Interplay between Mechanochemical Patterning and Glassy Dynamics in Cellular Monolayers

Living tissues are characterized by an intrinsically mechanochemical interplay of active physical forces and complex biochemical signaling pathways. Either feature alone can give rise to complex emergent phenomena, for example, mechanically driven glassy dynamics and rigidity transitions, or chemically driven reaction-diffusion instabilities. An important question is how to quantitatively assess the contribution of these different cues to the large-scale dynamics of biological materials. We address this in Madin-Darby canine kidney (MDCK) monolayers, considering both mechanochemical feedback between extracellular signal-regulated kinase (ERK) signaling activity and cellular density as well as a mechanically active tissue rheology via a self-propelled vertex model. We show that the relative strength of active migration forces to mechanochemical couplings controls a transition from a uniform active glass to periodic spatiotemporal waves. We parametrize the model from published experimental data sets on MDCK monolayers and use it to make new predictions on the correlation functions of cellular dynamics and the dynamics of topological defects associated with the oscillatory phase of cells. Interestingly, MDCK monolayers are best described by an intermediary parameter region in which both mechanochemical couplings and noisy active propulsion have a strong influence on the dynamics. Finally, we study how tissue rheology and ERK waves produce feedback on one another and uncover a mechanism via which tissue fluidity can be controlled by mechanochemical waves at both the local and global levels.

Figure 1

(a) Schematic of the three-dimensional forces exerted on cells in confluent monolayers. The in-plane cell area is determined by a balance of cytoskeletal forces on the basal and lateral sides, which can be modulated by ERK signaling activity [22, 24]. (b) Schematic of the mechanochemical couplings considered in the model. The ERK signaling activity impacts on preferred cell area $A_0$ with coupling strength $\alpha$, creating mechanical stresses for cells with area $A$ below or above this preferred value. This, together with stresses from self-propulsion forces $f_0$, results in changes in area $A$ which feeds back on ERK with coupling strength $\beta$. (c) Schematic of the in-plane 2D vertex model, its associated energy, and persistent random motility forces $f_0$.

Figure 2

(a) and (b) Relative amplitude of area to ERK oscillation ${\sigma }_A/{\sigma }_{\text{ERK}}$ vs ratio of mechanochemical coupling constants $\alpha /\beta$, showing that different values of the product $\alpha \beta$ robustly scale along the same master curve, allowing us to fit $\alpha /\beta$ from the experimentally observed value of ${\sigma }_A/{\sigma }_{\text{ERK}}$ (dashed lines; see also Fig. S3B in [36]). (c) Phase diagram of mechanochemical patterning in a 2D vertex model with ERK signaling activity and self-propulsion, as a function of active self-propulsion forces $f_0$ (which introduce persistent noise in the system) and the relative strength of mechanical and chemical couplings $\alpha /\beta$ (see Fig. S4 in [36] for a phase diagram as a function of the product $\alpha \beta$).

Figure 3

(a) Overview of the tissue-level analysis of ERK patterning. Local cellular phases of ERK signaling activity are smoothed into continuous fields containing $+/-$ topological defects. (b) Phase field of ERK activity (color coded for phase), for different values of active self-propulsion $f_0$ together with the identification and tracking in time of topological defects (white and black squares indicate $+1$ and $-1$ charges, respectively). (c) Phase field of ERK activity in MDCK monolayers, with the same analysis as in (b). (d) Experimental lifetime of ERK phase topological defects in MDCK monolayers, showing a good fit to an exponential distribution as observed in simulations. (e) Average lifetime of ERK phase topological defects in the simulations as a function of active self-propulsion $f_0$, for different values of mechanochemical coupling strength ${\epsilon }_{\alpha \beta }=(\alpha \beta -{\alpha \beta }_{\text{c}})/{\alpha \beta }_{\text{c}}$. Shaded intervals indicate experimental values of mean defect lifetime and estimates of $f_0$, showing that model values of ${\epsilon }_{\alpha \beta }\approx 0.8$ and $f_0=0.125–1.5$ explain the experimental lifetime data while also being consistent with predictions of $\alpha , \beta$, and $f_0$ from ERK and area amplitudes (Figs. S3D– S3F in [36]). (f) Representative tracks of ERK dynamics in the simulations for different values of $f_0$ (top) together with corresponding autocorrelation functions (bottom), showing that larger active self-propulsion noise (larger $f_0$) causes rapid decays, as quantified by the amplitude of the first peak (dashed horizontal lines). (g) Distribution of first-peak amplitudes of ERK autocorrelation across MDCK cells (with fit to normal distribution, see the Supplemental Material [36] for details). (h) First-peak amplitude of the ERK autocorrelation in simulations as a function of active self-propulsion $f_0$ and mechanochemical couplings ${\epsilon }_{\alpha \beta }$. Shaded intervals indicate estimates of $f_0$ as in (e) and the experimental measurement of first-peak amplitude from (g).

Figure 4

(a) Representative snapshots for the mapping of cell-cell rearrangements (T1 transitions, white circles) to local ERK activity (or phase; see Fig. S7 in [36] for color code) in vertex-model simulations. (b) Distribution of T1 transition probability as a function of ERK phase, for different values of active self-propulsion force $f_0$, showing strong anticorrelation with ERK activity (the black curve shows absolute value and color shows phase) and T1 transitions.