phase behaviour of disordered proteins underlying …spikelab/papers/140.pdfphase behaviour of...

Phase behaviour of disordered proteins underlyinglow density and high permeability of liquidorganellesMing-Tzo Wei1†, Shana Elbaum-Garfinkle1†, Alex S. Holehouse2†, Carlos Chih-Hsiung Chen1,Marina Feric1, Craig B. Arnold3, Rodney D. Priestley1, Rohit V. Pappu2* and Clifford P. Brangwynne1*

Many intracellular membraneless organelles form via phase separation of intrinsically disordered proteins (IDPs) orregions (IDRs). These include the Caenorhabditis elegans protein LAF-1, which forms P granule-like droplets in vitro.However, the role of protein disorder in phase separation and the macromolecular organization within droplets remainelusive. Here, we utilize a novel technique, ultrafast-scanning fluorescence correlation spectroscopy, to measure themolecular interactions and full coexistence curves (binodals), which quantify the protein concentration within LAF-1droplets. The binodals of LAF-1 and its IDR display a number of unusual features, including ‘high concentration’ binodalarms that correspond to remarkably dilute droplets. We find that LAF-1 and other in vitro and intracellular droplets arecharacterized by an effective mesh size of ∼3–8 nm, which determines the size scale at which droplet properties impactmolecular diffusion and permeability. These findings reveal how specific IDPs can phase separate to form permeable, low-density (semi-dilute) liquids, whose structural features are likely to strongly impact biological function.

Living cells are complex solutions of thousands of differentproteins, nucleic acids, lipids and small molecules. To organizetheir contents, cells form many different types of intracellular

organelles that localize distinct sets of molecules, allowing spatio-temporal control of molecular interactions. In addition to canonicalvesicle-like organelles, there are dozens of non-membrane bound,RNA- and protein-rich organelles within the cell nucleus1,2

and the cytoplasm3,4. Despite their lack of an enclosing membrane,these organelles are still able to concentrate molecular componentsand play important roles in key intracellular functions suchas RNA transcription and processing, and the regulation ofprotein translation.

It is now recognized that membraneless organelles, including Pgranules, nucleoli and stress granules, are condensed liquid-likedroplets of RNA and protein that form via phase separation.Indeed, many such organelles exhibit classic signatures of liquids,including rapid exchange dynamics of their contents with their sur-roundings, spherical shapes, coalescence upon contact and flowingand dripping in response to shear stresses1,5. These properties allowmembraneless organelles to concentrate molecular reactants whilemaintaining fluidity to facilitate interactions among the constituentmolecules. A growing number of studies have demonstrated theliquid-like nature of membraneless organelles and the relevance ofliquid–liquid demixing as a fundamental physical mechanismexplaining their formation6–9. There is also increasing support fora link between the material properties of membraneless organellesand cell physiology as well as disease states4,10–14.

A number of key questions remain unanswered regarding thephysicochemical driving forces for phase separation and macromol-ecular organization within membraneless organelles. Intrinsicallydisordered proteins (IDPs) or regions (IDRs) are, in many cases,

the drivers of phase-separation that give rise to membraneless orga-nelles12,14–16, although how protein disorder contributes to phaseseparation remains unclear. In Caenorhabditis elegans, germ-lineP granules are droplets rich in RNA and protein that are implicatedin the specification of germ cells. P granule assembly is driven byseveral proteins with IDRs17,18, including LAF-1, an abundantDDX3 family protein which contains an arginine/glycine-rich(R/G or RGG) domain that is necessary and sufficient for phase sep-aration12; PGL-3 is another P granule protein that contains RGGdomains19. R/G-rich IDRs are also found in the nucleolar proteinFIB-1 (ref. 7) , which drives assembly of a core droplet within thenucleolus20. Other examples include WHI3, which contains aQ-rich IDR and drives the formation of liquid-like puncta in thecytoplasm of fungi11. Similarly, the stress granule proteinshnRNPA1 and FUS contain IDRs and are also involved in neurode-generative diseases4,13,14. The molecular concentration within suchdroplets is expected to influence behaviours including molecularsequestration21, promotion of various reactions22, and the nuclea-tion of amyloid-like fibres that are associated with disease4,13,14.

Despite the importance of intra-droplet concentration, there aredifficulties associated with measuring the full coexistence curves(that is, binodals) that define the protein concentrations insideand outside of the droplet. As a result, little is known about howdroplet properties emerge from the underlying RNA–protein inter-actions22. Here, we utilize a novel method based on fluorescence cor-relation spectroscopy (FCS) measurements to infer second virialcoefficients, molecular diffusion coefficients, and binodals forLAF-1 and its intrinsically disordered RGG domain in the presenceand absence of RNA molecules. By combining these measurementswith a theoretical framework and insights from atomistic simu-lations, we uncover a rich physical picture of the interactions that

1Department of Chemical and Biological Engineering, Princeton University, Princeton, New Jersey 08544, USA. 2Department of Biomedical Engineering andCenter for Biological Systems Engineering, Washington University in Saint Louis, Saint Louis, Missouri 63130, USA. 3Department of Mechanical andAerospace Engineering, Princeton University, Princeton, New Jersey 08544, USA. †These authors contributed equally to this work.*e-mail: [email protected]; [email protected]

ARTICLESPUBLISHED ONLINE: 26 JUNE 2017 | DOI: 10.1038/NCHEM.2803

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underlie the phase behaviour and properties of LAF-1 droplets.These results show that intra-droplet concentrations are surprisinglylow, and suggest that condensed phases are akin to semi-dilutepolymer solutions. Large-scale conformational fluctuations orig-inating from the intrinsically disordered RGG domain in LAF-1are critical for the formation of such low-density droplets. Wealso determine a structural length scale, the mesh size, whichcharacterizes the molecular organization within droplets both invitro and in vivo. The inferred mesh sizes of P granules in livingC. elegans embryos, as well as other membraneless organelles,suggest the broader relevance of our findings for droplets withinliving cells.

ResultsUltrafast-scanning FCS measurements of coexistence curves. FCSis a powerful technique that relies on measuring the fluorescenceintensity fluctuations of labelled molecules within small,femtolitre excitation volumes23. FCS allows for precisemeasurements of molecular concentrations and diffusioncoefficients, and has been employed for studying proteinaggregation24. However, standard FCS methods have well-knownlimitations25, including the need to calibrate the fluorescenceexcitation volume. This can become problematic in a droplet-forming system due to refractive index variations. To overcomethese limitations, we developed a novel approach, called ultrafast-scanning FCS (usFCS). This approach uses a tunable acousticgradient index of refraction (TAG)26,27 lens placed in the backfocal plane of an oil immersion objective, as shown in Fig. 1a.The TAG lens allows axial scanning of the sample at very highfrequency (70 kHz). The axial scan range is adjustable bychanging the applied voltage28,29. The tunable scanning distanceserves as an external ruler for measuring the unknown detectionvolume within droplets. This allows us to estimate the size of themeasurement volume and thus determine molecular diffusioncoefficients, D, from the characteristic decay times, τD, ofmeasured autocorrelation functions (Supplementary Fig. 1). Weare also able to measure the internal viscosity and the localmolecular concentration within droplets.

We used usFCS to measure concentrations within the dilute anddense phases, to quantify the low- and high-concentration arms ofthe LAF-1 binodal, which is the coexistence curve that specifies theenvelope of the two-phase region as a function of salt concentration.For a given salt concentration, the equilibrium protein concen-tration outside the droplet, cS, defines a point on the left arm ofthe binodal (solid curve in Fig. 1b) whereas the protein concentration

inside the droplet, cD, defines the corresponding point on the rightarm of the binodal. At 125 mM NaCl, the value of cS for LAF-1 is0.124 ± 0.009 mgml–1 (1.5 ± 0.11 μM); the droplets that condensefrom solution are at a concentration of cD = 6.88 ± 1.52 mgml–1

(86.5 ± 19.2 μM; Fig. 1c; Supplementary Fig. 2). These values aresurprisingly low, given that the folded proteins lysozyme30 andγ-crystallin31, although fundamentally different from IDPs, arealso known to phase separate, but at concentrations that are approxi-mately two orders of magnitude higher (∼100–500 mgml–1) thanwhat we measure here. We confirmed these low-concentrationusFCS measurements using different fluorescent labels, as well asan orthogonal three-dimensional confocal microscopy approach(Supplementary Fig. 3). These findings indicate that although LAF-1 droplets are roughly 50 times more concentrated than the dilutephase, they are still at a very low concentration, which correspondsto a number density of 5 × 10−5 molecules nm–3 (that is, assuminga uniform 3D distribution of protein, the average distance betweenmolecular centres-of-mass is ∼27 nm).

The width of the two-phase regime, quantified in terms of theratio of cD to cS, decreases with increasing salt concentrations.This yields a concave down paraboloid binodal for LAF-1(Fig. 1c), which is characteristic of many polymeric systems32. TheRGG domain of LAF-1 is necessary and sufficient to drive phaseseparation12. Interestingly, however, the right and left binodalarms of the RGG domain alone are at mass concentrations thatare comparable to that of full length LAF-1, although the criticalsalt concentration is lower than for full-length LAF-1. We alsomeasured binodals in the presence of different types of genericRNA molecules, which may be expected to impact the phasediagram, since they are known to modulate the fluidity of LAF-1droplets12. In the presence of polyadenylate RNA (poly-rA) ofvarious lengths, the low-concentration arm of the LAF-1 binodaland the concentrations corresponding to the critical regionremain essentially invariant. However, upon addition of RNAwe observe a marked shift of the high-concentration arm of theLAF-1 binodal, toward lower values of cD (Fig. 1c).

Quantifying the strengths of intermolecular interactions. Theremarkably low concentration of LAF-1 droplets must arise fromthe underlying protein–protein interactions, which can bemodulated by RNA. Indeed, in mean field models, such as theFlory–Huggins theory, the sign and magnitude of the effectivetwo-body interactions determine the phase behaviour of polymersolutions33,34. These interactions are quantified using thedimensionless Flory interaction parameter χ, and are measured in

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Figure 1 | Measured binodals for the RGG domain and LAF-1. LAF-1 is measured in the absence or presence of RNA using the usFCS approach.a, Schematic of the microscope with an acoustically modulated beam that is controlled by a TAG lens. The system focus can be axially scanned along theoptical axis at a frequency of 70 kHz. b, Schematic showing a typical binodal with increasing protein concentration along the abscissa and increasing saltconcentration along the ordinate. Our measurements show that the salt concentration decreases the strengths of two-body interactions for RGGdomain–LAF-1 systems. c, The measured binodals of the RGG domain as well as LAF-1 in the presence and absence of RNA. Error bars represent standarddeviation (N = 10).

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terms of molecular dissociation constants KD or second virialcoefficients B2. We used usFCS to estimate the apparent values ofB2 as a function of salt concentration. For concentrations that arebelow cS, the diffusivity of a protein molecule can be influencedby interactions with other proteins35,36. Interactions that are, onaverage, attractive will diminish the protein diffusivities, whereastwo-body interactions that are, on average, repulsive will lead tolarger effective diffusion coefficients (Fig. 2a). We estimate B2 bymeasuring the dependence of the diffusivity on proteinconcentration (c) and analysing the data using the relation35:D ≈ D0(1 + 2B2Mc) (see Supplementary Information for a detaileddiscussion of this approximation). Here, D is the diffusioncoefficient, D0 is the diffusivity at infinite dilution, and M is themolecular weight of the protein. The B2 values for LAF-1 extractedusing usFCS are numerically equivalent to values obtained usingright-angle laser light scattering32 (Supplementary Fig. 4).

In the presence of 1 M NaCl, LAF-1 diffusivity is only moder-ately dependent on protein concentration, with a slope that isnear zero, indicating that LAF-1 is only weakly self-associative athigh salt concentrations (Fig. 2b,c). However, as salt concentrationdecreases, LAF-1 diffusivity becomes more strongly dependent onprotein concentration, thus yielding negative B2 values of increasingmagnitude. The addition of short unlabelled RNA molecules givesrise to less-negative B2 values, implying that the RNA moleculesweaken the strengths of two-body interactions between LAF-1 mol-ecules. In contrast, in the presence of long RNAmolecules we obtainmore-negative B2 values, implying a strengthening of the effectivetwo-body interactions between LAF-1 molecules. These results arequalitatively consistent with the changes in diffusivities within thedroplets (Supplementary Fig. 5). Additionally, measurements ofB2 values for the RGG domain show that these values are themost negative of all the constructs we tested, consistent with thisbeing a highly ‘sticky’ domain that drives phase separation.

Theoretical framework for the measured binodals. The lowprotein concentration inside LAF-1 droplets comes as a surprisegiven previous suggestions, including recent measurements ofelastin-like-polypeptides (ELPs), that point to concentrations atleast two orders of magnitude higher37. Moreover, our findingsreveal an unusual invariance of critical points and left binodalarms to the addition of RNA, features that cannot be explainedusing simple mean-field theories (Supplementary Fig. 6). Forexample, Flory–Huggins theory suggests that as B2 becomes morenegative (self-interactions are effectively more attractive), cSshould decrease and cD should increase, but this is not borne outin comparative measurements of the binodals for LAF-1 versusthe RGG domain. A clue to explaining the curious behaviour

comes from all-atom simulations, which show that the RGGdomain exhibits large-scale conformational fluctuations, wherebycompact, globular conformations, and expanded coil-like statesare sampled with roughly equivalent probabilities (Fig. 3a). Thenaive expectation is that these conformational features reflect alack of preference for interaction of chains with themselves versussolvent, which would be associated with B2 values of ≈0 (ref. 32);this is contradicted by our measurements of negative values of B2.Therefore, the phase behaviour of RGG domains appears to derivefrom a combination of large conformational fluctuations, andnegative B2 values; the latter likely arise from polyvalency of stickymotifs comprising charged and aromatic residues. Importantly,the large conformational fluctuations should generate largepervaded volumes, thus dramatically increasing the likelihood thatRGG domains will overlap with one another, even at ultra-lowconcentrations (Supplementary Fig. 7).

The concept of overlap volume fraction (ϕ*) is central to describ-ing the phase behaviour of polymer solutions. This is the concen-tration threshold beyond which inter-chain interactions becomemore likely than intra-chain interactions—that is, the concentrationat which different chains begin to overlap significantly with oneanother (Supplementary Figs 7 and 8). The overlap concentrationthreshold defines the boundary between the dilute (<ϕ*) and thesemi-dilute (>ϕ*) regimes. In a semi-dilute solution, polymerdensity fluctuations play a crucial role in determining the inter-actions between chains32. The large conformational fluctuationsassociated with the RGG domain combined with the low proteindensity within droplets points to the direct relevance of thephysics and chemistry of polymers in semi-dilute solutions38.Numerical reproduction of the measured binodals, for both LAF-1and the RGG domain alone, requires the adaptation of an advancedtheory38 that explicitly accounts for the combined effects of chaindensity fluctuations, as well as two- and three-body interactions(derived respectively from second and third virial coefficients) (Fig. 3b).

Above the overlap concentration, chain density fluctuations willcontribute to screening the interactions between pairs of residues ona single chain, provided the spatial distance between residues islarger than the correlation length, ξ. This characteristic lengthscale is also referred to as the mesh size because it pertains to theaverage size of voids between polymer chains. By fittingMuthukumar’s theory38 to the measured binodals, we generateestimates of construct-specific values for ξ and w. The inferredstrengths of three-body interactions are encoded in w, which forpositive values imply a weakening of attractive inter-molecularinteractions (Supplementary Fig. 9). The measured differencesbetween the binodals of the RGG domain and LAF-1 are partiallyexplained by a more positive w associated with RGG compared to

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Figure 2 | RNA and salt influence intermolecular interactions of LAF-1 and RGG. a, Schematic illustration of mutual diffusion. b, Mutual diffusion coefficientof LAF-1 strongly depends on the protein concentration. The dashed lines show the linear fits obtained using the equation shown for D in the text. The slope,which is proportional to B2, decreases with increasing salt concentration. c, The second virial coefficients, B2, approach the ideal solution limit of zero withincreasing salt concentration. The B2 values are most negative across the entire salt range for the RGG domain implying stronger effective pairwiseinteractions for the RGG domain when compared with LAF-1 in the absence or presence of RNA. Error bars represent standard deviation (N = 10).

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LAF-1 (inset of Fig. 3c). Similarly, RNA molecules lead to anincrease in w, a result that can be interpreted as the ability ofRNA to dilute the attractive interactions between LAF-1 molecules.

The overlap concentration for the RGG domain that we calculatefrom simulation results, ϕ* = 8.8 × 10–3, is of the same magnitude asthe measured cD (Supplementary Figs 6 and 7 and associated discus-sion). This implies that ξ should be quantitatively similar to thedimensions of an individual molecule. Our numerical reproductionof the measured binodals yields estimates for ξ as a function of χ(Fig. 3c). At 125 mM NaCl, the predicted value of ξ is between3 and 8 nm. These values of ξ are equal to the average dimensionsof the RGG domain inferred from simulations (between 3 and5 nm, see Fig. 3a); the agreement of these two sets of estimates isremarkable given that they were determined through entirelyindependent approaches. Our analysis thus reveals that proteinconcentrations in the dense phase are of the same magnitude asthe very low overlap concentrations (ϕ*), which arise from large-scale conformational fluctuations of individual molecules(Supplementary Fig. 7). Therefore, chemical information in theform of sequence-encoded conformational fluctuations controlsthe dimensions of the disordered RGG domain, and the resultingdroplet phase behaviour.

Droplet nanorheology. To quantify the impact of low intra-dropletconcentration/volume fraction on molecular motions andrheological properties of droplets, we used usFCS to determinethe diffusion coefficients of embedded 14 nm fluorescent sphericalnanoparticles. We then use the Stokes–Einstein relation tocalculate the viscosity, η = kBT/6πRD, where kBT is the thermalenergy scale, R is the nanoparticle radius and D is the measureddiffusion coefficient. This gives a LAF-1 droplet viscosity of27.2 ± 5.9 Pa s at 125 mM NaCl, which is consistent withmeasurements based on particle tracking microrheology12. Usinga similar approach, we find that RGG droplets are roughly twiceas viscous as full-length LAF-1 droplets (Fig. 4a), in agreementwith the finding that B2 values for RGG are significantly morenegative than full-length LAF-1. Moreover, measurements withinRGG droplets show that the RGG domains diffuse more slowly inthese droplets when compared to full-length LAF-1 molecules indroplets formed by full-length LAF-1 (Supplementary Fig. 5).Both full-length LAF-1 and RGG droplets exhibit a decreasedviscosity and increased molecular diffusivity upon increasing salt

concentration (Fig. 4a; Supplementary Fig. 5). This is consistentwith the decreasing magnitudes of B2 values as salt concentrationsincrease (Fig. 2c).

When we added RNA of either 15 or 30 nucleotides into LAF-1droplets in vitro, the droplet viscosity decreased to 16.1 ± 2.8 Pa s at125 mM NaCl. Similar mass concentrations of longer 3,000 nucleo-tide poly-rA cause the opposite effect, whereby the droplet viscosityincreases to 60.9 ± 10.3 Pa s. Nonetheless, in all cases, the dropletviscosity still decreases with increasing salt concentration. Thesechanges are also mirrored in the diffusivities of molecules withinthe droplets (Supplementary Fig. 5). However, changes indroplet viscosity are not fully captured by considering B2 alone(Supplementary Fig. 10). Consistent with simple theories ofviscosity in polymeric systems32, changes in droplet viscosity alsodepend on the protein concentration within the droplet, cD; thesecombined effects can be captured by plotting viscosity as aproduct of, B2cD, as shown in Fig. 4b. Interestingly, however, theability to collapse viscosity data as a function of B2cD breaks downfor the long poly-rA (poly-rA3k).

The agreement between the viscosity determined from the diffu-sive motion of 14 nm particles and micrometre-sized particles(Fig. 5a) suggests that the effective mesh size (ξ) of the intra-droplet protein network is less than 14 nm. To infer the value of ξfor LAF-1 droplets, we measured the diffusion coefficient for avariety of molecular probes of smaller sizes, and use their hydro-dynamic radius Rh to calculate an apparent viscosity as above; wenote that using the Stokes–Einstein equation to estimate viscosityis only strictly valid for spherical probe particles (SupplementaryInformation for a detailed discussion). Small solutes (Rh ∼ 0.5 nm)and the globular protein mCherry (Rh ∼ 1.4 nm) exhibit values inthe range of 0.07–0.2 Pa s. These values are roughly two orders ofmagnitude lower than the bulk viscosity, consistent with theirmotion primarily reflecting diffusion through the aqueous solventthat permeates the droplet mesh. To interrogate larger lengthscales, we used dextran molecules of differing molecular weights.In dilute aqueous buffers, the 10 kDa dextran has a hydrodynamicradius (Rh) of ∼2.3 nm. By plugging this value of Rh and themeasured diffusion coefficient into the Stokes–Einstein equation,we obtain an apparent viscosity value that is comparable to thoseof the other small probes. However, a similar analysis applied tothe measured diffusion coefficients of 40 kDa (Rh ∼ 4.5 nm) andlarger molecular weight dextran molecules suggests significantly

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Figure 3 | Summary of computational and theoretical analyses. a, Results from atomistic simulations of the RGG domain. The plot shows a two-dimensionalprobability density map of chain dimensions in terms of radius of gyration, Rg and asphericities. RGG samples a broad range of conformations leading tolarge fluctuations and low values for the overlap volume fraction (Supplementary Fig. 7). b, Comparison of the binodals derived from numericalimplementation of Muthukumar’s theory38 (open symbols) with experimental data (solid symbols). While the data help to identify the critical χ-region, theprecise critical point cannot be reliably located because it is characterized by fluctuations that occur on all length scales. Therefore, the analysis wasrestricted to reproducing the low- and high-concentration arms of the binodals away from the critical point. The dashed lines are drawn to guide the eye.c, χ-dependent values of ξ are shown for each of the constructs and are calculated as described in Supplementary Information. The horizontal grey stripecorresponds to values of ξ obtained at 125 mM NaCl. The inset shows inferred values of construct-specific three-body interaction coefficients, w and thecolour coding of the bars follows the format used in panels b and c. Error bars represent standard deviation (N = 10).






hindered motion, implying that the bulk properties of the dropletbecome increasingly dominant. Since dextran molecules, especiallyof higher molecular weights, are not well approximated as spheres,we also analysed the diffusivity data using a previously describedframework39; this analysis provides additional support for our con-clusions (Supplementary Fig. 11). Our dextran diffusivity data arealso consistent with the partitioning of different molecular weightdextran into droplets. We find that 10 kDa dextran moleculesstrongly partition into LAF-1 droplets (Fig. 5c,e), while 70 and155 kDa dextran molecules (>6 nm) are mostly excluded. These

findings suggest that the characteristic mesh size within droplets isbetween 3 and 6 nm, in agreement with results from our theoreticalanalysis and simulations (Fig. 3c).

We also measured the partitioning of dextran into LAF-1::GFPlabelled P granules in C. elegans embryos (Fig. 5c,d). Consistentwith our in vitro data, we find that the smaller 10 kDa dextranpartitions favourably into P granules, while the larger 155 kDadextran is significantly excluded; similar in vivo results have beenreported for P granules40 and for nucleoli41 (Fig. 5d andSupplementary Fig. 12; LAF-1 labelled P granules in C. elegans

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Figure 4 | Nanoscale rheology of RGG and LAF-1 condensed droplets. a, Increasing the concentration of NaCl decreases the viscosity within LAF-1 droplets.Adding short RNA (poly-rA30 and poly-rA15) also decreases the viscosity within LAF-1 droplets. However, adding long RNA (poly-rA3k) increases viscosityof LAF-1 droplets. b, Viscosity within droplets is proportional to the product of B2cD. On addition of the short RNA the droplet viscosity decreases and followsthe same universal curve with LAF-1 and RGG. Error bars represent standard deviation (N = 20).

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Figure 5 | Low-density semidilute liquid droplets. a, Apparent viscosities extracted from measurements of diffusion coefficients of dyes, mCherry, dextranand polystyrene beads within LAF-1 droplets at 125 mM NaCl. The grey bar corresponds to ξ in Fig. 3c. b, Permeability of different in vitro droplets tofluorescent dextran (red). 10 kDa dextran permeates droplets, while 70 and 155 kDa dextran molecules are excluded from the droplets. The inset figureshows the bright-field image of NPM1 droplets. Scale bar, 10 μm. c, Permeability of in vivo LAF-1::GFP labelled P granules in C. elegans to fluorescent dextran.Perinuclear P granules in ∼16-cell embryos are indicated with arrows. Scale bar, 10 μm. d, Partition coefficients were calculated from fluorescent intensitiesinside and outside droplets. The dashed lines are drawn to guide the eye. The grey bar corresponds to ξ in panel a and Fig. 3c. e, Schematic illustrating thevoid-rich nature of LAF-1 droplets, and their probe-size-dependent permeability. The RGG domain in LAF-1 is depicted in blue and envelopes defined by theRg of LAF-1 are shown in black-dash circles. Error bars represent standard deviation (N = 10).






and NPM1 labelled nucleoli in oocytes of frog Xenopus laevis,respectively). Moreover, we see similar size-dependent exclusionin vitro for two other well-known droplet forming proteins,WHI3 and NPM1 (Fig. 5b,d). These results suggest that the semi-dilute, void-rich nature of droplets (Fig. 5e) is likely a feature ofmany liquid-phase organelles that are driven by the sequence-encoded conformational fluctuations of IDRs.

DiscussionPhase separation has recently been recognized as a ubiquitousmechanism for organizing the contents of living cells. IDRs ofproteins appear to play an important role in driving phase separ-ation. However, there is a lack of clarity regarding the connectionbetween sequence-encoded nanoscale fluctuations of conformation-ally heterogeneous molecules and the microscale organization anddynamics of droplets that results from phase separation. Here, webegin to uncover these connections using a new usFCS approachto measure the phase behaviour and intra-droplet properties ofdroplets formed by LAF-1, which contains an archetypal disorderedR/G-rich domain (Supplementary Fig. 13). By quantifying thestrengths of pairwise interactions and resulting coexistence curves,together with measurements of nanoscale viscosity, molecularpartitioning and theoretical analysis, our results provide a holisticpicture of how emergent properties of membraneless organellesderive from the amplitudes of conformational fluctuations andinteractions of component molecules.

As in many membraneless organelles, LAF-1 and other P granuleproteins function by interacting with RNA42. Previous work showedthat short (50 nt) RNA molecules decrease the viscosity of LAF-1droplets, consistent with RNA impacting protein–protein inter-actions12. However, in that work, RNA had no effect on the saturationconcentration required for phase separation, which was unusual sincethe coexistence curve should arise from the same molecular inter-actions that govern fluidity. Our results help resolve this apparentparadox. We find that RNA does indeed impact the coexistencecurve, albeit by shifting only the high-concentration arm to lowervalues, while leaving the low-concentration arm and critical pointinvariant. Interestingly, while our results reveal a robust shift in thepresence of RNA for all lengths tested (15 to 3,000 nt), we find thatonly short RNA decreases droplet viscosity, while long RNA hasthe opposite effect. This suggests that additional physical processessuch as protein–RNA entanglements might be important indescribing molecular transport in the presence of longer RNAmolecules. Systematic investigations of ternary phase diagrams areneeded to obtain a complete understanding of how polydispersityof RNA lengths, sequences and structural motifs regulate theoverall phase behaviour of proteins such as LAF-1. This is biologicallyrelevant because RNA molecules of varying lengths are found in Pgranules. We speculate that their relative abundance could tune Pgranule viscosity and phase behaviour by modulating the effectiveinteractions between LAF-1 molecules or entangling with them.

A surprising finding is that LAF-1 and its IDR phase separateinto liquid droplets of ultra-low protein concentration, which corre-spond to the semi-dilute regime. We identify the characteristic meshsize within these permeable droplets to be ∼3–8 nm (Figs 3c and 5a,c). To account for this behaviour, we adapted an analytical modelthat explicitly accounts for the effects of conformational andchain density fluctuations. For LAF-1, the key region for under-standing the multiscale structural features of droplets is the RGGdomain, which is necessary and sufficient for phase separation12,and underlies the intriguing properties of P granule-like LAF-1 dro-plets. In particular, the sequence of the RGG domain imparts aunique and unexpected combination of attractive interactions(strongly negative B2), with large-scale conformational fluctuationsand average preference for expanded conformations. These com-bined effects readily engender overlap among chain molecules,

even at very low protein concentrations. This allows the RGGdomain to drive the LAF-1–LAF-1 interactions underlying phaseseparation, while still resulting in remarkably low-density droplets.Our findings provide an interesting contrast with those fromanother recent study of the phase behaviour of elastin-like poly-peptides (ELPs), which are IDPs lacking charge residues37. Themeasured binodals of ELPs correspond to concentrations for cSand cD that are at least two orders of magnitude larger than thosemeasured here for LAF-1 and the RGG domain. These differenceslikely arise from sequence-encoded differences in the amplitudesof conformational fluctuations, and their impact on the resultingdroplet phase behaviour32,38.

Our results reveal that LAF-1 droplets, as well as intracellularRNA–protein droplets, are dense when compared to the surround-ing solution, but are nevertheless solvent-rich and full of permeablevoids that accommodate the free diffusion of small solutes, foldedproteins, and flexible polymers up to a specific threshold in size/molecular weight. We find that molecular scale motions within dro-plets can be decoupled from the mesoscale droplet properties. Forexample, the bulk viscosity of the droplet has little effect on the dif-fusion of molecules that are smaller than the mesh size, because theyare free to move through the free volume within the droplet(Fig. 5a). By contrast, larger macromolecules and complexesrecruited within droplets will be subject to the viscous dragarising from the dynamic network of IDR–self associations.Because protein sizes span the droplet mesh size, from ∼2 nm foran average monomeric protein, to >10 nm for multimeric com-plexes, these effects are likely to have significant consequences forintracellular droplet functions. We further speculate that lowdensity droplets with large mesh sizes could allow for size-selectivefiltering, which could potentially be regulated, in a manneranalogous to that of FG Nups in the nuclear pore, which exhibit acomparable passive mesh size (∼4 nm)43.

Our findings are likely to shed light not only on P granules, butalso many other membraneless organelles. Indeed, IDRs withsequence properties resembling the LAF-1 IDR are found in manyRNA-binding proteins, including those that are known to drivephase separation7,11,20,44. Our findings provide a new frameworkfor understanding the length-scale-dependent properties of low-density liquid phase organelles throughout the cell. Changes inthese properties will be relevant not only for physiological function,but also in disease-associated pathological aggregation4,11,13,14.

MethodsUltrafast-scanning fluorescence correlation spectroscopy. Samples are excitedusing a diode-pumped solid-state laser (Cobolt Calypso, Cobolt) with emissionwavelengths of 491 nm. After passing through a TAG lens (2.5 BETA, TAG Optics),the light is focused into the sample using an oil immersion objective (Plan Apo100X/1.4, Nikon). The fluorescence emission is collected through the same objective,separated from the excitation light by a dichroic mirror (FF495-Di03-25 × 36,Semrock) and focused into a confocal pinhole unit (MPH16, Thorlabs). Thefluorescence light is filtered by a long pass filter (FF01-496/LP, Semrock). Photonsare detected by a photomultiplier tube (H10682-210, Hamamatsu), and their arrivaltimes are registered by a data acquisition card (PCI-6115, National Instruments).Here, the scanning distance was kept at ∼2 μm, which is an order of magnitudesmaller than the size of the liquid droplets.

Protein preparations. LAF-1–RGG constructs with an N-terminal His tag werepurified on Ni-NTA resin followed by a heparin column (GE) purification step,according to previously published protocols12. Dylight488 NHS-Ester wasconjugated to LAF-1 proteins as needed according to manufacturer protocols(Thermo). Proteins were stored at −80 °C, frozen in high salt buffer (20 mM Tris,pH 7.4, 1 M NaCl, 10% (vol/vol) glycerol, and 1 mM DTT). For dropletexperiments, LAF-1–RGG aliquots were centrifuged at 16,873g for 2 min andbuffer exchanged into high salt buffer (20 mM Tris, pH 7.4, 1 M NaCl, and 1 mMDTT). Then, protein solutions containing ∼1% fluorophore labelled LAF-1–RGGwere mixed with varying volumes of no salt buffer (20 mM Tris, pH 7.4, and 1 mMDTT). Different lengths of RNA oligonucleotides substrates were added,maintaining the same RNA mass concentration of ∼78 μg ml–1 (15 μM poly-rA15,7.5 μM poly-rA30, and 75 nM poly-rA3k).






Data analysis. When the measurement volume is axially scanned, Z, at a constantfrequency f, the autocorrelation function for simple diffusion is45:

G(τ)

= G(0) 1 +τ

τD

( )( )−1

1 +τ

κ2τD

( )( )−0.5

exp−(Z sin (πf τ))2

(2ωz)2

11 + (τ / κ2τD)

( )

(1)

Here, G(0) is magnitude at short time scales, τ is the lag time, τD is the half decaytime, κ is the ratio of axial to radial of measurement volume, and ωz is the depth offocus. The parameters τD, G(0), and ωz were optimized in the fit while theparameters Z and f were kept fixed. ωz provides a measurement of the volume, whichin turn can be used to determine the diffusion coefficient and moleculeconcentration in conjunction with τD and G(0).

The dependence of the diffusivity (D) on protein concentration (c) can bewritten as35:

D ≈ D0[1 + (2B2M − ks − �v)c] (2)

Here, M is the molecular weight, B2 is the second virial coefficient, ks issedimentation interaction parameter, and �v is partial specific volume. In thepresence of 1 M NaCl, LAF-1 diffusivity is only weakly dependent on proteinconcentration. This indicates that the effective two-body interaction,parameterized in terms of B2, has a greater contribution to diffusivity than thesedimentation interaction and volume effect, which are expected to dependonly weakly on salt concentration. In this approximation, B2 can be obtainedby fitting the observed diffusion coefficient versus protein concentration data toobtain a linear fit (Fig. 2b). For a more extensive discussion, see theSupplementary Information.

Simulation methods. All-atom Monte Carlo simulations were run using theCAMPARI software package (campari.sourceforge.net) and the ABSINTH implicitsolvent model46. Simulations use parameters from the abs_3.2_opls.prm parameterfile. Lennard-Jones and electrostatic interactions are subject to 10 and 14 Å cutoffs,respectively. CAMPARI uses a range of local and global moves to exploreconformational space through a combination of torsional and rigid body moves. Thecombination of the ABSINTH model and the CAMPARI simulation engine hasbeen extensively used to explore the conformational properties of a wide range ofdisordered proteins47.

Nano- and microrheology experiments. Data for diffusion of micrometre-sizedpolystyrene beads were obtained using particle-tracking-based microrheology anddata for diffusion of 14-nm-sized polystyrene beads were obtained using usFCS.Probes larger than ∼10 nm accurately probe the bulk viscosity of the droplets, whilesmaller probes do not. Data for dyes (RhodamineB, Sigma; and Alexa488-hydrazide,Alexa488-C5-maleimide, Alexa488-Carboxy, and Alexa488-NHS, MolecularProbes) and mCherry (BioVision) were obtained through standard FCS andcorrected for changes to a measurement of the volume based on analysisfrom usFCS.

Dextran experiments. Tetramethylrhodamine dextrans (10 k, 40 k, 70 k, Thermo;and 155 k, Sigma-Aldrich) were added to droplet solutions of unlabelled LAF-1,WHI3 or NPM1 at final concentrations of ∼0.01–0.07 mgml–1. Samples wereimaged on a Nikon laser scanning confocal microscope ∼2–3 h after dextranaddition. Partition coefficients were calculated from background correctedfluorescent intensities inside/outside droplets. Droplet conditions were as follows:LAF-1 ∼3–5 μM in 125 mM NaCl; WHI3 9 μM with 50 nM BIN1 RNA in 150 mMKCl; NPM1 ∼25 μMwith 0.1 mg ml–1 ribosomal RNA in 150 mMNaCl. Cover slipswere pretreated with 1% PF127, 30 mg ml–1 BSA, and SigmaCote for LAF-1, WHI3,and NPM1 respectively. For C. elegans, dextrans diluted to 4 mgml–1 in injectionbuffer (20 mM KPo4pH 7.5, 3 mM K citrate, 2% peg-1000) were injected into thesyncytial gonad of LAF-1–Crispr worms (CPB132[ptnIs077[laf-1::gfp(A206K)]]).After incubation for 4–5 h at 25 °C, worm gonads were dissected and embryos wereimaged on a Zeiss spinning disc confocal microscope.

Data availability. The data that support the findings of this study are available fromthe corresponding author upon reasonable request.

Received 30 August 2016; accepted 5 May 2017;published online 26 June 2017

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AcknowledgementsWe thank H. Zhang and D. M. Mitrea for purifying WHI3 and NPM1, respectively. Weacknowledge funding from the Princeton Center for Complex Materials, an MRSECsupported by NSF grant DMR 1420541, and the Eric and Wendy Schmidt TransformativeTechnology Fund. This work was also supported by an NIH Director’s New InnovatorAward (1DP2GM105437-01 to C.P.B.), an NSF CAREER award (1253035 to C.P.B.),NIH grants (1K99NS096217-01 to S.E.G. and 5RO1NS056114 to R.V.P.), and an HFSPProgram grant (RGP0007/2012 to C.P.B.). A.S.H. is a Bonnie and Kent Lattig graduatefellow in the Center for Biological Systems Engineering at Washington University inSaint Louis. We thank C. Theriault from TAG Optics for providing the TAG lens usedin this study.

Author contributionsM.W. acquired and analysed data in usFCS development and nano-scale rheology.S.E.G. acquired and analysed data in particle tracking microrheology, FCS and dextranpermeability. A.S.H. performed computational simulations and theoretical analysis. C.C.C.created in vivo LAF-1 constructs and injected dextran molecules into C. elegans. M.F.created in vivoNPM1/FIB-1 constructs and injected dextranmolecules intoX. laevis. M.W.,C.B.A., C.P.B. and R.D.P. designed the usFCS measurements. A.S.H. and R.V.P. designedthe theoretical analysis with input from M.W., S.E.G. and C.P.B.; M.W., S.E.G. A.S.H.,R.V.P. and C.P.B. wrote the paper.

Additional informationSupplementary information is available in the online version of the paper. Reprints andpermissions information is available online at www.nature.com/reprints. Publisher’s note:Springer Nature remains neutral with regard to jurisdictional claims in published maps andinstitutional affiliations. Correspondence and requests for materials should be addressed toR.V.P. and C.P.B.

Competing financial interestsThe authors declare no competing financial interests.





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