# Does sperm weight causes sex ratio?

Chromosome X in female sperm is heavier than male Y chromosome. Does it causes difference in fertility of sperm and heavier female sperm is unable to fertilize better than male sperm?

This is given in AK Jain of physiology, chapter on reproduction. I doubt this explanation.

Probably not! There are certainly some physical reasons to doubt it. Looks like the mass difference between X and Y sperm is on the order of 0.1 picograms: X chromosome "weight"?

First, mass differences are not likely to affect swimming and motility of sperm, because sperm are at low Reynolds number -- the forces of fluid drag vastly overwhelm inertial forces. See, e.g. Purcell's lecture "Life at Low Reynolds Number" (http://aapt.scitation.org/doi/abs/10.1119/1.10903 but also available online). For this reason, even much larger differences in mass are not likely to matter to swimming.

If motility is not the issue, you could imagine that, during the fertilization or insemination process, sperm might be under the force of gravity, leading to different sedimentation rates. A sperm's sedimentation speed is equal to the force on it divided by its friction coefficient $\gamma$, $$v_{sperm} = \frac{(m_{sperm}-m_{displaced}) g}{\gamma}$$ where $g$ is the gravitational acceleration and $m_{displaced}$ is the amount of mass displaced by the sperm. You can estimate $\gamma$ with Stokes' law (https://en.wikipedia.org/wiki/Stokes%27_law) as about $6\pi R \mu$ with $R$ being the sperm size and $\mu$ the fluid viscosity. We're interested in the maximum possible difference in speed, so we'll choose $R$ to be at the small scale of sperm size, $5$ microns and $\mu$ to be that of water $\mu \approx 0.01 \frac{g}{cm s}$. This gives us $\gamma \sim 10^{-4} g/s$. The difference between $v_X$ and $v_Y$ is then $$v_X - v_Y = \frac{(m_X - m_Y) g}{\gamma} \approx 0.01 \,\textrm{micron}/s$$

This means, for there to be a significant difference between X and Y sperm you'd have to keep them sedimenting under force for quite a while. This can be used (especially in a centrifuge, where you can increase the gravitational force) to select between genders - but it seems unlikely to happen in vivo.

To see why this is a small speed in practice, you have to ask whether the sperm would also have diffused a larger distance or managed to swim while it was sedimenting. Sperm velocities are on the order of tens of microns per second, so anything that changes the sperm swimming speed by even 0.1% is more important than the mass difference in sedimentation.

Putting this together, it suggests that mass differences are not a likely origin for sex ratios slightly deviating from one - if they are tuned, it would make more sense to change sperm length or swimming stroke. In fact, I believe there are some small geometric changes between X and Y sperm - but could those geometric changes happen simply because there is less chromosomal material in the Y? That, I'm not sure.

• It would be better to add this : ncbi.nlm.nih.gov/pmc/articles/PMC1440662
– JM97
Jul 27 '17 at 1:55
• Thanks JM97 for link. I would have accepted that as answer. Jul 27 '17 at 3:06