Primary cilium mechanotransduction of tensile strain in 3D culture: Finite element analyses of strain amplification caused by tensile strain applied to a primary cilium embedded in a collagen matrix

Abstract

Human adipose-derived stem cells (hASC) exhibit multilineage differentiation potential with lineage specification that is dictated by both the chemical and mechanical stimuli to which they are exposed. We have previously shown that 10% cyclic tensile strain increases hASC osteogenesis and cell-mediated calcium accretion. We have also recently shown that primary cilia are present on hASC and that chemically-induced lineage specification of hASC concurrently results in length and conformation changes of the primary cilia. Further, we have observed cilia length changes in hASC cultured within a collagen I gel in response to 10% cyclic tensile strain. We therefore hypothesize that primary cilia may play a key mechanotransduction role for hASC exposed to tensile strain. The goal of this study was to use finite element analysis (FEA) to determine strains occurring within the ciliary membrane in response to 10% tensile strain applied parallel, or perpendicular, to cilia orientation. To elucidate the mechanical environment experienced by the cilium, several lengths were modeled and evaluated based on cilia lengths measured on hASC grown under varied culture conditions. Principal tensile strains in both hASC and ciliary membranes were calculated using FEA, and the magnitude and location of maximum principal tensile strain determined. We found that maximum principal tensile strain was concentrated at the base of the cilium. In the linear elastic model, applying strain perpendicular to the cilium resulted in maximum strains within the ciliary membrane from 150% to 200%, while applying strain parallel to the cilium resulted in much higher strains, approximately 400%. In the hyperelastic model, applying strain perpendicular to the cilium resulted in maximum strains within the ciliary membrane around 30%, while applying strain parallel to the cilium resulted in much higher strains ranging from 50% to 70%. Interestingly, FEA results indicated that primary cilium length was not directly related to ciliary membrane strain. Rather, it appears that cilium orientation may be more important than cilium length in determining sensitivity of hASC to tensile strain. This is the first study to model the effects of tensile strain on the primary cilium and provides newfound insight into the potential role of the primary cilium as a mechanosensor, particularly in tensile strain and potentially a multitude of other mechanical stimuli beyond fluid shear.

Keywords: Adipose derived stem cells; Ciliary membrane; Ciliary pocket; Finite element analysis; Mechanobiology; Mechanotransduction; Primary cilia; Tensile strain.

Figure 1

Primary cilia on hASC visualized by acetylated -tubulin (green), in 3D collagen I culture with further staining for IFT88 (red) (a) and in 2D culture with further staining for actin (red) (b). DAPI = Nuclei (Blue). Scale bar represents 25 μm.

Figure 2

Boundary conditions and geometry for linear elastic model. A) Primary cilium model shown with cell and ciliary membrane in purple. Collagen gel is shown in pink. B) Perpendicular strain is applied along the x-axis. C) Parallel strain is applied along the z-axis.

Figure 3

Boundary conditions and applied forces for the hyperelastic model. A) Perpendicular strain is applied along the x-axis by holding one face of the cube and displacing the opposite face. B) Parallel strain is applied along the x-axis by holding one face of the cube and displacing the opposite face.

Figure 4

Representative images showing strain amplification at the cilium base in the linear elastic model. Principal tensile strain is shown in the cell and ciliary membrane for a primary cilium 3.05μm in length. Cilium strained perpendicular to cilium orientation (A, B) exhibited less membrane strain than cilium strained parallel to cilium orientation (C, D). Both directions of applied tensile strain result in strain concentrations at the cilium base.

Figure 5

Maximum principal tensile strain in the ciliary membrane in the linear elastic model for cilium with 10% tensile strain applied to surrounding collagen gel either parallel or perpendicular to the cilium. Perpendicular strain induces maximum tensile strain in the range of 150-200% while parallel strain shows maximum strains between 300-400%. There is no apparent trend between cilium length and magnitude of maximum principal tensile strain. ODM = osteogenic differentiation medium; CGM = complete growth medium; ADM = adipogenic differentiation medium.

Figure 6

Representative images showing strain amplification at the cilium base in the hyperelastic model. Principal tensile strain is shown in the cell and ciliary membrane for a primary cilium 3.05μm in length. Cilium strained perpendicular to cilium orientation (A, B) exhibited less membrane strain than cilium strained parallel to cilium orientation (C, D). Both directions of applied tensile strain result in strain concentrations at the cilium base.

Figure 7

Maximum principal tensile strain in the ciliary membrane in the hyperelastic model for cilium with 10% tensile strain applied to surrounding collagen gel either parallel or perpendicular to the cilium. Perpendicular strain induces maximum principal tensile strains within the ciliary membrane around 30% while parallel strain induces maximum principal tensile strains within the ciliary membrane between 50-70%. There is no apparent trend between cilium length and magnitude of maximum principal tensile strain. ODM = osteogenic differentiation medium, 2.72 m = primary cilium length used for ODM model; CGM = complete growth medium, 3.05 m = primary cilium length used for CGM model; ADM = adipogenic differentiation medium, 3.90 m = primary cilium length used for ADM model.