Artificial protocells operating under non-equilibrium conditions offer a new approach to achieve dynamic features with life-like properties. Using coacervate micro-droplets comprising polylysine (PLL) and a short single-stranded oligonucleotide (ss-oligo) as a membrane-free protocell model, we demonstrate that circulation and vacuolization can occur simultaneously inside the droplet in the presence of an electric field. The circulation is driven by electrohydrodynamics and applies specifically to the major components of the protocell (PLL and ss-oligo). Significantly, under low electric fields (E = 10 V cm⁻¹) the circulation regulates the movement of the vacuoles, while high levels of vacuolization produced at higher electric fields can deform or reshape the circulation. By taking advantage of the interplay between vacuolization and circulation, we achieve dynamic localization of an enzyme cascade reaction at specific droplet locations. In addition, the spatial distribution of the enzyme reaction is globalized throughout the droplet by tuning the coupling of the circulation and vacuolization processes. Overall, our work provides a new strategy to create non-equilibrium dynamic behaviors in molecularly crowded membrane-free synthetic protocells.

Using Brownian dynamics, we study the dynamical behavior of a polymer grafted onto an adhesive surface close to the mechanically induced adsorption-stretching transition. Even though the transition is first order (in the infinite chain length limit, the stretching degree of the chain jumps discontinuously), the characteristic relaxation time is found to grow according to a power law as the transition point is approached. We present a dynamic effective interface model which reproduces these observations and provides an excellent quantitative description of the simulation data. The generic nature of the theoretical model suggests that the unconventional mixing of features that are characteristic for first-order transitions (a jump in an order parameter) and features that are characteristic of critical points (an anomalous slowdown) may be a common phenomenon in force-driven phase transitions of macromolecules.

We use Brownian dynamics simulations and analytical theory to compare two prominent types of single molecule transitions. One is the adsorption transition of a loop (a chain with two ends bound to an attractive substrate) driven by an attraction parameter ε and the other is the loop-stretch transition in a chain with one end attached to a repulsive substrate, driven by an external end-force F applied to the free end. Specifically, we compare the behavior of the respective order parameters of the transitions, i.e., the mean number of surface contacts in the case of the adsorption transition and the mean position of the chain end in the case of the loop-stretch transition. Close to the transition points, both the static behavior and the dynamic behavior of chains with different length N are very well described by a scaling ansatz with the scaling parameters (ε − ε*)N^ϕ (adsorption transition) and (F − F^*)N^ν (loop-stretch transition), respectively, where ϕ is the crossover exponent of the adsorption transition and ν is the Flory exponent. We show that both the loop-stretch and the loop adsorption transitions provide an exceptional opportunity to construct explicit analytical expressions for the crossover functions which perfectly describe all simulation results on static properties in the finite-size scaling regime. Explicit crossover functions are based on the ansatz for the analytical form of the order parameter distributions at the respective transition points. In contrast to the close similarity in equilibrium static behavior, the dynamic relaxation at the two transitions shows qualitative differences, especially in the strongly ordered regimes. This is attributed to the fact that the surface contact dynamics in a strongly adsorbed chain is governed by local processes, whereas the end height relaxation of a strongly stretched chain involves the full spectrum of Rouse modes.