Fig. 8: Numerical simulations of the directional motion.

a Representative schematic of the model used. Photoreversible ‘Liquid’ and ‘Dissociated’ states in a DNA condensate undergo events (1) – (5) over two intervals, UV-to-Vis and Vis-to-UV, each with an interval length T. Besides an elapsed time t from the start, a lap time \({t}^{{\prime} }\) periodically runs from 0 to T within each interval. \(u\left(t\right)\) and \(x(t)\) are the 1D velocity and position, respectively, of ‘Liquid’ domain. It is driven by b photoswitched mass transport between the binary states during each interval. The alternate opposite transfers over a time step \(\Delta t\) are illustrated. The masses of the binary states are respectively denoted as \({m}_{\rm L}(t)\) and \({m}_{\rm D}(t).A\left({t}^{{\prime} }\right)\) and B (constant) are disassembly ratios, which refer to a fraction of the constituting motifs being transferred from one state to the other per unit time. Halfway through the transfers, the state-switching motifs diffuses away from the cycle reactions with disengagement ratios: \(\lambda ({t}^{{\prime} })\) in UV-to-Vis and κ (constant) in Vis-to-UV intervals. c Simulated time evolutions of the masses of the binary states, \({m}_{\rm L}(t)\) and \({m}_{\rm D}(t)\), and the velocity \(u(t)\) and position \(x(t)\) of ‘Liquid’ domain. Low, intermediate, and high switching frequencies f are highlighted. Simulations started with \({m}_{\rm L}\left(t\right)=100,{m}_{\rm D}\left(t\right)=0\), and Δt = 0.01. \({t}^{*}\) refers to a characteristic diffusion time of 800Δt.