Sequence design-based control of DNA droplets formed from phase separation of DNA nanostructures

DNA has the potential to realize a controllable liquid-liquid phase separation (LLPS) system, because the design of its base sequences results in programmable interactions. Here, we have developed a novel DNA-based LLPS system which enables us to create 'DNA droplets' and to control their dynamic behaviour by designing sequences of the DNA nanostructure. We were able to change the phase separation temperature required for the formation of DNA droplets by designing the sequences. In addition, the fusion, fission, and formation of Janus-shaped droplets were controlled by sequence design and enzymatic reactions. Furthermore, modifications of proteins with sequence-designed DNAs allowed for their capture into specific droplets. Overall, our results provide a new platform for designing the phase behaviour of macromolecular structures, and paves the way for new applications of sequence-designed DNA in the creation of cell-mimicries, synthetic membraneless organelles, and artificial molecular systems.

Liquid-liquid phase separation (LLPS) of water-soluble molecules induces the formation of macromolecular droplets in water. In polymer chemistry and soft matter physics, LLPS has been studied to elucidate underlying mechanisms of phase separation [1][2][3] and to construct cell-like structures 4 or bioreactors 5 . With recent advances in LLPS in biological research fields, studies have found that macromolecular droplets comprised of proteins and RNAs are formed within living cells via moderate interactions among the biomolecules [6][7][8][9][10][11] . LLPS of biomolecules has garnered considerable attention as the droplets have an important role in regulating several biological functions 12 . Although several in vitro studies have reproduced droplet formation by changing the concentrations of proteins/RNAs and salts 6,9,13,14 , no study has demonstrated the regulation of droplet formation depending on the biological information encoded in the biopolymer sequence. The sequence of biopolymers is an essential factor influencing droplet formation 15 because it determines intra-and inter-molecular interaction strength 16 . However, the potential of regulating LLPS by the sequence design of biopolymers remains unexplored, although it is expected that such a technology would provide new insights into not only LLPS mechanisms, but also LLPS applications.
Considerable progress is being made in modulating molecular interactions by biopolymer sequence design in the field of DNA nanotechnology, where sequence-specific hybridization of nucleic acids plays an important role. DNA nanotechnology is a promising avenue for the construction of nanostructures [17][18][19][20][21][22][23][24] and for the investigation of their phase behaviour 25-27 because the self-assembly of DNAs is precisely predictable from sequence information. The nanostructures can be further assembled into micro-sized structures. For example, a DNA hydrogel can be formed from the selfassembly of branched-DNA nanostructures [28][29][30][31][32] , and it can serve as a substrate for cell-free protein expression 29 , cytoskeleton for artificial cells 30 , or carrier for drug delivery 33 . On the other hand, a few studies have reported the phase behaviour of DNA nanostructures, such as the phase separation of DNA nanostructures into DNA-poor and rich phases 25 , formation of a coacervate-like DNA liquid 26 , and re-entrant phase dynamics 27 . These studies focused on the effects of temperature, DNA concentration, and ionic strength. However, sequence dependency in the interaction between DNAs 3 has not been translated into the ability to regulate phase behaviour. Sequence-design-based phase behaviour of DNA nanostructures will enable us to develop a novel LLPS system with controllability at the molecular level.
We herein report the formation and control of a 'DNA droplet' made of sequence-designed DNAs ( Fig. 1). We first show that DNA nanostructures (Fig. 1a) exhibit the LLPS that results in droplet formation depending on the surrounding temperature (Fig. 1b). Next, we show how the sequence design influences the phase behaviour of DNA nanostructures. Then, we demonstrate that control of the dynamic behaviour of DNA droplets, including fusion, fission, and segregation of DNA droplets can be achieved by rational design of DNA sequences (Figs. 1c-1e). Finally, as a potential application of our DNA-based LLPS system, we demonstrate the capture and partitioning of protein-cargos in DNA droplets in a sequence-specific manner (Fig. 1f). 4 5 Fig. 1. Droplet formation of DNA nanostructures based on phase separation. a, Schematic of the Y-shaped DNA nanostructure (Y-motif), and strand sequences of the Y-motif. b, Temperaturedependent phase-changes of the Y-motifs. The Y-motifs are dispersed in solution at a high temperature ('dispersed phase'). Decreasing the temperature induces phase separation into a 'droplet phase' that is a liquid-liquid biphasic system composed of a Y-motif-rich liquid droplets phase in a continuous Y-motif-poor phase. By further decreasing the solution temperature, the phase changes from the droplet to a 'gel phase' that is a gel-liquid biphasic system composed of Y-motif-rich gel phase in the Y-motif-poor phase. The phase-change temperature is dominated by the sequence of DNAs. c, d, e, and f, Schematic representations for the control of DNA droplet and selective cargo capture and partitioning.

Formation of DNA droplets via the phase separation of DNA nanostructures
We designed a Y-shaped DNA nanostructure (hereafter referred to as Y-motif) with three 'sticky ends' (SEs) (Fig. 1a). The Y-motif is composed of three single-stranded DNAs (ssDNAs): Y1, Y2, and Y3 (Fig. 1a). The 'stems' of the Y-motif have 16 base pairs that hybridized at 75 ºC in a buffer condition (20 mM Tris-HCl (pH: 8.0), 350 mM NaCl) ( Supplementary Fig. 1); the SE was a palindromic 8 nucleotide (nt) sequence and the same for three branches of the Y-motif, allowing for connection between the Y-motifs.
We first observed the Y-motif solution using a confocal laser scanning microscope and a stage heater. The Y-motifs were stained with a dye molecule (SYBR Gold). At 70 °C, the Y-motifs were dispersed in a buffer solution ('dispersed phase') ( Fig. 1b) and no micrometre-sized structures were observed owing to dehybridization of the SE at this temperature ( Fig. 2a(I)). When the temperature was lowered to 62 °C, spherical microparticles (from several to several tens of micro-meters) were observed in the solution, although the temperature was still much higher than the melting temperature (Tm) of the 8 nt SE (Tm: 45.9 °C) ( Fig. 2a(II)). Interestingly, fusion of the two particles occurred when they collided with each other (Figs. 2b and 2d, and Supplementary Movie 1); the fusion behaviour is similar to that of the droplets formed via LLPS in living cells 8 . We called the particles that exhibit such fusion 'DNA droplets', where Y-motifs spontaneously phase separate into Y-motif-rich liquid droplets in equilibrium with a Y-motif poor phase 34 ('droplet phase') (Fig. 1b). The DNA droplets grew in size via collision with one another (Supplementary Fig. 2).
To evaluate the mobility of the Y-motifs in the droplets, fluorescence recovery after photobleaching (FRAP) experiments were performed. In the FRAP experiments, the Y-motifs were labelled using FAM-modified Y2 without SE to avoid the detection of the reattaching the dye molecules to the Y-motifs. The half region of droplets was photo-bleached and the changes in fluorescence intensity were measured in the bleached regions. The fluorescence intensity in the droplets was immediately recovered after the bleaching (Figs. 2f and 2h), which suggests that the Y-7 motifs can diffuse inside droplets (do not form static networks) and the dynamic dissociation and association of the Y-motifs result in the formation of the droplet.
When the temperature was further decreased to 25 °C ( Fig. 2a(III)), the microparticles did not fuse (Figs. 2c and 2e). In addition, in the FRAP experiments, the fluorescence intensity did not immediately recover at around this temperature (Figs. 2g and 2i). Thus, the Y-motifs formed static networks and the DNA droplets became Y-motif-rich hydrogels ('gel phase') ( Fig. 1b). A previous study using a microrheological technique reported that DNA nanostructures exhibited a gradual transition into a hydrogel with decreasing temperatures 27 . Our results suggest that DNA nanostructures transition through a droplet phase before gelation.
We further found that this phase behaviour between the dispersed, droplet, and gel phases was reversible. The hydrogels changed into droplets when temperatures increased to 62 °C ( Fig. 2a (IV)), and the Y-motifs dispersed at 70 °C ( Fig. 2a(V)). These temperature-dependent phase-changes were confirmed with further continuous temperature changes ( Supplementary Fig. 3).

Effects of the sequence and the number of branches on phase separations and changes
We next investigated the effects of the SE sequences on the phase-change temperatures between the dispersed and droplet phases (Td), and between the droplet and gel phases (Tg). We defined Td as the temperature at which droplet formation was observed ( Supplementary Fig. 4), and Tg as the temperature at which less recovery of fluorescence in the FRAP experiment was detected ( Supplementary Fig. 5). Td and Tg were identified by decreasing the temperature from 85 ºC at a rate of -1 ºC/min. The phase diagram (Fig. 3a)  for the Y-motifs whose SEs that were 4-12 nt long ( Supplementary Fig. 6), but not with those that were 2 nt SE (ΔH: -9.6 kcal/mol) ( Supplementary Fig. 7).
We also investigated the effects of the number of branches in the motifs on the Td and Tg. We additionally designed two motifs that had four or six branches with 8 nts long SEs (Supplementary Table 2 The fact that the DNA droplets were formed at higher temperatures than the Tm of the SEs suggests that unstable hybridization between the SEs plays a key role in the formation of the DNA droplets. Such weak interactions of the SEs would allow for the dynamic association/dissociation of the motifs (Figs. 2f and 2h), which leads to the fluidic behaviour of DNA droplets, e.g. fusion of the droplets.
On the other hand, the increase of the number of branches in a motif resulted in the increase of Td We considered that Tg was attributed to the stability of SEs and entanglement of motifs. Previous studies have reported that the gelation process in the branched-DNA nanostructures occurs at around the Tm of SEs 32 . On the other hand, our results show that Tg for the Y-motif with 4 nt SE was higher than the Tm of the 4 nt SE (Fig. 3a). DNA nanostructures can be concentrated by the phase separation, also decrease the mobility of the motifs. The Tg in motifs having four or six branches was higher than their Tm (Fig. 3c), and the Tg in the six SE motifs was higher than that in four. Therefore, the effects of the entanglement on Tg would become more dominant than the stability of the hybridization of the SEs.

Orthogonality in DNA droplets
We expected that the rational design of the motif sequence allowed for the control of the dropletdroplet interactions. We designed an 'orthogonal Y-motif' with 8 nt SE ( orth Y-motif) whose sequences were not complementary to the Y-motif with 8 nt SE, but had almost similar thermodynamic parameters (ΔH and Tm) in their stem and SEs (Supplementary Tables 3 and 4). The orthogonality of the SE sequences between the Y-and orth Y-motifs enables us to acknowledge the sequence-specific fusion of DNA droplets (Fig. 4a). The Y-and orth Y-motifs were labelled with FAM (green) and Alexa 405 (blue), respectively. Then all strands for both of the motifs were mixed in a solution, and the motifs were annealed on the stage heater from 85 °C at a rate of -1 °C/min to 60 °C.
As we expected, the Y-and orth Y-motifs were individually phase separated into droplets. Fusion events were observed between the droplets composed of the same motifs but not between the droplets  Table 5). The S-motifs play a role for the cross-bridging between the Y-and orth Ymotifs and can eliminate the orthogonality between the two types of motifs, which results in the formation of DNA droplets composed of Y-, orth Y-and S-motifs (Fig. 4d). The Cy5-labelled S-motif, FAM-labelled Y-motif, and Alexa405-labelled orth Y-motif were mixed in a 1:3:3 molar ratio and visualized at 65 °C. In the experiment, the fluorescence of Cy5, FAM, and Alexa405 were observed in one droplet, suggesting that the Y-and orth Y-motifs were mixed via the S-motifs in the droplets (Fig. 4e). The elimination of the orthogonality was also confirmed in a two-dimensional histogram of FAM/Alexa405 fluorescence intensities ( Supplementary Fig. 20). In addition, the droplets composed of Y-, orth Y-and S-motifs exhibited fusion (Fig. 4f) similar to the droplets of a sole motif composition. Thus, selective fusion of the DNA droplets was achieved in two motifs that were orthogonal and the addition of the motif for cross-bridging eliminated the selectivity.

Fission and segregation of DNA droplets
To further demonstrate the controllability of the DNA droplets, we designed a mechanism for their fission (Figs. 5a and 5b). DNA-RNA chimera strands were introduced into the S-motif, termed 'chimerized-S-motif (CS-motif)' that also has SEs for both the Y-and orth Y-motifs ( Fig. 5a and Supplementary Table 5). Two RNA regions were located at around the centre of the CS-motif and ribonuclease A (RNase A) decomposes the RNA parts. The enzymatic reaction results in splitting CS-motif into two three-branched portions with affinity to the Y-motif ('Y-portion') and the orth Ymotif (' orth Y -portion') ( Fig. 5a, Supplementary Fig. 21). After splitting, the cross-bridge ability of the CS-motif disappears, and the Y-and orth Y-motifs cannot be mixed owing to their intrinsic orthogonality. As a result, the DNA droplets exhibit micro-phase separation in a spinodal decomposition manner, and finally fission into multiple droplets composed of Y-motif/Y-portion or orth Y-motif/ orth Y-portion (Fig. 5b).
The Y-, orth Y-, and CS-motifs formed droplets, representing the mixing of the Y-and orth Y-motifs via CS-motifs. (Fig. 5c) By using S-motifs (non-cleavable by RNase A) in addition to CS-motifs (cleavable by RNase A), we demonstrated the formation of complex-shaped droplets. When the ratio of the CS-motif was large but a few S-motifs existed, addition of RNase A did not induce fission but caused the segregation of the droplets owing to the immiscibility and the partial cross-bridging by a few S-motifs (Fig. 5f).
Experimental results showed that in the 90 % ratio of the CS-motifs, the DNA droplets segregated 16 and finally formed Janus-shaped droplets that have two portions for the Y-and orth Y-motifs in the droplets ( Fig. 5g and Supplementary Figs. 25 and 26). Fluorescence of Cy3 ( orth Y-portions) and Cy5 (Y-portions) were colocalized to Alexa405 ( orth Y-motif) and FAM (Y-motif), respectively. Furthermore, the 50 % ratio of the CS-motifs resulted in the patchy-like pattern formation in the DNA droplets ( Supplementary Figs. 27 and 28). These results showed the existence ratio of the S-and CSmotifs determined the shape of the DNA droplets after the addition of the RNase A, and indicated that the S-motifs played a role for not only the cross-bridging but also for a 'surfactant' between the Y-and orth Y-motifs.

Selective cargo capture and partitioning in DNA droplets
The combination of our DNA-based LLPS system and other molecules would provide an application basis and increase the functionality of the DNA droplets. We focused on the capture of cargo into the DNA droplets via DNA-modification. DNA-streptavidin conjugates that have SEs for Y-or orth Y-motifs were prepared (Fig. 6a) and the selective capture of streptavidin in the DNA droplets was visualized (Fig. 6b).
DNA-modified streptavidin, labelled with DyLight 549 fluorophores, was added during the visualization of DNA droplets composed of Y-or orth Y-motifs. The streptavidin was successfully localized in specific DNA droplets, depending on the modified DNA sequence (Figs. 6c and 6d). In addition, the accumulation processes of the streptavidin into DNA droplets were also visualized ( Supplementary Fig. 29).
Moreover, by adopting the technique to prepare the Janus-shaped DNA droplets (Fig. 5f), partitioning of the cargos in DNA droplets was achieved (Fig. 6e-6j). Streptavidin, modified with SE sequences, were homogeneously distributed in DNA droplets in which the Y-and orth Y-motifs were mixed by the S-and CS-motifs ( Fig. 6f and 6i). After the addition of RNase A, DNA droplets segregated into the Janus shape, and streptavidin were partitioned into the complementary sides depending on the modified sequence ( Fig. 6g and 6j). As we demonstrated here, modification of targets with SE sequences, which encode interaction information, allowed us to capture them in DNA droplets and to control their partitioning in a sequence-dependent manner. These results suggest that DNA droplets have a potential to be carriers of designated molecules and to provide reaction environments for biochemical processes as artificial membraneless organelles.

Discussion
In this paper, we reported the sequence-dependent phase behaviour of the DNA nanostructures and the control of DNA droplets according to the information encoded in the SE sequences. The sequencedependent phase-changes were reversible between the dispersed, droplet, and gel phases in response to the surrounding temperature (Fig. 2a), which is similar to the gas-liquid-solid phase transition of matter. We expect that these findings will be applicable to other nanostructures such as DNA origami 22 , DNA-modified proteins 37 , or nanoparticles covered with DNA strands [38][39][40] . In other words, the phase behaviour shown in the present study could be expanded to matters that can be modified with DNAs, which may enable us to design the phase and create droplets for any material.
A remarkable point in our DNA droplet system is the controllability of the interaction and dynamic behaviour of the droplets (Figs. [3][4][5]. As living systems are well organized-dynamic structures whose behaviour is regulated by the information encoded in biopolymers 41 , our DNA-based LLPS system would provide a new basis for the development of artificial cell engineering. Additionally, our demonstration for the capture of proteins in DNA droplets with sequence specificity (Fig. 6) can also make significant contributions to synthetic biology to generate a biochemical reaction environment composed of designed molecules.
From the viewpoint of material science, the successful creation of the Janus-shaped DNA droplets ( Fig. 5g) would give us a fundamental technique to construct water-soluble complex-shaped droplets in an aqueous phase, which is intrinsically different from the conventional Janus-droplets 42 based on the water/oil immiscibility. Furthermore, the Janus DNA droplets were created owing to a surfactantlike role of DNA nanostructures for the cross-bridge of the two types of Y-motif. It suggests that multi-affinity surfactants would be achieved by the modification of DNAs to designated molecules.
Finally, we envision that their combination with biochemical circuits that can be programmed to produce and decompose specific DNA strands [43][44][45] , will lead to the design and control of autonomous dynamic behaviour of DNA droplets as if living organisms. Ultimately, such autonomous behaviour of macromolecular structures could serve for the development of molecular robotic systems 46, 47 , 23 which become comparable with living cellular systems in the future. We believe that this study is an important step toward the development of a novel LLPS system whose dynamical behaviour can be controlled by information encoded in component molecules.

Oligonucleotide preparation
Sequences for the DNA and DNA-RNA chimera strands are provided in the Supplementary Tables 1-3, and 5. The oligonucleotides were purchased from Eurofins Genomics (Tokyo, Japan) and were of OPC grade purification, except for the fluorophore-labelled and chimerized strands, that were purified to an HPLC grade. The oligonucleotides were dissolved in ultrapure water (18 MΩ cm in resistance) at 100 µM concentrations and stored at -20 ºC until use.

Repetitive phase-change of Y-motifs
DNA strands for the Y-motifs with 8 nucleotide long sticky ends were mixed in a test tube with the buffer, 5 µM for each strand. SYBR Gold was also added at 1 × concentration to the test tube to stain the DNA. The test tube was heated at 85 ºC for 3 min; then gradually cooled to 25 °C at a rate of -1 °C/min, using a thermal cycler (Mastercycler nexus X2, Eppendorf, Hamburg, Germany). The  Supplementary Fig. 3.

Measurement of the phase-change temperatures and FRAP experiments
Each motif was labelled with dye-modified DNA without sticky ends, that was mixed at a 10 % molar ratio in the solution. (e.g., 5 µM for Y-1 and Y-3, 4.5 µM for Y-2, and 0.5 µM for Y2_0_FAM). The sample solution was poured in the chamber on the stage heater and incubated at 85 °C for 3 min.
Subsequently, the temperature was decreased to a designated temperature at a rate of -1 °C/min. To determine the temperature at which the DNA droplets were formed, the sample was visualized at the 1 °C interval. To evaluate the phase-change from the droplet phase to the gel phase, the fluidity of the motifs in the particles formed by the phase separation was analysed using FRAP experiments.  Supplementary Table 5. Sequences of six-junction motifs (S-motif) and the chimerized-S-motif

Measurement of Tm for the Y-motif
DNA strands for the Y-motifs without sticky ends were mixed in a test tube at 5 µM of each strand with a buffer, consisting of 20 mM Tris-HCl (pH 8.0) and 350 mM NaCl. SYBR Green I (Takara Bio, Kusatsu, Japan) was added at 1× concentration to the test tube to detect the formation of the double helix. The test tubes were set on a real-time PCR detection system (CFX Connect, Bio-Rad, Hercules, CA, USA). The sample was heated at 85 ºC for 3 min; then cooled to 5 °C at a rate of -1 °C/min.
Subsequently, the temperature was increased from 5 °C to 85 °C at the same rate. The fluorescence intensity was measured at 1 °C intervals during the decrease and increase of temperature ( Supplementary Fig. 1).

Concentration estimation
The concentrations of the Y-motifs in the droplets and gel phases were estimated by measuring the fluorescence intensity of the supernatant, after centrifugation, that precipitates the DNA droplets and hydrogels. First, the calibration curve for the intensity-based concentration values was prepared using Y-motifs without sticky ends (composed of Y-1_0, Y-2_0, Y-3_0 and 10 %(mol) Y-2_0_FAM). The Y-motif without a sticky end was annealed at 5 µM in a 20 µl volume in the PCR test tube with the buffer, using the thermal cycler from 85 °C to 4 °C, at a rate of -1 °C/min. The annealed Y-motifs without sticky ends were then diluted to 100, 10, and 1 nM for a 20 µl volume using the buffer, and the fluorescence intensity was measured using a spectrometer (FP-6500, JASCO, Hachioji, Japan).
Next, the Y-motifs with 4, 6, 8, 10, and 12 nucleotide long sticky ends were also annealed by the same procedure. After annealing, to precipitate the DNA droplets and hydrogels at the bottom of the test tubes, the PCR tube was placed in a larger test tube as a support during centrifugation ( Supplementary   Fig. 18 a). Then, the tubes were centrifuged at 2000 ´ g at 4 °C for 20 min. The precipitation of the phase separated Y-motifs were confirmed using a gel imager (Gel Doc EZ system, Bio-Rad, Hercules, CA, USA) ( Supplementary Fig. 18 b). The PCR tubes containing the precipitate were set on the thermal cycler. For measuring the concentrations in the droplet and gel phases, the temperatures were set at 1 °C lower than the Td for each length of the sticky end or 4 °C, respectively. The test tubes were incubated for 10 min at each temperature, and the supernatant was collected using a gel loading tip (BM Equipment, Tokyo, Japan). Ten micro-litres of supernatant was diluted to 200 µl using the buffer, and the fluorescence intensity was measured. The concentration of Y-motifs was estimated using the calibration curve.

Observations of orthogonality in the DNA droplets and its elimination
For the orthogonality experiments, DNA strands were mixed in a test tubes with the buffer at the concentrations shown in Table 6. This mixture was poured in the observation chamber and set on the stage heater. Then, the temperature was kept at 85 °C for 3 min, and decreased at a rate of -1 °C/min.
The fusion events of the DNA droplets were visualized at 60 °C using the confocal microscope at a scanning velocity of 7 s per frame.
To confirm the elimination of the orthogonality, the Y-, orth Y-, and S-motif were mixed in a test tube with the buffer at the concentrations shown in Table 7. The mixture was then visualized using the same method as described above. Supplementary

Fission of DNA droplets
To achieve fission of the DNA droplets, part of the DNA strands constituting the S-motif were replaced with DNA-RNA chimera strands, considering the motif geometry for the split into the Yand orth Y-portions. DNA and DNA-RNA chimera strands were mixed at the concentrations given in Supplementary

Segregation of DNA droplets
The Janus-shape and patchy-like patterns in the DNA droplets, were created by adjusting the concentrations of DNA-RNA chimera strands. For the Janus-shape and patchy-like pattern, 90 and 50 mol % of the DNA strands were replaced with the chimera strands, respectively (Supplementary Table 9 and 10). Sample solutions in the test tubes were annealed from 85 °C to 25 °C at a rate of -1 °C/min using the thermal cycler; then, 1 µl of the RNase A solution was added to the solutions for the 20 µg/ml final concentration. These mixtures were poured into the observation chamber on the stage heater and the temperature was increased to 62 °C, and visualized using the confocal microscope. Supplementary

Supplementary Discussion
The phase diagram (Fig. 3a in the main text) showed that the phase-change temperature between the dispersed and droplet phase (Td) for each sticky end (SE) was higher than the Tm of the SEs. The Tm is generally defined as the temperature at which half of the DNA strands in a solution formed double helixes when two complementary DNA strands were present. On the other hand, our motifs have multiple SEs (e.g., Y-motif has three SEs). Thus, the Tm for the SEs should not be considered, but instead, the Tm for the motifs (Tm-Motif) at which half of the motifs in a solution are connected, should be considered.
In the branched motifs, the hybridization of one of multiple SEs would be sufficient for the connection between the motifs. Based on this idea, we considered that the Tm-Motif can be described as the temperature at which at least one of the multiple SEs can hybridize at a 50 % ratio. It is calculated by the following equation:  Fig. 13); this trend is consistent with the experimental results (Fig. 3c). However, there were still gaps between the Td and Tm-Motif, in particular, for the shorter SEs, which suggests that another parameter can influence the phase-change temperature.
The phase diagram also showed that the difference between the Td and Tg (the phase-change temperature between the droplet and gel phase) becomes larger with decreasing SE length. As the hybridization stability of the SEs would play a key role in determining the phase-change temperature of both the Td and Tg, the width of the melting range (Tw) provides an indication for the phase-change temperature.
In addition to Tm, Tw is also an important parameter for the characterization of melting behaviour.
Tw can be defined as the difference between the temperatures at the end and the start of DNA melting ( Supplementary Fig. 14). DNA strands transfer from ssDNA to dsDNA states in the range of Tw and vice-versa. At the start of the melting, SEs can exhibit weak interactions, and at the end of melting, SEs form stable double helixes. As the self-assembly of motifs into droplets and gel structures results from weak interactions and stable network-formations, we supposed that temperature differences between Td and Tg (ΔTdroplet-gel) related to Tw.
We calculated Tw for each of the SEs from the melting curve using NUPACK 1 (Supplementary Fig.   15). The ΔTdroplet-gel and Tw were shown in Supplementary Fig. 16. ΔTdroplet-gel and Tw exhibited closer values and the differences between ΔTdroplet-gel and Tw are smaller in the shorter SEs. Although the entanglement of motifs can influence Tg, as we discussed in the main text, this graph suggests that Tw may be one of the parameters that determines the phase-change temperature.
Taken together, the entanglements of motifs, multiple SEs in motifs that provide new parameters of Tm-Motif, and Tw of SEs could be possible factors influencing the phase-change temperature and their combinatorial effects may determine Td and Tg. Model-based numerical simulations could be a