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Register a new userSemiflexible polymer in a gliding assay: reentrant transition, role of turnover and activity
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We consider a model of an extensible semiflexible filament moving in two dimensions on a motility assay of motor proteins represented explicitly as active harmonic linkers. Their heads bind stochastically to polymer segments within a capture radius, and extend along the filament in a directed fashion before detaching. Both the extension and detachment rates are load-dependent and generate an active drive on the filament. The filament undergoes a first order phase transition from open chain to spiral conformations and shows a reentrant behavior in both the active extension and the turnover, defined as the ratio of attachment-detachment rates. Associated with the phase transition, the size and shape of the polymer changes non-monotonically, and the relevant autocorrelation functions display double-exponential decay. The corresponding correlation times show a maximum signifying the dominance of spirals. The orientational dynamics captures the rotation of spirals, and its correlation time decays with activity as a power law.
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By means of Metropolis Monte Carlo simulations of a coarse-grained model for flexible polymers, we investigate how the integrated autocorrelation times of different energetic and structural quantities depend on the temperature. We show that, due to critical slowing down, an extremal autocorrelation time can also be considered as an indicator for the collapse transition that helps to locate the transition point. This is particularly useful for finite systems, where response quantities such as the specific heat do not necessarily exhibit clear indications for pronounced thermal activity.
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We characterize cell motion in experiments and show that the transition to collective motion in colonies of gliding bacterial cells confined to a monolayer appears through the organization of cells into larger moving clusters. Collective motion by non-equilibrium cluster formation is detected for a critical cell packing fraction around 17%. This transition is characterized by a scale-free power-law cluster size distribution, with an exponent $0.88pm0.07$, and the appearance of giant number fluctuations. Our findings are in quantitative agreement with simulations of self-propelled rods. This suggests that the interplay of self-propulsion of bacteria and the rod-shape of bacteria is sufficient to induce collective motion.
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By embedding inert tracer particles (TPs) in a growing multicellular spheroid the local stresses on the cancer cells (CCs) can be measured. In order for this technique to be effective the unknown effect of the dynamics of the TPs on the CCs has to be elucidated to ensure that the TPs do not greatly alter the local stresses on the CCs. We show, using theory and simulations, that the self-generated (active) forces arising from proliferation and apoptosis of the CCs drive the dynamics of the TPs far from equilibrium. On time scales less than the division times of the CCs, the TPs exhibit sub-diffusive dynamics (the mean square displacement, $Delta_{TP}(t) sim t^{beta_{TP}}$ with $beta_{TP}<1$), similar to glass-forming systems. Surprisingly, in the long-time limit, the motion of the TPs is hyper-diffusive ($Delta_{TP}(t) sim t^{alpha_{TP}}$ with $alpha_{TP}>2$) due to persistent directed motion for long times. In comparison, proliferation of the CCs randomizes their motion leading to superdiffusive behavior with $alpha_{CC}$ exceeding unity. Most importantly, $alpha_{CC}$ is not significantly affected by the TPs. Our predictions could be tested using textit{in vitro} imaging methods where the motion of the TPs and the CCs can be tracked.
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