Diffusiophoresis promotes phase separation and transport of biomolecular condensates

Doan, Viet Sang; Alshareedah, Ibraheem; Singh, Anurag; Banerjee, Priya R.; Shin, Sangwoo

doi:10.1038/s41467-024-51840-6

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Published: 03 September 2024

Diffusiophoresis promotes phase separation and transport of biomolecular condensates

Nature Communications volume 15, Article number: 7686 (2024) Cite this article

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Abstract

The internal microenvironment of a living cell is heterogeneous and comprises a multitude of organelles with distinct biochemistry. Amongst them are biomolecular condensates, which are membrane-less, phase-separated compartments enriched in system-specific proteins and nucleic acids. The heterogeneity of the cell engenders the presence of multiple spatiotemporal gradients in chemistry, charge, concentration, temperature, and pressure. Such thermodynamic gradients can lead to non-equilibrium driving forces for the formation and transport of biomolecular condensates. Here, we report how ion gradients impact the transport processes of biomolecular condensates on the mesoscale and biomolecules on the microscale. Utilizing a microfluidic platform, we demonstrate that the presence of ion concentration gradients can accelerate the transport of biomolecules, including nucleic acids and proteins, via diffusiophoresis. This hydrodynamic transport process allows localized enrichment of biomolecules, thereby promoting the location-specific formation of biomolecular condensates via phase separation. The ion gradients further impart directional motility of condensates, allowing them to exhibit enhanced diffusion along the gradient. Coupled with a reentrant phase behavior, the gradient-induced enhanced motility leads to a dynamical redistribution of condensates that ultimately extends their lifetime. Together, our results demonstrate diffusiophoresis as a non-equilibrium thermodynamic force that governs the formation and transport of biomolecular condensates.

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Introduction

Biomolecular condensates are a group of non-membraneous organelles that carry out a myriad of intracellular functions including stress response¹, intracellular signaling², and genome organization³. These condensates concentrate organelle-specific proteins and nucleic acids in a spatiotemporal manner to achieve their desired functions in the cell. Segregative transitions, such as phase separation, have been heavily cited as the most plausible mechanism for the formation of biomolecular condensates⁴. Phase separation is a density transition that occurs through a hierarchy of attractive chain-chain and repulsive chain-solvent interactions leading to the formation of compositionally distinct macromolecular phases⁵.

The spatial location and active transport of biomolecular condensates within the cell are often tightly regulated. For example, P granules, which are RNA- and protein-rich condensates, form near the posterior of the cytoplasm during C. elegans zygote polarization⁶. The asymmetric spatial patterning of P granules has been attributed to the intracellular concentration gradients of proteins and RNA⁷. Similar observations were made for bacterial PopZ condensates that regulate cell division in bacteria⁸. PopZ condensates locally form at the poles of bacterial cells. Although not fully understood, it has been hypothesized that PopZ condensates localize to the poles of the bacterial cells due to less crowded chromatin at the poles⁹. Plant cells provide further examples of the spatially controlled formation of condensates¹⁰. These examples and many others suggest that the site-specific localization of condensates within the cell is a prerequisite to their function¹¹. For these reasons, a deeper understanding of the biophysical mechanisms that dictate condensate spatial localization and transport is a topic of significant importance.

The biological cell is intrinsically heterogeneous in space and time, exhibiting several types of thermodynamic gradients of solutes, pH, pressure, ions, and biological macromolecules^12,13. For instance, a recent study has shown that a significant pH gradient is present between the nucleolus and the nucleoplasm due to the distinct charge composition and patterning of the proteins that drive the spatially distinct tripartite mesoscale organization of the nucleolus¹⁴. Pressure gradients are also evident within the living cells where the variations in the ion concentration lead to both osmotic and hydraulic pressures across the cell¹⁵. Such intracellular chemical gradients often lead to intriguing nonequilibrium processes, such as the asymmetric diffusion of molecules and particles up and down the gradients¹⁶.

The directional migration of particles induced by solute gradients is referred to as diffusiophoresis^17,18. In a metabolically active cell, it is speculated that diffusiophoresis may facilitate the transport of macromolecular assemblies across the cell cytoplasm¹⁹. However, it is unknown whether thermodynamic gradients within the cell can cause nonequilibrium forces to drive the motility of biomolecular condensates in space and time through diffusiophoresis. Importantly, the diffusiophoretic response of biomolecular condensate to a gradient would depend on the interfacial properties of the condensate and the type of gradients present. Therefore, understanding how biomolecular condensates behave in the presence of gradients is critical for elucidating their spatial patterning and advective motion within the cell.

In this work, we study the effect of salt concentration gradients on the formation and transport of biomolecular condensates formed by associative phase separation of multivalent disordered proteins and nucleic acids. We postulate two types of effects that a gradient may impart on a biomolecular condensate system: (a) the gradient dictates the regions where the formation of biomolecular condensates via phase separation is favorable, and (b) the gradient leads to directional motility of a biomolecular condensate by biasing the condensate diffusion towards a certain direction with respect to the gradient axis. Both of these effects are plausible and may occur concurrently.

To understand these two effects and their interplay with the biophysical properties of condensates, we employ an in vitro model system comprised of Arg/Gly-rich multivalent peptide [RGRGG]₅ (25 amino acids) and a single-stranded homopolymeric DNA [dT]₄₀ (40 nucleotides). Arg/Gly-rich disordered protein domains have been shown to drive ribonucleoprotein phase separation with RNA²⁰ and are present in a large percentage of the RNA-binding and condensate-forming proteome²¹. These positively charged multivalent domains undergo phase separation with nucleic acids through a combination of their attractive electrostatic forces with the negatively charged backbone of nucleic acids and cation–π and π–π interactions with nucleobases^22,23,24. Several recent studies have characterized the phase behavior and material properties of RGG domains with ssDNA and RNA^{20,24,25,26,27}. Importantly, RGG-nucleic acid (NA) phase separation is reentrant, meaning that phase separation is only favored within a finite window of mixing ratios that are usually centered around the stoichiometric charge-balanced mixture composition²⁸. The stoichiometry of RGG-NA mixtures also dictates the interfacial charge of these condensates via a charge inversion mechanism^22,29,30. The tunable phase behavior and interfacial properties of RGG-NA condensates make them suitable systems for studying the effect of ion gradients on condensate motility.

Using a controlled microfluidic setup alongside fluorescence microscopy, we find that concentration gradients of the peptide and the ssDNA promote spatially patterned condensate formation in specific regions along the salt gradient. We show that the formation of condensates is more robust in the presence of salt gradients due to the local enrichment of the oppositely charged biomolecules via diffusiophoresis. After their formation, the presence of the salt gradient enhances the motility of condensates along the gradient and establishes their directional transport that is dependent on the condensate surface charge. Microfluidics studies on peptide and ssDNA solutions reveal that spatial patterning of condensates is dictated by the location-specific concentration and stoichiometry of peptide and ssDNA mixtures. These results are extended to other biomolecular systems where phase separation is driven by obligate heterotypic electrostatic interactions, such as in the mixtures of cationic nucleic acid binding protein protamine and homopolymeric RNA, poly(rU). Overall, our results show that the controlled spatial localization of biomolecular condensates can be spontaneously achieved with macromolecular and ionic concentration gradients. Furthermore, the enhanced motility of condensates in the presence of salt gradients can add additional control over their localization. Together, these findings shed light on the role of ion and chemical gradients in controlling the localization and transport of biomolecular condensates and highlight diffusiophoresis as a plausible mechanism of localization control of biomolecular condensates within cells.

Results

Phase separation is promoted in the presence of salt gradients

To investigate the associative phase separation of ssDNAs and cationic polypeptides in the presence of salt gradients, we employ a controlled microfluidic platform (Fig. 1, Supplementary Fig. S1). In an H-shaped microfluidic channel, we initially fill the entire channel with the polypeptide [RGRGG]₅ (0.5 mg/ml; 0.17 mM) in Tris buffer (pH 7.5) with additional NaCl of concentration c₁ (Fig. 1a). Then, along the left reservoir channel, we supply an oppositely charged ssDNA [dT]₄₀ (0.63 mg/ml; 0.13 mM) in Tris buffer (pH 7.5) with NaCl of concentration c₂. Finally, the [RGRGG]₅ in Tris buffer with NaCl of concentration of c₁ is injected into the right reservoir.

**Fig. 1: Salt gradients promote the transport and phase separation of biomolecular condensates.**

The microfluidic channel is made out of a UV-curable epoxy (NOA-81) due to its low surface charge (zeta potential = −12.3 mV) and excellent compatibility with in situ photopolymerization of polyethylene glycol diacrylate (PEGDA) hydrogels^31,32. A thin PEGDA membrane is patterned at the right end of the horizontal channel to suppress undesired advective flows in the horizontal channel while allowing the diffusive transport of the molecular solutes (Supplementary Fig. S1). This ensures that only salt gradients are established while keeping the buffer conditions identical throughout the channel. The PEGDA membrane also suppresses [dT]₄₀ and [RGRGG]₅ from permeating through the gel. The side channels thus act as reservoirs that provide and sustain gradients of salts and biomolecules within the center channel. Therefore, the experiments are performed such that a finite amount of initially present polypeptide is gradually diffused out while ssDNA is continuously provided through the left reservoir in the presence (or absence) of salt gradients. Overall, our microfluidic setup can robustly create thermodynamic gradients of ions and biological macromolecules mimicking heterogeneous subcellular microenvironment³³.

We monitor the phase separation and transport of [dT]₄₀ and [RGRGG]₅ using fluorescence microscopy, as shown by the time-lapse images in Fig. 1b–d (Supplementary Movie 1) and their corresponding fluorescence intensity profiles in Fig. 1e–g (averaged over the channel width) and Supplementary Fig. S2 (local maximum intensity). The condensates are visualized using Cy5-labeled [dT]₄₀ (1.2 mol% of the total [dT]₄₀). Once [dT]₄₀ is introduced to the left reservoir, it starts to interact with [RGRGG]₅ and undergoes phase separation via multivalent heterotypic interactions²⁷. These condensates are polydispersed submicron-sized coacervates with mean diameters ranging between 230–660 nm depending on the buffer salt concentration (Supplementary Fig. S3).

Similar to complex coacervates, RGG-NA phase separation is suppressed with an increasing salt concentration in the buffer since electrostatic interactions are one of the major drivers of phase separation of the mixture^22,30. Consistent with this, we observe that with less NaCl in the background (c₁ = c₂ = 1 mM; Fig. 1c, f), phase separation is more robust compared to the higher salinity case (c₁ = c₂ = 20 mM; Fig. 1b, e) as evidenced by the higher fluorescence intensity of the condensates. What is remarkable is that when a salinity gradient is introduced (c₁ = 20 mM and c₂ = 1 mM; Fig. 1d, g), the fluorescence intensity becomes even stronger, despite the overall salinity being higher than the low salinity case (c₁ = c₂ = 1 mM) and the similarity in biomolecular concentrations. With NaCl gradients, the fluorescence intensities are significantly higher than the experiments performed without the gradients (Fig. 1g, Supplementary Fig. S2). These results indicate that NaCl gradients enhance peptide-ssDNA coacervation.

We further observe that peptide-ssDNA condensates are not only formed locally inside the channel but also display wave-like patterns that move along the channel. Notably, the wave speed is faster and moves further down the channel when the NaCl gradient is present, as shown in Fig. 1h, where we track the position of the wave peaks x_peak over time. We note that the condensates under NaCl gradients eventually reach the far right end of the channel where the PEGDA membrane is present. The condensates subsequently accumulate adjacent to the membrane, displaying an extremely localized distribution (Fig. 1i).

We posit that the observed directional migration of the condensates in the NaCl gradients is caused by diffusiophoresis. Given that the concentration of [dT]₄₀ in the left reservoir is higher than the initial [RGRGG]₅ concentration in the center channel, the condensates are generally rich in [dT]₄₀. These condensates are expected to be negatively charged with excess [dT]₄₀ populated preferentially at the surface of the condensate³⁴. Indeed, the electrophoretic light scattering measurements of the condensates at the mixture ratio of [dT]₄₀:[RGRGG]₅ = 1.25:1 confirms the negative surface charge with a zeta potential ζ = −27.4 mV (Supplementary Fig. S4). These negatively charged condensates migrating toward the higher NaCl concentration side are consistent with previously reported diffusiophoresis of negatively charged colloids in NaCl gradients^35,36,37,38. When we impose NaCl gradient in the opposite direction (negative gradient), the wave tends to move slower and the phase separation seems to be less robust (Supplementary Fig. S5). The logarithmic sensing of diffusiophoresis, i.e., the diffusiophoretic velocity varies with the gradient of the logarithm of the salt concentration (Supplementary Fig. S5), further strengthens the nature of the directional migration being diffusiophoresis^39,40.

We next employed image analysis to resolve individual condensates within the wave in order to understand the detailed dynamics of the condensate wave motion. In Fig. 2a–c (Supplementary Movie 2), we plot kymographs showing the spatiotemporal dynamics of the wave and the condensates. In the absence of NaCl gradient, we find that individual condensate trajectories are stochastic and do not exhibit a directional bias, appearing as flat tracks over time (Fig. 2a, b). This indicates that the condensate wave is propagating while the condensates dissolve at the rear side of the wave and form at the wavefront. Contrastingly, in the presence of salt gradients, the advective trajectories of the condensates show that they actively migrate toward the higher NaCl concentration side (Fig. 2c). This directional migration of trailing condensates effectively delays their dissolution. Overall, these findings indicate that NaCl gradients not only enhance condensate formation compared to the uniform salt conditions, but also lead to a directional migration of peptide-ssDNA condensates toward higher NaCl concentrations.

**Fig. 2: Spatiotemporal dynamics of biomolecular condensates reveal the influences of diffusiophoresis on their formation, transport, and dissolution.**

The promotion of phase separation is a result of the local enrichment of biomolecules driven by diffusiophoresis

Diffusiophoresis alters the transport of not only charged colloidal particles but also charged molecular species^41,42. Given that [dT]₄₀ and [RGRGG]₅ are oppositely charged, we speculate that the stronger phase separation of the [dT]₄₀-[RGRGG]₅ mixtures under NaCl gradients is due to the local enrichment of the individual biomolecules driven by diffusiophoretic transport. To test this idea, we conducted similar microfluidic experiments with only either [dT]₄₀ or [RGRGG]₅ present in the same setup with or without the NaCl gradients (Fig. 3a–d). In these experiments, not only [dT]₄₀ is fluorescently tagged (1.2 mol% of the total [dT]₄₀), but also [RGRGG]₅ is tagged with Alexa-488 fluorophore (3.7 mol% of the total [RGRGG]₅). The migration of [dT]₄₀ entering from the left reservoir without the NaCl gradient is driven solely by diffusion, which shows a monotonically decaying distribution along the channel (Fig. 3a). In contrast, with the presence of the NaCl gradient, negatively charged [dT]₄₀ molecules experience a non-monotonic distribution where the molecules locally accumulate as they diffuse down the channel (Fig. 3b).

**Fig. 3: Diffusiophoresis enhances the transport of biomolecules.**

This behavior is likely due to the logarithmic nature of diffusiophoresis^39,40. As the diffusiophoretic velocity (${u}_{d}$) scales with the gradient of the logarithm of the salt concentration ($c$), viz., ${u}_{d}\, \sim \,{\partial }_{x} {{{\mathrm{ln}}}} \,c$, the velocity is influenced by the absolute salt concentration where the biomolecules undergoing diffusiophoresis slow down as they migrate toward higher salt concentrations, leading to their accumulation. This peculiar feature has been observed in a variety of biocolloids including bacterial cells⁴³, liposomes^44,45, DNAs^46,47, and proteins⁴¹. Notably, Riback et al. recently reported similar wave-like advective migration of ribosomal RNAs in the nucleolus, a nuclear biomolecular condensate associated with ribosome biogenesis⁴⁸, for which the migration is speculated to be due to the viscoelasticity gradients present in the nucleolus⁴⁹. A recent report by King et al. showed that a noticeable pH gradient is established between the nucleolus and the nucleoplasm, raising an intriguing possibility that the advective inside-out migration of the ribosomal RNAs might be due to the diffusiophoretic transport induced by proton gradients¹⁴. Finally, similar to the ssDNA migration, positively charged [RGRGG]₅ molecules also experience enhanced transport via diffusiophoresis, but they migrate down the gradient due to the reversed charge polarity (Fig. 3c,d).

To quantify the diffusion coefficient and the diffusiophoretic mobility of [dT]₄₀ and [RGRGG]₅ moving up and down the NaCl gradient from the fluorescence intensity distributions, we consider a one-dimensional transport equation for the individual biomolecules³⁵, which reads

$$\frac{\partial {n}_{i}}{\partial t}+\frac{\partial {j}_{i}}{\partial x}=0,\,\, {j}_{i}=-{D}_{i}\frac{\partial {n}_{i}}{\partial x}+{n}_{i}\cdot {M}_{i}\frac{\partial {{{\mathrm{ln}}}}\,c}{\partial x},$$

(1)

where n_i is the mass concentration, j_i is the mass flux, D_i is the diffusivity, and M_i is the diffusiophoretic mobility of the biomolecular species i (i ∈ {DNA (D), polypeptide (P)}). The mobility M_i quantifies the tendency of a biomolecule’s migration in response to local concentration fields c. The second term on the right-hand side for the flux equation is the phoretic advection driven by the salt concentration gradient. Here, [dT]₄₀ molecules diffuse into the channel with the bulk diffusivity of D_D = 1.2 × 10⁻¹⁰ m²/s (Fig. 3b). With diffusiophoresis, an advective velocity ${u}_{d}={M}_{i}{\partial }_{x} {{{\mathrm{ln}}}}\, c$ is added to the transport of [dT]₄₀ molecules, boosting the migration with additional mobility of M_R = 0.78 × 10⁻¹⁰ m²/s (Fig. 3a). Given the units for mobility being identical to the diffusivity, diffusiophoretic mobility can alternatively be viewed effectively as an enhanced diffusivity since diffusiophoresis of the condensates is ultimately dictated by the diffusion of solutes^50,51.

For [RGRGG]₅, which diffuses out through the left reservoir, the diffusivity without NaCl gradient is estimated as D_P = 2.3 × 10⁻¹⁰ m²/s (Fig. 3c). As the NaCl gradient is introduced, [RGRGG]₅ diffuses out of the channel much faster, accelerated by the diffusiophoretic mobility of M_P = −0.3 × 10⁻¹⁰ m²/s (Fig. 3d). The negative sign indicates that [RGRGG]₅ migrates down the NaCl gradient. Unlike [dT]₄₀ migrating up the concentration gradients by which the molecules locally accumulate, the logarithmic dependence now causes dispersion of [RGRGG]₅ toward the lower salt concentration front. Therefore, while [dT]₄₀ is enriched from lower to higher NaCl concentration, [RGRGG]₅ is quickly brought from higher to lower NaCl concentration. The opposing actions of diffusiophoresis on [dT]₄₀ and [RGRGG]₅ effectively create an attractive interaction over a longer distance, where the length scale is effectively set by the salt diffusion length⁵². This local enrichment of the oppositely charged biomolecules directly enhances the formation of [dT]₄₀-[RGRGG]₅ condensates.

We further confirm the diffusiophoretic transport of [dT]₄₀ and [RGRGG]₅ by performing experiments in other similar monovalent chloride salts, namely LiCl and KCl. For charged molecular species, their diffusiophoretic mobility is linearly proportional to the diffusivity contrast factor, β = (D₊ −D₋)/(D₊ + D₋), where D₊ and D₋ are the diffusivity of cations and anions, respectively⁵³. β sets the magnitude of the diffusion potential that provides the electrokinetic driving force for diffusiophoresis. Indeed, we observe a linear dependence of the mobility on β for both [dT]₄₀ and [RGRGG]₅ (Fig. 3e and Supplementary Fig. S6). Also, their distinct mobility signs confirm once again that the transport of oppositely charged biomolecules is accelerated toward each other by diffusiophoresis, providing a non-equilibrium driving force to phase separate. These results collectively highlight the importance of non-equilibrium interactions of ionic species with biomolecules and their condensates. The equilibrium electrostatics of the monovalent cations Na⁺, K⁺, and Li⁺ are more or less identical, yet their non-equilibrium electrokinetics vary significantly, as manifested by β.

Formation and propagation of the condensate waves are the results of reentrant phase behavior and non-linear diffusiophoresis

Regardless of the presence of NaCl gradients, the biomolecular condensates are distributed in a wave-like fashion where the condensates are formed only within a narrow region in the channel (although the wave speed is significantly influenced by the NaCl gradients), as shown in the intensity profiles in both cases (Fig. 1e–g). These profiles are replotted in Fig. 4a, b where we now delineate the phase-separated regions (solid curves) from the regions of no visible condensates (dashed curves). This behavior in which the phase separation occurs locally is reminiscent of the reentrant phase behavior where the phase separation takes place only within a specific range of biomolecule stoichiometry²⁸. Since [dT]₄₀ enters from the left while [RGRGG]₅ migrates from the right, the concentration ratio of the two biomolecules (i.e., n_D/n_P where n_D and n_P are the mass concentration of [dT]₄₀ and [RGRGG]₅, respectively) gradually decreases along the channel. Such a distribution results in the localized zone of phase separation that is set by a finite window of n_D/n_P.

**Fig. 4: Reentrant phase behavior results in wave-like distribution of condensates that move along the gradients.**

From the intensity distributions for the individual biomolecules presented in Fig. 3a–d, by taking the ratio of the two, we can plot the mixture composition ratio n_D/n_P versus x/L (Fig. 4c, d). The concentrations of the biomolecules, n_D and n_P, are assumed to be linearly proportional to the fluorescence intensity, which is a valid assumption in dilute systems⁵⁴. As we compare the reconstructed n_D/n_P plot (Fig. 4c) with the condensate distribution (Fig. 4a, b), we indeed observe that the range of n_D/n_P over which the phase separation occurs remains more or less constant over time when the NaCl concentration is uniform throughout the channel. This is also shown in the inset of Fig. 4c, where we explicitly plot the phase separation range of n_D/n_P (gray region). As [dT]₄₀ and [RGRGG]₅ diffuse toward each other, the local concentrations of the two biomolecules, and thus the ratio of the two (n_D/n_P), change dynamically in space and time. This gradually shifts the phase-separated region in the positive x-direction by forming new condensates in the leading front and dissolving the existing condensates in the trailing end (Fig. 5a), thus creating a wave-like condensate profile. This is also captured in the kymograph (Fig. 2a), where the condensate streaks that fade in and out indicate, respectively, condensation and dissolution. Despite the dynamically changing n_D/n_P, the condensates are always formed within a fixed range of stoichiometry (n_D/n_P), as also indicated by the constant width of the gray region in the inset of Fig. 4c. This suggests that the formation and dissolution of the condensates occur much faster than the migration of the phase-separation region, thus indicating that the phase separation occurs in a quasi-equilibrium manner. Specifically, our microfluidics experiments indicate that condensates form when 1.0 < n_D/n_P < 3.3.

**Fig. 5: Enhanced phase separation and transport of condensates through diffusiophoresis.**

To confirm the quasi-equilibrium nature of the condensate formation, we performed turbidity measurements of [dT]₄₀-[RGRGG]₅ mixtures under equilibrium by quantifying the amount of light scattered from the condensates at a given wavelength (350 nm)²². Plotting turbidity as a function of mixture composition n_D/n_P shows that condensates form between 0.28 < n_D/n_P < 3.5 (Supplementary Fig. S7). The wider reentrant window may be attributed to the difference in the measurement methods, where the smaller spatial resolution of the turbidity measurements compared to optical microscopy will likely detect smaller clusters that form at stoichiometries far from the charge neutral conditions⁵⁵. Nonetheless, the agreement of the two methods suggests that the phase separation behavior under non-equilibrium conditions of our microfluidic experiments is dictated by local equilibrium thermodynamics. This is consistent with a recent report that suggested that local thermodynamic equilibrium governs phase separation in living cell cytoplasm despite their inherent non-equilibrium nature⁵⁶.

In the case of NaCl gradients (Fig. 4b, d), we observe that the phase-separation range gradually broadens, as also indicated by the widening of the gray region in the inset of Fig. 4d. This is attributed to the increase in the local biomolecule concentration driven by diffusiophoresis (i.e., molecular diffusiophoresis), where the local enrichment of biomolecules by diffusiophoresis broadens the two-phase coexistence window. This behavior is consistent with the previous observations under equilibrium conditions with a similar biomolecular system comprised of RNAs and proteins, where the increase in the absolute concentration of RNA [poly(rU)] and cationic proteins results in a wider range of mixture stoichiometry that promote phase separation in equilibrium environments²². In our system, [dT]₄₀ and [RGRGG]₅ undergo diffusiophoresis, causing a local increase in their concentrations in the presence of a NaCl gradient and directly expanding the stoichiometric range of the two-phase region. Unlike the condensates formed without the NaCl gradient, the condensates under the non-equilibrium environments effectively move along with NaCl gradient via diffusiophoresis (i.e., condensate diffusiophoresis). This directional motility allows the condensates to keep up their position within the moving front of the phase-separated region (Fig. 2c).

The spatial variation within the given stoichiometry window suggests that the condensates’ surface charge may also vary spatially since the surface charge, and thus the diffusiophoretic mobility, of the condensates is governed by the mixture stoichiometry³⁴. To confirm this, we performed electrophoretic mobility measurements of condensates at varying mixture compositions (Supplementary Fig. S4), which showed that the zeta potential of the condensates changes from −17.2 mV when n_D/n_P = 1 to −32.3 mV when n_D/n_P = 3. This zeta potential variation translates to the mobility difference from M_P = 1.0 × 10⁻¹⁰ m²/s (n_D/n_P = 1) to M_P = 2.4 × 10⁻¹⁰ m²/s (n_D/n_P = 3). This implies that, in addition to the logarithmic dependence, the condensates will experience slower diffusiophoresis near the front of the wave than the back, causing even more accumulation of the condensates. This is evidenced by tracking the position of the individual condensates shown in Fig. 2c, where the leading condensates near the front of the wave move considerably slower (~0.28 µm/s) than the trailing condensates at the rear (~0.37 µm/s). Therefore, the simultaneous action of logarithmic sensing and stoichiometry dependence of diffusiophoresis, combined with an enlarged reentrant phase separation window, makes the trailing condensates catch up with the slower leading condensates, which would otherwise have dissolved, reinforcing the local accumulation and migration of the condensates along the salt gradient (Fig. 5b).

We note that the condensate migration velocity (~0.1 µm/s) agrees quantitatively with the theoretical estimates for the diffusiophoretic velocity of charged rigid spheres of similar zeta potential^57,58. This suggests that these condensates behave close to a solid, where liquid-like phoretic transport, i.e., Marangoni propulsion, is negligible. This is likely due to the viscoelastic nature of [dT]₄₀-[RGRGG]₅ condensates^27,30,59. For highly viscous liquid drops, the viscous shear inside the drop should dominate over the viscous shear acting on the exterior, yielding the condition $(\lambda /R)\cdot ({\eta }_{c}/\eta )\, \gg \, 1$, where $\lambda \, \sim \,1$ nm is the Debye layer thickness, ${R} \sim \,240$ nm is the condensate radius, $\eta \, \sim \,1$ mPa·s is the dynamic viscosity of the external solution, and ${\eta }_{c}$ is the dynamic viscosity of the condensates. Based on our previous measurements of similar peptide-nucleic acid condensates^27,30, the viscosity ${\eta }_{c}$ ranges between 1 and 10 Pa·s, indeed satisfying the above condition. The overall migration of the condensates being identical regardless of their size, shown by the kymographs in Fig. 2c, also suggests that their motion is dictated by diffusiophoresis³⁵ rather than the Marangoni effect, which strongly depends on the drop size⁶⁰.

Furthermore, while one may reason that the gradients of [dT]₄₀ and [RGRGG]₅ may also induce the diffusiophoresis of the condensates, this is likely to be negligible due to the biomolecules being dilute while the background solutes are relatively concentrated. For multi-species (electro)diffusiophoresis, one may express the particle velocity as ${u}_{d}=\frac{\varepsilon {kT}}{\eta e}\frac{{\sum }_{i}{z}_{i}{D}_{i}\nabla {n}_{i}}{{\sum }_{i}{z}_{i}^{2}{D}_{i}{n}_{i}}\zeta+\frac{\varepsilon }{8\eta }\frac{{\sum }_{i}{z}_{i}^{2}\nabla {n}_{i}}{{\sum }_{i}{z}_{i}^{2}{n}_{i}}{\zeta }^{2}$, where ε is the permittivity, k_B is the Boltzmann constant, T is the temperature, e is the elementary charge, and z is the charge number^57,58. Taking the summation over all the known background solute species including the buffer, the velocity is estimated to be about ${u}_{d}=0.4$ nm/s, which is indeed negligible compared to the condensate diffusiophoretic velocity driven by salt gradients.

Discussion

A number of recent studies have identified that a variety of dynamical processes of biomolecular condensates are associated with thermodynamic activity gradients. For instance, concentration and temperature gradients established by evaporation at liquid-vapor interfaces are shown to promote phase separation in various biomolecular systems^61,62. These gradients may further segregate biomolecular condensates by convective transport processes such as Marangoni or gravity-driven flows, having implications in prebiotic compartmentalization and localization^61,62. Self-generated chemical gradients via enzymatic reactions can lead to a dynamical response of the condensates. Testa et al. showed that pH gradients established by the enzymatic reactions of urease-containing condensates could induce hydrodynamic flow within and around the condensates via Marangoni flow⁶³. Similar enzyme catalysis-driven gradients may also enable freely suspended condensates to self-propel^64,65. It was also recently predicted that the activity gradients in the nucleus expedite nucleolar coalescence, which helps in the positioning of nucleolus towards the nuclear periphery, a key factor in the localized organization of the nucleus^3,66. Other types of gradients, such as protein gradients, have been proposed to drive the localization of biomolecular condensates, such as the asymmetric patterning of P granules in germline polarized cells due to an underlying MEG3 gradient⁷. Chromatin density gradients have also been suggested to drive the local enrichment of PopZ condensates on the poles of bacterial cells⁸. Therefore, thermodynamic gradients are expected to play a ubiquitous role in regulating the formation and localization of intracellular biomolecular condensates in space and time.

In this work, we provided an elaborate study on the effect of salt gradients on biomolecular condensates formed by RGG repeat polypeptides and ssDNA. Using a controlled microfluidic platform, we showed that heterotypic condensates form non-monotonic patterning along salt and biomolecular gradients due to the reentrant nature of their phase separation. We further delineated two effects of salt gradients on RGG-ssDNA condensates that are both driven by diffusiophoresis on different length scales (molecular and mesoscale). The first is that salt gradients enhance the formation of condensates due to their non-linear effect on the diffusiophoresis of the individual protein and ssDNA molecules. The second effect is that salt gradients can impart directional migration of the charged condensates, which is controlled by the stoichiometry of peptide-ssDNA mixtures. Both of these effects can have important implications in living cells and can provide multiple levels of localization control over biomolecular condensates by either dictating the spatial location where the condensate formation is favored or by enhancing the diffusion of preformed condensates towards a particular location with respect to the underlying gradient.

Although further studies are needed to ascertain whether diffusiophoresis can drive phase separation in living cells, our experiments show that this process, if strong enough, could play a vital role in spatiotemporal regulation of multi-component biomolecular condensates that are formed by charge-driven interactions. This is also consistent with our observations that diffusiophoresis enhances the formation and transport of positively charged [dT]₄₀-[RGRGG]₅ or negatively charged poly(rU)-protamine condensates in NaCl gradients (Supplementary Fig. S8). Recent studies on diffusiophoresis with a variety of other biomolecules and biocolloids, such as membrane proteins⁶⁷, exosomes⁴⁵, bacteria^43,68, and blood cells⁶⁹, or other phase-separating systems⁷⁰ further suggest the ubiquity of diffusiophoresis in biological systems where chemical gradients are ever-present, potentially providing suitable conditions for diffusiophoresis to arise⁷¹. The presence of a concentrated, active, and nonuniform mixture of proteins, nucleic acids, metabolites, and ions such as ATP, Na⁺, K⁺, and Ca²⁺ inside the cytoplasm and nucleoplasm makes the movement of particles and molecules subjected to various gradients. For instance, the interdiffusion of equimolar multicomponent solutes of Na⁺ and K⁺ can also induce significant diffusiophoresis and enhanced phase separation (Supplementary Fig. S9).

Finally, the gradient-induced changes in the microenvironment may lead to different dynamical and non-equilibrium properties of the biomolecular condensates. Our work shows that diffusiophoresis is an important phenomenon for the formation and regulation of biomolecular condensates. The methods we presented here can be utilized to study the effect of diffusiophoresis on many levels beyond salt gradients, including other types of biochemical gradients such as ligands, protein/nucleic acid, crowding, enzymes, and other types of co-solutes. Such studies can illuminate our understanding of the spatiotemporal regulation of biomolecular condensates within the active microenvironment of a living cell and can enable technology development toward synthetic membrane-less organelles with precise localization and functionalities.

Methods

Microfluidic device fabrication

The channel was created using the microfluidic sticker technique with UV-curable epoxy (Norland Optical Adhesive, NOA-81)⁷². In this method, a polydimethylsiloxane (PDMS, Dow Inc.) mold was cast from the SU-8 mold. Subsequently, the NOA-81 channel was molded from the PDMS mold (depth = 40 µm) and partially cured under UV light (IntelliRay 400, Uvitron). Another flat piece of NOA-81 was then combined with the molded channel and exposed to UV light for complete curing. Once the channel is formed, a solution of PEGDA, Sigma-Aldrich (20%(v/v) PEGDA, 2%(v/v) photoinitiator 2-hydroxy-2-methylpropiophenone, Sigma-Aldrich) was injected into the empty epoxy channel. The PEGDA membrane was selectively cured within a thin region using a photomask and a 40× objective lens^31,32,73. After the thin membrane is cured near the inlet, any uncured PEGDA was flushed out by deionized water for 30 min (Supplementary Fig. S1).

Sample preparation

ssDNA oligos of length 40 were purchased from Integrated DNA Technologies (NJ, USA). The dry stocks were reconstituted in RNase-free water. The reconstituted solutions were centrifuged at 23,000 × g for 2 min to remove any particles. After extracting the supernatant, DNA concentrations were subsequently measured using a NanoDrop 1C^TM spectrophotometer. The DNA stocks were then aliquoted and stored at −20 °C for further use. The peptide [RGRGG]₅ was synthesized by Genscript Inc, USA., and was reconstituted in RNase-free water containing 50 mM DTT (dithiothreitol, ThermoFisher Scientific). The purity of the peptides was higher than 90% as per manufacturer specifications. All the peptide sequences contain a C-terminal cysteine that is used for site-specific labeling with fluorescence dyes. The site-specific peptide labeling was performed as described previously^22,34. Polyuridylic acid [poly(rU); molecular weight = 600–1000 kDa] was purchased from Sigma-Aldrich. Poly(rU) RNA was re-suspended in RNase-free water at concentrations ≥80 mg/ml, then aliquots were made and stored at −20 °C for later use. All the ssDNA, RNA, and peptide stocks were checked for complete solubilization and absence of aggregates under the microscope. Salmon protamine (P4005) was purchased from Sigma-Aldrich and used without any further purification.

Microscopy visualization of diffusiophoresis and phase separation

The entire channel was first flushed with the solution consisting of salt, protein, Tris-HCl (10 mM), and DTT (20 mM) in RNase-free water using a syringe pump (Pump 11 Pico Plus Elite, Harvard Apparatus). Subsequently, a second solution consisting of DNAs at different salt concentrations was injected into the left side channel with a flow rate of 20 µl/h to initiate the phase separation experiment in the salt gradient. The transport and phase separation dynamics were observed under an inverted fluorescence microscope (DMi8, Leica) equipped with an sCMOS camera (ORCA-Flash4.0 LT3, Hamamatsu). The recorded images were analyzed using ImageJ and MATLAB. For the visualization of the condensates, Alexa488-labeled peptide [RGRGG]₅ and Cy5-labeled ssDNA [dT]₄₀ (purchased from Integrated DNA Technologies) were used.

Estimation of condensate size distribution

To determine the condensate size distribution using confocal microscopy, condensates at three different salt concentrations were prepared by mixing 0.5 mg/ml peptide [RGRGG]₅ and 0.625 mg/ml ssDNA [dT]₄₀ in a buffer containing 10 mM Tris-HCl (pH 7.5), 20 mM DTT, and either 1, 10, or 20 mM NaCl with 150 nM each of Alexa488-labeled [RGRGG]₅ and Cy5-labeled [dT]₄₀. 5.0 µl of the condensate forming samples were drop-casted on a Tween20 [20%(v/v)] coated coverslips (0.17 mm thickness, 18 × 18 mm² dimensions). The sample was then sandwiched using a glass slide, creating a sample chamber using double-sided tape strips. 100 µl of mineral oil was injected into the sample chamber to prevent evaporation by filling the vacant space in the sample chamber. A laser scanning confocal microscope (Q2, ISS Inc.) with a 60× water objective was used for acquiring the fluorescence images of the condensates. The condensates in the fluorescence images were approximated as circles using Hough Circle Transform algorithm under UCB Vision Sciences plugin in ImageJ (https://imagej.net/plugins/hough-circle-transform)⁷⁴. The diameters of the circles were determined, and a distribution of the estimated diameters was plotted for 1 mM, 10 mM, and 20 mM NaCl concentration (Supplementary Fig. S3a, b).

The size distribution was also measured using dynamic light scattering (Lite Sizer 500, Anton Paar). The condensates were formed with the same mixing conditions as the above confocal microscopy measurement. The sample with a total volume of 60 µl was loaded into a low-volume cuvette (Univette). The measurement was initiated immediately after forming the condensates to prevent sedimentation. The sizes of the condensates were obtained using the General analysis mode and Advanced cumulant model. The size distribution is reported in Supplementary Fig. S3c with different NaCl concentrations, ranging from 1 mM to 20 mM.

Zeta potential measurements of biomolecular condensates and NOA-81

Zeta potential measurements (Lite Sizer 500, Anton Paar) of two types of biomolecular condensates ([dT]₄₀-[RGRGG]₅ and poly(rU)-protamine) are presented in Supplementary Fig. S4. Samples were prepared by mixing the protein ([RGRGG]₅ or protamine) and the nucleic acid ([dT]₄₀ ssDNA or poly(rU) RNA) at the desired concentration ratio in a buffer containing 10 mM Tris-HCl and 10 mM NaCl. For [dT]₄₀-[RGRGG]₅ mixtures, the peptide concentration was fixed at 0.5 mg/ml while the DNA concentration was varied. For poly(rU)-protamine mixtures, the protein concentration was fixed at 0.15 mg/ml while the RNA concentration was varied. Next, the sample was placed in a cuvette and inserted into Litesizer 500 particle size analyzer to perform dynamic light scattering measurements. We observe a charge inversion of protein-nucleic acid complex upon increasing the mixing ratio. [dT]₄₀-rich droplets (ssDNA-to-protein ratio n_D/n_P = 1.25) have a negative charge (zeta potential = −27.2 ± 1.5 mV), while [RGRGG]₅-rich biomolecular condensates show a weakly positive charge (zeta potential = 9.8 ± 1 mV at n_D/n_P = 1/9). On the other hand, poly(rU)-rich condensates (RNA-to-protein ratio n_R/n_P = 4) have a zeta potential of −41.7 ± 1 mV while the charge of the condensates is reversed (zeta potential = 58.8 ± 1 mV) as the concentration shifts to the protamine-rich region (n_R/n_P = 1/4).

We also measured the zeta potential of NOA-81 microparticulates (diameter = 1–2 µm), which we obtained by grinding a fully cured NOA-81 film. The zeta potential of the NOA-81 particles in 10 mM NaCl solution is measured to be −12.3 ± 0.4 mV, suggesting negligible diffusioosmotic flow.

Salt-dependent diffusiophoretic mobilities of biomolecules

While diffusiophoretic mobility is often treated as constant³⁵, it is a property that is sensitive to the local zeta potential, thus the local salt concentration. Due to the small size of the biomolecules, the contribution of chemiphoresis can be effectively neglected. Therefore, diffusiophoretic mobility M_i is directly proportional to the zeta potential of the protein

$${M}_{i}=\zeta \frac{\varepsilon }{\eta }\frac{{k}_{B}T}{{ze}}\beta$$

(2)

where $\varepsilon$ is the permittivity, $\eta$ is the viscosity, ${k}_{B}$ is the Boltzmann constant, T is the temperature, z is the valence, and e is the element charge and ${\beta}=\left({D}_{+} {-} {D}_{ - } \right)/\left({D}_{+}+{D}_{-}\right)$, is the diffusivity contrast, where D₊ and D₋ are the diffusivity of cations and anions, respectively⁴¹. For weakly charged particles, the zeta potential scales with the local salt concentration c as $\zeta \sim 1/\sqrt{c}$⁷⁵. Hence, Eq. 2 can be rewritten as

$${M}_{i}={\zeta }_{0}\sqrt{\frac{{c}_{0}}{c}}\frac{\varepsilon }{\eta }\frac{{k}_{B}T}{{Ze}}\beta$$

(3)

where ${\zeta }_{0}$ is the zeta potential at ${c}_{0}$ = 1 mM. The concentration of solutes within the channel depends both on position and time $c=c\left(x,t\right)$, which can be determined by solving the one-dimensional diffusion equation ${\partial }_{t}c={D}_{s}{\partial }_{{xx}}c$, where ${D}_{s}=2{D}_{+}{D}_{-}/({D}_{+}+{D}_{-})$ is the ambipolar diffusion coefficient. Here, instead of accounting for the full solute concentration distribution for determining the concentration-dependent M_i, we make an approximation where we average the local concentration across the channel at a given time such that the averaged concentration only depends on time, shown as

$$c=\bar{c}(t)=\frac{1}{L} {\int }_{ \!\!\!\! x=0}^{L} {c(x,t){dx}.}$$

(4)

This allows us to approximate the concentration-dependent mobility (which is position and time-dependent) as only time-dependent

$${M}_{i}\left(t\right)={\zeta }_{0}\sqrt{\frac{{c}_{0}}{\bar{c}\left(t\right)}}\frac{\varepsilon }{\eta }\frac{{k}_{B}T}{{Ze}}\beta .$$

(5)

This position-averaged mobility is used to plot Fig. 3b, d in the main text and Supplementary Fig. S6. The time-averaged mobility values $\langle M\rangle$ reported in Fig. 3e are the mobility in Eq. 5 time-averaged over the course of the experiments.

Turbidity measurements

Samples were prepared in a tube by mixing the peptide and the ssDNA at the desired mixing ratio and a fixed peptide concentration of 1.0 mg/ml. The buffer of these samples contained 10 mM Tris-HCl (pH 7.5) and 20 mM NaCl. The sample was then placed on a UV–Vis spectrophotometer (NanoDrop 1C) and the solution turbidity at 350 nm was measured for three independent samples. Before measuring the turbidity of peptide-ssDNA samples, the instrument was blanked using the experimental buffer. The values of the turbidity were averaged for each mixing ratio, and the error was estimated as half the range of experimentally measured values (Supplementary Fig. S7).

Reporting summary

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

Data availability

All relevant data are included in the paper and/or its Supplementary Information files. Source data for all graphs are provided in the Source Data file. Source data are provided with this paper.

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Acknowledgements

This work was supported by grants from the National Science Foundation (2223737 and 2237177 to S.S.) and the National Institute of General Medical Sciences of the National Institutes of Health (R35 GM138186 to P.R.B.). The authors acknowledge members of the Banerjee and Shin labs for valuable discussions during different stages of the manuscript preparation.

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Authors and Affiliations

Department of Mechanical and Aerospace Engineering, University at Buffalo, The State University of New York, Buffalo, NY, USA
Viet Sang Doan & Sangwoo Shin
Department of Physics, University at Buffalo, The State University of New York, Buffalo, NY, USA
Ibraheem Alshareedah, Anurag Singh & Priya R. Banerjee

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Viet Sang Doan
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Ibraheem Alshareedah
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Anurag Singh
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Priya R. Banerjee
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Sangwoo Shin
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Contributions

Conceptualization: P.R.B. and S.S.; Methodology: V.S.D., I.A., P.R.B., and S.S.; Investigation: V.S.D., I.A., A.S., P.R.B., and S.S.; Resources: P.R.B., and S.S.; Writing—original draft: V.S.D., I.A., P.R.B. and S.S.; Writing—reviewing and editing: all authors; Funding acquisition: P.R.B., and S.S.

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Correspondence to Priya R. Banerjee or Sangwoo Shin.

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P.R.B. is a member of the Biophysics Reviews (AIP Publishing) editorial board. This affiliation did not influence the work reported here. All other authors declare no competing interests.

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Nature Communications thanks Richard Sear and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

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Doan, V.S., Alshareedah, I., Singh, A. et al. Diffusiophoresis promotes phase separation and transport of biomolecular condensates. Nat Commun 15, 7686 (2024). https://doi.org/10.1038/s41467-024-51840-6

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Received: 14 July 2023
Accepted: 16 August 2024
Published: 03 September 2024
DOI: https://doi.org/10.1038/s41467-024-51840-6

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