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The LLPS REDIFINE protocol described here was applied to the FUS N-terminal domain (NTD). FUS NTD readily phase separates under ambient conditions at micromolar concentrations19,21. This particular sample was prepared at a concentration of 200 µM in 30 mM HEPES buffer containing 200 mM KCl at pH 7.5, with 0.5% regular agarose. Upon phase separation, FUS NTD signals remain observable in the condensed phase (Figure 1A,B). This makes it a perfect candidate for LLPS REDIFINE to study. Namely, most LLPS-prone proteins contain long intrinsically disordered regions that usually remain observable in the condensed phase; however, in more structured proteins, this is not the case.
The REDIFINE fit (Figure 1D and Figure 3A,B) revealed multiple unique parameters for this FUS NTD sample. Specifically, it determined the diffusion coefficients in the dilute and condensed phase (Ddil and Dcond), population of protein in the condensed phase (νcond), average droplet size R, and interphase permeability p. Droplet size and permeability define the interphase exchange rate from the condensed to the dilute phase kcd=3p/R, allowing us to obtain the information about exchange dynamics19.
These results can be visualized in different ways (Figure 3B). Using a spider plot, one could compare results across different conditions or samples. On the other hand, one can pictorially represent the REDIFINE parameters in the model to visualize them most effectively. Note that REDIFINE provides all these results label-free in just a couple of hours using only one sample.
As the NMR signal of FUS NTD remains detectable in the condensed phase (Figure 3C), the CONDENSE-MT will most likely not be applicable due to the lack of relaxation contrast. We recorded the CONDENSE-MT data set on FUS NTD, and indeed, no difference in the MT profile is observed between the agarose reference and FUS NTD biphasic sample (Figure 3C). This renders the CONDENSE-MT methodology inapplicable to this particular FUS NTD sample.
However, the CONDENSE-MT provides dynamic characterization of repeat-expansion RNA condensates (Figure 3C,D)20. Note that CONDENSE-MT could provide multiple parameters uniquely characterizing the RNA in the condensed phase (Figure 3D), despite the fact that its signal is unobservable in conventional NMR (Figure 3C). The obtained parameters are the proton-exchange kinetics between condensate and bulk water (kcondensate,H2O and kH2O, condensate), the T2 relaxation rate for the condensate (T2,condensate), reflecting the extent of dynamic arrest of the biomolecules upon condensation, and the apparent R2 rate of bulk water (R2,water). This last parameter is a linear combination of the tumbling rate of bulk, dilute water, and slow-tumbling, condensed water. Higher R2,water values indicate a higher population of water in the condensate, which elevates the apparent overall water R2 rate20 (Figure 2E and Figure 3D).
DATA AND CODE AVAILABILITY
LLPS REDIFINE raw data and processing codes are available in the Zenodo repository: https://doi.org/10.5281/zenodo.15228787 . CONDENSE-MT raw data and processing codes have been deposited to Zenodo repository https://doi.org/10.5281/zenodo.15789697. MATLAB is required for the processing. They are also provided within this article (Supplementary Coding Files).

Figure 1: REDIFINE workflow. (A) Diffusion measurements yield complex biphasic diffusion decay curves in condensed samples. The resulting decay contains deconvolved parameters describing the diffusion coefficients of the species in the condensed and dilute phase, their populations, droplet size, and interphase exchange rate. (B) To decode these isolated parameters, one needs to record a pseudo-3D dataset by varying not only the gradient strength but also the diffusion delays. It is absolutely essential for quantification that every slice from these measurements be properly phased and baseline-corrected. (C) After checking the quality of the measured and processed data, these 1D slices are fed into the MATLAB code for analysis and final plotting. (D) The data are then fitted by a nonlinear programming solver. The fitting and resulting parameters are illustrated for the biphasic FUS NTD sample. Please click here to view a larger version of this figure.

Figure 2: CONDENSE-MT workflow (A) A unique CONDENSE-MT profile observed on the water resonance illustrating the broadening due to the presence of condensed biomolecules and water. (B) Water is observed for every irradiation offset. (C) For quantification, it is essential that all spectra be phased correctly. (D) After acquiring the water resonance at different irradiation offsets, the experiment is repeated at different irradiation powers. This will yield a dataset of the relative water signal as a function of both irradiation offset and irradiation power (E). The data are then fitted by a nonlinear programming solver. The fitting and resulting parameters are illustrated for the biphasic 31xCAG RNA sample. Please click here to view a larger version of this figure.

Figure 3: Presentation of REDIFINE and CONDENSE MT results. (A) Spider plot representation of REDIFINE parameters for comparative analysis across samples or conditions. (B) Schematic model illustrating REDIFINE-derived parameters, including diffusion coefficients, droplet radius, partitioning, and interphase exchange rate. (C) Comparison of CONDENSE-MT profiles acquired for agarose reference and biphasic FUS NTD in agarose at 500 Hz irradiation.
(D) CONDENSE-MT analysis of 31xCAG repeat-expansion RNA condensates showing parameter extraction and visualization of condensate-associated magnetization transfer effects. Please click here to view a larger version of this figure.
Supplementary Figure 1: REDIFINE setup. (A) FUS N-terminal domain remains observable upon preparation of the biphasic condensed sample. A strong amide/amino and aromatic proton signal is observed. (B) The signal decay observed in the diffusion DOSY experiment illustrates faster decay of the dilute-phase protein population and slower decay of the protein in the condensed phase. Please click here to download this file.
Supplementary Figure 2: REDIFINE processing. (A) Matlab code used for REDIFINE fitting, with highlighted parameters where the specific input is needed. The inset illustrates how one picks the integration area. (B) Minimization of the fitting function and the ensuing results.Please click here to download this file.
Supplementary Figure 3: CONDENSE-MT setup. (A) Overview of the NMR experiments required for CONDENSE-MT analysis, including the water inversion-recovery experiment (expno. 5) and the CONDENSE-MT experiments at different irradiation powers (expno 11-18). (B), (C) Overview of the Matlab script for reading and integrating the water 1D spectra for CONDENSE-MT datasets. The CONDENSE-MT experiments are given as main – main8. The integration boundaries are entered as water_left and water_right. Please click here to download this file.
Supplementary Figure 4: CONDENSE-MT processing. (A) First section of the CONDENSE-MT fitting script, which includes water inversion recovery fitting (section 1) and input of the previously determined agarose background parameters. (B) Fitting and parameter uncertainty determination of CONDENSE-MT datasets. Starting parameters for the fit can be set within fit0. (C) Plotting section of the CONDENSE-MT fitting result. Please click here to download this file.
Supplementary Coding Files: MATLAB Scripts for REDIFINE and CONDENSE-MT Analysis. Bruker Topspin codes to set up the CONDENSE-MT experiment and MATLAB scripts used for processing and fitting REDIFINE diffusion datasets and CONDENSE-MT magnetization-transfer datasets, including data integration, relaxation analysis, and global model fitting routines. MATLAB is required to run the scripts.Please click here to download this file.