Matching material and cellular timescales maximizes cell spreading on viscoelastic substrates

Cell spreading speed is significantly different based on the elastic and viscous parameters (ka,kl, η) of the substrate. (A) Heat maps of spreading speed, Vs, plotted as a function of long-term stiffness, kl, and viscosity, η, from the ODE method. The substrate additional stiffness, ka, increases from 0.1 pN/nm to 10 pN/nm from Left to Right. (B) Mean spreading speed versus viscosity, η, under different values of ka (corresponding to the dashed lines in A) and a fixed kl of 0.1 pN/nm. There is an optimum viscosity that maximizes cell spreading, which becomes more significant as ka increases from 0.1 pN/nm to 0.5 pN/nm. Above ka = 5 pN/nm, the substrate behaves like a Kelvin−Voigt material with a sharp increase in cell spreading with viscosity. (C) The heat map of the optimum viscosity (for inducing maximum spreading speed) plotted as a function of long-term and additional stiffness. The spreading speed is maximized at intermediate viscosity in regime I, while a monotonic increase of the spreading speed with viscosity is observed in regime II. The symbols in C correspond to three cases for different k_a in B. Based on typical length of FAs (∼1 μm), a substrate stiffness of 1 pN/nm is equivalent to a modulus of 1 kPa (Supporting Information).

Optimal substrate viscosity is determined by the ratio between the substrate relaxation (τs) and clutch binding (τb) timescales. (A) Mean spreading speed plotted as a function of τs/τb for three different values of kl (with fixed initial stiffness ka+kl=1.1 pN/nm) shows that the greatest cell spreading occurs on a substrate where τs is slightly greater than τb. (B) Heat map of spreading speed, Vs, plotted as a function of the long-term stiffness, kl, and viscosity, η, calculated using the ODE method for ka=1 pN/nm. (C) Spreading speed vs. time for three typical values of η corresponding to the cross points in B, with dash-dotted lines representing the time average. The black line represents a highly viscous substrate that relaxes slowly such that the cells only sense the initial substrate stiffness (i.e., τs>τl>τb). The red line represents a substrate with low viscosity that relaxes quickly on which cells mainly sense the long-term stiffness (i.e., τs≪τb). The green line represents the optimal viscosity where the substrate relaxes during the FA lifetime (i.e., τs≈τb). (D) Schematic of three regimes for effect based on relaxation timescales: (I) when τs≪τb, the viscoelastic substrate has the same effect on cell spreading as an elastic substrate with the long-term stiffness kl; (II) when τs≈τb, the maximum spreading is observed on viscoelastic substrates; and (III) when τ_s τ_b, the viscoelastic substrate gives the same spreading speed as an elastic substrate with the initial stiffness ka+kl.

Model explains that viscosity increases cell spreading for substrates synthesized by combining a network of cross-linked polyacrylamide with linear acrylamide. (A) The method used to prepare viscoelastic gels: combining a network of cross-linked polyacrylamide (elastic) with linear polyacrylamide (viscous). (B) The relaxation stiffness as a function of time for cross-linked polyacrylamide substrate (elastic, blue dots) and cross-linked polyacrylamide and linear acrylamide substrate (viscoelastic, red dots). (Inset) Fitting of the relaxation time spectra (black line) for the normalized stiffness of the viscoelastic substrate (red dot markers). (C) Relaxation spectra of the viscoelastic substrate shows that τ=1 s is the dominant relaxation timescale greater than the binding timescale. (Inset) The generalized Maxwell model with multiple relaxation timescales. (D) For gels synthesized with this method (A), viscosity increases cell spreading 4 h after seeding, where a significant difference (n ≥ 180 cells, **P < 0.01, Student’s test) is observed. Note that cross and triangle symbols show the simulated cell spreading area on elastic and viscoelastic substrate, respectively. (E) The relevant positions are also marked on the heat map of spreading speed for ka=1 pN/nm. The trend predicted by the model agrees with the experimental cell spreading area.

Model explains that viscosity has no effect on cell spreading for substrates synthesized by combining covalent and supramolecular cross-linkers. (A) The method used to prepare viscoelastic gels: combining covalent and supramolecular cross-linkers (see Methods). (B) The relaxation stiffness as a function of time for covalently cross-linked substrate (elastic, blue dots) and covalent and supramolecular cross-linked substrate (viscoelastic, red dots). (Inset) Fitting of the relaxation time spectra (black line) for the normalized stiffness of viscoelastic substrates (red dot markers). (C) The relaxation spectrum H(τ) was plotted as a function of the relaxation timescale τ, which represents (Inset) the generalized Maxwell model. There is no apparent relaxation timescale that is larger than (or comparable to) the binding timescale (τb ≈ 1 s). (D) For substrates synthesized with the method in A, cell spreading area was similar for elastic and viscoelastic substrates; n≥ 80 cells, and n.s. indicates that no statistically significant difference is observed (using the Student’s test). Note that cross and triangle symbols show the simulated cell spreading area on elastic and viscoelastic substrate, respectively. (E) The relevant positions are also marked on the heat map of spreading speed for ka=0.1 pN/nm. The trend predicted by the model agrees with the experimental cell spreading area.

Model explains experimental findings that viscosity increases cell spreading for low initial stiffness and suppresses cell spreading for high initial stiffness. (A–C) Heat maps of spreading speed, Vs, plotted as a function of the long-term stiffness, kl, and viscosity, η, calculated using the ODE method for a fixed initial stiffness of (A) 1.4 kPa, (B) 3.4 kPa, and (C) 9 kPa. Crosses and circles indicate the measured properties of the elastic and viscoelastic substrates used for experiments in ref. 4. (see Supporting Information for more details). The viscoelastic relaxation spectrum for this system is given in Fig. S6. (D) Quantification of the cell spreading area as a function of the initial moduli of cells on elastic (gray) or viscoelastic (maroon) substrates. Reprinted with permission from ref. 4. Data are shown as mean ± SD, and ***P < 0.001 (Student’s t test). (E) Model predictions for cell spreading on elastic (gray) or stress-relaxing (maroon) substrates exhibit a behavior similar to the experimental results, where substrate viscosity leads to an increase in cell spreading at a low initial stiffness and decrease in spreading at high initial stiffness.