Supplementary MaterialsMovie S1. in a significant deformation of the underlying substrate if it is softer than the cells. This smooth substrate effect leads to an underestimation of a cells elastic modulus when analyzing data using a standard Hertz model, as confirmed by finite element modelling (FEM) and AFM measurements of calibrated polyacrylamide beads, microglial cells, and fibroblasts. To account for this substrate deformation, we developed the composite cell-substrate model (CoCS model). Correcting for the substrate indentation exposed that cortical cell tightness is largely self-employed of substrate mechanics, which has significant implications for our interpretation of many physiological and pathological processes. and the overall sample indentation is MCHr1 antagonist 2 mostly modeled using the Hertz model14, which in the case of a spherical probe is as follows: is the probe radius, and its deflection is used to calculate the applied push is the cantilevers spring constant. The indentation depth C is definitely inferred from these quantities based on the important assumption the sample is definitely deformed but not the underlying substrate. However, while this condition is clearly fulfilled for cells cultured on glass or cells tradition plastics, it may no longer hold for cells cultured on smooth matrices mimicking the mechanical properties of the physiological cell environment16. Results AFM indentation pushes cells into smooth substrates Indeed, when we cultured microglial cells on polyacrylamide substrates with stiffnesses ranging from = of around 0.1m/nN for stiff substrates MCHr1 antagonist 2 (Fig. 1c) and a significantly larger deformability of c~0.9m/nN for soft substrates (Fig. 1d) (observe also Supplementary Figs. 1g-i, 2e). Open in a separate window Number 1 Quantification of substrate displacements in AFM indentation measurements of cells. (a, b) Confocal profiles of microglial cells (orange) cultured on (a) stiff ( 2 kPa) and (b) smooth ( 100 Pa) substrates (green). The AFM probe (blue) is definitely applying a loading push of = 1 nN on each cell. Level bars: 10 m. (c, d) Relationship between substrate displacements from confocal images of the cells demonstrated in (a) and (b) and the applied push on (c) stiff and (d) smooth substrates (observe also Supplementary Fig. 1g-i). Causes exerted on cells by AFM indentation result in significant deformations particularly of smooth substrates. Experiments are representative for (a, c) and 6 (b, d) self-employed measurements on = 5 cells each with related results. (e) Schematic of an AFM cantilever having a spherical probe of radius pushing on a cell with elastic modulus bound to a substrate with elastic modulus is a combination of the indentation of the cell, MCHr1 antagonist 2 denotes vertical cantilever displacement, cantilever deflection. (f) Schematic of the mechanical ENTPD1 system, consisting of the two springs in series, which both experience the same push. The tip-cell contact follows the nonlinear Hertz model14, and the cell-substrate contact follows a linear force-indentation connection due to the mainly constant contact area, MCHr1 antagonist 2 similar to other analytical contact models19. Hence, the indentation inferred from AFM measurements is actually the sum of the indentation of the cell C = = 7 self-employed measurements with related results. We consequently assumed an axisymmetric stress distribution with maximum stress of 0 below the cell center and linear decrease from the center to zero inside a range approximated from the cell radius (Fig. 2b). The substrate deformation can then become approximated from the elastic response of a semi-infinite half space due to axisymmetric stress distribution on a circular region, also known as the Boussinesq remedy19: = 2/3, and may become interpreted as the effective substrate deformability, and as free parameters, allows the determination of the cells elastic modulus and the substrate deformability individually of each additional. We termed this approach the composite cell-substrate model (CoCS model). The CoCS model can easily become adapted to additional Poissons ratios or tip geometries (for example for conical/pyramidal suggestions using = 1/2 and a different connection for according to the respective contact model21,22), and that the tip geometry only affects = 0.5 indicates the measured total.