Following in the footsteps of E. coli: sperm in microfluidic "strictures"

TL;DR

This paper compares sperm motion experiments in microfluidic structures to similar studies on E. coli, highlighting hydrodynamic similarities and suggesting that prior bacterial research can inform understanding of sperm migration.

Contribution

It identifies hydrodynamic parallels between sperm and E. coli experiments and proposes leveraging bacterial motion insights to better understand sperm migration in microfluidic environments.

Findings

Hydrodynamic similarities between sperm and E. coli motion

Potential for bacterial studies to inform sperm migration understanding

Comparison of experimental setups and results

Abstract

We briefly describe the similarities of the experiments of sperm motion in microfluidic "strictures" by Zafeeani et al. in 2019 (Sci. Adv. 5, eaav21111, 2019) and those by Altshuler et al. in 2013 (Soft Matter 9, 1864, 2013). We shortly discuss the hydrodynamic elements justifying the strong resemblance between the two types of experiments, and suggest that other previous results in E. coli motion (Soft Matter 11, 6248, 2015) may shed further light on the understanding of sperm migration.

Equations

$$-D\frac{d^{2}n(x)}{d{x}^2}+\frac{d}{dx}[u_a(x)n(x)]=S(x)$$

Full text

Following in the footsteps of E. coli: sperm in microfluidic “strictures”

E. Altshuler1,2, G. Miño3,2, A. Lindner2, A. Rousselet2, and E. Clément2

††footnotetext: 1 Group of Complex Systems and Statistical Physics, Physics Faculty, University of Havana, 10400 Havana, Cuba

2 PMMH, UMR 7636, CNRS, ESPCI Paris, PSL Research University, Universitè Paris Diderot, Sorbonne Universitè, Paris, 75005, France

3 LAMAE, Facultad de Ingeniería, Universidad Nacional de Entre Ríos (FI - UNER) and Instituto de Investigación y Desarrollo en Bioingeniería y Bioinformática (IBB) - CONICET - UNER, Argentina

In a very interesting paper, Zaferani et al. study the locomotion of sperm into “strictures” made on microfluidic channels that resemble an hourglass through which a liquid flow is established 1. Their experiments are, in fact, extremely similar to those published by Altshuler et al. in 2013 on another micro-swimmer, E. coli bacteria 2.

Figure 1 shows the clear parallel between the findings for bacteria and sperm in terms of motion: both tend to move against the flow along lateral boundaries; both detach and re-attach to lateral boundaries, depending on the relation between the local shear and the “strength” of the swimmer. But it should not surprise us. Firstly, because E. coli and sperm share a lot of similarities. Both are “pushers”, i.e., their hydrodynamic center lies near the “head” of the swimmer, defined with respect to its direction of self-propelled motion and the resulting hydrodynamic interactions with bounding walls lead in both cases to an attraction 3. In addition, both swimmer shapes show a fore-aft asymmetry, which is thought responsible for the upstream motion observed for both micro-swimmers 5, 4, 6, 7. Secondly, because the geometry and dimensions of the “hourglass” micro-channel structures used in 1 are very similar to the ones used in 2.

Interestingly, equation (1) proposed by Zaferani et al. can be assumed as a “microscopic” version of the advection-diffusion equation proposed by Altshuler et al. 2:

[TABLE]

where $n(x)$ is the volume concentration of bacteria, $u_{a}(x)$ is their mean advection velocity along the flow, $D$ is an effective longitudinal dispersion coefficient and $S(x)$ is a conservative bulk source/sink term coming from the lateral wall contributions (i.e., absorption-erosion processes). By extracting from the experiment the effect of the lateral walls given by $S(x)$, Altshuler et al. used the equation above to reproduce quantitatively the bacterial distribution not only near the constriction, but far from it, as illustrated in Fig. 3 in 2.

The PMMH-ESPCI group’s more recent work reveals the complex nature of $S(x)$ through systematic experiments on E. coli bacteria confined into microfluidic channels at different flows 8 –a very relevant study in connection to hospital infections. We believe that many features of the swimmer-boundary interaction in the presence of shear found in those experiments are valid to many pushers, so they have good chances to be extended for the important case of sperm.