Fig. 7: Collective behaviors of binding memory.

Source data are provided as a Source Data file. a Temporal fluctuations in the total number of bound molecules within the system, analyzed across three independent simulation systems. b Autocorrelation function analysis of binding fluctuations, \({C}_{f}\). c Time evolution of the total binding pairs between initially selected molecules in 2D and 3D systems, both showing power-law tails. d Response of the binding pairs to a sudden weakening of binding affinity in a nonequilibrium simulation, exhibiting a power-law behavior during the transition. In the inset, the high-affinity state of the molecules is shown in red and the low-affinity state in black. The data points correspond to averages over 500 independent simulations for \({C}_{f}\), 25 for binding pair counting, and 100 for the response analysis. Error bars are obtained as standard deviations from these averages. Power-law fits and corresponding fitting errors for panels (b), (c), and (d) are included in the figure, with fitting range spanning \(2\times {10}^{4}\)−\(1.5\times {10}^{5}\) steps for (b), \(7\times {10}^{7}\)−\(3\times {10}^{8}\) (2D) and \(5\times {10}^{7}\)−\(1.2\times {10}^{8}\) (3D) for (c), and 300–6000 steps for (d).