a, Schematic illustration of dynamic properties near a phase boundary. Orange particles have self-association properties (green dotted lines) and concentrate into a phase (orange background, right side). An orange particle in the orange phase can move in any direction and encounter only orange particles (eight arrows) until it contacts a blue particle, which prevents self-association between two orange particles and limits the potential diffusion dimensions of the orange particle (red squiggle, loss of arrows). This results in two properties of particles near the phase boundary: net slower diffusion and higher likelihood that two orange particles will move in the same direction. b, Schematic illustrating number and brightness technique22. If particles are moving independent of one another (left, blue), variations in fluorescence intensity measured in the pixel volume over time will be small. If particles are moving together in and out of the pixel volume (right, red), intensity variation will be larger. This can result from bound molecules (that is, complex) or unbound molecules moving in the same direction (coordinated movement). c, A cultured Drosophila S2 cell expressing GFP-tagged fibrillarin to mark the nucleolus (left). Inset shows entire nucleus (dotted line) and region of interest (white box). Visual representation of increased variance measured by number and brightness (middle), colour scale represented in quantification graph (right). Quantification of variance (right) across the border from nucleoplasm to nucleolus (example line drawn in middle). Dotted line represents approximate nuclear boundary. d–g, Image, variance map, and quantified variance of HP4 in S2 cells (d), HP5 in S2 cells (e), HP1γ in mammalian NIH3T3 cells (f), and HP1c in S2 cells (g). h, Diffusion rate (D) for fibrillarin across the nucleoplasm–nucleolus boundary (left), and HP4 (middle) and HP5 (right) across the euchromatin–heterochromatin boundary. For c–h, n = 25 nuclei, error bars are s.d. i, Representative image, variance map, and quantified variance across boundary for HP4 in control cells (bw RNAi, top), HP1a-depleted cells (HP1a RNAi, middle), and HP1a-depleted and rescued cells (HP1a RNAi + mCherry–HP1a, bottom). n = 25 nuclei per condition, error bars are s.d. j, Predictions of inert probe variance and diffusion near ‘H2A edges’, which have a >2 fold increase in H2A density (purple bar) with <1.25 fold change in HP1a density (green bar), and ‘HP1a edges’, which have >3 fold increase in HP1a density (green bar) with <1.25 fold change in H2A density (purple bar). The chromatin compaction model (left) predicts that inert probe variance and diffusion rate would be influenced by increasing H2A density, but unaffected by HP1a density. The phase-separation model (right) predicts that inert probe variance and diffusion rate would be influenced by HP1a density, but unaffected by H2A density. k, Summary of RICS and N&B data. Heterochromatin proteins can move freely in the heterochromatin domain (i) but are hindered near the hetero-euchromatic border (ii). Similarly, euchromatic proteins move freely in euchromatin (iii) but are hindered near the border (iv), mostly preventing their entry. Euchromatic proteins that do enter heterochromatin move more slowly owing to energetically costly interactions with surrounding phase particles (v) or crowded environments (vi). l, Models of how liquid properties could influence heterochromatin domain formation and functions. We speculate that nucleation of heterochromatic (HP1) foci could occur independently of chromatin and H3K9me2/3, then associate with the chromatin fibre (top left), or nucleation could require H3K9me2/3 (top right). Heterochromatin could spread along the chromatin fibre (in cis) due to HP1 liquid ‘wetting’, followed by H3K9 HMTase recruitment and H3K9 methylation (‘HP1 first’), or as previously proposed, HP1 recruitment of the HMTase could result in H3K9 methylation of adjacent nucleosomes, followed by HP1 binding (H3K9me2/3 first). Finally, non-contiguous segments of chromatin (on the same or different chromosomes) can coalesce into one 3D domain, owing to liquid-like fusion events between H3K9me2/3–HP1-enriched regions.