Chiral Matching between Nucleic Acids and Polypeptides Facilitates Liquid–Liquid Phase Separation

Abstract

Liquid–liquid phase separation (LLPS) is a newly discovered phenomenon to modulate a multitude of cellular functions. Despite its importance, the full evolution mechanism of LLPS starting from intramolecular interactions to intermolecular condensations has yet to be revealed. In this study, we investigated a representative LLPS formed between negatively charged nucleic acids poly(G-quadruplex) and positively charged peptides poly(lysine). Harnessing the chiral nature of these two components, we elucidated an exquisite chirality effect on the LLPS formation using optical-tweezer-based single-molecule force spectroscopy, which revealed four states of intramolecular condensation at low component concentrations, and a microscopy-based ensemble clouding assay, which, in a complementary manner, discloses the shape and density of macroscopic intermolecular condensates at higher concentrations. We found that, with increasing concentrations, intramolecular interactions evolve to intermolecular condensations, resulting in liquid-like condensates followed by solid-like droplets. The entire evolution was facilitated by the matching chirality between poly(G-quadruplex) and poly(lysine), which confirmed that the intermolecular interaction is the driving force for the LLPS process. The elucidation of the full LLPS evolution offers ample opportunities to interfere with the LLPS process via chirality factors, which provides new avenues for targeted therapeutics and development of functional biomaterials.

Graphical Abstract

Liquid–liquid phase separation (LLPS) is a physicochemical process that drives the separation of two aqueous phases in a solution mixture, providing spatial and temporal regulation of biochemical reactions. This phenomenon has garnered intensive research attention due to its pivotal role in organizing intracellular components and its implications in various biological processes and diseases.^1,2 Almost all LLPS in cells involve proteins,^1,3 whereas a significant portion of LLPS droplets contain nucleic acids.² Recent studies have high-lighted the importance of electrostatic interactions between negative-charged nucleic acids and cationic residues in peptides to facilitate LLPS formation^4,5 by affecting protein conformations for example.⁶ However, a detailed evolution mechanism starting from intramolecular interactions between these two key components at low concentrations to the intermolecular interactions at higher concentrations remains elusive.

Given that natural nucleic acids and peptides have predominately d and l chiralities, respectively, it is intriguing to understand the chiral effect of these two key components in LLPS formation. Chirality is critical in many biological interactions, such as molecular recognition and structural formation of biomolecules.^7–9 Therefore, the chiral communication between nucleic acid and proteins is expected to exert an important role yet to be determined in the LLPS formation.¹⁰ Recently, studies have shown that naturally non-predominant d-amino-acid-containing peptides¹¹ also exist in phase-separated protein aggregates, such as plaques, responsible for diseases such as Alzheimer’s and Parkinson’s diseases.^12,13 Therefore, it becomes even more significant to scrutinize the chiral effect on LLPS formation, which provides insights into the fundamental principles governing the properties of biomolecular interactions.

Given the potentially subtle chiral interactions in nucleic acids and polypeptides, we employed single-molecule mechanical unfolding in optical tweezers to investigate intramolecular interactions at low component concentrations and a high-resolution clouding assay in a video microscope to study the intermolecular interactions at increased concentrations. The submolecular sensitivity¹⁴ of optical-tweezer-based mechanical unfolding allows for investigation of conformation changes of individual macromolecules with nanomolar effective concentrations¹⁵ during intramolecular condensations. At higher concentrations where macroscopic LLPS occurs, we used video microscopy to examine the multivariable information, such as the size, shape, and number of LLPS droplets, which is beyond the reach of conventional clouding assays using absorbance or light-scattering principles.

With these two complementary methods, we dissected the interactions between poly(DNA-G-quadruplex (GQ)) with either left- (l-) or right- (d-) handed GQ topologies and poly(lysine) containing either d- or l-lysine units [i.e., poly(d-lysine) (PDL) or poly(l-lysine) (PLL)]. G-quadruplexes are four-stranded DNA structures stabilized by Hoogsteen hydrogen bonds, playing vital roles in genomic stability and regulations,¹⁶ through the process involving LLPS.^17,18 Nucleic acid strands with tandem GQ formation [i.e., poly(GQ)] exist inside cells.^19–21 In nature, G-quadruplexes adopt the right-handed (d) conformation; however, recent studies have also reported the presence of left-handed (l) GQ structures, commonly referred to as Z-G4s, in genomic DNA fragments.^22–24 Our results have demonstrated that matching chirality between poly(GQ) and poly(lysine) facilitates every stage of the LLPS likely due to the better association between the two macromolecular components. These findings rendered a full picture of the evolution mechanism of the LLPS between nucleic acids and peptides, starting from intramolecular interactions (i.e., single-molecular level) that undergo four progressive states to intermolecular condensations (i.e., macroscopic bulk level) in which liquid-like droplets are followed by solid-like condensates. Surprisingly, we found that there exists a trapped state in the intramolecular condensation that does not convert to liquid-like or solid-like intermolecular LLPS droplets. This study not only elucidates the molecular mechanism of LLPS but also underscores the generic nature of chirality effects across different macromolecules. By systematic investigation of the chirality-dependent phase behavior, this work lays the foundation for future research to design chiral-specific biomolecular assemblies for potential applications in materials, biotechnology, and medicine.

Intramolecular Condensation of Poly(DNA-d-GQ) Prefers Poly(d-lysine) (PDL) over Poly(l-lysine) (PLL).

We first synthesized a long ssDNA template that consists of a tandem array of a human telomeric GQ-forming sequence²⁵ (5′ TTA GGG TTA GGG TTA GGG TTA GGG TTA 3′) via the RCA protocol^26,27 (Figure 1A; see section S4 of the Supporting Information for details). To this end, we designed a linear ssDNA that consists of a sequence complementary to the GQ-forming sequence. After this fragment was circularized by splint ligation,²⁸ the splint was removed by toehold-mediated strand displacement.²⁹ The resultant fragments of noncircular DNA were removed by exonucleases I and III (NEB). The RCA was performed using a 5′ biotin-modified primer on the circular DNA template by a Phi29 DNA polymerase. After RCA, the 3′ end of ssDNA was modified with a digoxigenin molecule by terminal deoxynucleotidyl transferase (TdT) (Thermo Fisher). Consistent with the literature,²² the CD spectrum of the GQ-forming sequences in the ssDNA template [i.e., poly(DNA-d-GQ)] confirmed the formation of right-handed G-quadruplex structures in 10 mM Tris buffer (pH 7.4) supplemented with 100 mM KCl (see Figure S8 for details).

Figure 1.

Chiral preference in the intramolecular condensation of poly(DNA-d-GQ) in the presence of PDL. (A) Synthesis of a tandem array of DNA d-GQ in a single-stranded DNA template. (B) Optical-tweezers setup to investigate single-molecule condensation between poly(DNA-d-GQ) and poly(d-lysine) (PDL). Schematics of four different condensation states are shown below. With an increasing PDL concentration, the end-to-end distance of poly(DNA-d-GQ) decreases, indicting the progress of intramolecular condensation. (C) Typical FX curves from the single-molecule assay represent different condensation stages in a concentration-dependent manner. Colored and black curves indicate stretching and relaxing FX curves, respectively. (D) Phase diagram of condensation stages in the single-molecule poly(DNA-d-GQ) strand in the presence of PLL and PDL with different concentrations. The data for PLL are redrawn from ref 5.

To investigate the condensation in a single nucleic acid template of poly(DNA-d-GQ) prepared above (hence, we call this intramolecular condensation), the template was tethered between two optically trapped polystyrene beads using biotin–streptavidin and digoxigenin (DIG)–DIG antibody interactions in the laser-tweezers instrument (Figure 1B). The end-to-end distance of the negatively charged poly(DNA-d-GQ) template was monitored when positively charged poly(d-lysine) (PDL) or poly(l-lysine) (PLL) solution was continuously introduced in 10 mM Tris buffer (pH 7.4) supplemented with 100 mM KCl inside a four-channeled microfluidic chamber (see sections S2 and S3 of the Supporting Information for details) at room temperature.⁵ Given the variability in literature reports^30–32 on the effect of the polymer length on nucleic acid condensation, we used commercial poly(lysines) of 150–350 amino acids in length. Tension was applied to the tethered single-molecule construct by mechanically moving the two optically trapped beads apart using a mirror that steered one of the trapping lasers³³ (see section S3 of the Supporting Information for details). This allowed the mechanical unfolding of the structures formed in the poly(DNA-d-GQ) template.

Without PDL or PLL, mechanical unfolding of the GQs in the tethered ssDNA template revealed distinct rupture events [Figure 1C, “state 1”; see Figure S9 for more force–extension (FX) curves]. Upon relaxation, a hysteresis was observed between the stretching and relaxing FX curves, characteristic of slow GQ unfolding and refolding events.^5,25 The addition of PDL resulted in changes in the FX curves (Figure 1C, “states 2, 3, and 4”). At lower PDL concentrations (0–0.01 μM or “state 1”), the rupture features, hysteresis area, and end-to-end distance (at 51 pN) of the poly(DNA-d-GQ) template remained unchanged in the FX curves (Figure 1B and C, “state 1”). As the PDL concentration increased from 0.1 to 1 μM, the FX curves shifted to the left, indicating shortening of the end-to-end distance of the construct (Figure 1B and C, “state 2”). This suggests that long-range interactions exist between PDL and poly(DNA-d-GQ), which shortened the construct by forming loops for example (Figure 1B). Since PDL and poly(DNA-d-GQ) are oppositely charged, these long-range interactions are primarily driven by electrostatic attractions, which facilitate loop formation beyond direct polymer contact. The appearance of large rupture events (~200 nm, see an event around 30 pN in the “state 2” F-X curves in Figure 1C) was consistent with this scenario.

Above 1 μM PDL, an elevated baseline force (i.e., the plateau force of 9.2 ± 3.4 pN) was observed instead of the expected baseline at 0 pN (Figure 1B and C, “state 3”). This phenomenon, consistent with our previous findings⁵ and other studies,^34,35 has been ascribed to the mechanical stretching of the condensed phase of the poly(DNA-d-GQ) template in the presence of positively charged polymers, like spermidine³⁵ or polyamidoamine.³⁴ Below this concentration (<1 μM), no such features were observed in the FX curves even after 20 min of incubation (see Figure S10 in section S12 of the Supporting Information for FX curves).

When the PDL concentration was increased to 200 μM, we observed short and clean FX curves without any rupture events (Figure 1B and C, “state 4”), similar to those observed previously between PLL and non-GQ-forming nucleic acids.⁵ At this high concentration, we hypothesize that the nucleic acid−PDL condensate matured to state 4, further reducing the end-to-end distance of the assembly. At the same time, the condensate became strong enough to resist a force up to 60 pN to pull it apart. Occasionally, the two trapped beads collapsed together in one of the optical traps when exposed to 200 μM PDL, indicating that the condensation force from the PDL and multi-GQ mixture exceeded the optical trapping force of the escaped polystyrene bead. Below this concentration (200 μM), no such features were observed in the FX curves even after 20 min of incubation (see Figure S11 in section S13 of the Supporting Information for FX curves).

Based on these data, we constructed a phase diagram for the four intramolecular condensation states of the poly(DNA-d-GQ) template at different PDL concentrations (Figure 1D). In comparison, we also plotted the phase diagram describing the same four states of the poly(DNA-d-GQ) construct in the presence of PLL.⁵ We found that, with PLL, state 4 was never observed at the PLL concentration up to 200 μM. Additionally, PLL began to promote state 2 of poly(DNA- d-GQ) at only 30 μM, which was 300 times higher than that (0.1 μM) for PDL to enter the state 2 of the same DNA template. The condensed phase (state 3) of the DNA template was only observed at 200 μM PLL, 200 times higher than PDL (1 μM). All these findings indicate that poly(DNA-d-GQ) interacts stronger with PDL than PLL to undergo different intramolecular condensation states. Given that the DNA backbone and GQ structures both have d chirality, it suggests that chiral matching between poly(lysine) and the nucleic acid template facilitates the intramolecular condensation of the nucleic acid template. To further confirm this chiral matching mechanism, we compared the effect of racemic poly(lysine) mixtures to that of poly-d-lysine and poly-l-lysine on the condensation process of poly(DNA-d-GQ). We observed that the poly(DNA-d-GQ) condensation was facilitated with a ranking order of poly-l-lysine, racemic mixtures, and poly-d-lysine (Figure S17). This ranking again supports that poly-d-lysine promotes condensation via chiral recognition, while the presence of poly-l-lysine in the racemic mixture may partially impede this effect due to chiral mismatch in the condensation process of poly(DNA-d-GQ).

Intramolecular Condensation of Poly(DNA-l-GQ) Prefers Poly(l-lysine) (PLL) over Poly(d-lysine) (PDL).

If this chiral matching principle (d-DNA prefers PDL) exists, then we expect the interaction between a l-DNA template and PLL would be stronger than that with PDL. However, there are no molecular biology tools available to prepare a long l-DNA strand. Instead, we introduced multiple left-handed G-quadruplex (l-GQ)²² units on a d-DNA template. First, we confirmed that the l-GQ-forming sequence (see Table S1) can fold into GQ at the single-molecular level. To this end, we first synthesized a single-unit l-GQ construct by ligating the l-GQ-forming ssDNA sequence (Table S1) between two dsDNA handles (1558 and 2391 bp duplex DNA; see sections S6 and S7 of the Supporting Information for details). The two handles were separately labeled with biotin and digoxigenin at the ends (Figures S4 and S5)³⁶ to facilitate the tethering of the construct between the two optically trapped polystyrene beads as described above. After the final construct was exposed to a 10 mM Tris (pH 7.4) buffer supplemented with 100 mM KCl, a tension was applied by moving one of the trapped beads apart from the other. When the tension was sufficiently high, the structure in the construct was unfolded, producing a rupture event in the FX curve (Figure S5B). In a control construct without the l-GQ-forming sequence [i.e., l-GQ was replaced by a short duplex DNA fragment containing an internal (dA)₂₁ loop (see Table S1 for the sequence)], the FX curves showed no rupture features (3 molecules, 27 FX curves; see section S8 of the Supporting Information for details), confirming that the rupture event was due to the folded structure in the l-GQ-forming sequence. After we examined the histograms of change in contour length (ΔL) and unfolding force (F) (Figure S5C and D) from 96 unfolding events (12 molecules), we found that ΔL was centered at 10.2 nm, close to the expected ΔL (9.5 nm) of the l-GQ structure (see section S9 of the Supporting Information for details). In addition, CD spectra showed a characteristic trough at ~270 nm, which is absent in d-GQ, and a crest at ~250 nm (see section S10 of the Supporting Information), both consistent with the formation of a left-handed GQ structure²² in the l-GQ-forming sequence. It is interesting that the unfolding force of this structure was significantly higher (p < 0.0001) than that of the human telomeric GQ studied above (38.2 pN vs 21.7 pN),³⁷ which may be due to the fact that l-GQ consists of four G-quartets in the quadruplex²² instead of the three G-quartets in telomeric GQ.

With the l-GQ conformation confirmed, next, we prepared a single-stranded DNA template containing an array of l-GQ-forming units [poly(DNA-l-GQ)] by using the RCA strategy described above (see section S4 of the Supporting Information). We then performed an intramolecular condensation assay on poly(DNA-l-GQ) by continuously flowing PLL or PDL into the microfluidic channel. Strikingly, we observed “state 4” in poly(DNA-l-GQ) with 200 μM PLL, which was absent even as high as 200 μM PDL (Figure 2B–D; see Figures S12 and S13 for more FX curves in sections S14 and S15 of the Supporting Information). This confirms that poly(DNA-l-GQ) undergoes a stronger condensation with PLL than with PDL.

Figure 2.

Confirmation of the chiral preference in the intramolecular condensation of the single-stranded poly(DNA-l-GQ) template in the presence of poly(lysine). (A) Single-molecule experimental setup to investigate condensation of the poly(DNA-l-GQ) template. Typical FX curves obtained from the condensed poly(DNA-l-GQ) template in the presence of (B) PLL or (C) PDL. Colored and black traces represent stretching and relaxing FX curves, respectively. States 1–4 depict different condensation states. (D) Phase diagram of intramolecular condensation of poly(DNA-l-GQ) in the presence of PLL or PDL.

Comparing the phase diagrams of the intramolecular condensations between poly(DNA-d-GQ)/PDL and poly-(DNA-l-GQ)/PDL mixtures (Figures 1D and 2D), we found that the “state 3” condensation began at 1 μM PDL for poly(DNA-d-GQ), whereas for poly(DNA-l-GQ), it started at 10 μM PDL (i.e., more difficult to form). At 200 μM PDL, poly(DNA-d-GQ) exhibited strong condensation (“state 4”), whereas poly(DNA-l-GQ) did not. In contrast, in the case of PLL, a reversed pattern in the phase diagram was observed. While poly(DNA-l-GQ) started to condense to the “state 3” with 10 μM PLL, poly(DNA-d-GQ) entered the same state with 200 μM PLL (i.e., more difficult to form). Despite the similar trends in the phase diagrams of the poly(DNA-l-GQ)/PLL and poly(DNA-d-GQ)/PDL mixtures, the impact at each concentration differed due to the presence of the d-DNA spacers in the poly(DNA-l-GQ) template (see section S4 of the Supporting Information for details), which increased chirality clash when interacting with PLL. Overall, these observations at the single-molecular level strongly support the hypothesis that chirality matching between DNA and poly(lysine) enhances the propensity for intramolecular condensation to proceed.

Intermolecular Condensation Also Showed the Chiral Matching Principle between Poly(DNA-d/l-GQ) Strands and PDL/PLL Polypeptides.

To investigate whether such a chirality preference exists in the intermolecular LLPS condensation at the bulk level, we conducted ensemble phase separation assays between poly(DNA-d-GQ)/poly(DNA-l-GQ) and PDL/PLL. We found that the LLPS droplets formed between poly(DNA-d-GQ) (1 mM equivalent of the charge concentration calculated by the phosphate groups) and PDL (200 μM equivalent of the charge concentration calculated by the lysine units) were significantly more than those formed with PLL (200 μM equivalent of the charge concentration; Figure 3A; see section S5 and Figure S15 for details), supporting that chirality matching exists in the intermolecular LLPS processes. Next, we mixed 1 mM (equivalent of the phosphate concentration) of poly(DNA-l-GQ) with 200 μM (equivalent of the lysine concentration) of PDL or PLL; again, we found that poly(DNA-l-GQ) more easily formed droplets (26 ± 2 vs 10 ± 3 droplets per 50 × 50 μm area in an image frame; Figure 3B; see Figure S15 for details) with PLL than PDL, confirming the chiral matching principle at the bulk level.

Figure 3.

Chiral matching in intermolecular LLPS condensations. (A) and (B) show the LLPS droplet density observed under a video microscope in the mixtures of chiral poly(DNA-GQ) and chiral poly(lysine). Images depict typical fields of view for each mixture. Circles at 100 μM concentrations indicate typical droplets. Scale bars: 10 μm. (C) and (D) represent turbidity measurements of the LLPS in the mixtures of chiral poly(DNA-GQ) and chiral poly(lysine) using 600 nm absorbance. The p values are indicated for different signals between PDL and PLL. Error bars depict standard deviations from at least 3 independent measurements. All concentration axes refer to those for poly(lysines) while DNA concentration is kept constant at 1 mM equivalent phosphate concentration.

The subtle differences in the number of LLPS droplets can also be distinguished at other PLL/PDL concentrations (Figure 3A, inset). However, above 1 mM PLL or PDL, droplets became too many to distinguish (Figure S15). To follow LLPS under these high PLL/PDL concentrations, we performed 600 nm absorbance-based turbidity assays (Figure 3C and D). Again, we found that LLPS formation was facilitated when there was chirality matching between poly(GQ) and poly(lysine). Interestingly, the absorbance assay could not detect turbidity at lower concentrations (<0.2 mM) due to sensitivity reasons.

Evolution Mechanism of LLPS Demonstrates Chiral Matching Principles.

Previously, chiralities in the two polyelectrolytes with opposite charges, such as PDL/PLL and poly(d-/l-glutamic acid) (i.e., PDE/PLE), have been found to play a critical role during the LLPS formation.³⁸ Although PDL or PLL does not assume secondary structures at neutral pH per se,^39,40 when their positive charges are neutralized by negatively charged polyelectrolytes, such as PDE/PLE, they assume stable secondary structures.^38,41 In our case, the positive charges in PDL or PLL are neutralized by the negatively charged nucleic acids, likely forming secondary structures with opposite chiralities in PDL or PLL. The electrostatic attraction between poly(lysines) and nucleic acids brings their respective secondary structures into proximity. As a result, the short-range intermolecular interactions, such as hydrogen-bonding forces, steric packing, and hydration, become critical in the condensates.³⁸ When the chirality of nucleic acid secondary structures matches that of poly(lysine) [i.e., PLL with poly(DNA-l-GQ) or PDL with poly(DNA-d-GQ)], it leads to stronger association between the polypeptides and nucleic acids due to their better alignments, facilitating the LLPS process as observed here (Figure 4A).

Figure 4.

(A) Proposed mechanism for the chirality matching principle in LLPS condensates. (Left) When the chirality is matched in secondary structures of two LLPS components, the intermolecular force between the two components is maximized. (Right) When chiralities are mismatched, intermolecular force is compromised due to steric hindrance, leading to weaker condensates. (B) Evolution of the LLPS process between nucleic acids and polypeptides [poly(lysines)].

In summary, bulk-level LLPS droplets occurred only when polypeptides and nucleic acids had high enough concentrations to allow intermolecular condensations (Figures 3A and 4B). At low concentrations, intramolecular condensations occur (Figure 4B), which has been uniquely investigated by mechanical unfolding in optical tweezers (Figures 1 and 2). Such a single-molecular approach revealed four progressive states of intramolecular condensations with increasing polypeptide concentrations.⁵ It is conceivable that intermolecular LLPS condensations occur after the state 4 of the intramolecular condensation, where additional nucleic acid strands join the nucleus of the intramolecular condensate. However, we found that FX curves of the state 4 did not change in the presence of extra single-stranded poly(DNA-d-GQ) molecules, indicating the absence of intermolecular condensations in these two cases, a feature consistent with the solid-like droplets that do not fuse with each other^42,43 (see Figure S16 for FX curves). This fact suggests that state 4 is a trapped state that cannot proceed further to the intermolecular LLPS condensation (Figure 4B). The trapped state 4 was confirmed when 1 mM poly(DNA-d-GQ) or poly(DNA-l-GQ) was mixed with <200 μM PDL, which produced rather small droplets (diameter of 0.5–1.2 μm) (Figure S15). These droplets did not fuse with each other, even when they were brought into contact inside the same laser focus, which was demonstrated by their rapid dispersion when the laser tweezers were turned off. The nonfusible observation confirmed the solid-like nature of these small droplets (see Figure S14). Since state 4 is a trapped state while state 2 is yet to undergo intramolecular condensation characterized by the force plateau (see “state 3” in Figures 1 and 2), it is likely that the intermolecular liquid LLPS condensation evolves from state 3 in which intramolecular condensation occurs (Figure 4B). With further increase in the concentrations of nucleic acids and/or polypeptides, liquid-like LLPS droplets transition to solid-like droplets (Figure 4B).

Since optical tweezers can isolate individual macromolecules involved in the LLPS process, they provide a unique perspective to understand the LLPS at the intramolecular level without interference from neighboring molecules. Such a capability enables us to reveal four distinct states of the condensation formed between negatively charged nucleic acids and positively charged polypeptides at the intramolecular level. Our focus on this more naturally prevalent two-component LLPS process, instead of the simpler one-component LLPS system, such as tau proteins,⁴² has allowed us to conveniently investigate intermolecular condensations in the LLPS, as concentrations of each component can be precisely controlled. In addition, such a dual-component LLPS platform enables us to dissect chiral interactions between two types of molecules with different chiralities. As a result, we have observed, for the first time, a chiral matching principle between nucleic acids and polypeptides in every stage of the intramolecular condensation as well as the intermolecular LLPS processes. On the other hand, the finding of the chiral matching unequivocally indicates that intermolecular interactions are the driving force for the LLPS evolution. Such a chiral matching phenomenon is expected to have a profound ramification in providing a new means to manipulate LLPS, which is critical for many biological functionalities. For example, chiral-matching-induced assemblies may inspire the design of synthetic systems, such as artificial biomolecular condensates, enantioselective molecular recognition platforms, or chiral biomaterials, where chirality can be changed to modulate LLPS behavior. In this way, our findings also open avenues for future applications in synthetic biology, nanotechnology, and molecular engineering.

Supplementary Material

The Supporting Information is available free of charge at https://pubs.acs.org/doi/10.1021/acs.jpclett.5c02218.

List of oligos, microfluidic chamber, optical tweezer platform to study intramolecular condensation at the single-molecular level, synthesis of an ssDNA template via rolling circle amplification (RCA), bulk-level LLPS assay, synthesis of a single-molecule DNA-l-GQ construct, force and change-in-contour-length histograms of DNA-l-GQ unfolding, typical FX curves obtained from a duplex DNA construct, calculation of change in contour length (ΔL), circular dichroism (CD) study of the G-quadruplex-forming sequences, typical FX curves of poly(DNA-d-GQ) with PDL, time course of FX curves of poly(DNA-d-GQ) with 0.1 μM PDL, time course of FX curves of poly(DNA-d-GQ) with 70 μM PDL, typical FX curves of poly(DNA-l-GQ) with PDL, typical FX curves of poly(DNA-l-GQ) with PLL, evidence of the trapped state 4 by droplet fusion assays, bulk LLPS assays of poly(d-GQ) and poly(l-GQ) with PDL/PLL, typical FX curves of the single-molecule constructs at “state 4” in the presence of DNA, materials, and references (PDF)