Fig. 2: The glassy motor-clutch model captures both sub- and super-diffusive migration modes modulated by substrate stress relaxation.

A Schematic representation of the 2D motor clutch model illustrating cell migration on a viscoelastic substrate. The model utilizes independent clutch modules in the X and Y directions. B Energy landscape depicting protein unfolding with multiple pathways, each with varying off rates. C Probability density function (PDF) for the off-rate time constant with varying glass coefficient (\(\beta=1.5,\,3,\,10\)). D Cumulative distribution function (CDF) of the power law distribution used for sampling off rates (\(\beta=1.5,\,3,\,10\)). E Heatmap illustrating variation in migration diffusivity parameter (\(\alpha\)) with viscosity \((\eta )\) and glass coefficient \((\beta )\). Higher values of \(\beta\) fail to capture both sub- and super-diffusive regimes, underscoring the importance of long-tails in distribution. F Glassy motor clutch model. (i) MSD time curves show that cells on fast-relaxing substrates tend to travel longer distances compared to their slow-relaxing counterparts and consequently have a higher slope. (ii) Diffusivity exponent (\(\alpha\)) values representing the diffusive mode. Cells on slow-relaxing substrates exhibit sub-diffusive behavior, while those on fast-relaxing substrates display super-diffusive behavior. The unpaired two-tailed Student’s t test was used for data analysis: P = 2.01E−06; n = 5 (fast) and 5 (slow) fits, each for 100 independent simulations. (iii) Glassy model captures trends in track straightness and VAC. Enhanced substrate relaxation promotes directional migration, reflected in the higher velocity autocorrelation observed for cells on fast-relaxing substrates. The unpaired two-tailed Student’s t-test was used for data analysis: P = 0.00048; n = 50 (fast) and 50 (slow) independent cell trajectory simulations. (iv) Normalized VAC function decays more slowly for fast-relaxing substrates compared to medium- or slow-relaxing substrates. (Black lines represent mean in the violin plots. ‘ns’ represents not significant p > 0.05, *p < 0.05, **p < 0.01, ***p < 0.001, ****p < 0.0001).