Author's response

Guillermina R. Ramirez-San Juan and Manu Prakash shared

Open questions

1. An interesting point you discuss towards the end of your paper, is that the mouse airway operates below the optimal regime of cilia orientation and patchiness allowing fast particle clearance, and you discuss the literature of what is known in other species. From your elegant model and experimental setup, what would be your hypothesis from a biology point of view, of the current parameters defining airway clearance in various animals?

Multiciliated tissues have the inherent constraint of having to accommodate other non-ciliated cell types (for example mucus secretory cells). Therefore, the coverage fraction by multi ciliated cells is always less than one, thus flow strength is by definition less than the maximum possible value. Given this constraint, the separation between clusters of multi ciliated cells, described by the patchiness parameter, becomes crucial. Our simulations show that indeed clearance time depends strongly on patchiness, therefore we hypothesized that this parameter would have similar values across species. We found that this is indeed the case, independently of the total length of a trachea, patchiness determines clearance time, thus this mechanism of clearance would work from a mouse up to a giraffe. It is important to note that the parameters we measure depend on one another, for example at the patchiness of the mouse airway having a moderate amount of orientational disorder is beneficial, however, this would not be the case if coverage by multi ciliated cells is one. It is important to note that this a multi-dimensional phase space and for most animals – many of these fundamental parameters have never been measured. Therefore, we think that these parameters must be tuned accordingly given the particular constraints of an organism with overall clearance that is good enough for function while preserving other function. As is often the case, things in biology don’t always need to be perfectly optimal.

2. Restricting the discussion and model to the airways, do you observe something different in the arrangement of cilia in the bronchi or other anatomical sections of the respiratory tract, compared to the trachea?

We have not looked at other tissues in the airway, however from the literature we know ciliation decreases in the lobar bronchi and more significantly in the terminal bronchioles. (E. Toskala et al. AJP-Lung Cell Mol Physiol 289, L454-L459 2005). The diameter of the airway also decreases, and we hypothesize that the thickness of the mucus layer does to. All these factors could modify the mechanism responsible for mucus clearance in these lower sections of the respiratory tract. Furthermore, in the future, we will explore the role of branching topology – so fundamental to the design of the lung – in determining clearance times in complex geometries so commonly seen.

3. Could you briefly explain the envelope approach on which you got inspired for your hydrodynamic model?

For the single cell scale, instead of modeling each individual cilia with point forces acting on the fluid, we consider a classical approach utilized in hydrodynamics (3,4) – an envelope that covers the tips of several beating cilia that together form a continuous moving sheet. This sufficiently models a dense patch of cilia moving concurrently. The boundary condition at the fluid surface thus becomes v=Up, an effective tangential slip velocity that follows the orientation field p of the underlying cilia with an average local flow velocity U. This approach coarse-grains the length-scales smaller than the cell, so it cannot resolve the flow around individual cilia, however it is suitable to model very large systems, as is pertinent to ciliary flows in the trachea, and for understanding how the spatial patterning of multi ciliated cells gives rise to directed flows.

Next, the model the entire flow velocity of the ciliary carpet with patches of multi-ciliated cells – we perform a simulation using a 3D computational fluid dynamics (CFD) solver for the incompressible Navier-Stokes equations, optimised for low Reynolds numbers. This algorithm is implemented on a staggered grid in x, y and z, corresponding to a liquid film of size L_x times L_y times H, where H is height of the mucus film. We utilize periodic boundary conditions in x and y directions, where x is defined as the distal-to-proximaldirection of the trachea. For modeling the fluid-air interface, we enforce the no-shear condition at z=H. Finally, on the tissue surface we apply the no-slip condition in the absence of cilia (c=0), and in the presence of cilia (c=1) we impose a slip velocity set by the envelope model, previously described. We simulate this system until the (unique) solution is reached at steady state, after which we save the three-dimensional velocity field and the pressure field of the ciliary flow.

4. Would you think the cilia arrangement you observed in mice is optimal for clearing fluid with different properties than those observed in homeostasis, such as those possibly induced during airway infection? For instance, increased mucus viscosity?

In our model the fluid parameter that influences the strongest the clearance time is the height of the fluid film, as could be considered in a chronic sickness or infection. The height of the fluid film determines directly the value of patchiness, defined as patchiness=lambda/H. Therefore as the height of the mucus layer decreases we expect longer clearance times. The viscosity of mucus will not impact the directionality of the flow but its amplitude. However, it is important to note that mucus is a complex viscoelastic fluid and it will be important for future work to include this feature in the current framework.

5. Are you interested in exploring with your model how it is that different pathogens cause respiratory conditions? For instance, if specific pathogens destroy large areas of multiciliated cell patches, or compromise the activity of cilia, how does this impact on dynamics of particle clearance?

Our model directly predicts the effects of changes to coverage fraction, patchiness, ciliary density and  orientational order in clearance time. As is mentioned above, reduced coverage fraction and increased orientational disorder are hallmarks of airway pathologies. We see in our model that these changes indeed lead to increased clearance times and thus compromised function. It is important to note that these changes also lead to the emergence of zones of mucus recirculation, it is possible that this local accumulation of mucus can lead to further loss of multi ciliated cells, making the situation even worse. However, future work will be needed to address the dynamics of mucus accumulation and their effect on cilia.

6. In your model, can you test known conditions which compromise ciliary function and movement, such as Kartagener’s syndrome? Altogether, can you introduce into your model different variables including known mutations compromising cilia, as well as particles or pathogens?

Our model coarse grains the beat of individual cilia, thus this particular model it is not suited for the study of the effect of mutations that alter the cilia beat frequency of waveform on clearance time and flow. We can indeed modify the underlying framework to find an effective lumped parameter that could simulate ciliary beat frequency defect. Several previous models in the literature explicitly implement ciliary beat frequency, however, it is not possible to simulate a system the size of the actual airway. And since the important phenotype (such as clearance time) might only emerge at larger length scales – it is important to account for the same. As is often the case with biological models, you have to pick your models according to the scale you’re interested in. This work explicitly tries to account for effects that occur only when we consider the multiple scales in the problem.

7. You used beads of specific shape to study particle clearance. Would shape differences in particles have an impact on clearance times as well, in addition to the parameters you studied?

We use spherical beads in our experiments as they are conveniently available. In the future we are interested in including particles – such as carbon black or pollen fragments – that are often lodged in the trachea. This would allow us to understand the role of surface chemistry – beyond shape which would be important. From a modeling perspective, shape of a particle can be accounted for in several other lumped parameters such as effective diffusion, which can be easily incorporated in the study.

8. In your discussion, you mention stochastic resonance as something not uncommon in biological systems. Can you discuss further examples, and how they are beneficial in a context of anatomy and physiology?

A fundamental question is biology is how form leads to function? Over the last several decades, this question has been explored in many biological systems where a parameter space can be mapped between form and function and hence this relationship between form and function can be teased apart quantitatively. In this context, stochastic resonance is a defined as phenomena where some noise in a specific parameter leads to optimal function. Discovered first in the context of neuronal circuits – it is most often described in biological systems with temporal noise. Here we describe a biological system where spatial noise (orientation) enables specific flow topologies that enhance physiological function. Spatial patterns are indeed being quantified more broadly in biology – most recently in retinal systems where the arrangement (and noise therein) is linked to function of light sensation.

9. You focused your work on the respiratory tract, and mention indeed cilia are present in multiple organs and systems. Do you envision exploring the relevance of cilia and their coordinated function in other organs?

Yes! Indeed, the airway is only a particular case where we see arrays of cilia. Beyond humans and organ systems, most often flow generation is needed for physiology, it is driven by a ciliary carpet. We are fascinated by ciliary carpets since the molecular constituents of the individual cilium are highly conserved across organisms, however the architecture of ciliary arrays and the flow patterns cilia generate are incredibly diverse.

 The first author of this study – Dr. Guillermina Ramirez-San Juan will also be starting her own lab soon, where research will be focused on understanding how the multiple cilia integrate their activity across several length scales to give rise to the diversity of flow patterns we see in nature, using model systems that range from swimming unicellular organisms to airway cells.

10. In your discussion, you mention the following prospect: ‘This could open new doors to fabricate active surfaces that drive fluid flows with programmable and adaptive topologies’. This is an exciting idea. Following on the translational philosophy of the Prakash lab, do you envisage taking this idea from ‘bench to bedside, as a direct application for human health?

First, we expect that understanding the biophysical basis of flow generation by ciliary arrays and defect therein will have a direct impact on treatment and diagnosis of airway pathologies. So far, we have been looking at the pathologies and the phenotypes they exhibit in isolation. Having the tools to link the two together allows us to understand what is missing, and make significant headway in pushing diagnosis and treatment for a range of ciliary pathologies. Current diagnostics are based in recording the activity of individual cilia, however we envision that by linking flow phenotypes to ciliary function via less invasive tests, that assess macroscopic variables can be potentially developed. Of course, this would also involve engaging physicians who understand deeply the challenges faced by patients every day.

 We are also excited about several applications that go beyond human health. There are several technological challenges that could benefit from understanding how to generate flows with particular topology and hydrodynamic properties at low Reynolds number. For example, giant biofuel tanks face the challenges of mixing but might not be able to use traditional turbulence generated mixing due to ill effects of the high shear rates seen traditionally. By generating active surfaces that enable enhanced mixing without inducing force based stress phenotypes would be a fruitful direction to explore.