Immotile cilia at the ventral node of mouse embryos are required for sensing leftward fluid flow that breaks left-right symmetry of the body. However, the flow-sensing mechanism has long remained elusive. In this work, we show that immotile cilia at the node undergo asymmetric deformation along the dorsoventral axis in response to the flow. Application of mechanical stimuli to immotile cilia by optical tweezers induced calcium ion transients and degradation of Dand5 messenger RNA (mRNA) in the targeted cells. The Pkd2 channel protein was preferentially localized to the dorsal side of immotile cilia, and calcium ion transients were preferentially induced by mechanical stimuli directed toward the ventral side. Our results uncover the biophysical mechanism by which immotile cilia at the node sense the direction of fluid flow.

When a red blood cell (RBC) is subjected to an external flow, it is deformed by the hydrodynamic forces acting on its membrane. The resulting elastic tensions in the membrane play a key role in mechanotransduction and govern its rupture in the case of hemolysis. In this study, we analyze the motion and deformation of an RBC in a simple shear flow and the resulting elastic tensions on the membrane. The large deformation of the red blood cell is modelled by coupling a finite element method to solve the membrane mechanics and a boundary element method to solve the flows of the internal and external liquids. Depending on the capillary number Ca, ratio of the viscous to elastic forces, we observe three kinds of RBC motion: tumbling at low Ca, swinging at larger Ca, and breathing at the transitions. In the swinging regime, the region of the high principal tensions periodically oscillates, whereas that of the high isotropic tensions is almost unchanged. Due to the strain-hardening property of the membrane, the deformation is limited but the membrane tension increases monotonically with the capillary number. We have quantitatively compared our numerical results with former experimental results. It indicates that a membrane isotropic tension $\mathcal{O}({10}^{-6}$ N/m) is high enough for molecular release from RBCs and that the typical maximum membrane principal tension for haemolysis would be $\mathcal{O}({10}^{-4}$ N/m). These findings are useful to clarify not only the membrane rupture but also the mechanotransduction of RBCs.

The squirmer model of Lighthill and Blake has been widely used to analyse swimming ciliates. However, real ciliates are covered by hair-like organelles, called cilia; the differences between the squirmer model and real ciliates remain unclear. Here, we developed a ciliate model incorporating the distinct ciliary apparatus, and analysed motion using a boundary element–slender-body coupling method. This methodology allows us to accurately calculate hydrodynamic interactions between cilia and the cell body under free-swimming conditions. Results showed that an antiplectic metachronal wave was optimal in the swimming speed with various cell-body aspect ratios, which is consistent with former theoretical studies. Exploiting oblique wave propagation, we reproduced a helical trajectory, likeParamecium, although the cell body was spherical. We confirmed that the swimming velocity of model ciliates was well represented by the squirmer model. However, squirmer modelling outside the envelope failed to estimate the energy costs of swimming; over 90 % of energy was dissipated inside the ciliary envelope. The optimal swimming efficiency was given by the antiplectic wave; the value was 6.7 times larger than in-phase beating. Our findings provide a fundamental basis for modelling swimming micro-organisms.

Significance: In this study, we clarified energetics of microbial locomotion by computing flow around a spherical swimmer covered with cilia. We showed a scaling law for microbial dynamics and revealed that microorganisms can swim optimally and enlarge their bodies by making multiple cilia. The optimal density of cilia was independent of the body size. Our estimated optimal density of cilia corresponded to those of actual microorganisms, including species of ciliates and microalgae. These results will help us to understand the mechanistic benefits of multiple cilia and open up an area of research that integrates fluid mechanics, biophysics, and microbiology.

A capsule is a liquid drop enclosed by a solid, deformable membrane. To analyze the deformation of a capsule accurately, both the fluid mechanics of the internal and external fluids and the solid mechanics of the membrane must be solved precisely. Recently, many researchers have used discrete spring network models to express the membrane mechanics of capsules and biological cells. However, it is unclear whether such modeling is sufficiently accurate to solve for capsule deformation. This study examines the correlations between the mechanical properties of the discrete spring network model and continuum constitutive laws. We first compare uniaxial and isotropic deformations of a two-dimensional (2D) sheet, both analytically and numerically. The 2D sheet is discretized with four kinds of mesh to analyze the effect of the spring network configuration. We derive the relationships between the spring constant and continuum properties, such as the Young modulus, Poisson ratio, area dilation modulus, and shear modulus. It is found that the mechanical properties of spring networks are strongly dependent on the mesh configuration. We then calculate the deformation of a capsule under inflation and in a simple shear flow in the Stokes flow regime, using various membrane models. To achieve high accuracy in the flow calculation, a boundary-element method is used. Comparing the results between the different membrane models, we find that it is hard to express the area incompressibility observed in biological membranes using a simple spring network model.

The dynamics of a capsule and a biological cell is of great interest in chemical engineering and bioengineering. Although the dynamics of a rigid spheroid is well understood by Jeffery's theory, that of a spheroidal capsule remains unclear. In this Letter, the motion of a spheroidal capsule or a red blood cell in creeping shear flow is investigated. The results show that the orientation of a nonspherical capsule is variant under time reversal, though that of a rigid spheroid is invariant. Surprisingly, the alignment of a nonspherical capsule over a long time duration shows a transition depending on the shear rate, which can be utilized for a particle-alignment technique. These findings form a fundamental basis of the suspension mechanics of capsules and biological cells.