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The respiratory tract of larger animals is cleared by sweeping bundled strands along the airway surface. These bundled strands can be millimetric in length and consist of MUC5B mucin. They are produced by submucosal glands, and upon emerging from these glands, the long axis of the bundled strands is oriented along the cilia-mediated flow toward the oral cavity. However, after release, the bundled strands are found to have turned orthogonal to the flow, which maximizes their clearance potential. How this unexpected reorientation is accomplished is presently not well understood. Recent experiments suggest that the reorientation process involves bundled strands sticking to MUC5AC mucus threads, which are tethered to the goblet cells. Such goblet cells are present in small numbers throughout the airway epithelium. Here, we develop a minimal model for reorientation of bundled mucus strands through adhesive interactions with surface goblet cells. Our simulations reveal that goblet cell interactions can reorient the bundled strands within 10 mm of release—making reorientation on the length scale of the tracheal tube feasible—and can stabilize the orthogonal orientation. Our model also reproduces other experimental observations such as strong velocity fluctuations and significant slow-down of the bundled strand with respect to the cilia-mediated flow. We further provide insight into the strand turning mechanism by examining the effect of strand shape on the impulse exerted by a single goblet cell. We conclude that goblet cell–mediated reorientation is a viable route for bundled strand reorientation, which should be further validated in future experiment.

During growth, a nerve cell creates protrusions that are called neurites. The intracellular active transport of the proteins is based on kinesin molecules walking on microtubules that have a chiral symmetry and thus a direction. The direction of this movement is towards the +END of the microtubule. Estimates suggest that in neurites 80% of microtubules are aligned in such a way that kinesin molecules walk to the tip of the neurite. In sharp con- trast, recent experiments found that kinesin molecules move collectively toward the cell body, away from the tip of the neurite. So far, there is no explanation on this unexpected observation. In this thesis, we introduce a mathematical description of the collective ki- nesin movement and investigate three different possible underlying mechanisms for the observed reversal. The most possible mechanism assumes that through cell signaling ki- nesin molecules exclusively can bind to different subsets of microtubules pointing either toward or away from the cell body. For this model, we approximate the full mathemati- cal system of transport-reaction equations with an equation for biased diffusion and fit the parameters so we reproduce the experimental data and describe quantitatively the environ- ment changes that the cell induces.

During growth, a nerve cell creates protrusions that are called neurites. The intracellular active transport of the proteins is based on kinesin molecules walking on microtubules that have a chiral symmetry and thus a direction. The direction of this movement is towards the +END of the microtubule. Estimates suggest that in neurites 80% of microtubules are aligned in such a way that kinesin molecules walk to the tip of the neurite. In sharp con- trast, recent experiments found that kinesin molecules move collectively toward the cell body, away from the tip of the neurite. So far, there is no explanation on this unexpected observation. In this thesis, we introduce a mathematical description of the collective ki- nesin movement and investigate three different possible underlying mechanisms for the observed reversal. The most possible mechanism assumes that through cell signaling ki- nesin molecules exclusively can bind to different subsets of microtubules pointing either toward or away from the cell body. For this model, we approximate the full mathemati- cal system of transport-reaction equations with an equation for biased diffusion and fit the parameters so we reproduce the experimental data and describe quantitatively the environ- ment changes that the cell induces.

Unrestricted particle transport through microfluidic channels is of paramount importance to a wide range of applications, including lab-on-a-chip devices. In this article, we study via video microscopy the electro-osmotic aggregation of colloidal particles at the opening of a micrometer-sized silica channel in the presence of a salt gradient. Particle aggregation eventually leads to clogging of the channel, which may be undone by a time-adjusted reversal of the applied electric potential. We numerically model our system via the Stokes-Poisson-Nernst-Planck equations in a geometry that approximates the real sample. This allows us to identify the transport processes induced by the electric field and salt gradient and to provide evidence that a balance thereof leads to aggregation. We further demonstrate experimentally that a net flow of colloids through the channel may be achieved by applying a square-waveform electric potential with an appropriately tuned duty cycle. Our results serve to guide the design of microfluidic and nanofluidic pumps that allow for controlled particle transport and provide new insights for anti-fouling in ultra-filtration.

The human body is nearly left-right symmetric on the outside, but this is not the case on the inside. During the development of the body, a leftward fluid movement in the node (a cavity that will turn into the embryo) is essential for the left-right symmetry-breaking process. However, the exact role of nodal flow and the hair-like appendages (cilia) that produce this is still debated. In this thesis we study a minimal model of a nodal cilium with only one degree of freedom. In this model, originally proposed by Vilfan and J¨ulicher, Phys. Rev. Lett. 96, 058102 (2006), a cilium is replaced by a spherical bead moving on a fixed elliptic orbit. The model cilia interact hydrodynamically which allows for the study of synchronization. In this thesis we compare the minimal model to an advanced model developed concurrently in another Bachelor project by Perugachi Israels. Surprisingly, we find that the minimal model semi-quantitatively captures the features and generates fluid dynamics comparable to the advanced model. Consequently, the minimal model can be used to qualitatively study processes like the flowinduced movement of small signaling molecules. Duplicating the minimal model allows us to study synchronization between neighboring cilia. Doing so, we notice that the model cannot take into account the change in the trajectory of a cilium due to the presence of a second cilium. This problem can be solved by adding another degree of freedom to the minimal model, which is left for future study.

The body plan of many mammals, including humans, shows a very clear internal left-right (LR) asymmetry. The process of LR symmetry breaking starts with asymmetric fluid flow generated by rotating cilia inside a short-lived embryonic cavity called the node. Although a significant amount of experimental and theoretical research has been conducted on the subject, there is no consensus on how fluid flow leads to asymmetric gene expression. At the moment there are two hypothesised mechanisms: chemosensing and mechanosensing. To contribute to the research being done on this subject we make a numerical model of mouse nodal cilia with which we reproduce the flow field inside the node. We discuss the low Reynolds number hydrodynamics of this system; important features include boundary effects and the flow generated by beads. The cilium itself consists of three interconnected filaments of beads attached to a no-slip boundary. Our model reproduces the key features of nodal flow quite well, despite the reducing assumptions made. We find that the flow generated by two cilia is not strong enough to bend an immotile cilium at the periphery of the node, as the mechanosensing hypothesis suggests. Moreover, the traction force on the surface generated by two cilia seems to be too weak to be noticeable. The fluid flow generated by two cilia does seem to be strong enough to create a chemical gradient inside the node, as the chemosensing hypothesis suggests. We conclude that the chemosensing hypothesis seems more likely to be correct than the mechanosensing hypothesis. However, it could be the case that the actual mechanisms for asymmetric gene expression involves a combination of both hypothesised mechanisms.

Jamming behaviour has been observed in epithelial tissue. We tried to get more insight into jamming behaviour in monolayers of cells through numerical modelling. In our simulation epithelial cells were modelled as soft-potential spheres and soft-potential dumbbells. Oscillations in cell length and size were used to study the effect of deformation of cells on the collective dynamics of epithelial tissue. Jamming was observed in systems of passive disks, but jamming disappeared as cell oscillations were introduced. All simulated systems with dumbbells were linearly diffusive. Adding oscillations to the dumbbells increased the diffusivity of the system, especially at higher densities. The model of oscillating dumbbells used in this thesis was successful in showing the effect of oscillations on the dynamics of diffusive systems. However, it did not succeed in simulating jamming. For future research it will be necessary to look further into creating a different model of deforming epithelial cells if we want to study jamming behaviour.