Numerous recent studies have reported the liquid-like behaviour of intracellular membraneless organelles, such as nucleoli, stress granules and processing bodies7. They are formed via promiscuous interactions among proteins and nucleic acids by liquid–liquid phase separation (LLPS), coacervation or condensation8,9,10,11. Reversible formation and dissolution of these organelles during the cell cycle and intracellular signalling plays critical roles in cellular responses and homoeostasis and is regulated by various post-translational modifications. Phosphorylation, one of the most common post-translational modifications occurring in cellular proteins, changes the structure, interactions and intracellular localization of substrate proteins and regulates several intracellular signalling pathways12,13. An increasing number of studies have reported phosphorylation-dependent regulation of LLPS and intracellular liquid-like organelles. Phosphorylation regulates not only protein-based phase separation in positive or negative manners1,2,3,4,5,6 but also protein–nucleic acid coacervation14. A recent study showed that viral replication is regulated by phosphorylation-dependent LLPS of viral nucleocapsid protein15.

In a protein with a rigid three-dimensional structure, the addition of a phosphate group induces a conformational change locally or allosterically, which in turn affects the interaction with its substrate and/or partner protein(s). However, how phosphorylation of intrinsically disordered regions (IDRs) of proteins regulates LLPS mechanistically remains elusive16,17,18,19. Recent studies using charged polymers and theoretical modelling demonstrated that a polyampholyte chain with segregated charged residues (charge blocks) exhibits stronger phase separation than the chain with the same number of charged residues randomly distributed20,21,22,23. Charge blocks also play important roles in phase separation in vivo24,25,26, and shuffling of the charged residues along a polypeptide results in the dispersion of liquid-like organelles in the cell24,25. As many IDRs of cellular proteins are hyperphosphorylated during mitosis, for example, Ki-67, RIF1, INCENP and NPM116, the addition of multiple negatively charged groups may enhance or reduce such ‘charge blockiness’ of IDRs and affect the propensity for LLPS in the cell. However, direct evidence for this hypothesis is lacking.

Ki-67, a nucleolar phosphoprotein, plays a critical role in organizing the periphery of mitotic chromosomes, which are thought to have a liquid-like property. Ki-67 separates chromosomes from each other and prevents their coalescence during mitosis27,28,29,30,31,32. Human Ki-67 is composed of multiple domains, including an N-terminal PP1-binding domain, a central repeat domain (RD) composed of 16 repeats of an ~110-amino-acid unit, and a C-terminal chromatin-targeting domain (LR domain) for chromosome binding (Fig. 1a). Phosphoproteomic analyses demonstrated that Ki-67 is hyperphosphorylated by CDK1 and other mitotic kinases33. Our quantitative mass spectrometric analysis of mitotic phosphorylation identified more than 70 residues in the RD that are significantly phosphorylated upon entry into mitosis16. Comparison of the charge distributions between the mitotic (hyperphosphorylated) form and interphase (dephosphorylated) form revealed that mitotic phosphorylation converts the individual repeats into strong diblock ampholytes, in which a positive charge block is followed by a negative block (Fig. 1b). This tendency was identified in most of the repeats present in the RD (Extended Data Fig. 1a), suggesting that mitotic phosphorylation enhances the alternating charge blocks throughout the RD. In contrast, mitotic hyperphosphorylation of nucleophosmin (NPM1), an IDR-rich nucleolar protein that interacts with Ki-67 and plays a critical role in assembling nucleolar components in interphase cells34, diminishes the alternating charge blocks that otherwise exist in the non-phosphorylated form (Extended Data Fig. 1b). Therefore, mitotic hyperphosphorylation may introduce negative charges to enhance or reduce the alternating charge blocks in the IDRs and modulate the propensity for LLPS (Fig. 1c). In this Letter, we tested the hypothesis that changes in charge blockiness, rather than the attachment of phosphate groups at specific sites, play critical roles in phase separation of Ki-67 and NPM1 and in the morphological dynamics of the periphery of mitotic chromosomes and nucleoli.

Fig. 1: Mitotic hyperphosphorylation of human Ki-67 enhances the charge blockiness of its RD and LLPS.
figure 1

a, Primary structure of human Ki-67 (long isoform). Phosphorylation sites increased and decreased upon mitotic entry16 are indicated by magenta triangles and brown triangles, respectively. FHA, forkhead-associated domain. b, Charge plot of R12 in interphase (left) and mitotic (right) forms (window size: 25 amino acids). The positions of phosphorylation are indicated by triangles. Positive and negative charge blocks (Methods) are depicted by blue and red bars, respectively. The BLC value, which quantifies the charge blockiness, is also shown. c, Illustration of how mitotic hyperphosphorylation enhances the charge blockiness and promotes phase separation. d,e, In vitro LLPS assay using ATTO488-labelled recombinant proteins. Fluorescence microscopic images of recombinant proteins carrying different RD stretches (40 µM R16, 5 µM R14–16 and 0.2 µM R8–16) (d) or increasing copy numbers of R12 (40 μM (R12)1, 40 μM (R12)2 and 20 μM (R12)4) (e) are shown. Scale bar, 30 µm. f,g, The turbidity of the droplet solution was measured as the OD600 and plotted against the protein concentration (f). One representative result is shown for each construct (out of three). Csat, which represents the protein concentration giving a half-maximal OD value, was obtained by curve fitting and plotted against the repeat number (g). Error bars reflect standard deviation of the mean (n = 3 independent measurements). h, Wild-type R12 was incubated with ATP or ADP in the absence or presence of purified CDK1–cyclin B and subjected to LLPS assay. Scale bar, 50 µm. Source numerical data are available in source data.

Source data

Recombinant proteins of human Ki-67 RD formed liquid-like droplets in vitro in the presence of 100 mM NaCl and 15% polyethylene glycol. (Fig. 1d and Extended Data Fig. 2a,b). Droplet formation increased with the number of repeats (Fig. 1d and Extended Data Fig. 2c). Tandem homogeneous repeats of repeat 12 ((R12)1, (R12)2 and (R12)4) showed a similar tendency (Fig. 1e and Extended Data Fig. 2d). A clear inverse correlation between the number of repeats and the propensity of LLPS (quantified by the saturation concentration, Csat10) was observed; Csat sharply decreased as the repeat number increased (Fig. 1f,g). The effect of phosphorylation on LLPS was examined. R12 contains nine mitotic phosphorylation sites (Fig. 1b), six of which harbour a consensus motif for CDK135. In vitro phosphorylation of recombinant R12 by CDK1 increased droplet formation (Fig. 1h and Extended Data Fig. 2e).

Phosphomimetic mutations in nine mitotic phosphosites (Pm9) in R12 enhanced droplet formation (Fig. 2a,b and Extended Data Fig. 3a). Phosphomimetic mutations in another repeat (R7) also enhanced LLPS (Extended Data Fig. 3b,c). Notably, the phosphomimetic mutations did not induce the formation of any secondary structures (Extended Data Fig. 3d). To demonstrate that alternating charge blocks are important and necessary for LLPS, we constructed a series of R12 mutants in which the charge distribution was modified by replacing the amino acids that are not involved in mitotic phosphorylation (charge-block mimetic mutant, CBm; Fig. 2a) and subjected these mutants to the LLPS assay (Fig. 2b and Extended Data Fig. 3a). Neutralization of the positive charge block at the amino-terminal region by substituting either the neutral amino acids with glutamic acid (E) residues (CBm-1) or K/R by Q (CBm-2) reduced the formation of liquid droplets (Fig. 2b). In contrast, replacement of neutral residues in the middle region with E residues, which mimics phosphorylated charge blocks (CBm-3), substantially promoted LLPS, as was observed in the phosphomimetic mutant (Pm9). A similar effect was observed when E residues were introduced in the carboxyl-terminal region (CBm-4) (Fig. 2b).

Fig. 2: Alternating charge blocks of RD are critical for LLPS.
figure 2

a, Amino-acid sequence of R12 WT and mutants. Mitotic phosphosites are indicated by an asterisk. Positively and negatively charged amino acids are shown in blue and red, respectively. Mutated residues are shown in bold. Positive and negative charge blocks (Methods) are highlighted in cyan and red, respectively. b, LLPS assay of R12 fragments shown in a. Charge plot (window size: 25 amino acids), BLC values and fluorescence images of liquid droplets are shown. Scale bar, 30 µm. c,d, Correlation between BLC and Csat. Csat values of R12 WT and mutants described in a were obtained by a turbidity assay and plotted against BLC values (c). The same analysis was performed with a series of charge block mutants carrying different net charges (−4, 0 or +5) (d). Amino-acid sequences and charge plots of individual mutants are shown in Extended Data Fig. 4b. Error bars reflect standard deviation of the mean (n = 3 independent measurements). Source numerical data are available in source data.

Source data

The relationship between charge blockiness and LLPS was investigated quantitatively. The extent of charge blockiness along the polypeptide was evaluated on the basis of either the blockiness of like charges (BLC) or degree of segregation (Dseg) (Methods). Plotting Csat against BLC and Dseg revealed a clear inverse correlation (Fig. 2c and Extended Data Fig. 4a). To characterize the relationship further, a series of mutants (CBm-5–16) carrying different net charges (between −4 and +5) and/or charge blockiness (Extended Data Fig. 4b) were constructed and subjected to LLPS assay. Csat more closely correlated with charge blockiness (BLC and Dseg) (Fig. 2d and Extended Data Fig. 4c) than with the net charge (Extended Data Fig. 4d). Together, these results demonstrate that the existence of alternating charge blocks governs LLPS in vitro and indicate that neither the exact position of the charged residues nor a negative shift of the net charge is a critical determinant.

Next, we tested whether the Ki-67 RD could form a liquid phase on an artificial chromosome surface in vitro. Diethylaminoethyl (DEAE) beads were coated with double-stranded DNA and incubated with LR-fused R12 (LR is necessary for DNA binding). All these constructs bound to the DNA-coated beads; however, both the phosphomimetic mutant (Pm9) and the charge-block mimetic mutant (CBm-3) assembled on the beads stronger than the wild type (WT) (Fig. 3a,b). As the mutation affected neither the affinity for DNA (Extended Data Fig. 5a) nor the efficiency of fluorescent labelling (Extended Data Fig. 5b), the protein layer observed in the Pm9 and CBm-3 sequences indicated stronger interactions among the RDs. To confirm this, fluorescently labelled LR-free (Pm9)1 was added to the DNA beads together with non-labelled (Pm9)2-LR. The labelled (Pm9)1 was incorporated into the layer only in the presence of (Pm9)2-LR (Extended Data Fig. 5c). The incorporation of LR-free molecules was stronger in Pm9 and CBm-3 than in WT (Fig. 3c,d). The liquid-like property of the protein layer was further confirmed by fluorescence recovery after photobleaching (FRAP) analysis of the LR-free molecules in the layer (Fig. 3e and Extended Data Fig. 2b).

Fig. 3: Ki-67 RD forms a liquid phase on a DNA-coated bead.
figure 3

a,b, λDNA-bound DEAE beads were incubated with purified R12 ((WT)2, (Pm9)2 and (CBm-3)2) fused with LR. DNA was labelled with YOYO-1 (green) and LR-fused proteins were labelled with ATTO-610 (red). Fluorescence images are shown (a). The signal intensity of the protein layer along the bead’s contour was measured and normalized to the median value of (Pm9)2-LR (b) (n = 7 for (WT)2-LR and (CBm-3)2-LR) and n = 12 for (Pm9)2-LR and (CBm-3)2-LR). Box plot shows the minimum and maximum value by whiskers, 25% and 75% percentile by box boundaries and median by bar inside the box. Numbers above graph indicate P values by one-tailed Mann–Whitney U test. Scale bar, 15 µm. ce, Assembly and behaviour of LR-free R12 on a bead. λDNA-bound DEAE beads were incubated with purified LR-fused R12 ((WT)2, (Pm9)2 and (CBm-3)2), together with ATTO610-labelled LR-free R12 ((WT)1, (Pm9)1 and (CBm-3)1). Fluorescence and differential interference contrast (DIC) images are shown (c). Signal intensity of the protein layer along the bead’s contour was measured and normalized to the median value of (Pm9)1 (d) (n = 8). Box plot shows the minimum and maximum value by whiskers, 25% and 75% percentile by box boundaries and outlier by dot above upper whisker. Numbers above graph indicate P values by one-tailed Mann–Whitney U test. Representative fluorescence images acquired during the FRAP analysis are shown (e). The region surrounded by a circle was bleached and the fluorescence intensity in the area was measured and plotted with a solid line of mean and a shade of standard deviation (right panels) (n = 4 for (Pm9)1 and n = 5 for (CBm-3)1). Scale bar, 15 µm. Source numerical data are available in source data.

Source data

We investigated how phosphorylation of the Ki-67 RD and its LLPS-promoting activity were related to the formation of the chromosome periphery in vivo. Enhanced green fluorescent protein (EGFP)-Ki-67 (full length) expressed in HeLa cells localized in the interphase nucleoli and at the mitotic chromosome periphery (Fig. 4a). The liquid-like behaviour of Ki-67 at the chromosome periphery was confirmed by treating the cells with ammonium acetate36, as well as by FRAP analysis (Extended Data Fig. 6a–c). The homogeneous repeats of R12 were fused with LR (required for binding to chromosomes; Extended Data Fig. 6d) and expressed in HeLa cells (Fig. 4b). These homogeneous repeats localized at the mitotic chromosome periphery in a repeat-number-dependent manner (Extended Data Fig. 6e). Replacement of all nine mitotic phosphosites with non-phosphorylatable residues ((A9)12-LR; Fig. 4b), which nearly completely abolished mitotic phosphorylation (Extended Data Fig. 7a), severely diminished the peripheral localization compared with that of the WT constructs containing the same number of repeats (Fig. 4c and Extended Data Figs. 6e and 7b). In contrast, the phosphomimetic mutant (Pm9)12-LR, as well as a charge-block mimetic mutant showing similar LLPS in the in vitro droplet assay ((CBm-3)12-LR) (Fig. 2b), localized at the chromosome periphery (Fig. 4c). These results indicate that the block-polyampholyte repeat is necessary and sufficient for localization at the mitotic chromosome periphery.

Fig. 4: Mitotic phosphorylation, phosphomimetic mutants and a charge-block mimetic mutant of R12 induce the formation of the mitotic chromosome periphery.
figure 4

a, EGFP-tagged full-length human Ki-67 expressed in HeLa cells. DNA was stained with Hoechst 33342. Scale bar, 5 µm. b, Schematic illustration of EGFP- and LR-fused homogeneous R12 repeat constructs. The amino-acid sequence of a single repeat unit is shown in Fig. 2a. In the CBm-3 mutant, nine mitotic phosphosites were replaced with alanine to avoid mitotic phosphorylation. c, Localization of R12 repeat constructs in mitotic HeLa cells. DNA was stained with Hoechst 33342. Magnified images (square (3.4 × 3.4 µm)) are shown in the insets. Scale bar, 5 µm. d, Expression of R12 constructs in Ki-67-KO cells. DNA was stained with Hoechst 33342. Scale bar, 5 µm.

The ability to form a functional chromosome periphery was examined using Ki-67 knockout (KO) cells. In these cells, mitotic chromosomes coalesced, forming a large single mass of chromatin (Fig. 4d). The depletion caused a slight mitotic delay in some cell lines37, although other cell lines showed proliferation similar to that of the WT counterpart38. The expression of full-length Ki-67 in KO cells nearly completely rescued the phenotype (Fig. 4d). Three-dimensional morphological analysis of the mitotic chromosomes indicated that chromosomes were more dispersed in the rescued cells than in non-rescued cells (Extended Data Fig. 7c). The recovery of the chromosome periphery was confirmed by the segregated localization of protein and DNA on mitotic chromosomes (Extended Data Fig. 7d,e). Notably, WT R12 ((WT)12-LR), but not the non-phosphorylatable form ((A9)12-LR), rescued the KO phenotype (Fig. 4d), although to a lower level than the full-length Ki-67 did (Extended Data Fig. 7c,d), probably because of its lower repeat number. Homogeneous repeat of R7 ((R7)12-LR) not only localized at the chromosome periphery of mitotic HeLa cells, but also rescued the phenotype of Ki-67-KO cells (Extended Data Fig. 7c,d,f,g), suggesting that the number of repeats rather than specific amino-acid sequence of R12 is important for the formation of the chromosome periphery. Notably, not only the phosphomimetic mutant ((Pm9)12-LR), but also the charge-block mimetic mutant ((CBm-3)12-LR) of R12 rescued the KO phenotype (Fig. 4d and Extended Data Fig. 7c, d). The charge-block mimetic mutant carrying the same net charge as A7 but larger charge blockiness (CBm-7; net charge +5 and BLC 35) also rescued the KO phenotype (Extended Data Fig. 7e), indicating that charge blockiness, but not a negative shift of the net charge, is critical for the formation of the chromosome periphery. Together, these results demonstrate that the alternating charge blocks of the Ki-67 RD are necessary and sufficient for efficient LLPS in vitro and for forming the functional mitotic chromosome periphery in vivo.

Next, we investigated whether mitotic phosphorylation regulates the intracellular dynamics of other phosphoproteins by changing the charge blockiness. NPM1 localizes in the GC region of the nucleoli and is heavily phosphorylated upon entry into mitosis16. Eleven mitosis-specific phosphorylation sites were identified in a long stretch of the IDR (Extended Data Fig. 1b). Comparison of the charge distributions revealed that the dephosphorylated (interphase) form has a strong block-polyampholytic charge distribution, whereas the hyperphosphorylated (mitotic) form loses positive charge blocks (Extended Data Fig. 1b). Therefore, mitotic hyperphosphorylation may reduce the propensity of NPM1 for LLPS, an effect opposite to that observed for Ki-67 (Fig. 5a). Indeed, CDK1-treated NPM1-IDR and the phosphomimetic mutant of the 11 mitotic phosphosites reduced the formation of liquid droplets in vitro (Fig. 5b and Extended Data Fig. 8a–c). Notably, a charge-block mimetic mutant of NPM1 showed reduced droplet formation (Fig. 5b and Extended Data Fig. 8b,c), demonstrating that mitotic phosphorylation suppresses LLPS of NPM1 by reducing its charge blockiness.

Fig. 5: Mitotic hyperphosphorylation reduces charge blockiness and the propensity for LLPS of the nucleolar phosphoprotein NPM1.
figure 5

a, Schematic illustration of how hyperphosphorylation of the IDR of NPM1 reduces charge blockiness. b, In vitro LLPS assay of recombinant NPM1 IDR. WT, CDK1-treated WT, phosphomimetic mutant, and a charge-block mimetic mutant (amino-acid sequences are shown in Extended Data Fig. 8b). Scale bar, 50 µm. c, Mitotic localization of NPM1. mCherry-fused WT, phosphomimetic mutant and charge-block mimetic mutant of full-length NPM1 were expressed in HeLa cells. DNA was counterstained with Hoechst 33342. The charge plot (window size: 25 amino acids) and BLC value are also indicated. Scale bar, 10 µm. Arrowheads and asterisks indicate cells in which NPM1 started to re-assemble among WT- and mutant-expressing cells, respectively. d, Mitotic localization of LR domain-fused 12 tandem repeats of Ki-67 R12 with or without N-terminal domain (1-639) (EGFP-NT-(R12)12-LR, EGFP-(R12)12-LR). DNA was counterstained with Hoechst 33342. Scale bar, 10 µm.

We found that the intracellular dynamics of NPM1 during mitosis were also modified by phosphomimetic and charge-block mimetic mutations (Fig. 5c). NPM1 diffused from the nucleoli into the cytoplasm when the cell entered mitosis and localized mainly in the cytoplasm, with weak localization around the chromosome periphery. It re-appeared at the chromosome periphery in anaphase and eventually assembled into many small loci in telophase (arrowheads in Fig. 5c), finally fusing to form several nucleoli in early G1 phase. Phosphomimetic and charge-block mimetic mutants localized not only in the nucleoli, but also in the nucleoplasm and cytoplasm in interphase cells (Fig. 5c). Similar to the WT, the mutants diffused into the cytoplasm during prophase and metaphase but did not re-assemble at the chromosome periphery even in anaphase and telophase and remained in the cytoplasm throughout mitosis. Finally, they started to localize to the nucleoli in early G1 phase (asterisk in Fig. 5c). These results demonstrate a close correlation between the block-polyampholytic property of NPM1 and its intracellular dynamics during mitosis.

As Ki-67 directly or indirectly interacts with NPM1 via its N-terminal conserved domain (Extended Data Fig. 8d), we investigated how the opposing effects of mitotic phosphorylation on these proteins are integrated to determine their behaviour during mitosis. The homogeneous repeat construct of Ki-67 ((R12)12-LR) localized exclusively in the nucleoplasm in interphase cells (interacting with the chromosome via LR), and addition of the N-terminal domain (1−639) (NT-(R12)12-LR) directed it to the perinucleolar region (an interface between the nucleoli and nucleoplasm) (Fig. 5d), suggesting that Ki-67 bridges NPM1 and the chromosome. Ki-67 constructs were localized at the chromosome periphery in prophase and metaphase regardless of the presence of the N-terminal domain (Fig. 5d). In this period, the interaction between Ki-67 and NPM1 was severely abrogated (Extended Data Fig. 8d). When the interaction between Ki-67 and NPM1 recovered in anaphase and telophase, NT-(R12)12-LR re-assembled with NPM1 and finally localized in the perinucleolar region, whereas (R12)12-LR did not associate with NPM1 and was redistributed from the periphery to the entire chromosome until the end of mitosis (Fig. 5d), demonstrating that the perinucleolar localization of Ki-67 requires interaction with NPM1. Overall, these results suggest a reciprocal regulatory mechanism of the nucleoli and chromosome periphery during the cell cycle.

We demonstrated that mitotic hyperphosphorylation of the RD of Ki-67 enhanced its charge blockiness and promoted its LLPS to form the periphery of mitotic chromosomes. Notably, a mutant mimicking the mitotically phosphorylated charge blocks not only displayed strong LLPS in vitro (Fig. 2b,c), but also rescued deficiencies observed in Ki-67-KO cells (Fig. 4d). Thus, the occurrence of alternating charge blocks, rather than the exact position of negative charges, plays an important role in chromosome periphery formation via LLPS. This ‘fuzzy’ regulatory mechanism, regulated by charge blockiness, clearly contrasts the conventional ‘tight’ mechanism via which site-specific addition of a phosphate group modulates stereospecific interactions between structured proteins or domains. This mechanism is distinct from a previously reported mechanism of multiple phosphorylation, in which stepwise accumulation of multiple phosphate groups confers high cooperativity or ultrasensitivity in enzymatic activation (such as that for the CDK1 inhibitor Sic1 (ref. 39)). The proposed mechanism also explains why protein phosphorylation frequently occurs at multiple neighbouring residues located in IDRs40,41,42.

Notably, the mode of cell cycle-dependent regulation is reversed in NPM1: mitotic hyperphosphorylation of NPM1 reduces, rather than enhances, its charge blockiness and suppresses its strong LLPS propensity, leading to dissolution of the nucleoli (Fig. 5). The opposing effects of mitotic phosphorylation of Ki-67 and NPM1 on their LLPS, together with their cell cycle-specific interaction (Extended Data Fig. 8d), underlie the morphological changes of nucleoli and the chromosome periphery during mitosis (Extended Data Fig. 8e). Our phosphoproteomic analyses demonstrated that mitotic hyperphosphorylation changes the charge blockiness of IDRs in several other nucleolar proteins (Extended Data Fig. 9), suggesting that their LLPS is also regulated by charge blockiness-enhancing or charge blockiness-reducing phosphorylation. Notably, the average charge block size converges to ~30–40 amino acids, indicating that this charge block size is the most suitable for a polypeptide to undergo regulatable LLPS in an intracellular milieu.

In summary, the blockiness-enhancing or blockiness-reducing phosphorylation described here is distinct from previously reported phosphorylation-based regulatory mechanisms and may represent a general mechanism that regulates the behaviour of a broad spectrum of phosphoproteins and assembly and disassembly of intracellular membraneless organelles and structures.



All chemical reagents used in this study were purchased from Nacalai Tesque unless otherwise indicated.

Protein sequence analysis

The mitotic phosphosites in human Ki-67 and NPM1 were reported in our previous study16. The human Ki-67 and NPM1 sequences were obtained from the UniProt database (accession numbers P46013 and P06748, respectively). Charge distribution was calculated as the sum of the charges (Arg and Lys, +1; Glu and Asp, −1; phospho-Ser and phospho-Thr, −2) in the indicated window range. A charge block was designated when the area of the charge plot (window size: 35 amino acids) was larger than 20. Multiple sequence alignment was performed using Clustal Omega ( Dseg and BLC were calculated with the equation described in Supplementary Note. We chose to use BLC over other charge patterning parameters such as sequence charge decoration43 and κ (ref. 44), because BLC employs a larger block size, more appropriately capturing the longer charge tracts that we believe are important in Ki-67.

DNA construction

Complementary DNA of human Ki-67 (short isoform) was obtained as described previously45. Fragments of the WT Ki-67 RD, LR domain (amino acids 2,578–2,896) and N-terminal domain (amino acids 1–639 (corresponding to amino acids 1–135 and 496–999 of the long isoform)) as well as human NPM1 (amino acids 105–250) were amplified by PCR and subcloned into pET28a(+) (Novagen) for expression in Escherichia coli and/or pEGFP for mammalian expression. The nucleotide sequences of primers are presented in Supplementary Table 1. cDNA fragments encoding phosphomimetic mutants and charge-block mimetic mutants of Ki-67 and NPM1 were synthesized at Thermo Fisher Scientific. The amino-acid sequences of all mutants that were used in this study are presented in Supplementary Table 2. For bacterial expression, the codon usage was optimized for E. coli without changing the amino-acid sequence. To generate tandem repeats of Ki-67 R12 and R7, the DNA fragment encoding R12 was cleaved out from the expression vector with Xho I and Sal I digestion and ligated into the same expression construct digested with Sal I. Through these procedures, the number of R12 was increased up to 12. All of these homogeneous repeat constructs contained the linker sequence ‘GHTEESVEDD’ between each repeat unit.

Cell culture, synchronization and transfection

HeLa cells (ATCC, CCL-2.2) were cultured in Dulbecco’s modified Eagle’s medium (DMEM, Sigma-Aldrich) supplemented with 10% foetal bovine serum (FBS, Gibco) at 37 °C in the presence of 5% CO2. The Ki-67 KO HCT116 cell line was described previously46 and was cultured in high-glucose DMEM supplemented with 10% FBS and penicillin–streptomycin at 37 °C in the presence of 5% CO2. Cells were transfected with the plasmids using PEI-MAX (Polysciences). To induce mitotic arrest, cells were treated with 0.2 µM nocodazole for 15 h. For microscopic observation, cells on a cover glass (Matsunami Glass) were fixed with 4% paraformaldehyde at room temperature for 15 min and mounted with Vectashield (Vector Laboratories) containing Hoechst 33342.

Protein purification

E. coli cells (BL21‐CodonPlus(DE3)‐RIL, Agilent Technologies) harbouring the expression vector for hexahistidine (His6)-tagged Ki-67 fragments were cultured in Luria–Bertani medium. Protein expression was induced by adding 0.1–1.0 mM IPTG, and the cultures were further incubated at 20 °C or 37 °C overnight. The cells were collected by centrifugation (5,000g, 15 min, 20 °C) and stored at −80 °C until use. For purification under a denaturing condition, the cell pellet was subjected to two rounds of freeze–thaw cycles and was finally dissolved in urea-containing buffer (8 M urea, 10 mM Tris–HCl, 100 mM NaH2PO4, 5 mM 2-mercaptoethanol and 10 mM imidazole, pH 8.0) at 4 °C for overnight to 2 days. The lysate was centrifuged (10,000g, 4 °C, 30 min) and the supernatant was collected and mixed with Ni-NTA agarose beads (Qiagen). The beads were gently agitated at 4 °C for 1 h, washed with wash buffer (8 M urea, 10 mM Tris–HCl, 100 mM NaH2PO4, 10 mM 2-mercaptoethanol and 20 mM imidazole, pH 8.0), and His6-tagged proteins were eluted with elution buffer (8 M urea, 10 mM Tris–HCl, 100 mM NaH2PO4, 5 mM 2-mercaptoethanol and 100, 300 or 500 mM imidazole, pH 8.0). Eluted proteins were sequentially dialysed at 4 °C against dialysis buffer 1 (0.1% (v/v) trifluoroacetic acid (TFA) and 2 mM 2-mercaptoethanol) for 3 h, dialysis buffer 2 (0.05% (v/v) TFA and 2 mM 2-mercaptoethanol) for 3 h or overnight and, finally, dialysis buffer 3 (0.05% (v/v) TFA) for 3 h. The purified proteins were lyophilized (FDU‐2200, EYELA) and stored at 4 °C.

To purify His6-tagged protein under a native condition, the cell pellet was dissolved in lysis buffer (50 mM Tris–HCl, 500 mM NaCl, 1 mM MgCl2, 2 mM 2-mercaptoethanol, 1 mM phenylmethylsulfonyl fluoride, 20 mM imidazole, lysozyme and DNase I, pH 7.4) and subjected to three rounds of quick freeze–thaw cycles. The cell debris was removed by centrifugation (12,000g, 20 min, 4 °C) and the supernatant was mixed with Ni-NTA beads at 4 °C for 1 h. The beads were then washed with wash buffer (50 mM Tris–HCl, 500 mM NaCl, 2 mM 2-mercaptoethanol and 20 mM imidazole, pH 7.4) three times and eluted stepwise with increasing concentrations (50, 100, 200, 300, 400 and 500 mM) of imidazole in wash buffer. The eluted protein was dialysed against low-salt buffer (50 mM Tris–HCl, 50 mM NaCl and 2 mM 2-mercaptoethanol, pH 7.4) at 4 °C for 3 h and then subjected to ion-exchange chromatography (Hi-Trap Q, GE Healthcare). The eluted fraction was collected, dialysed against assay buffer (50 mM HEPES and 100 mM NaCl, pH 7.4) at 4 °C, concentrated using Amicon centrifugal filters (Millipore) and stored at −80 °C in small aliquots. The amount of RNA contamination in the individual protein preparations was quantified using a fluorescent probe for RNA (QuantiFluor RNA, Promega) and was 0.1–0.7% (w/w).

In vitro LLPS assay

Lyophilized protein was dissolved into dissolving buffer (2 M guanidine hydrochloride, 100 mM Tris–HCl pH 8.0 and 10 mM HEPES) to a final concentration of 4 mM. For fluorescence microscopic observation, protein was incubated with 10 µM ATTO488-maleimide (ATTO-TEC) at room temperature for 1 h and then with 5 mM dithiothreitol at room temperature for 1 h or at 4 °C overnight. The labelled protein solution was diluted in droplet buffer (50 mM HEPES, 100 mM NaCl and 15% (w/v) PEG3350 (Sigma-Aldrich), pH 7.4) at a 1:100 ratio, incubated at room temperature for 30 min and transferred to a 96-well clear-bottom plate (Greiner Bio-One) for microscopic observation (FV3000, Olympus). The final concentration of protein was 40 μM unless otherwise indicated. For protein with multiple repeats, the final protein concentration is indicated in the figure legend. For the turbidity assay, protein in dissolving buffer was sequentially diluted with the same buffer, and then mixed with droplet buffer at 1:50. The mixture was incubated at room temperature for 10 min and transferred to a microcuvette. The optical density at 600 nm (OD600) was measured using a V-630 spectrophotometer (JASCO). The Csat value was defined by the concentration at which the turbidity was at half-maximal value10. The data obtained were fitted using the equation (Supplementary Note) in OriginPro (v.9.8).

In vitro phosphorylation by CDK1

Protein purified under the native condition was incubated with CDK1–cyclin B1 (Abcam) in kinase buffer (50 mM HEPES–NaOH, 100 mM NaCl, 10 mM MgCl2 and 50 μM ATP, pH 7.4) at room temperature for 30 min. Phosphorylation was confirmed by SDS–PAGE containing Phos-tag acrylamide (Fuji Film, Wako). Protein was then incubated with 10 µM ATTO488-maleimide for 1 h, mixed with droplet buffer at a 1:100 ratio and transferred to a 96-well clear-bottom plate for microscopic observation.

DNA bead assay

Lyophilized proteins were dissolved into dissolving buffer and labelled with ATTO610-maleimide (ATTO-TEC) as described above, if necessary. λDNA (Takara) (26.25 µg) was attached to 1.65 µl DEAE sepharose beads (DEAE Sepharose Fast Flow, GE Healthcare) and stained with YOYO-1 (Thermo Fisher Scientific) if necessary in bead buffer (50 mM HEPES and 100 mM NaCl, pH 7.4). The bead suspension was then incubated with protein (0.8 μM) in a 96-well clear-bottom plate (Greiner Bio-One) at room temperature for 2.5 h. To examine the incorporation of LR domain-free RD, the ATTO610-labelled protein was added to a final concentration of 40 μM after 2.5 h of incubation of the DNA beads with LR-fused repeat protein. For the FRAP assay, ATTO610 signal on the beads was bleached using 561-nm laser light and observed by time-lapse imaging (FV3000, Olympus).

Microscopic observation, image processing and image analysis

For the observation of fluorescence signals, a confocal laser-scanning microscope system (FV3000, Olympus) was used. For live-cell imaging, a stage chamber (Tokai Hit) was used to maintain the temperature and moisture and CO2 levels. Phenol red-free DMEM supplemented with 10% FBS and 1 µg ml−1 Hoechst 33342 was used to visualize chromosomes if necessary. The images obtained were processed and analysed using MetaMorph (Molecular Devices), Fiji47 or Python 2 or 3 with add-on libraries (Numpy, Scipy, Pandas, Matplotlib, OpenCV and seaborn).

Statistics and reproducibility

Methods of statistical analysis and sample size are indicated in the figure legends.

No statistical methods were used to predetermine sample size. Sample sizes were estimated empirically on the basis of pilot experiments and previously performed experiments with similar setup to provide sufficient sample sizes for statistical analysis. No data were excluded from the analyses with the exception of the image analysis of droplet. For the quantification of droplet, ones with higher eccentricity than criterion (0.7) were excluded. For droplet assay, sample and measurement order was randomized. The area of microscopic observation was randomly determined. The investigators were not blinded to allocation during experiments and outcome assessment. Turbidity assay was performed three times, and microscopic observation, gel electrophoresis, western blotting and electrophoretic mobility shift assay were performed at least twice.

Reporting Summary

Further information on research design is available in the Nature Research Reporting Summary linked to this article.