Fig. 4: Evolution of dielectric permittivity with macromolecule concentration and ATP modulation.

a Effect of BSA concentration on the permittivity of PEG-BSA condensate systems. Top: average intensity projections of hyperspectral stacks for different initial BSA concentrations (indicated in white). Bottom: corresponding permittivity maps of the same regions, showing a gradual decrease in the depleted phase permittivity with increasing protein concentration. Scale bars: 10 µm. b Increasing the total BSA concentration lowers the permittivity of homogeneous protein solutions in water (blue circles) and BSA-depleted phase (diamonds), but has no significant effect on the PEG-BSA condensates (stars); see Fig. S6 for the respective permittivity maps. c Schematic phase diagrams of the PEG–BSA system (top) and the K₁₀-D₁₀ system (bottom). The solid black curves denote binodals; black dotted lines represent tie lines through given initial compositions (black dots). Black crosses indicate the compositions of the coexisting dense and depleted phases for these initial compositions in the absence of ATP. The purple dotted curves illustrate the expected shift of the binodal upon ATP addition, reflecting weakened intermolecular interactions. Correspondingly, purple crosses indicate the altered compositions of the coexisting phases in the presence of ATP. d Permittivity maps illustrating the effect of increasing ATP concentration on K₁₀-D₁₀ and BSA-PEG condensates. Each frame represents a 36.9 × 36.9 µm² sample area. The color bar (logarithmic scale) indicates permittivity. Left: permittivity maps of K₁₀-D₁₀ condensates showing increasing permittivity with ATP concentration. Right: permittivity maps of BSA-PEG condensates (10 wt% PEG, 0.375 mM BSA) demonstrating a similar trend. e Impact of ATP concentration on the permittivity of K₁₀-D₁₀, and BSA-PEG condensates (shown in d) and glycinin condensates (10 g/L total protein in 100 mM NaCl). Permittivity values in the absence of ATP are given in Fig. 2.