Shifting the optimal stiffness for cell migration

Abstract

Cell migration, which is central to many biological processes including wound healing and cancer progression, is sensitive to environmental stiffness, and many cell types exhibit a stiffness optimum, at which migration is maximal. Here we present a cell migration simulator that predicts a stiffness optimum that can be shifted by altering the number of active molecular motors and clutches. This prediction is verified experimentally by comparing cell traction and F-actin retrograde flow for two cell types with differing amounts of active motors and clutches: embryonic chick forebrain neurons (ECFNs; optimum ∼1 kPa) and U251 glioma cells (optimum ∼100 kPa). In addition, the model predicts, and experiments confirm, that the stiffness optimum of U251 glioma cell migration, morphology and F-actin retrograde flow rate can be shifted to lower stiffness by simultaneous drug inhibition of myosin II motors and integrin-mediated adhesions.

Figure 1. Cell migration simulator.

(a) Schematic of a motor–clutch module attached to the central cell body. Additional modules may also extend from the cell body but are not shown here for simplicity. (b) Representative schematic of the cell migration simulator overlaid on top of a phase-contrast image of U251 glioma cell. This image demonstrates how the simulator captures the three main protrusions of the cell. (c–f) Plots of simulator outputs for the cases of low (1,000 motors and 750 clutches) and high (10,000 motors and 7,500 clutches) are shown. (c) For the low case, the actin retrograde flow minimum occurs around a spring constant of 0.1 pN nm⁻¹, and for the high case it occurs at ∼1 pN nm⁻¹. (d) For both the low and high number of motor and clutches cases, the traction force maximum occurs at ∼0.1 pN nm⁻¹ and the high case producing ∼10-fold more force. (e) For both low and high motors and clutches, cell aspect ratio has a maximum of ∼10 pN nm⁻¹. (f) For low motors and clutches, random motility coefficient peaks at ∼10 pN nm⁻¹, whereas for high motors and clutches, it peaks at ∼1 pN nm⁻¹. (g) The composite metric, created to mathematically combine all four metrics, and fit Gaussian curves' peaks show a statistically significant shift in the optimum stiffness for the low and high motors and clutches cases (P=0.0001). All error bars are s.e.m. The number of observations for each condition can be found in Supplementary Table 3.

Figure 2. U251 glioma cell migration and morphology have maxima with respect to substrate Young's modulus.

(a) Representative images of U251 glioma cells on 4.6, 100 and 200 kPa Young's moduli polyacrylamide gels. (b) Wind-rose plots of cell trajectories on 4.6, 100 and 200 kPa. Ten randomly selected cell trajectories over 10 h are shown for each condition. (c) Cell random motility coefficient has a maximum between 20 and 200 kPa (P=0.04). (d) Projected cell area has a potential maximum at ∼200 kPa or higher. (e) Cell aspect ratio has a potential maximum at ∼9 kPa. All error bars are s.e.m. The number of observations for each experiment can be found in Supplementary Table 3.

Figure 3. Actin retrograde flow and traction strain energy of U251 glioma cells versus ECFNs.

(a) Representative fluorescent image of an EGFP-actin U251 glioma cell on a 100 kPa polyacrylamide gel. The boxed region represents an area selected for an actin flow kymograph. (b) Actin flow kymograph for a U251 glioma cell on a 100 kPa polyacrylamide gel. Horizontal bar is 2 μm. Vertical bar is 30 s. (c) Embryonic chick forebrain neuron (ECFN; data taken from Chan and Odde7) and U251 glioma cell actin retrograde flow versus substrate stiffness. U251 actin flow has a minimum between 9 and 200 kPa (P=0.004). (d) Representative phase-contrast images with traction field overlays of an ECFN and a U251 glioma cell on 700 Pa polyacrylamide gels. Traction vectors were thinned fourfold for ease of visualization. (Inset) Region of ECFN with traction vectors expanded by 60-fold. (e) Mean strain energy of ECFNs and U251 glioma cells on 700 kPa polyacrylamide gels. U251 strain energy is significantly higher than for ECFNs (P=10–24). (f) U251 stain energy has a maximum between 4.6 and 20 kPa (P=0.0002). ECFN data were adapted from Chan and Odde. All error bars are s.e.m. The number of observations for each experiment can be found in Supplementary Table 3.

Figure 4. Simultaneous inhibition of motors and clutches shifts the optimum stiffness to lower Young's modulus.

(a) Addition of both drugs shifted the minimum actin flow rate to ∼4.6 kPa. cylco(RGDfV) alone increased actin flow on both 4.6 and 100 kPa, while blebbistatin alone reduced actin flow on 4.6 kPa but not significantly on 100 kPa. The combined drug treatment reduced actin flow on 4.6 kPa but did not significantly affect actin flow on 100 kPa. (b) Addition of both drugs decreased traction strain energy by approximately fourfold on all stiffnesses. The maximum traction strain energy maintained its maximum at ∼9 kPa. However, the combined drug treatment increased the traction strain energy compared with either individual drug treatment on 4.6 kPa. (c) Addition of both drugs caused the maximum area to be ∼9 kPa. On 4.6 kPa, the addition of both drugs increased the cell area, while on 100 kPa they decreased the cell area. (d) Addition of both drugs did not shift the maximum aspect ratio. On 4.6 kPa, blebbistatin individually and both drugs combined increase the aspect ratio. None of the drugged cases had a significant effect on the aspect ratio on 100 kPa. (e) Simultaneous addition of 6 μM blebbistatin and 0.6 μM cyclo(RGDfV) shifts the potential maximum U251 glioma cell random motility coefficient to ∼4.6 kPa. On 4.6 kPa, addition of both drugs increases the random motility coefficient compared with the no drug, blebbistatin and cylco(RGDfV) cases. On 100 kPa, all three drugged cases are lower than the no drug case, but addition of both drugs increases the random motility coefficient compared with either single drug case. (f) A composite metric with corresponding Gaussian fit curves demonstrates the shifting in stiffness optimum among U251 glioma cells, U251 glioma cells treated with blebbistatin and cyclo(RGDfV) and ECFNs. Gaussian fit curves peaks show a statistically significant shift in the optimum stiffness for the untreated and treated U251 glioma cell composite metric (P=0.015). (g) Illustration of how same drug treatment may result in opposite effects in different mechanical environments. P values for all bar chart comparisons are presented in Supplementary Table 4. All error bars are s.e.m. The number of observations for each experiment can be found in Supplementary Table 3.