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. 2024 Jan 29;35(3):mr1. doi: 10.1091/mbc.E23-07-0289

NAGPKin: Nucleation-and-growth parameters from the kinetics of protein phase separation

Zsuzsa Sárkány a,b, Francisco Figueiredo a,b,†, Sandra Macedo-Ribeiro a,b, Pedro M Martins a,b,*
Editor: Huaiying Zhangc
PMCID: PMC10916857  PMID: 38117593

Abstract

The assembly of biomolecular condensate in eukaryotic cells and the accumulation of amyloid deposits in neurons are processes involving the nucleation and growth (NAG) of new protein phases. To therapeutically target protein phase separation, drug candidates are tested in in vitro assays that monitor the increase in the mass or size of the new phase. Limited mechanistic insight is, however, provided if empirical or untestable kinetic models are fitted to these progress curves. Here we present the web server NAGPKin that quantifies NAG rates using mass-based or size-based progress curves as the input data. A report is generated containing the fitted NAG parameters and elucidating the phase separation mechanisms at play. The NAG parameters can be used to predict particle size distributions of, for example, protein droplets formed by liquid-liquid phase separation (LLPS) or amyloid fibrils formed by protein aggregation. Because minimal intervention is required from the user, NAGPKin is a good platform for standardized reporting of LLPS and protein self-assembly data. NAGPKin is useful for drug discovery as well as for fundamental studies on protein phase separation. NAGPKin is freely available (no login required) at https://nagpkin.i3s.up.pt.

  • Protein phase separation (PPS) is a ubiquitous phenomenon with vital roles in human health and disease. Drug discovery in PPS has been hampered by the lack of quantitative methods characterizing nucleation and growth rates.

  • NAGPKin is the first computational tool dedicated to quantifying PPS kinetics from the mass -or size-increase of biomolecular condensates over time. Fundamental insights are gained from the automatic analysis of raw experimental data.

  • NAGPKin is useful for the development of new drugs targeting PPS, for standardized data reporting and, on the whole, for understanding the molecular mechanisms of functional and pathological PPS.

INTRODUCTION

The liquid-liquid phase separation (LLPS) of biomolecular condensates and the aggregation of proteins into amyloid fibrils are examples of protein phase separation in cell physiology and disease. Pathological hallmarks of several neurodegenerative diseases, amyloid fibrils form through the phase separation step of primary nucleation and proliferate through the secondary nucleation of new fibrils on the surface of existing ones (Hadi Alijanvand et al., 2021). While nucleation increases the number of fibrils, autocatalytic growth increases the size of the fibrils (Bentea et al., 2017), which can reach >1000 nm in length (Gade Malmos et al., 2017). Nucleation and growth (NAG) are also present during the formation of aberrant and functional membraneless organelles through the LLPS of proteins and nucleic acids (Strom and Brangwynne, 2019; Darling and Shorter, 2021). Distinctively from the highly ordered structure of amyloid fibrils, biomolecular condensates formed by LLPS present liquid-like properties such as the spherical shape, the ability to coalesce and deform under shear flow, and the short recovery times from fluorescence recovery after photobleaching (FRAP) experiments (Garaizar et al., 2022).

A good understanding of the NAG kinetics is important for knowing how candidate drugs modulate the phase separation rates and the size distributions of protein assemblies (Shimobayashi et al., 2021; Kar et al., 2022). For the kinetic analysis of amyloid aggregation, the mass concentration of protein assemblies ([M]) is measured over time (t) and subject to a min-max normalization (Figure 1, A and B). The normalized curves are then fitted by a physical model to yield rate constants for the primary nucleation, growth, and secondary nucleation steps (Knowles et al., 2009; Linse, 2019; Sárkány et al., 2023). Mass-based progress curves are readily measured using amyloid dyes such as Thioflavin-T (ThT) or by estimating the mass of aggregates from the depleted concentration of monomer in solution (Gade Malmos et al., 2017; Xue et al., 2017; Bellomo et al., 2018). To test whether the fitted model does provide reliable mechanistic information about the NAG steps, complementary measurements of size-based progress curves and particle size distributions are needed using dynamic light scattering (DLS) and advanced microscopy techniques (Silva et al., 2017, 2018), for example. Size-based progress curves are, however, less commonly studied because the size distributions of amyloid fibrils can be too complex to be deconvoluted by conventional light scattering or image analysis techniques.

FIGURE 1.

FIGURE 1.

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Schematic representations of mass-based and size-based progress curves. (A) Mass-based progress curves monitor the mass of protein assemblies either directly or indirectly (e.g., through fluorescence measurements) from an initial point with signal [M]i to a final point [M]f. These curves can have hyperbolic (solid line) or sigmoidal (dashed line) shapes. (B) The same curves are represented in normalized units of reaction conversion (α). The maximal growth rate (vmax, red line), the time required to reach vmax (tmax), the half-life coordinates t50 and v50 (red line), and the duration of the lag phase (tlag) are examples of commonly used kinetic measurables. (C) Size-based progress curves monitor the increase in the size of protein assemblies from an initial value Ri to a final value R∞.

The intense research presently devoted to the LLPS of biomolecular condensates instigates an interest in size-based progress curves in which a characteristic droplet size (R) is monitored over time (Figure 1C) either in the test tube or in cells (Berry et al., 2015; Matsarskaia et al., 2019). Typically, these curves are represented in a log-log scale to extract power-law scaling exponents: the scaling exponents take values of ∼1/2 in purely diffusional regimes and of ∼1 in kinetic regimes determined by surface attachment (Berry et al., 2018); spontaneous LLPS by spinodal decomposition (without nucleation) is characterized by a scaling exponent of ∼1/3 (Matsarskaia et al., 2019). More in-depth mechanistic investigations have been hampered by the absence of phase separation models able to describe the R versus t dependencies and, above all, explain the recurrent observation of sharp NAG of a few droplets with large and uniform sizes (Mohapatra et al., 2017; Sárkány et al., 2023).

These challenges were recently addressed with the proposal of a “general” NAG model that, besides describing the kinetics of protein crystallization and aggregation (Crespo et al., 2012), also predicts the evolution of particle size distributions of amyloid fibrils (Silva et al., 2017) and liquid droplets (Sárkány et al., 2023). The initial motivation behind the general NAG model was to study protein aggregation as a phase separation process and not as a protein polymerization reaction (Crespo et al., 2012). Analogous to crystallization processes, the elementary rate equations of primary nucleation, growth, and secondary nucleation were expressed as a function of supersaturation thus helping to elucidate the important role of protein solubility as a thermodynamic determinant of protein aggregation (Crespo et al., 2012). Moreover, the phase separation view accounted for hyperbolic-shaped aggregation curves measured in the absence of preformed aggregates, which was a fundamental advance relative to the existing physical models (Crespo et al., 2012). More recently, the crystallization-like model was developed to include the effect of surface tension on protein aggregation and LLPS (Sárkány et al., 2023).

Here we present the NAGPKin web server for automated quantification NAG parameters from the kinetics of protein phase separation. NAGPKin requires minimal intervention from the users, who, after uploading their raw data, follow an informative tour through the steps of chemical kinetic analysis. A final report provides quantitative information about the general NAG parameters that best fit the measured mass or size progress curves. To improve the quality of the predictions, global fittings to multiple curves obtained at different protein concentrations are encouraged. The application examples that follow illustrate the usefulness of NAGPKin for drug discovery, standardized kinetic data reporting and, on the whole, for understanding the molecular mechanisms of protein phase separation.

RESULTS AND DISCUSSION

NAGPKin provides different types of information depending if mass-based or size-based curves are uploaded (Supplemental Table S1). In the first level of analysis, “descriptive” kinetic measurables such as the half-life coordinates are determined by a systematic, user-independent method. In the subsequent levels, the phase separation mechanism and the elementary steps of primary nucleation, secondary nucleation, and growth are characterized quantitatively from the kinetic analysis of scaling laws (level 2) or through global numerical fitting (level 3) using the physical NAG model of Sárkány et al., 2023.

As an application example of level 1 analysis, we study how different concentrations of dopamine (DA) affect the aggregation of an Atx3 variant containing a pathological polyglutamine (polyQ) tract size of 77Q (Atx3-77Q). The curves of ThT fluorescence increase were previously measured by us in triplicate experiments for 12 serially diluted concentrations of DA (Figueiredo et al., 2023). The NAGPKin’s template was filled with the values of time (first column) and ThT fluorescence (36 subsequent columns) and then saved keeping the .ods extension. The used concentration of Atx3-77Q (3 μM) is not a piece of relevant information if only level 1 analysis is performed. So, for descriptive-only studies, the row destined for protein concentration values can be left with blank cells. Because NAGPKin does not analyze the effect of modulators on protein phase separation, no information about the adopted DA concentrations is requested in the spreadsheet template. After the .ods file is uploaded, the initial data processing produces a graphic with experimental and numerically fitted curves (Figure 2A) and two .csv files summarizing the fitted kinetic measurables and progress curves. The user can download these files and use the data to customize new graphs or to find dose−response relationships (Figure 2B). In general, kinetic modulators of protein aggregation influence the values of t50 (via the primary nucleation and autocatalytic steps) and v50 (via the autocatalytic steps), whereas thermodynamic modulators influence the values of [M]∞ (via the effect on protein solubility) (Sárkány et al., 2019, 2023). Because the uploaded data were obtained at a fixed protein concentration (c0), moving forward to the second level of analysis is not possible − the minimum requirement is four different c0 values. A global fit to all curves to estimate a single set of NAG parameters (level 3 analysis) is also undue because changeable inhibitor concentrations are adopted.

FIGURE 2.

FIGURE 2.

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Systematic analysis of 36 aggregation curves of Atx3-77Q measured by Figueiredo et al. in the presence of different concentrations of DA (Figueiredo et al., 2023). (A) NAGPKin’s output graph with the uploaded (symbols) and fitted (line) curves. (B) The values of t50 (top), v50 (middle), and [M]∞ (bottom) produced by NAGPKin are represented as a function of DA concentration. Symbols and error bars: mean and SD values. In two of the conditions studied (5.0 and 0.31 μM DA), one replicate is excluded.

By default, NAGPKin assumes the submitted data to consist of mass-based progress curves. For the analysis of size-based progress curves, the “size-based” option in the lefthand expander should be selected at any point, before or after file upload. To exemplify the fundamental interpretation of particle size measurements, we used DLS data obtained during the LLPS of the low-complexity domain (LCD) of TAR DNA-binding protein 43 (TDP-43) (Van Lindt et al., 2021), and during the aggregation of nonexpanded Atx3 (Silva et al., 2017). The evolution of the hydrodynamic radii follows dissimilar trends in each of the cases, either increasing with time for liquid droplets of TDP-43-LCD (Figure 3A) or decreasing with time for Atx3 fibrils (Figure 3B). Importantly, the two types of curves are resolved by NAGPKin both in level 1 and level 3 of analysis. Level 2 analysis is again not performed because the required c0-scaling data is not included in the input file. The final reports (Supplemental Figure S1) disclose that the importance of secondary nucleation relative to the other autocatalytic step (growth) is minimal for TDP-43-LCD (∼0%) and maximal for Atx3 (∼100%). Because the secondary nucleus is smaller than the primary nucleus, systems dominated by secondary nucleation exhibit decreasing mean sizes over time, even in the absence of significant breakage/fragmentation, as confirmed for Atx3 (Silva et al., 2017). As we move from level 1 to level 3, the quality of the numerical fittings improves for TDP-43-LCD and worsens for Atx3. The explanation for this fact can also be found in the NAGPKin’s report (Supplemental Figure S1): in the case of TDP-43-LCD, the underperformance of the numerical fittings in level 1 is due to STEs that play a significant role in the nucleation of these liquid droplets (25% importance) but are not considered in the first stage of analysis. Level 3 is a more constrained analysis because it takes into account the effects of protein concentration and solubility. Therefore, level 3 is more trustworthy than level 1 even if the quality of the numerical result is worse. For reproducible assays, imperfect goodness-of-fit statistics are suggestive of the occurrence of parallel phenomena, which, in the case of Atx3 are indeed present through nonamyloid aggregation pathways (Silva et al., 2017).

FIGURE 3.

FIGURE 3.

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Comparison between measured and theoretical size-based curves. (A and B) Evolution of the hydrodynamic radius measured by DLS (symbols) and numerically fitted after level 1 (dashed line) and level 3 (solid line) analyses by NAGPKin. Experimental data obtained by (A) Van Lindt et al. during LLPS of TDP-43-LCD in the absence of NaCl (Van Lindt et al., 2021) and (B) Silva et al. during the formation of Atx3 fibrils (Silva et al., 2017).

As an illustrative example of all levels of NAGPKin analysis, we use mass-based progress curves measured by Hurshman et al. (Hurshman et al., 2004) for different concentrations of monomeric transthyretin (mTTR) (Figure 4). The ThT fluorescence data obtained by those authors were previously digitized and normalized by us (Sárkány et al., 2023) and are made available to NAGPKin users as a workable “prefilled example” for which no file upload is required. The kinetic measurables tmax, vmax, or tlag are not quantified by NAGPKin because only t50 and v50 are suitable to describe sigmoidal, but also hyperbolic curves (Figure 1), such as those obtained during mTTR aggregation. The selection between the results from levels 2 or 3 is automatic and relies on the values of r-squared (r2) obtained using t50 vs. c0 scaling properties (level 2) or the the global numerical fitting (level 3). The t50 versus c0 analysis will be preferred over the global fit analysis only if the difference in the values of r2 is > 0.03 in favor of level 2. Values of r2 > 0.98 are obtained in the example of mTTR for both levels of analysis (Supplemental Figure S2). Even in such cases of high r2, the occurrence of (undetected) parallel processes cannot be excluded; in fact, significant amounts of TTR dimers were identified in the initial sample of mTTR (Hurshman et al., 2004), an observation that may explain differences between the values of fitted parameters in levels 2 and 3.

FIGURE 4.

FIGURE 4.

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NAGPKin analysis of the aggregation kinetics of mTTR. (A) Symbols: normalized values of ThT fluorescence increase measured by Hurshamnn et al. for mTTR concentrations of (from top to bottom) 400, 300, 250, 200, 150, 100, and 50 μg/mL (Hurshman et al., 2004). Lines. NAGPKin’s global fit (level 3). (B) Representation of the measured (symbols) and numerically fitted (line) dependencies of t50 on c0 (level 2).

DISCUSSION

NAGPKin is the first computational tool dedicated to the kinetic analysis of phase separation processes. To the best of our knowledge, none of the practical examples here investigated could have been processed by alternative software for automated kinetic analysis. In the first of the given examples, the inhibition of protein aggregation was characterized through the quantification of both kinetic (t50 and v50) and thermodynamic measurables ([M]∞). Detailed mechanistic information could be extracted from size-based progress curves obtained during the LLPS of TDP-43-LCD and the aggregation of Atx3. Similar mechanistic insights were then obtained from hyperbolic curves of ThT fluorescence increase and chemical kinetic properties of mTTR aggregation. We expect that NAGPKin will be useful for processing data of condensate size increase measured in cells (Zwicker et al., 2014; Snead et al., 2022), especially during the initial phase of coalescence-free self-assembly (Berry et al., 2018; Matsarskaia et al., 2019). Additional applications such as the study of NAG during protein and industrial crystallization processes (Arruda et al., 2023) will be investigated in the future.

When mass-based progress curves showing a sigmoidal shape are obtained, fundamental studies can alternatively be performed using the web tools AmyloFit (Meisl et al., 2016) and Kfits (Rimon and Reichmann, 2018). These tools are based on polymerization principles that are distinct from phase separation principles of protein self-assembly. In particular, the used protein polymerization model was originally developed by Oosawa and Kasai to describe actin-like polymerization (Oosawa and Kasai, 1962) and then expanded to include secondary nucleation steps and Michaelis−Menten-like kinetics for elongation and secondary nucleation (Knowles et al., 2009; Meisl et al., 2016). Although the analogies with “a gas-liquid transition” or “condensation phenomenon” are used since the original work by Oosawa and Kasai (Oosawa and Kasai, 1962), the “nucleation” and elongation steps during actin-like polymerization do not follow phase equilibrium principles. For this reason, the AmyloFit and Kfits tools cannot be used to process 1) mass-based, hyperbolic curves, 2) LLPS data, or 3) the modulation of phase equilibrium parameters such as protein solubility. Moreover, NAGPKin is the only web server analyzing size-based progress curves, whereas the general NAG model (on which NAGPKin is based) is the first to rationalize the sharp formation of large assemblies with Gaussian size distributions (Sárkány et al., 2023).

The NAGPKin’s report may reveal unsatisfactory fitting results, even when high-quality reproducible data are subject to analysis. Those situations likely result from parallel phenomena such as off-pathway aggregation, coalescence, and mixed liquid-liquid and liquid-solid nucleation pathways, whose occurrence can be checked by complementary methods for monitoring phase separation (Crespo et al., 2016, 2017; Ferreira et al., 2017; Lee et al., 2018; Babinchak and Surewicz, 2020; Martins et al., 2020; Garaizar et al., 2022). To avoid the problem of overparameterization, our algorithm does not include additional parameters describing parallel microscopic events whose number and nature cannot be known a priori. Instead, the report issued by NAGPKin identifies possible reasons for the poor fittings and suggests ways to address this problem. It may happen, for example, that the scaling of t50 with c0 follows the expected trend but the global fitting results are poor. In cases such as this, the NAGPKin report would alert for the possible occurrence of off-pathway aggregation, which is known to severely affect the shape of the kinetic curves but has little effect on the values of t50 (Crespo et al., 2016).

The predictions from the general NAG model are testable. For example, the NAG rate constants fitted to size-based progress curves should also describe mass-based progress curves (Silva et al., 2017, 2018). Similarly, the fitted NAG rate constants can be used to predict the evolution of size distributions of protein droplets (Sárkány et al., 2023). It is therefore advised that, when possible, results obtained using mass- and size-based methods are submitted to NAGPKin for consistency analysis.

MATERIALS AND METHODS

Overview

NAGPKin performs automated kinetic analysis with different levels of detail depending on what type of experimental data is uploaded (Figure 5). In level 1a, the half-life coordinates t50 and v50 and the total mass increase [M]∞ = [M]f – [M]i are estimated from mass-based progress curves. If, instead, size-based curves are uploaded, the fitted values of the primary nucleus size (R1) and final size (R∞) are provided together with an indicative estimate of the half-life time t50 expected for mass-based progress curves (level 1b). In levels 2 and 3, NAG rate constants are obtained following different methods independently of what type of progress curves are used as input. The NAGPKin algorithm automatically selects what method is more reliable and what rate constants should be included in the final report. Level 2 is based on the scaling properties of measurable t50 with protein concentration c0. As such, level 2 analysis is only possible if four or more progress curves are measured at different c0 values. Level 3 analysis includes a global fit of the model equations to the experimental data. Although this can be done using a single progress curve as the input, the simultaneous analysis of multiple curves decreases the risk of numerical convergence to local minima rather than to the global optimum. From the comparison of the level 2 and level 3 results, the NAGPKin algorithm can identify the possible occurrence of parallel self-assembly pathways or suggest ways to improve the quality of the kinetic analysis.

FIGURE 5.

FIGURE 5.

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Overview of the NAGPKin web server. Left: the raw data measured during protein phase separation experiments can be copied and pasted into the NAGPKin’s spreadsheet file. Right: NAGPKin’s workflow. The user selects whether the uploaded data correspond to mass or size progress curves; then, automatic curve fitting analyses are performed to provide level 1, 2, and 3 information. The equations used for parameter estimation are numbered as in Supplemental Figure S3.

Input file

A single spreadsheet file containing mass-based or size-based progress curves is used as the input for the NAGPKin web server. An example of this file is available for download at the beginning of the analysis and can be modified to remove the exemplifying data and add the user’s data. The OpenDocument Spreadsheet (.ods) format of this file is compatible with applications such as Microsoft Excel or LibreOffice and should be kept upon saving the file. The first rows of the template contain instructional information that can be left unmodified. The experimental data should be added as indicated by the instructions, with the values of time over the blue column, the values of protein concentration over the yellow row, and the values of protein mass or size over the green cells (Figure 5, left). It is assumed that all curves are obtained simultaneously and, therefore, the values in the first column (time) are common to all the individual contours. No distinction between mass or size progress curves is required at this point. Data obtained during mass-based experiments (such as turbidimetry and ThT fluorescence measurements) or size-based experiments (such as average size measurements) can be copied and pasted directly from the raw data files. Each curve may contain blank cells corresponding to, for example, experimental outliers or noisy data. After saving the modified .ods template, the user can upload it into NAGPKin by dragging and dropping the file or by file browsing.

Algorithm

The NAGPKin algorithm is based on the general NAG model of phase separation (Crespo et al., 2012; Silva et al., 2017; Sárkány et al., 2023). In this model, the principal moments of the size distribution (Eq. 1 in Supplemental Figure S3) can be numerically solved to obtain the evolution with time of the mass concentration [M](t), number concentration [P](t), and mean size (in number of protein units) N(t) of new assemblies. Through mathematical programming, it is also possible to fit the master equation to size-based progress curves and estimate the rate constants for primary nucleation (kn), growth (k+) and secondary nucleation (k2). While the growth and secondary nucleation steps affect particle size in drastically different ways, their effect on the total mass of assemblies is difficult to discriminate as k+ and k2 are both elementary rate constants describing a supersaturation-dependent, autocatalytic step (Crespo et al., 2012; Silva et al., 2017; Sárkány et al., 2023). This means that numerical fittings to mass-based progress curves yield an autocatalytic rate constant kα = k+ + k2 and not the individual estimates of k+ and k2. The importance of the primary nucleation rate relative to the autocatalytic rates is given by the parameter kb = kn/kα. In the NAGPKin algorithm, the exact solution of model equations is only used in the last stage (level 3) of the analysis (Figure 5, right). Before, simplified model equations (level 1) and, if possible, NAG scaling laws (level 2) are fitted to the experimental data to obtain complementary mechanistic information and good initial guesses for the global fitting. The simplified equations used in level 1 are only valid in the absence of surface tension effects (STEs) (Sárkány et al., 2023). Since the simplified equations produce robust numerical fittings both in the presence and absence of STEs (Sárkány et al., 2023), they are used to obtain descriptive measurables but not in-depth mechanistic information. STEs change the protein solubility of small, curved assemblies from the saturation value c∞ to a critical value cc, with cc ≥ c∞. Both c∞ and cc can be obtained experimentally, for example, from the linear plot of the total mass of assemblies versus protein concentration (Sárkány et al., 2023). By default, NAGPKin assumes very low solubility (c∞ << c0), while the ratio cc/c∞ is a fitted parameter. However, the user may choose to set c∞ and cc to fixed values known experimentally. Level 2 analysis is only performed if four or more progress curves are available for different c0 values. Global fit analysis (level 3) of mass-based progress curves produces estimates of kα/c∞ and kβ = kb (c∞/cc)2; in addition, the combined parameter k2N1/(kαN2) can be fitted during the analysis of size progress curves. Here, N1 and N2 are the number of protein units constituting primary and secondary nuclei, respectively. A ratio of N1/N2 = (R1/R2)3 = 223 was previously estimated for amyloid fibrils of Atx3 (Silva et al., 2018). Whenever possible, a final report is generated summarizing the values and physical meaning of the NAG rate constants, quantifying the importance of STEs, and evaluating the possible occurrence of parallel processes such as off-pathway aggregation and coalescence. The selection between NAG rate constants obtained during level 2 and 3 analysis is based on goodness-of-fit statistics; in the case of equally good statistics, the global fit analysis (level 3) is preferred.

Implementation

NAGPKin’s code was written with the programming language Python (version 3.9.16) and the web tool is made using Streamlit (www.streamlit.io). The up-to-date codes and new releases are available on GitHub (https://github.com/pmartins2106/NAGpkin/). The GNU general public license is also added to the source package on GitHub.

CONCLUSIONS

NAGPKin analyzes mass-based progress curves (exhibiting both hyperbolic and sigmoidal shapes) as well as size-based progress curves. Descriptive information but also detailed mechanistic insights are provided into phase separation dynamics. The uniqueness of the NAGPKin toolkit is demonstrated in a series of application examples, from drug discovery to fundamental chemical kinetic analysis. The user-friendly interface of NAGPKin makes it an accessible tool to both experimentalists and bioinformaticians with or without previous experience in kinetic data modeling.

Supplementary Material

mbc-35-mr1-s001.pdf (1.1MB, pdf)

Acknowledgments

We thank Professor José Paulo Leal, Department of Computer Science − Faculdade de Ciências da Universidade do Porto, for his invaluable help during the Implementation of NAGPKin. This work is part of a project that has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement no. 952334 (PhasAGE). This research was funded by the Portuguese Foundation for Science and Technology (FCT) in the framework of project PTDC/QUI-COL/2444/2021.

Abbreviations used:

Atx3

ataxin-3

DA

dopamine

DLS

dynamic light scattering

LCD

low-complexity domain

LLPS

liquid-liquid phase separation

mTTR

monomeric transthyretin

NAG

nucleation and growth

polyQ

polyglutamine

STEs

surface tension effects

TDP-43

TAR DNA-binding protein 43

ThT

Thioflavin-T

Footnotes

This article was published online ahead of print in MBoC in Press (http://www.molbiolcell.org/cgi/doi/10.1091/mbc.E23-07-0289) on December 20, 2023.

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