Riding the Wave: Polymers in Time-dependent Nonequilibrium Baths

TL;DR

It is shown that the response of polymeric systems to temporal stimuli can be controlled by the topology or the length of the polymer, showing that the response of polymeric systems to temporal stimuli can be controlled by the topology or the length of the polymer.

Abstract

Directed transport is a characteristic feature of numerous biological systems in response to signals such as nutrient and chemical gradients. These signals often depend on time owing to the high complexity of interactions in these systems. In this study, we focus on the steady-state behavior of polymeric systems responding to such time-dependent signals. We model them as ideal Rouse polymers submerged in a nonequilibrium bath, which is described by a spatially and temporally varying self-propulsion wave field. Through a coarse-graining analysis, we show that these polymers display rich emergent response to the temporal stimuli as a function of their length and topology. In particular, long polymers and structures with ring and star topologies ride the wave, displaying a positive drift in the direction of the wave. Whereas, shorter polymers and fully connected structures drift against the wave signal. We confirm these analytical predictions with robust numerical simulations, showing that the response of polymeric systems to temporal stimuli can be controlled by the topology or the length of the polymer.

Figures (5)

• Figure 1: Schematic of active polymers of varying lengths and connectivity experiencing an activity signal, varying in space and time. The signal is represented as a traveling wave $v_a(\boldsymbol{x},t)$ propagating along $\hat{e}_w$. Polymers with a higher degree of polymerization and low connectivity follow the wave peaks and drift in the wave direction, whereas, shorter polymers and fully connected structures follow the wave valleys and drift against the wave.
• Figure 2: Steady state density profiles for linear active polymers of different lengths in $2$-dimensions. The bottom panel shows the activity field $f_s(x) = v_0[1+\sin(4\pi x/L)]$ experienced by the active monomers. The $y$-axis in the top panel is normalized with the bulk density, defined as $\rho_b = 1/L$, where $L=10.0$ is the simulation box size with periodic boundary conditions. The parameters of the simulation are $v_w=10^{-2}$, $k_{B}T=10^{-3}$, $k=5.0$, $\gamma=1.0$, $D_{R} = 10.0$, and $v_0 = 1.0$.
• Figure 3: Steady state density profiles for active polymers of different architecture (topology) in $2$-dimensions, each composed of $N=6$ monomers. The bottom panel shows the activity field $f_s(x) = v_0[1+\sin(4\pi x/L)]$ experienced by the active particle. The $y$-axis in the top panel is normalized with the bulk density, defined as $\rho_b = 1/L$, where $L=10.0$ is the simulation box size with periodic boundary conditions. The parameters of the simulation are $v_w=10^{-2}$, $k_{B}T=10^{-1}$, $k=5.0$, $\gamma=1.0$, $D_{R} = 5.0$, and $v_0 = 1.0$.
• Figure 4: Average drift for different lengths of the linear active polymers in $2$-dimensions. The activity profile is the same as in Fig. \ref{['fig:steady_state_density_waves_length']}. Simulation parameters are: $k_{B}T=10^{-2}$, $k=5.0$, $\gamma=1.0$, $D_{R} = 10.0$, and $v_0 = 1.0$. The results are obtained by running $10^{3}$ independent trajectories and averaging $(X_{\text{COM}}(t) - X_{\text{COM}}(0))/t$ over these trajectories.
• Figure 5: Average drift for different architectures of the active polymers with $N=6$ monomers in $2$-dimensions. The activity profile is the same as in Fig. \ref{['fig:steady_state_density_waves_topology']}. Simulation parameters are: $k_{B}T=10^{-1}$, $k=5.0$, $\gamma=1.0$, $D_{R} = 5.0$, and $v_0 = 1.0$. The results are obtained by running $10^{3}$ independent trajectories and averaging $(X_{\text{COM}}(t) - X_{\text{COM}}(0))/t$ over these trajectories.