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Journal of Theoretical Biology journal homepage: www.elsevier.com/locate/yjtbi

Primary cilia mechanics affects cell mechanosensation: A computational study Hanifeh Khayyeri a,b, Sara Barreto a, Damien Lacroix a,n a

INSIGNEO – Institute for in silico medicine, Department of Mechanical Engineering, The University of Sheffield, Sir Frederick Mappin Building, Mappin Street, Sheffield S1 3JD, United Kingdom b Department of Biomedical Engineering, Lund University, Lund, Sweden

H I G H L I G H T S







A first computational study on primary cilium interaction with cell components. The length and stiffness of primary cilia affect internal cell strain levels. The cell nucleus is strained during primary cilium deflection. Cells’ mechanosensitivity can be altered by targeting primary cilia lengths.

art ic l e i nf o

a b s t r a c t

Article history: Received 29 August 2014 Received in revised form 19 December 2014 Accepted 23 April 2015

Primary cilia (PC) are mechanical cell structures linked to the cytoskeleton and are central to how cells sense biomechanical signals from their environment. However, it is unclear exactly how PC mechanics influences cell mechanosensation. In this study we investigate how the PC mechanical characteristics are involved in the mechanotransduction process whereby cilium deflection under fluid flow induces strains on the internal cell components that regulate the cell's mechanosensitive response. Our investigation employs a computational approach in which a finite element model of a cell consisting of a nucleus, cytoplasm, cortex, microtubules, actin bundles and a primary cilium was used together with a finite element representation of a flow chamber. Fluid–structure interaction analysis was performed by simulating perfusion flow of 1 mm/s on the cell model. Simulations of cells with different PC mechanical characteristics, showed that the length and the stiffness of PC are responsible for the transmission of mechanical stimuli to the cytoskeleton. Fluid flow deflects the cilium, with the highest strains found at the base of the PC and in the cytoplasm. The PC deflection created further strains on the cell nucleus but did not influence microtubules and actin bundles significantly. Our results indicate that PC deflection under fluid flow stimulation transmits mechanical strain primarily to other essential organelles in the cytoplasm, such as the Golgi complex, that regulate cells’ mechanoresponse. The simulations further suggest that cell mechanosensitivity can be altered by targeting PC length and rigidity. & 2015 Published by Elsevier Ltd.

Keywords: Cell mechanics Biophysics Mechanobiology Mechanosensation Finite element model

1. Introduction Primary cilia are singular, non-motile extensions of the cell that protrude into the extracellular environment. They have been found on cells from many different tissues such as kidneys (Praetorius and Spring, 2001), cartilage (McGlashan et al., 2006b), liver (Masyuk et al., 2004), tendons (Donnelly et al., 2010; Lavagnino et al., 2011) and bone (Malone et al., 2007), where the impairment of cilia is associated with diseases like polycystic kidney disease (Yoder, 2007), Meckel–Gruber syndrome

n

Corresponding author. Tel.: þ 44 114 220156. E-mail address: d.lacroix@sheffield.ac.uk (D. Lacroix).

(Dawe et al., 2007) and osteoarthritis (McGlashan et al., 2008). Extending from the cell body, the cilia play a key role in cell cycle, signalling and mechanosensation during development, homoeostasis as well as regeneration (Satir et al., 2010). The organelle is often described as an “antenna” that collects biomechanical signals from the surrounding pericellular environment (Satir et al., 2010; Singla and Reiter, 2006). However, the exact mechanisms of primary cilia mechanosensation are not fully understood, which impedes the development of new clinical therapies that target primary cilia and their role in regulating cell and tissue health. For example, experiments have shown that primary cilia are flow sensors as they deflect under fluid flow. This in turn induces a cascade of molecular events, like hedgehog, Wnt and PDGF

http://dx.doi.org/10.1016/j.jtbi.2015.04.034 0022-5193/& 2015 Published by Elsevier Ltd.

Please cite this article as: Khayyeri, H., et al., Primary cilia mechanics affects cell mechanosensation: A computational study. J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.04.034i

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signalling, by engaging the many receptors, ion channels and transporter proteins that are localised on the cilium and its basal body (Satir et al., 2010), such as integrin alpha and beta receptors, NG2, and PDK channels (Delling et al., 2013; McGlashan et al., 2006a). Researchers have further discovered that the degree of deflection regulates the strength of the molecular response, for example the degree of calcium release (Malone et al., 2007; Praetorius and Spring, 2003; Praetorius et al., 2003; Wann et al., 2012) and cAMP signalling (Besschetnova et al., 2010; Kwon et al., 2008; Masyuk et al., 2004). Other studies have also shown that the removal of primary cilia reduces sensitivity of cells to external biophysical signals, measured as for example reduced calcium release and blocked TGF-beta signalling in endothelial cells under fluid flow (Egorova et al., 2011) or the down-regulation of hedgehog signalling in chondrocytes subjected to mechanical strain (Thompson et al., 2014). This loss of sensitivity to mechanical stimulation can have detrimental effects in many load-bearing and adaptive tissues, such as bone and cartilage. In bone implant interfaces, the deletion of primary cilia in pre-osteoblasts has resulted in reduced differentiation into bone forming cells and reduced proliferation in response to mechanical stimuli (Leucht et al., 2013). This suggests that the mechanosensory role of the primary cilium has not only short term effects like calcium signalling, but also affects the long term response of cells and tissues, crucial for tissue maintenance and regeneration. But due to the limited knowledge about the primary cilium interactions with other cell organelles, and considering that most cell culture studies can only measure short term effects of primary cilium mechanosensation, it is unclear how cilium mechanics would have prolonged effects on cell and tissue function. Studies have shown that there might be an adaptive relationship between the length of the primary cilium and the biophysical loading which the cell is subjected to. In a study by Besschetnova et al. (2010) the authors reported that the length of primary cilia on endothelial cells and mesenchymal stem cells decreases with increased biophysical stimulation. Gardner et al. (2011) and McGlashan et al. (2010) have further shown that the removal of biophysical stimulation on cells results in longer primary cilia. These studies suggest that there is an inverse relationship between the length of primary cilia and mechanical stimulation. It has also been proposed that the mechanical properties, such as flexural rigidity, of primary cilia, determining the degree of ciliary deflection under mechanical stimulation, control cell biochemical response (Hoey et al., 2012). However, the mechanical properties of primary cilia are not well known and several studies, combining in vitro and computational models, have been performed to investigate the flexural rigidity of primary cilia on different cell phenotypes. One of the first computational models of a primary cilium was developed by Schwartz et al. (1997) who proposed the heavy elastica model describing the primary cilium as an elastic beam when subjected to fluid flow. By calibrating the computational model with images of cells in vitro, Schwartz et al. (1997) were able to establish the flexural rigidity of the axoneme. Later, Rydholm et al. (2010) created a finite element model of a primary cilium, distinguishing the cilium microtubules and ciliary membrane, which was attached to the apical membrane of the cell. Using the flexural rigidity derived by Schwartz and colleagues (1997), Rydholm et al. (2010) showed that the flow-induced deflection of the primary cilium creates high stresses at the base of the cilium, where it is attached to the cell. The authors concluded that the high stresses are likely to activate calcium channels located at the base of the cilium, where the viscoelastic properties of the ciliary membrane could be responsible for the short delay in calcium signalling response after flow stimulation. More recent computational models have shown that apart from the flexural rigidity, the position of the cilium (i.e. the angle

between the cilium and the cell membrane) is crucial for how the cilium deflects and therefore, transmits the external biophysical signal (Downs et al., 2012; Young et al., 2013). However, the effects of primary cilia angular positions on signal mechanotransduction are still to be verified and quantified. Chen et al. (2009) developed a more complex finite element model of a primary cilium including its nine microtubule doublets. Their simulations showed that deformations of cilia under flow are large enough to induce intracellular signalling; however, like its predecessors, their model does not cover how primary cilia may interact with the rest of the cell during flow stimulation nor how cilium mechanical properties influence this interaction. Previous mechanobiological studies have shown that cells are responsive to mechanical strain, either through their stretchactivated channels, focal adhesion sites, integrins or cytoskeleton (e.g. Discher et al., 2005; Ingber, 2006; Kamm and KaazempurMofrad, 2004; Lee et al., 2007; Tarbell et al., 2005; Tschumperlin et al., 2004; Wang et al., 1993). It is believed that mechanical stimuli modulates the integrin-mediated signals that are transmitted through the focal adhesion sites and the actin bundles (Kuo, 2013). Many studies have investigated how these mechanotransduction mechanisms alter the cytoskeleton organisation of the cell as well as its mechanosensitive response. Despite advances, the synergies of primary cilium mechanics with other mechanosensory organelles of the cell have not been fully explored. Computational models are advantageous in this regard since they have the capacity to investigate biomechanical and mechanobiological hypotheses that might be very difficult to test otherwise with existing experimental approaches with which isolating the influence of specific cellular structures on cells’ response is extremely difficult. In this paper, we investigate whether the mechanics of the primary cilium influences cell mechanosensation. More specifically, we aim to show how the mechanical characteristics of the primary cilium, such as length and stiffness properties, modulate the cilium’s mechanosensory role by affecting the mechanotransduction to other cell organelles as well as the strain on the cilium itself. This study looks if the primary cilium deflection under fluid flow induces strains on, not only the cilium and its base but also on the internal cell components involved in regulating the cell’s mechanosensitive response such as the actin bundles, microtubules and the nucleus. This is tested using a computational approach where a model of a single cell, equipped with a primary cilium, is subjected to fluid flow stimulation. Our findings suggest that the degree of mechanosensitive response of ciliated cells depends partly on the mechanics of the primary cilium, which regulates the mechanical stimuli transduced to important cell organelles such as the nucleus and to specific locations of the cytoplasm where the Golgi apparatus is located.

2. Materials and methods 2.1. Single cell model geometry and material properties A three dimensional finite element model of a single cell, originally created by Barreto et al. (2013), was used and further developed. The cell had a semi-ellipsoidal shape and was 19 mm long, 4 mm height and 8 mm wide. It was equipped with a primary cilium and the cell interior was composed of a nucleus, cytoplasm, cortex, microtubules and actin bundles (see Fig. 1). The nucleus was modelled as an ellipsoid as reported by Caille et al. (2002) and was located 2.5 mm from the centre along the long axis of the cell. The primary cilium was modelled as a three dimensional cylindrical solid continuum rod and was 5 mm long (Downs et al., 2012) and 0.2 mm in diameter (Rydholm et al., 2010). The cilium is an

Please cite this article as: Khayyeri, H., et al., Primary cilia mechanics affects cell mechanosensation: A computational study. J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.04.034i

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Fig. 1. Illustration of the single cell model and its cytoskeleton components.

Table 1 List of material properties used for the different components of the cell model. Cell component

Young’s modulus (kPa)

Poisson’s ratio

Cytoplasm Nucleus Actin cortex Microtubules Actin bundles Primary Cilia

0.25 (Caille et al., 2002) 1.00 (Caille et al., 2002) 2.00 (Stricker et al., 2010) 2  106 (Pampaloni and Florin, 2008) 340 (Deguchi et al., 2006) 178 (Rydholm et al., 2010)

0.49 0.3 0.3 0.3 0.3 0.3

extension of the basal body that sits just beneath the cell surface. The basal body is derived from the mother centriole in the centrosome, which in proliferating cells migrates to the cell surface and attaches to the plasma membrane (Fry et al., 2014). To capture this polarisation, the microtubules where modelled with a star-shaped morphology in the cell cytoplasm. The microtubule configuration was modified from the original cell model by Barreto et al. (2013) such that the microtubule origin at the centrosome was located at the base of the primary cilium docked on the cell surface. From the centrosome, the microtubules could extend until they reached the cell cortex. The actin bundles of the model were depicted as parallel actin fibres that run along the long axis of the cell. A combination of discrete and continuum finite elements were used in the cell model. The nucleus and cytoplasm were meshed with 563 046 hexahedral solid elements (average mesh size 0.1 mm) whereas the cortex was modelled as 0.2 mm thick shell. The microtubules were assigned linear beam element properties to resist both tension and compression, and truss elements were used to depict the lack of resistance to compression for the actin bundles (see Barreto (2013) for more detailed description of the original cell model). The primary cilium was modelled with 600 deformable hexahedral second order finite elements. For simplicity, all other internal cell components were modelled as linear elastic materials and properties were assigned to organelles according to literature data (see Table 1). Even though the material behaviour is assumed linear, the whole cell response is non-linear due to the lack of resistance to compression by the actin bundles. Since the primary cilium undergoes large deformations, the structure was modelled as compressible neo-Hookean material. The bulk modulus and shear modulus of the cilium were

Fig. 2. Highlighted area marks the tie constraints used to attach the primary cilium to the cell. The central node in the highlighted region was common for the primary cilium, cortex, microtubules and actin bundles.

calculated as K¼

E 3ð1  2vÞ

G¼

E 2ð1 þ vÞ

respectively, where E is Young’s modulus of the primary cilium and v is Poisson’s ratio. 2.2. Boundary conditions for cell organelles The cell was assumed to lie on a substrate, modelled as encastre boundary condition at the bottom of the cell. The actin bundles were organised in the internal periphery of the cell volume and were assumed to anchor to the cell cortex in intersecting nodes. The centrosome was assumed to be attached on the top cell surface, also anchored to the cortex and the actin bundle by sharing one finite element node. Extending from the centrosome, the microtubules beams joined nodes with the cell cortex and actin bundles at the other end of the beams. The primary cilium was attached on top of the cell, linked to the microtubules (centrosome), actin bundles and cell cortex by sharing the same node as described previously. The cilium was modelled to sit on top of the cell surface and its bottom element surfaces were assigned tied constraints to those of the cell cortex (i.e. four cortex elements were tied to the base of the cilium in this model, see Fig. 2). Since the cell surface is curved, the cilium rod had to be cropped to create the same curvature at the base of the rod needed for imposing the surface constraints. 2.3. The perfusion flow bioreactor model To model the cell in a perfusion flow bioreactor environment, a finite element model of the fluid domain in a bioreactor system was created. The fluid domain was assumed to be rectangular with the dimensions of 10  5  5 mm3, representing a flow chamber

Please cite this article as: Khayyeri, H., et al., Primary cilia mechanics affects cell mechanosensation: A computational study. J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.04.034i

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system. The geometry of the cell was cut out in the centre of the fluid domain to ensure that the model captures the fluid profile surrounding the cell under flow in the middle of the bioreactor. The fluid domain was meshed with 0.4 mm hexahedral fluid elements on the surface closest to the cell and a global average element size of 10 mm, resulting in more than 7 million elements. Non-slip wall boundary conditions were assigned around the external surfaces of the fluid domain, and a zero pressure outlet condition was assumed at the end of the domain. An inlet velocity of 1 mm/s fluid flow was simulated in the flow chamber (Koch et al., 2010) (see Fig. 3 for illustration of boundary conditions). The fluid was modelled as water with a density of 1000 kg/m3 and viscosity of 0.001 Pa s. The pre and post-processing of the CFD model was performed on a high performance visualisation node equipped with Nvidia M2070Q graphic card.

Fig. 3. The fluid model of the cell inside a perfusion flow chamber.

2.4. Fluid structure simulations A one-way decoupled fluid–structure interaction (FSI) computational routine was developed with Cþ þ and Abaqus V. 6.11-3 (Dassault Systemes) to simulate the cell under fluid flow. The entire simulations follow a computation scheme where initially a fluid domain of the extracellular flow chamber environment is created and submitted for computational fluid dynamics (CFD) analysis. Once the CFD analysis has completed and converged, the Cþ þ subroutine reads in the fluid pressure created by the fluid flow and translates it to shear force applied on the corresponding finite elements belonging to the cell surface and the primary cilium on the solid cell model and in the direction of flow. Next, the single cell model is submitted to Abaqus for finite element analysis (see Fig. 4 for computational scheme). This scheme was only repeated once for every single cell simulation with a new cilium configuration. In order to investigate how the mechanical characteristics, such as length and stiffness of primary cilia interact with other cell organelles and test whether their role in mechanosensation is affected by their mechanical characteristics, six simulations of the cell under perfusion fluid flow were performed. Simulations in which the length of the primary cilium were altered to 3 and 10 mm (corresponding to reported cilium lengths in literature, see Table 2) were run. Changes in the stiffness of the primary cilium was also investigated in simulations where Young’s modulus of the cilium was decreased to 0.017 kPa and increased to 1.057 kPa (length and diameter of cilium were kept constant) (see Table 2 for a list of simulations). In total 4 CFD simulations and 6 FEA cell simulations were performed.

3. Results 3.1. Simulations results of the cell with and without a primary cilium

Fig. 4. The computational scheme of the framework developed for the decoupled fluid–structure interaction analysis of the cell inside a flow chamber.

In the CFD simulations, the fluid velocity around the cell dropped due to frictional drag forces and at convergence the results showed an average fluid shear pressure of 0.12 Pa around the cell with and without cilium. By applying the local fluid pressures on the cell model, the simulations of the cell with primary cilium showed that the structure deflects under fluid flow creating strains on the surface of the organelle and its base. Highest strains were observed at the base of the cilium where it is attached to the cell cortex. The results showed that this deflection induces higher strains on the cell body and cell components compared to simulations of the cell without primary cilium but subjected to the same fluid flow condition (see Fig. 5 images labelled no cilium vs. baseline cilium). In the cell equipped with a primary cilium, the strains due to deflection were transmitted mainly to the cortex, cytoplasm and nucleus (see Table 3). The microtubules and actin bundles were only minimally strained (in the order of 10  7–10  6) and so the influence of primary cilium

Table 2 List of simulations performed with different primary cilia mechanical properties. Simulations of a cell with no cilia were also run to investigate the overall role of primary cilia. Simulation

Young’s modulus of primary cilia (MPa)

Primary cilia length (mm)

Cell Cell Cell Cell Cell Cell

– 0.178 (Schwartz et al., 1997) 0.178 (Schwartz et al., 1997) 0.178 (Schwartz et al., 1997) 1.057 (Young et al., 2012) 0.017 (Herzog, 2010)

– 5 (Downs et al., 2012) 3 (Herzog, 2010) 10 (Praetorius and Spring, 2001) 5 (Downs et al., 2012) 5 (Downs et al., 2012)

with with with with with with

no cilium baseline cilium short cilium long cilium stiff cilium soft cilium

Please cite this article as: Khayyeri, H., et al., Primary cilia mechanics affects cell mechanosensation: A computational study. J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.04.034i

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Fig. 5. Simulation results of the cell under fluid flow. The contour plots are in undeformed configuration and showing a close up cross section of the cell where the cilium is attached. Contours show the magnitude of strain created in the cell due to primary cilia deflections. Simulations of cell with a primary cilium show all higher strains on the cell compared to cells without primary cilium. The strain induced on the cell is significantly affected by the length of the cilium, but also by its stiffness. Longer and softer cilium also induced higher strains on the cilium body.

Table 3 Summary of results from the 6 simulations performed showing the maximum principal strain in the different components of the cell. Ratios are calculated as the strains in the cell component with specified cilium properties divided by maximum principal strains in the cell component without primary cilium. Simulation No cilium Baseline cilium Short cilium Long cilium Stiff cilium Soft cilium

Cytoplasm 3

2.0  10 1.1  10  2 5.9  10  3 9.0  10  2 1.1  10  2 1.2  10  2

Strain ratio cytoplasm 1 5.50 2.95 45.0 5.50 6.00

Cortex 3

1.9  10 9.8  10  3 5.6  10  3 7.4  10  2 1.0  10  2 8.7  10  3

on microtubules and actin bundles was not as significant as on the other cell components (results not shown).

3.2. The role of primary cilia mechanics Increased length of the primary cilium resulted in much higher strains on both the cilium structure and the internal cell components, particularly the cytoplasm. Conversely, simulations of a shortened primary cilium predicted reduced deflection as well as strains on the cell organelles, compared to baseline simulations. This is a result of the cilium deflection, where the longer cilium is exposed to higher drag forces by the fluid compared to the shorter cilium; in turn longer cilia deflect more than shorter cilia when subjected to identical fluid flows, thus creating higher magnitudes of strains on the respective cell and the primary cilium itself (see Tables 3, 4, and Figs. 5, 6). Higher flexural rigidity, i.e. stiffer cilium, showed smaller deflections and reduced magnitudes of strain on the cilium (see Figs. 5 and 6). Following this, lower flexural rigidity resulted in larger ciliary deflections and higher strains on the structure, and the cytoplasm and the cell cortex (see Tables 3 and 4). In general, the simulations also showed a relationship between degree of deflection and strains on the different cell components. However, this trend was mainly obvious for strains on the primary cilium itself and not always the other cell components, where although softer cilia exhibited larger deflections than baseline, the simulations showed similar magnitudes of strain on the cortex and the cytoplasm for both cilium configurations (see Fig. 7). Interestingly, a cross section of the single cell shows that the deflection of the cilium strains a region in the cytoplasm just below where the primary cilium protrudes into the extracellular space (see Fig. 5). Simulations of a cell without primary cilium

Strain ratio cortex

Nucleus 5

5.4  10 1.4  10  4 2.1  10  4 1.1  10  3 1.5  10  4 1.3  10  4

1 5.16 2.95 38.9 5.26 4.58

Strain ratio nucleus

Primary cilia

1 2.59 3.89 20.4 2.78 2.41

– 7.3  10  3 3.4  10  3 6.0  10  2 1.6  10  3 3.6  10  2

Table 4 Deflection of the tip of the primary cilia during 1 mm/s perfusion fluid flow. Simulation

Tip deflection (μm)

Baseline cilia (5 mm) Short cilia (3 mm) Long cilia (10 mm) Soft cilia (E ¼0.017 MPa) Stiff cilia (E¼ 1.057 MPa)

0.35 0.03 8.59 1.80 0.20

were not strained in this region (see Fig. 5 cell without primary cilium). The results also showed that the nucleus of the cell is exposed to relatively high strains when the primary cilium deflects (see Figs. 7 and 8). The cell with the longer primary cilium induced higher strains on the nucleus compared to the other cells. Despite that the tip of the soft cilium was displaced more than the baseline, stiff and short cilium, the strains transduced to the nucleus were not significantly higher.

4. Discussion To the best of the authors’ knowledge this work is the first computational study to investigate how primary cilia mechanics interacts with the cell and its components when subjected to fluid flow. The multi-structural cell model presented, enables us to deconstruct cellular components and scale down the biological complexity to better understand how each component is involved in cell mechanosensation. The results of this study have demonstrated that the deflection of the primary cilium under fluid flow creates large strains on the cilium surface and at its base where it

Please cite this article as: Khayyeri, H., et al., Primary cilia mechanics affects cell mechanosensation: A computational study. J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.04.034i

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is connected to the cell, as also reported in previous computational findings (Rydholm et al., 2010). Stimulation of primary cilium transmits mechanical strain to essential cell organelles located in the cytoplasm, but also to the cell nucleus. The simulations further suggest that cell mechanosensitivity can be altered by targeting primary cilium length. As with any model, this model is a simplification of the biological complexity, which is necessary to better understand the interactions between different complex structures and their individual function. However, it should be mentioned that this model is one of the most complete single cell models existing in the field, and uniquely equipped with a primary cilium. The cell model used in this study has been previously tested and corroborated with in vitro cell experiments, and captured the whole cell behaviour of U2OS cells under compression (Barreto et al., 2013). But like its predecessor it does not consider the cell membrane due its low mechanical integrity compared to the cortex and the other modelled components. Also, due to lack of geometric and material data, and to focus on the basic interaction between primary cilia and cell components, a simplistic cilium model has been adopted. For example, this model has not included the nine doublets of microtubules that reside within the cilium nor does it consider the ciliary pockets around the attachment of cilium to the cell surface (Fry et al., 2014). Surprisingly, our simulations did not find any significant effect caused by the primary cilium deflection on the actin bundles and microtubules within the cell (however, actin bundles and microtubules were strained due to fluid flow stimulation). Nonetheless, studies have shown that actin bundles are a highly mechanosensitive network of the cytoskeleton, responsible for cytoskeleton remodelling and formation of focal adhesion sites (Alenghat et al., 2004; De Santis et al., 2011; Wang et al., 1993). This indicates that perhaps a multi-scale approach including molecular dynamics must be adopted to model the cilium microtubules anchorage to the mother and daughter centrosomes to get a better understanding of how these components influence one another. Furthermore, the myosin–actin filament interactions are believed to further sensitise the cell to mechanical loads. A mathematical model of the myosin–actin network has been developed previously by Borau et al. (2012) where a 3D Brownian dynamic

approach could describe the role of myosin motors in mechanosensation. Such models could give an even better representation of the cytoskeleton force transmission under fluid flow stimulation. Our model has no time dependent aspect and does not consider cytoskeleton remodelling, which may change the pattern and magnitudes of the transduced strains. But although it is wellestablished that cytoskeleton remodelling occurs during mechanical loading, it is not clear whether the strains created by primary cilium deflection are involved in regulating the remodelling process. Moreover, research often describes the cytoplasm as a fluid with high viscosity (Chee et al., 2008; Lubyphelps et al., 1986). Therefore it would be interesting to test if a liquid cytoplasm enables load transfer through the cytoskeleton network or if cilium deformations will cause wave propagation and load transfer via the cytoplasm still.

Fig. 7. Maximum principal strain is plotted against the degree of deflection of the different primary cilia (PC). The plot shows clearly that longer cilium induces both larger deflections and strains on the cell components. However no major difference is observed on strains transduced on the cortex and cytoplasm for stiff, baseline and soft primary cilium simulations, despite increased deflections. The cilium on the other hand is exposed to twice as high strains when it is lengthened and softened. The maximum principal strains on the cell nucleus (right axis, green line) shows higher strain magnitudes due to the mere existence of the cilium on the cell, but the clear influence of cilium deflection on the nucleus is only visible for the longer cilium. (Please note that the left axis applies for strains on the cytoplasm, cortex and primary cilium, whereas the right axis of the plot shows strains on the nucleus only). (For interpretation of the references to colour in this figure legend, the reader is referred to the web version of this article.)

Fig. 6. Simulation results showing the deflection of the primary cilia under fluid flow. The plots are an overlay of the undeformed and deformed configuration of the cells with cilia. Significantly larger cilium deflections were observed for longer cilium length.

Please cite this article as: Khayyeri, H., et al., Primary cilia mechanics affects cell mechanosensation: A computational study. J. Theor. Biol. (2015), http://dx.doi.org/10.1016/j.jtbi.2015.04.034i

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Fig. 8. Contour plots of the principal strains transmitted to the cell nucleus. The mere existence of the primary cilium induces higher strains transduced to the nucleus. The magnitude of strains on the nucleus are correlated to the deflection of the ciliary tip, where larger deflections also induce higher strains on the nucleus.

This computational framework also involves CFD simulations of perfusion fluid flow on the cell, which only considers one cell located in the centre of the flow chamber and does not model the substrate stiffness interactions nor cell–cell interactions. Coming from the equations of fluid dynamics for flow in a pipe, there is always a pressure drop along the length of the pipe that depends on its length and diameter. Therefore, the pressure sensed by the cell close to the opening of the flow chamber will be higher than those on cell in the middle and the end of the chamber. It must be emphasised that this phenomena is rarely reported in literature and is something that must be discussed and reported more widely when conducting in vitro experiments or computational fluid dynamics simulations of flow chambers and bioreactors. In fact, the change in pressure could be responsible for part of the variation and discrepancies observed in experiments. It should be noted that a fully coupled fluid–structure-interaction was not feasible in this study due to the lack of data regarding the material density properties of each component (needed to solve the mass and momentum equations). Future experimental research in this direction would enable coupled fluid–structure-interaction computations and time-dependent simulations of dynamic loading, such as fluctuating fluid flow, and time-dependent material models for the cell, like viscoelasticity. Despite the limitations, we believe that our model has shown novel results in terms of strain transmission to the different cellular components as a result of primary cilia deflection. It further consolidates results from previous research where larger cilium deflections result in higher strains that activate stretchsensitive channels on the primary cilium and at its base (e.g. Malone et al., 2007; Praetorius et al., 2003; Wann et al., 2012, their studies have shown a positive correlation between larger primary cilium deflections and activation of stretch-sensitive channels at the base of the cilium). The cilium mechanical properties have been investigated in several experimental and computational studies of primary cilium (Downs et al., 2012; Young et al., 2013) as this enables accurate predictions of cilium deflection under specific loading conditions. Using the derived mechanical properties from these experiments, our simulations indicate that the flexural rigidity (stiffness) of the cilium does not always result in increased strains on the cell. In fact, our single-cell simulations show similar strain magnitudes on the cytoplasm and cortex of

cells with primary cilia of different flexural rigidities, but at constant lengths, and different degrees of deflection. Reduced stiffness did however induce twice as high strains on the cilium body, indicating that stiffness of cilium regulates the activation of sensory channels located on the primary cilium itself. The simulations show that the length of the cilium has a very significant effect on the strain transmission to the internal cell components; here, nucleus, cortex and cytoplasm. Longer cilium induced overall much higher strains compared to the shorter cilium under identical fluid stimulation. Thus, the results indicate that the length of the cilium is more critical than the stiffness of the structure for mechanotransduction to the cell. In experimental studies the lengths of primary cilia have been correlated with mechanical stimulus, where longer cilia are often observed at reduced magnitudes of stimulation (such as stress-deprivation), whereas shorter cilia are observed after cyclic loading (Gardner et al., 2011; McGlashan et al., 2010). Together with our findings, this suggests that the length of the primary cilium is a mechanism that allows the cell to control mechanosensation. It seems that in environments with low biophysical stimulus, the cell increases the length of its cilium to increase its mechanosensitivity as the longer cilium would induce higher strains on the cell. Conversely in high stimulus environments, the cell would shorten its cilium to reduce the strains to maintain ‘normal’ activity or prevent mechanically induced apoptosis. The deflection of the primary cilium creates further strain transmission to the cell’s nucleus, which could affect the regulatory activities of the cell (Satir et al., 2010). This strain transmission has been reported in experimental studies where researchers have strongly indicated that external mechanical strains are transduced into the cell nucleus and resisted by the nucleus lamina (see review by Dahl et al. (2008)), which is involved in tissue differentiation (Martins et al., 2012; Swift et al., 2012, 2013). But in order to elucidate whether primary cilium deflection actually affects the nucleus mechanoresponse, novel challenging in vitro experiments must be conducted that test whether nuclear shape is adapted to sole primary cilium deformations and whether the cilium deformations alter gene-transcription factors. Perhaps most interestingly are the simulations that show how cells equipped with primary cilia are also exposed to larger strains in the cytoplasm, in regions where the Golgi apparatus is known to

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be located. This organelle is believed to be involved in mechanosensation and alters cells’ synthesis in response to mechanical stimulation (Hicks and Machamer, 2005; Poole et al., 1997). Studies have previously shown that the Golgi centrosome and the microtubule centrosome are co-localised (Poole et al., 1985). This co-localisation could mean that the Golgi is also interconnected to the primary cilium, arguing that the close location of the two organelles normally implies a functional relationship (Poole et al., 1997) as experiments have found vesicular transport mechanisms between the two organelles (Hsiao et al., 2012). A recent study by Asante and colleagues has further shown that the Golgi protein Giantin is necessary for ciliogenesis (Asante et al., 2013). Considering that the Golgi apparatus plays a pivotal role in posttranslational modifications of proteins and the assembly of extracellular matrix, our simulation findings further agree with Poole et al.’s hypothesis (1997). They hypothesised that the primary cilium is involved in a sensory feedback loop where it collects extracellular signals, which are translated to the Golgi complex to enable new extracellular synthesis. In summary our simulations suggest that intra and extracellular signal translation may not only be biochemical but also biomechanical where essentially the length of the primary cilium regulates the magnitude of strain transmission to important intracellular components, regulating protein synthesis. If such interconnection is true, then this could be one of the mechanism behind for example the development of osteoarthritis (Chang et al., 2012), reduction of articular cartilage mechanical properties (Irianto et al., 2014), and impediment of growth plate proliferation, differentiation and organisation (Song et al., 2007), reported in transgenic mice with depleted primary cilia. Future studies must focus on investigating the interconnection between the primary cilium length and the centrosomal region, where the signalling between microtubules of the cell and primary cilium are likely to be affected by mechanical stimulation.

Conflicts of interest The authors have no conflicts of interest.

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