 3 are the means of the distributions created by pooling together values from the individual cycles of all the sperm samples in each genotype.

QuantityWTKOtp
Cycle time (s)0.160.182.720.01
Reciprocal cycle time (Hz)7.197.20.035010.97
Full tail hyd. dissn. (fW)89.0766.396.911.26 × 10−11
Mid-piece hyd. dissn. (fW)6.694.806.891.49 × 10−11
Principal piece hyd. dissn. (fW)82.2161.486.714.63 × 10−11
Full tail motor dissn. (fW), ηn= 103 Pa s μm4135.0648.7226.89<10-16
Full tail int. dissn. (fW), ηn= 103 Pa s μm4240.05200.914.556.54 × 10−6
Mid-piece motor disspn. (fW), ηn= 103 Pa s μm4109.7529.1425.57<10-16
Mid-piece int. dissn. (fW), ηn= 103 Pa s μm4108.4332.4024.59<10-16
Principal piece motor dissn. (fW), ηn= 103 Pa s μm425.0819.495.623.01 × 10−8
Principal piece int. dissn. (fW), ηn= 103 Pa s μm4131.11168.285.033.01 × 10−8
Full tail motor dissn. (fW), ηn= 0 Pa s μm4155.5877.6124.87<10-16
Mid-piece motor dissn. (fW), ηn= 0 Pa s μm4112.5635.2329.10<10-16
Principal piece motor dissn. (fW), ηn= 0 Pa s μm442.7142.280.220.82

Additional files

Download links

A two-part list of links to download the article, or parts of the article, in various formats.

Downloads (link to download the article as PDF)

Download citations (links to download the citations from this article in formats compatible with various reference manager tools)

Open citations (links to open the citations from this article in various online reference manager services)