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Deciphering how naturally occurring sequence features impact the phase behaviors of disordered prion-like domains

Prion-like low complexity domains (PLCDs) have distinctive sequence grammars that determine their driving forces for phase separation. Here, we uncover the physicochemical underpinnings of how evolutionarily conserved compositional biases influence the phase behavior of PLCDs. We interpret our results in the context of the stickers-and-spacers model for phase separation of associative polymers. We find that tyrosine is a stronger sticker than phenylalanine whereas arginine is a context dependent auxiliary sticker. In contrast, lysine weakens sticker-sticker interactions. Increasing the net charge per residue destabilizes phase separation while also weakening the strong coupling between single-chain contraction in dilute phases and multi-chain interactions that give rise to phase separation. Finally, glycine and serine residues act as non-equivalent spacers, thus making glycine vs. serine contents an important determinant of the driving forces for phase separation. The totality of our results leads to a set of rules that enable comparative estimates of composition-specific driving forces for PLCD phase separation.

Protein expression and purification: All hnRNPA1-LCD variants were expressed in E. coli BL21-Gold (DE3) strain in ZYM5052 auto induction media at 37°C for 24 hours. For NMR samples, cultures were grown in isotopically labeled M9 media, induced at OD600=0.8 with 1 mM IPTG and cultured at 37°C for an additional 6 hours. Cell pellets were resuspended in 50 mM MES pH 6.0, 500 mM NaCl, 20 mM 2-mercaptoethanol and lysed via sonication. Cell lysates were centrifuged, and the variants were purified from insoluble inclusion bodies as previously described 1 . The inclusion bodies were resuspended in 6 M GdmHCl, 20 mM Tris pH 7.5, 15 mM imidazole overnight at 4°C. Solutions of solubilized inclusion bodies were cleared by centrifugation, and supernatants were loaded onto selfpacked columns of chelating Sepharose fast flow beads (GE Healthcare) charged with nickel sulfate. The columns were washed with 4 column volumes of 4 M urea, 20 mM Tris pH 7.5, 15 mM imidazole. Proteins were eluted from the Ni-NTA resin with 4 M urea, 20 mM Tris pH 7.5, 500 mM imidazole. TEV cleavage of the 6xHis-tag was done in 2 M urea, 20 mM Tris pH 7.5, 50 mM NaCl, 0.5 mM EDTA, 1 mM DTT overnight at 4°C. Cleaved protein solutions were loaded onto Ni-NTA columns. The flowthrough and wash fractions were collected and concentrated using a 3000 MWCO Amicon centrifugal filter. As a final purification step, the samples were passed in 2 M GdmHCl, 20 mM MES pH 5.5 over a S75 Superdex size exclusion column (GE Healthcare). The identity of each protein was confirmed via intact mass spectrometry. All proteins were stored in 4 M GdmHCl, 20 mM MES pH 5.5 at 4°C. For the -2R-2K+3D construct, the procedure was modified as follows. The sample was cleaved in a minimum of 30 mL of buffer per 1 L of culture. Following the post-cleavage nickel column, the sample was rapidly exchanged into 20 mM MES pH 5.5 and 6 M GdmHCl using a 10K MWCO 15 mL Amicon centrifugal filter prior to size exclusion by a Superdex 75 column to avoid the protein being concentrated at a pH near its theoretical pI. For the -4R-2K+5D construct the procedure was modified such that the protein was cleaved in a minimum of 30 mL of buffer per 1 L of culture. The sample pH was then rapidly increased after the post-cleave nickel column by adding 1/10 volume of 1 M CAPS pH 10.5 before concentrating with a 10K MWCO 15 mL Amicon centrifugal filter. The sample was then subjected to size exclusion chromatography using a Superdex 75 column equilibrated with 20 mM CAPS pH 10.5, 2 M GdmHCl.
Buffer exchange to remove denaturant: Buffer exchange was achieved in two-steps. First, the protein in 4 M GdmHCl, 20 mM MES pH 5.5 storage buffer was exchanged into 1 M MES pH 5.5 by multiple dilution and concentration steps using a 3K MWCO Amicon centrifugal filter as previously described 1 . The protein was then dialyzed overnight against 20 mM HEPES pH 7.0 (without excess salt) at room temperature. The pH of the buffer was adjusted using ammonium hydroxide to prevent the introduction of excess salt into the sample. The protein was filtered through a 0.22 mm Millex-GV filter (Merck) to remove potential aggregates from the solution, which might have formed during dialysis.

SDS-PAGE:
All gel electrophoresis was carried out using NuPAGE 4-12% Bis-Tris gradient gels (Invitrogen). The gels were run using NuPAGE MES SDS Running buffer (Invitrogen) diluted to 1x until the dye-front had traveled a suitable distance. The gels were washed with water and stained with SimplyBlue SafeStain (Thermo Fisher Scientific) before destaining with water. PageRuler Plus Prestained protein ladder (Thermo Fisher Scientific) was used as a molecular weight reference.
Measurements of saturation concentrations for specific variants that required special handling: Experiments on variant +8D was carried out in 20 mM HEPES, 150 mM NaCl pH 8.0 because of its net neutral charge. Because +7F-7Y lacks Tyr residues, its protein concentration was determined at 205 nm using a Cary 300 UV-Vis spectrophotometer (Agilent). For determination of low protein concentrations, a 10 mm pathlength quartz cuvette was used.
We also measured saturation concentrations for variant +7K+12D as a function of pH. The sample of variant +7K+12D in denaturing buffer was rapidly exchanged into non-denaturing buffers using Zeba spin columns (Thermo Fischer) following standard procedures. The columns were equilibrated with buffers prepared at room temperature to contain 150 mM NaCl and 20 mM of one of the following buffering agents, MES at pH 5.5, and 6.5, HEPES at pH 6.5, 7, and 8, Tris at pH 8, and 9, and HEPBS at pH 8, 8.3, 8.7, and 9. The pH of each buffering condition was measured at 4ºC to account for temperature dependent pKa shifts of the buffer. The saturation concentration at 4ºC was then measured by separating dilute and dense phase by centrifugation as described in the Methods. All measurements were done as at least 3 replicates. The theoretical protein net charge at each pH was calculated using protpi.ch. The protonated state of the lysine side chain at each pH was calculated using the estimated net charge of the protein and accounting for the charge state of the amino terminal at the given pH, assuming the remainder of the charge difference results from deprotonated Lys residues.
Far UV-CD spectra: CD spectra were recorded with a J-1500 spectrophotometer (Jasco). ~0.5mg/mL protein solutions were measured in a 0.1 mm pathlength cuvette (Hellma). The spectra were accumulated with a response time of 4 s, 1 nm data pitch, 1 nm band width from 195 to 260 nm. The CD spectra were collected at 25ºC and at least two replicates were measured and averaged for each condition.
Small Angle X-ray Scattering (SAXS) measurements: All measurements were performed at BioCat (beamline 18ID at the Advanced Photon Source, Chicago) with in-line size exclusion chromatography (SEC-SAXS) as previously reported 1, 2 . Experiments were conducted at room temperature in 20 mM HEPES, 150 mM NaCl, pH 7.0. Protein samples stored in 4 M GdmHCl, 20 mM MES pH 5.5 were loaded onto either a Superdex 75 5/150 GL or a Superdex 75 Increase 10/300 column (GE Life Science) with a flow rate of 0.4 mL/min. The column eluent passed through the UV monitor and proceeded through the SAXS sheath flow capillary in the coflow system 3 . Scattering intensity was recorded using a Pilatus3 1 M (Dectris) detector placed 3.5 m from the sample providing a q-range of 0.004-0.4 Å -1 . Exposure time was 0.5 sec. Raw SAXS data was reduced at the beamline using BioXTAS RAW 1.6.3 and 2.0.2 4 . Buffer subtraction, Guinier fits, and Kratky transformations were performed using the BioXTAS Raw software 4 . Raw data were additionally fit using an empirically derived molecular form factor (MFF) developed by Riback et al. 5 .
Microscopy: Differential interference contrast microscopy (DIC) images were obtained at room temperature using a Nikon Eclipse Ni Widefield microscope with a 20X objective. Samples were prepared by adding NaCl to 150 mM to the protein stock solution. Protein concentrations were selected such that they were slightly above their corresponding csat at 20°C. 2 µL of the protein solution was sandwiched between two coverslips sandwiched with 3M 300 LSE high-temperature double-sided tape (0.34 mm) with a window for microscopy cut out.
NMR spectroscopy: NOESY and TOCSY experiments for A1-LCD Dhexa were acquired on either a Bruker Avance 1.1 GHz or 850 MHz spectrometer equipped with TCI triple-resonance cryogenic probes and pulse-field gradient units. A 13 C-resolved 1 H aromatic -1 H aliphatic NOESY spectrum (64 scans, 2048 ( 1 H) ´ 64 ( 13 C) ´ 80 ( 1 H) complex data points, with 14.2 ppm, 16.0 ppm, and 1.5 ppm as 1 H, 13 C and 1 H sweep width, respectively) and a mixing time of 250 ms were measured at 1.1 MHz and 313 K in 20 mM HEPES, 200 mM NaCl, 5 mM TCEP, 150 µM DSS, and 5% D2O at pH 6.3. 13 C editing was not necessary for aromatic protons as they are well separated, but all post-NOE protons were 13 C resolved. The concentration of the Dhexa LCD was ~800 µM. 2D planes from the 3D spectra corresponding to the arginine d-position were assessed for NOEs between the arginine d-proton and the aromatic protons. A triple resonance (H)CC(CO)NH spectrum (16 scans, 2048 ( 1 H) ´ 80 ( 13 C) ´ 200 ( 1 H) complex data points, with 16.3 ppm, 22.0 ppm, and 54.0 ppm as the 1 H, 13 C and 1 H sweep width, respectively) was used to assign the arginine sidechain frequencies. Data were processed using BRUKER Topspin version 4.0, NMRPipe version 10.4 6 and analyzed using NMRfam SPARKY 7 . All spectra were referenced directly using DSS for the 1 H dimension; 13 C and 15 N frequencies were referenced indirectly.
NMR data for A1-LCD +7K+12D were acquired on Bruker Avance 600 and 800 MHz spectrometers equipped with TCI triple-resonance cryogenic probes and pulsed-field gradient units. All samples were prepared in a buffer consisting of 20 mM HEPES pH 6.8, 0.5 mM EDTA and 10% D2O at 20°C. For assignment, samples of 15 N, 13 C +7K+12D with concentrations between 85 and 220 µM were used to acquire standard triple-resonance backbone assignment experiments based on a sensitivity enhanced 1 H- 15  Data were processed using BRUKER Topspin version 3.2, or NMRPipe (v.7.9) 6 and analyzed using NMRviewJ 8 . All spectra were referenced directly using DSS for the 1 H dimension, 13 C and 15 N frequencies were referenced indirectly. 15 N R2 relaxation experiments were acquired at 600 MHz at 293 K using a standard Carr-Purcell-Meiboom-Gill (CPMG)-based Bruker pulse program (32 scans, 2048 ( 1 H) x 256 ( 15 N) complex data points) with the following delays of 16.8, 33.5, 67, 100.5, 134.1, 167.6, 251.4, and 335.2 ms with a recovery delay of 3 s. Due to significant overlap in the spectra Peakipy was used to attempt to deconvolute the peak intensities. The relaxation rates for residues 13, 15, 17, 19, 20, 21,  , and 132 were omitted as the overlap was too great for deconvolution. Fitting of the R2 rate profile to an analytical model was done as previously described 1 . To account for gaps in experimental data, the maximum cluster height was limited to 9 s -1 .
Bioinformatics analysis: Homologous sequences were identified using version 5.0 of the EggNOG database 9 . Sequences of homologs were aligned using the EMBL-EBI Clustal Omega tool 10 . The sequences were then trimmed to include only intrinsically disordered regions using the UniProt annotation 11 of the canonical human isoform. Sequence analyses were performed using the localCIDER tool 12 . The sequences culled for LCDs from homologs of hnRNPA1 and FUS / FET family proteins are included in separate Supplementary spreadsheets.

Analysis of sequence compositions:
Pairwise compositional similarities were determined in the following manner: (1) For each sequence, we create a 20´1 compositional vector. Each vector is of the form: (fA, fC, … fY). Here, each element quantifies the fraction of each amino acid within a sequence. (2) For a pair of compositional vectors, we compute the dot product of the two vectors. (3) Next, we divide the dot product by the product of the magnitudes of the vectors. This gives a value between 0 and 1, where values closer to 1 indicate higher compositional similarity. In Fig. 1b, Fig. 3a,b, Fig. 7a-c,  Extended Fig. 1b,c, and Extended Fig. 6, the sequences analyzed share a compositional similarity with the WT sequence of at least 0.8 (770 sequences) to limit the effects of strong outliers and/or partial homologs on the sequence analyses.
Analysis of csat data using a mean-field, stickers-and-spacers model: Wang et al. 13 adapted the mean-field stickers and spacers model of Semenov and Rubinstein 14 to a system with nA stickers of type A and nB stickers of type B. In this model, the saturation concentration csat was shown to be proportional to (nAnB) -1 providing the heterotypic interactions among A and B stickers are the only determinants of csat. The model of Wang et al. 13 was generalized by Choi et al. 15 to account for the competing effects of homotypic A-A and B-B interactions. Additionally, Choi et al., accounted for cooperative effects, whereby the strengths of inter-sticker interactions can either be enhanced or weakened due to the influence of three-body interactions on the strengths of inter-sticker interactions. We adapted the approach of Choi et al. 15 to obtain rescaled values of csat that were analyzed as a function of NCPR. Here, we choose the aromatic residues (Tyr / Phe) as the primary stickers and Arg as auxiliary stickers.
In the generalized mean-field model of Choi et al. 15 , csat is governed by the numbers of aromatic residues (na), the numbers of Arg residues (nR), and the strengths of inter-aromatic (laa) and aromatic-Arg (laR) interactions. Note that the l-values are dimensionless quantities. Accordingly, the functional form for csat, written in terms of a multiplicative constant is as shown in Equation (1). ; (1) Here, k is a constant that converts the right-hand side into units of concentrations. The value for k can be extracted by linear regression of measured csat values plotted against the quantity in the parenthesis on the right-hand side of Equation (1) 13 . In our analysis, we focus on a rescaling of csat and therefore we do not need an estimate for k. The first step in the rescaling, which accounts for the contributions of aromatic and Arg residues as stickers is written as: ; ( Note that we set laa = 1 and hence the only free parameter in the regression analysis is the value of laR. If the only determinants of csat were inter-sticker interactions, then the expectation would be that, with appropriate parameterization of laR, the values of csc,1 would be similar to one another for all A1-LCD variants. Instead, we observe the emergence of a V-shaped profile for csc,1 plotted against NCPR, especially for the Arg and Asp/Glu variants (Fig. 5c).
We also notice that the Lys variants have considerably higher csc,1 values than would be expected based on the numbers of aromatic and Arg residues in these variants. The implication is that Lys plays a distinctive role, not just as a high-excluded volume spacer, but also in terms of its impact on the strengths of inter-sticker interactions. This model emerges from findings regarding the influence of positive and / or negative cooperativity on pi-pi and cation-pi interactions 16 . Here, we reason, based on the model of Choi et al. 15 that Lys residues appear to weaken inter-sticker interactions via threebody interactions. This effect is captured in Equation (3) as: ; (3) Here, lK quantifies the extent to which Lys residues impact the effective strengths of inter-sticker interactions and nK is the number of protonated Lys residues. Notice that the effects of Lys residues are incorporated as contributions that affect csat via three-body interactions. The impact of accounting for the destabilizing effects of Lys residues is summarized in Fig. 5d. This requires parameterization of laR and lK. This two-parameter fit of Equation (3) shows that the rescaled csat values at 4˚C collapse onto the V-shape profile that is plotted against NCPR (Fig. 5e). c sat = k λ aa n a 2 + 2λ aR n a n R ( ) c sc,1 = c sat λ aa n a 2 + 2λ aR n a n R ( ) c sc,2 = c sat n a 2 λ aa + 3λ K n K ( ) + n a n R 2λ aR + 6λ K n K ( ) Finally, since we have measurements of csat at a series of different temperatures, we account for the temperature dependence by noting that the dilute arms of the binodals are linear on a semi-log scale implying that the temperature dependence of csat may be written as: ; (4) Here, csat(T0) is the csat value at the reference temperature of 277 K and T is the actual temperature at which csat is measured. We combine Equations (3) and (4) to arrive at a final rescaled form for csat plotted against NCPR to assess the extent to which the data can be collapsed onto a master V-shaped profile. The final rescaled form of csat takes the form: We applied Equation (5) to analyze the totality of variant-specific temperature dependent data for csat. The results are shown in Fig. 5e. Here, the dashed red lines show linear fits of each arm of the V-shaped plot. The associated Pearson r-values that quantify the linear correlation are also shown on the plot. In calculating the fits, the rescaled csat values for a given variant are averaged to one value so that each variant is weighted equally. The l-values in Equations (2) -(5) were found by optimizing the Pearson correlation coefficients of the linear fits while keeping laa fixed at unity. The m values in Equations (4) -(5) were determined by averaging the slopes of the dilute arms of the binodals of the relevant constructs. Accordingly, the fit of Equation (5) to all of the data has three free parameters viz., laR, lK, and m. The parameters we obtain are: laR = 1.69, lK = 0.0479, and m = 8.26 K.
We tested the accuracy of this model by overlaying csc,3 values for variants that were not used in the optimization. The results are shown in Fig. 5e. We find that the magnitudes of the Pearson rvalues that quantify the strengths of linear correlations are still at least 0.95. The key message that is uncovered from the analysis in Fig. 5e and Equation (5) is that it helps us unmask the sticker and spacer determinants of the driving forces for phase separation. Importantly, it helps identify the contributions of NCPR to the driving forces for phase separation of PLCDs, even for PLCDs that are not enriched in charged residues.
Estimating csat values of A1-LCD homologs using our mean-field model: We applied our meanfield model to the set of A1-LCD homologs culled from our bioinformatics analysis to estimate their csat values at 4˚C. Specifically, we used the NCPR of a given homolog to estimate its csc,3 value based on the two linear fits in Fig. 5e. Next, we solved directly for csat in Equation (5) by inputting na, nR, nK, and the estimated csc,3 for the given homolog and setting T = 277 K. We restricted our analysis to homologs whose length ranged from 100 -200 residues to limit the effects of length, since this is not directly accounted for in the mean-field model. The results are shown in Figure 5f. We find that the estimated csat values range over three orders of magnitude, demonstrating how similar sequences can display divergent phase separation behaviors based on small changes to sequence compositions.  Shifts in electrophoretic mobility are expected for certain mutations, particularly when multiple charged or bulky residues are substituted. This figure demonstrates the lack of contaminating proteins and that there is no evidence for proteolysis. Fig. 2, Fig. 3 and Fig. 4. (a) Measured binodals of A1-LCD variants that titrate Phe and Tyr balance (Fig. 2a) as a function of temperature. (b) Measured binodals of A1-LCD variants that titrate Arg residues (Fig. 3c). (c) Measured binodals of A1-LCD variants that titrate Arg / Lys content (Fig. 4a). (d) Measured binodals of A1-LCD variants that titrate the content of negatively charged residues (Fig. 4c). (e) Measured binodals of A1-LCD variants that titrate the content of oppositely charged residues (Fig. 4e).  SAXS data for all A1-LCD variants that were analyzed in this manner presented as I(q) versus q normalized by the forward scattering. The raw data (black) is overlaid with logarithmically smoothed data for visualization (red circles). The results from the fit to the empirical MFF 5 are indicated in the upper right corner. Results are summarized in Table S2. The inset is the Guinier fit with the resulting Rg. Deviations from the linearity in the Guinier region prevented a Guinier fit for variant +4D; a fit to the MFF was possible, nonetheless. Here, R = 1.98717´10 -3 kcal/mol*K. The +7R variant is omitted due to the proximity of the measurements to the critical point restricting one from performing a van't Hoff analysis. Among the aromatic variants, Dh˚ increases as the Tyr:Phe ratio increases, indicating Tyr is a stronger sticker than Phe. In addition, among positively charged variants, Dh˚ increases as the number of Arg residues increases, which is attributable to the role of Arg as an auxiliary sticker.