Emergence of Compact Oligomers inside the Small-World Network of TDP-43 Condensates

Abstract

Liquid-liquid phase separation (LLPS) of TDP-43 mediates the formation of pathological inclusions in various neurodegenerative diseases, with the condensate structures and their related amyloid aggregation remaining elusive. Here, by developing a data-driven bottom-up coarse-grained model using discrete molecular dynamics simulations, proteins in the condensates of TDP-43 were found to form a dynamic network of fluctuating sizes. While dominated by peptides engaged with a small number of peptides connected by a low number of inter-peptide contacts, the condensates also contained peptides with large numbers of connections, serving as hubs of a small-world network. Importantly, peptides in these high-contact states were intertwined to form oligomers that were stable for relatively long periods inside the weakly connected network. These oligomers were likely the aggregation intermediates towards nucleation of amyloid fibrils. Therefore, this transferable coarse-grained model may serve as a powerful tool for unravelling the inner workings of LLPS and amyloid aggregation.

Graphical Abstract

The TAR DNA-binding protein 43 (TDP-43) is a versatile DNA and RNA processing protein that plays essential physiological roles in RNA metabolism, neuronal physiology, cell proliferation.^1,2 Meanwhile, pathological amyloid-like deposits of TDP-43 are the main inclusions found in the brain and spinal cord of patients with amyotrophic lateral sclerosis (ALS) and frontotemporal dementia (FTD).^3–5 Mounting evidence indicates that TDP-43 can undergo liquid-liquid phase separation (LLPS) by partitioning a homogeneous solution into a high-density membraneless condensate, which often resembles a liquid droplet, and a dilute phase.^6–10 The LLPS of TDP-43 is essential for cellular functions by mediating the formation of biomolecular condensates in nucleoli, Paraspeckles, Cajal bodies, stress granules, and transport granules.¹¹ Formation of the condensates is also required for the regulatory function of TDP-43 on a subset of its mRNA partners.¹ Moreover, aberrant phase separation of TDP-43 is intimately related to neurodegenerative diseases.^12,13 Aberrantly phase separated condensates impair the RNA regulatory functions in neurons, and dysregulate local and global translation by sequestration of mRNAs and RNA-binding proteins.¹⁰ Disrupted axonal transport dynamics were found for ALS-related mutations, where the viscosity of the TDP-43 condensates was altered by the mutations.¹⁴ Meanwhile, transient stress granules consisted of TDP-43 lose reversibility and dynamic liquid-like properties under chronic stress conditions to form insoluble solid or gel-like structures, perturbing the formation-dissociation kinetic balance of the stress granules.¹⁰

Although increasing evidence has revealed the crucial roles of LLPS and the resultant condensates of TDP-43 in neurodegenerative diseases, the exact relationship between LLPS and amyloid aggregation remains poorly understood, particularly regarding the formation of oligomers that are widely considered to be the dominant cytotoxic species and the primary cause of neurodegenerative diseases.^15,16 The stress granules are found to co-localize with cytoplasmic aggregates formed by TDP-43, suggesting the potential role of condensates as a nucleation site for the TDP-43 amyloid aggregates.¹⁷ It has been postulated that the high concentration of amyloid proteins in the condensates facilitates the formation of toxic oligomers by reducing the free-energy barrier, which further promotes the amyloid aggregation of TDP-43 by converting the protein into irreversible fibrils through a liquid-to-solid transition.¹¹ However, the condensates are a dense, viscous, and crowded peptide complex with remarkable internal structures and interface properties that can offer a completely different environment for oligomer formation compared with homogeneous solutions¹⁸. Thus, how the unique structure of the condensates mediates oligomer formation remains elusive, a knowledge essential for guiding potential mitigation strategies against the aberrant phase transitions of LLPS and amyloid aggregation.¹⁹

In this study, we developed a novel coarse-grained model to investigate LLPS and oligomer formation within the condensates of TDP-43 using discrete molecular dynamics (DMD, details in Supporting Information). DMD is a rapid molecular dynamics algorithm used widely to study protein folding, dynamics of multi-domain proteins, and the assembly of amyloid aggregation.^20–22 We focused on the low complexity domain (LCD) of TDP-43 (residues 267–414),^23,24 which is the major component of neuronal inclusions and harbors most of the ALS-associated mutations.^25,26 TDP-43 LCD was experimentally found to form condensates by LLPS, which enhanced the formation of the aggregates.⁹ The coarse-grained model was established by a bottom-up training of atomic interaction information and a data-driven implementation of overpacking free energy penalty. Then, the accuracy and transferability of the model were validated by reproducing experimentally observed phase separation behaviours of TDP-43 LCD wild type (WT) and mutants. After that, the internal structures of the TDP-43 LCD condensates were investigated. We found that the dynamic condensates featured small-world-like network structures that enabled the emergence of oligomers with strong inter-molecular interactions inside the condensates, serving as the aggregation intermediates towards nucleation of amyloid fibrils. Oligomers emerged within the peptide network were flexible to adopt distinct conformations, including compact structures with collapsed peptides, and extended structures with flexible branches or linkers. Overall, our results revealed for the first time the small-world protein-interaction network of the TDP-43 LCD condensates and offered a direct observation of oligomer formation in the condensates.

The Coarse-Grained Model Reproduced Details of Atomic Interactions.

The coarse-grained model was constructed by bottom-up training of the atomic information and data-driven corroboration of high-resolution experiment data. We first built the coarse-grained DMD model by mapping each residue of TDP-43 LCD to its Cα atom (Figure 1A). Interaction potentials between the coarse-grained beads were determined by benchmarking with atomistic DMD simulations on the dimerization of TDP-43 LCD using iterative Boltzmann inversion method (Supporting Information). TDP-43 LCD is an intrinsically disordered protein featuring residual helical structures within residues 269–275, 320–344, and 350–370 (Figure S1), which agreed well with nuclear magnetic resonance results.^27,28 The helical structures have been experimentally shown to play an essential role in mediating the LLPS of TDP-43 LCD.^27,28 In the coarse-grained model, the helical structures were well reproduced by iteratively adjusting the intra-peptide-contact potentials between residues i and i + 2 (Figure 1B&S1). Equilibrated residue-wise contact frequencies obtained by the coarse-grained model were consistent with atomistic simulations (Figures S2&S3). High inter-peptide contact frequency patterns were observed between residues 275–285, 310–340, and 380–385, which have been shown to facilitate the phase separation of TDP-43 LCD experimentally.^27,28 Additionally, high-contact frequencies between the hydrophobic and aromatic residues as observed in experiments and atomic simulations²⁹ were evident in the inter-peptide contact frequency map (Figure S3), suggesting that the coarse-grained model could capture detailed interactions in atomistic simulations. Accuracy of the coarse-grained model was further evaluated by correlating contact frequencies obtained by the atomistic and coarse-grained simulations (Figures 1C&D). Pearson correlation coefficients r and slope of the linear regression k were 0.94 and 0.80 for inter-chain contact frequencies, and 0.99 and 0.94 for intra-chain contact frequencies, indicating that the contact frequencies of the coarse-grained model were quantitatively consistent with the atomistic simulations. Therefore, the developed coarse-grained model could reproduce atomic interactions with high accuracies.

Figure 1.

Construction of the coarse-grained model. (A) Amino acid sequence of the TDP-43 LCD (top panel) and the all-atom and coarse-grained structures of the TDP-43 LCD (bottom panel). (B) Contact frequencies between residues i and i + 2 obtained by the all-atom and coarse-grained DMD simulations. (C, D) Correlations of the residue-wise contact frequencies between the all-atom and coarse-grained simulations for (C) inter-peptide and (D) intra-peptide contact frequencies. (E) Free energy as a function of the number of neighborhood residues for a tryptophan (TRP) amino acid. (F) Phase diagrams of the TDP-43 LCD WT and A321G with respect to temperature and peptide concentration. Temperature is in the reduced unit of kcal/mol·k_B. (G) Typical conformation of the condensate and dilute phases in the slab model with a large dimension in z direction. Periodic boundary conditions are applied in the x, y, and z direction to model an infinite system.

During the formation of condensates that involves a large number of peptides, attractions between the coarse-grained beads could result in an unrealistic overpacking of coarse-grained beads. To address this issue, energy penalties for the overpacking of residues were introduced. Specifically, energy as a function of the proximity residue number for each of the twenty amino acids was obtained by calculating the distribution of packed residue numbers based on a large dataset of available high-resolution protein structures in the protein databank (e.g., Figure 1E for tryptophan). By fitting the free energy with a linear function, the packing valence n_v and the energy penalty coefficient dE (the slope of the fitting line) were determined (Table S1). By implementing an amino acid specific energy penalty E_overpack = dE ∙ (n − n_v) for coarse-grained beads with the number of contacting residues n larger than n_v, the coarse-grained model effectively avoided unrealistic overpacking and kinks around coarse-grained beads (details in Supporting Information, Figures S5&S6). Since overpacking occurs when multiple peptides are involved, it is unnecessary to include the overpacking penalty in the dimerization simulations.

With the benchmarked accuracy of reproducing detailed atomistic interactions and overpacking energy penalties, the established model was further utilized to investigate the phase separation of TDP-43 LCD. Mutants including A321G, W334G, G335D, and M337V that have been widely investigated by experiments,^10,27,28 were considered to validate the model and its transferability. The slab simulation method was employed to simulate the formation of co-existing low-density and high-density phases^30–32 (Figure 1G). Equilibrium all-atom DMD simulations of dimerization were first carried out for each mutant, and corresponding coarse-grained interaction potentials were obtained afterwards. The phase boundaries of the LLPS were obtained by measuring the peptide concentrations of dilute phase and condensed phase at various temperature for twenty independent simulations. The bottom-up coarse-grained models showed good correlations with the atomic simulations (Figures S7–S10), indicating that the coarse-grained models are robust and effective in describing various mutations. Moreover, the two-phase region below the coexistence curve became narrower for A321G, W334G and M337V compared to the WT while G335D broadened the two-phase region (Figure 1F&S11). The phase diagrams agreed well with the trends of the mutants to form droplets in vitro, showing mutations A321G, W334G, and M337V disrupted the phase separation, whereas G335D promoted it.^6,27,28,33 Furthermore, the peptide binding affinities of the WT and mutations obtained in the all-atom DMD dimerization simulations showed consistent trends with phase separations,²⁹ indicating that the mutants altered the LLPS propensities by changing intermolecular interactions. The consistency between phase diagrams obtained by the coarse-grained simulations and experimental results suggests that the developed coarse-grained model was an accurate tool for investigating the phase separation with high transferability.

Internal Structures of the TDP-43 LCD Condensates.

The dynamic behavior and molecular structure of the condensates were further investigated based on the coarse-grained model. The sizes of the equilibrated condensates, which were described by the number of peptides in the condensed phase, kept fluctuating rapidly (Figure 2A), suggesting that the sizes of the condensates evolved over time. To describe the dynamics of the condensate components, the peptides were classified by whether they were in a dilute or condensed phase. Peptides embedded in the condensates could dissociate into the dilute phase and peptides in the dilute phase could diffuse to reassociate into condensates (Figure S12). The frequent dissociation and reassociation of the peptides enabled an exchange of molecules between the condensates and their surroundings.

Figure 2.

Internal structures of condensates formed by TDP-43 LCD. (A) Number of peptides in condensates as a function of simulation time at T = 0.58 kcal/mol·k_B for WT TDP-43 LCD. (B) Evolution of peptides in contact with the randomly selected peptide. (C) Number of residue contacts between randomly selected peptide and the rest peptides. (D) Time-averaged contact probability of each peptide with randomly selected peptide. (E) Radial distribution function of coarse-grained beads in the condensates of TDP-43. (F) The radius of gyration distributions of peptides in the dilute and condensed phases differ significantly (Kruskal-Wallis test, p ~ 1e-12).

To investigate the condensate internal dynamics at the molecular scale, contacts between peptides in the condensates were monitored. We randomly chose a peptide (the 50^th peptide as an illustration) and calculated contacts between the selected peptide and the rest of the peptides. The contacting state between each peptide was transient and changed rapidly with time, as reflected by a random evolution of contact peptides in Figure 2B. The weak and transient interactions between TDP-43 peptides enabled a rapid rearrangement of the condensates and are crucial for the reversibility of functional TDP-43 species including nuclear bodies, stress granules, and myo-granules.²³ The time-averaged contact frequency of peptides showed that although each peptide in the condensates made contacts with a few peptides simultaneously, it could establish dynamic contacts with almost all remaining peptides via diffusion in the condensates (Figure 2D). This further confirmed that the condensates were fluid-like, consistent with the experimental data acquired with small-angle neutron scattering, fluorescence recovery after photobleaching, and coarse-grained molecular dynamics simulations.³⁴ Most of the contact frequencies were evenly distributed with some peptides exhibiting exceptionally high contact frequencies, suggesting that most of the inter-peptide interactions were weak and transient, while some inter-peptide interactions could be strong and maintained for a relatively long time. Meanwhile, obvious oscillations were also observed for the number of residue contacts between the peptides (Figure 2C), indicating contacts between the peptides in the condensates were highly dynamic at the single residue level. Taken together, the condensates were highly dynamic and fluid-like, whose components frequently exchanged with the dilute phase and the contacts within which were random and dynamic at both the peptide and residue levels.

Although it has been well established that TDP-43 LCD can undergo LLPS to form the high-density liquid phase, little is known about the structure of its condensates. Here, the internal structures of condensates formed by TDP-43 LCD were characterized by the radial distribution function g(r) of the residues (Figure 2E). There were three peaks in the short range (within the cutoff range of 7.5 Å) at 3.9 Å, 5.5 Å, and 6.5 Å, corresponding to covalent bonds, helical and β-sheet structures between second nearest residues. No significant peaks were observed in the long range (>7.5 Å). This apparently homogeneous structure of the condensates resulted from time and space averages of the heterogeneous yet dynamic network structures for the g(r) calculation. The local environment of the condensates was different from that of the solution, which in turn would alter the structure of the component peptides. Indeed, the radius of gyration (R_g) of peptides in the condensed phase was shifted from that for peptides in the dilute phase (Figure 2F). This is because peptides in the dilute phase were flexible for conformational changes, whereas peptides in the condensed phase were extended and constrained by surrounding peptide contacts. Taken together, structures of peptides in the condensates were extended due to inter-peptide interactions, which renders the amyloid nucleation and aggregation in the condensate distinct from those in the dilute solution.

Peptides within the Condensate Formed a Small-World Network.

The structure of the condensed phase was further analyzed by connectivity of each peptide, defined as the number of peptides that it made contacts with (i.e., the valence of peptides). As indicated by Figure 3A, more than 60% of peptides in the condensates formed contacts with 2 to 5 surrounding peptides. The low value of peptide connectivity suggests that the condensates were porous with sparse connections. Meanwhile, there were peptides with high connectivity engaging up to 20 peptides simultaneously. The peptide connections of the four mutants exhibited similar trends to the WT (Figure S13). Mutations inhibiting the phase separation, i.e., A321G, W334G and M337V, featured a higher probability to establish low peptide connections, whereas the LLPS-promoting mutation G335D tended to form higher peptide connections (Figure S13).

Figure 3.

Small-world network structure of the condensates formed by TDP-43 LCD at T = 0.56 kcal/mol·k_B. and the concentration of the condensed phase was and 0.01 nm⁻³. (A) Distribution of peptide connections. (B) Network graph of a typical condensate formed by TDP-43 LCD. (C) Cumulative probability, CP(n), defined as the fraction of a peptide having at least n connections. (D) Representative conformation of a peptide with a large valence. Right-top panel: overall conformation of a condensate. The peptides in the simulation box are shown in cyan with the neighboring peptides in gray to illustrate the periodic boundary conditions; Right-bottom panel: conformation of the condensate in the simulation box. Left-bottom panel: zoom-in conformation of the peptide possessing a large valence. The peptide of a large valence is shown in red, and the connected peptides are shown in green.

To detail structures of peptides with high connections, the internal connections between peptides in a condensate of TDP-43 LCD were visualized by network graphs (Figure 3B). Specifically, each peptide is represented by one node with the size and color proportional to the number of connections it possessed. The edges between the nodes represent connections between peptides, with the edge width reflecting the number of residue contacts between each interacting peptide pair. As indicated by the network graph of the condensates, the peptide that served as the joint or hub of a network involved a large portion of the condensate components. The presence of peptides with high connectivity suggests that it is possible to connect any two peptides in the condensates through just a few links, indicating the peptides in the condensates formed a small-word network. To further investigate the network structure, the cumulative probability distribution of peptide connectivity was calculated in a log-log plot (Figure 3C). The tail of the cumulative probability distribution can be well fitted by a power-law, shown as a linear function in the log-log plot. The existence of peptides with high connections and the tail of power-law distribution indicates a small-world network structure,³⁵ formed in the context of a growing network where new vertices (peptides) preferentially connect to the more connected vertices in the network.

The peptides of high connections formed a compact core embedded in the condensates, as shown by typical conformations of the condensates (Figure 3D). The peptides with large valences usually connected with neighboring peptides possessing low residue contacts, whereas the high residue contact states occurred between peptides with low valences, as elucidated by the edge widths in Figure 3B and Figure S14. The presence of a peptide with a large valence effectively enhanced the network stability. The rendered networks of the condensates of TDP-43 LCD were heterogeneous at both the peptide and residue levels, with low peptide connections and low residue contacts being the dominant states. High peptide connection and strong inter-peptide contact states were rare but vital for the stability and evolution of the condensates.

Oligomer Formation Within the Condensate of TDP-43 LCD.

Oligomers are low-molecular-weight aggregation intermediates before the nucleated conformational conversion into high-ordered fibril seeds, usually separated by a high free-energy barrier. Although lacking ordered cross-b fibril structures, oligomers are assumed to be formed by stronger inter-molecular interactions than droplets. The aberrant phase separated TDP-43 can facilitate the formation of amyloid fibrils, but the oligomerization processes inside the condensates, which are critical steps of fibrillization, remain unclear. Here, the number of residue contacts between peptides in condensates were calculated to characterize their intermolecular interaction strength. The semi-log plot of the residue contacts can be linearly fitted by two lines of divergent slopes, suggesting that peptides in the droplets exhibited different behaviors when the residue contacts were low and high. Thus, contacts between peptides can be divided into two distinct states, namely the low contact and high contact states (Figure 4A&S15). In the low contact state, the probability decreases relatively slowly with the increase of residue contacts, while it decreases rapidly in the high contact state. The probability profile was fitted by two lines with different slopes by minimizing the errors between the simulation results and fitted results. The crossover of the two fitting lines was found to be n_c=160, which was used to differentiate the low contact state and high contact state approximately. The existence of the two contact substates between peptides indicated heterogeneity of condensate structures at the residue level. Similar results were observed in our prior all-atom TDP-43 LCD dimerization simulations,²⁹ suggesting that LLPS can be reflected by peptide interactions in dimerization. Low residue contacts between peptides were prevalent and transient, contributing to the formation of dynamic network within the condensates. Dominance of the low contact state provided a molecular explanation for the liquid-like properties of the condensates such as their fusion and reversibility. In contrast, the high residue contact state entailed abundant interpeptide contacts required to overcome the loss of entropy during oligomerization.

Figure 4.

Formation of oligomers in the condensates of TDP-43 LCD. (A) Distribution of the number of residue contacts within the condensates. The coarse-grained simulation result (black line) was fitted by two lines with different slopes (red lines). (B) Time-variations of oligomers with residue contacts greater than the threshold n_c. (C) Distribution of oligomer size formed in the condensates. (D) Representative conformation of oligomers formed in the condensates. The oligomers with high residue contacts are highlighted in red with detailed structures illustrated. Structures of peptides with weak and transient contacts are also shown as a comparison. (E) R_g of dimers, trimers, and tetramers formed in the condensates (left panel). Typical conformations of the oligomers labeled with R_g values (right panel).

Peptides in the high contact state, i.e., residue contacts larger than n_c, were identified as the oligomers formed in the condensates. Peptides with weak and transient contacts were regarded as ‘monomers’ in the condensates. A typical time-evolution of oligomers in the condensates is shown in Figure 4B. Low molecule-weight oligomers up to pentamers with high residue contacts can be formed in the condensates. The frequent associations and dissociations reflect the dynamic and transient characteristics of oligomers formed in the condensates. Size distribution of the oligomers showed that oligomers formed by peptides in the high contact state were dominated by dimers and trimers with the propensities decreasing with the oligomer size (Figure 4C). The probability distribution of oligomers follows an exponential-decay with the increasing size of the oligomer, which may result from fluctuations in a density system. However, the high-contact interaction defining oligomers is not just the fluctuations of inter-peptide interactions stabilizing the droplets. In Figure 4A, the logarithm of probability for two peptides forming a given number of intermolecular residue contacts is proportional to the free energy of the pair, while the number of residue contact is approximately proportional to the enthalpy. The distinct exponents (i.e., the linear fitting slope in the semi-log plot) of the two states suggest different entropies of the two high- and low-contact states. The weaker slope for the low-contact state suggested a weaker entropic penalty upon contact, consistent with the dynamic, nonspecific interactions stabilizing the droplets. The higher slope for the high-contact state suggested a stronger entropic penalty upon forming the compact oligomers (Figure 4E). This observation is consistent with our previous work on the atomic simulations of the dimerization of TDP-43 LCD, where the low contact and high contact states were identified based on the distribution of the residue contacts²⁹. Hence, the emergence of oligomers by peptides of high contacts was not the trivial fluctuation of the intermolecular interactions stabilizing the droplets.

To illustrate formation of oligomers in the condensates, a typical condensate and detailed structures of the formed oligomers are shown in Figure 4D. The peptides in the oligomers intertwined with each other, forming a complex structure with obvious entanglements. These oligomers can serve as the loci for nucleated conformational conversions into fibril seeds with cross-b structures, and subsequent liquid-to-solid transition or fibrillization in the condensates.³⁶ In contrast, peptides in the low contact state are relatively flexible connecting with each other by a small portion of residues (Figure 4D). No entanglements were observed in the low contact state, enabling fast dissociation of the peptides and thus efficient rearrangement of the peptide network. The oligomers formed in the condensates were analyzed for their molecular structures. The R_g of the oligomers increased with size and spanned across a wide range from ~2.0 nm to nearly 5.0 nm (Figure 4E), suggesting that the oligomers emerged within the peptide network were flexible to adopt distinct conformations. Both compact oligomers with collapsed peptides and extended oligomers with flexible branches or linkers can be formed, indicating heterogeneity of the oligomer structures. The R_g distributions of dimers, trimers, and tetramers were asymmetric with long tails. Compact oligomers with a smaller R_g had a relatively higher propensity than the extended structures with a larger R_g. Furthermore, interaction strengths between the peptides forming the oligomers exhibited a significant diversity (Figure S16). Tetramers, for example, were formed by three peptide pairs with high contacts, while the rest three peptide pairs were connected weakly. The diverse interaction strengths simultaneously enabled the stability of oligomers by peptide pairs with strong contacts and efficient conformational changes by peptide pairs with weak contacts. By calculating the dwell time of the oligomers, oligomers with compact and entangled structures can survive for a relatively longer period than the extended oligomers with flexible and loosely connected conformations (Figure S17), suggesting the essential role of high contact states in the formation of oligomers in the condensates.

Based on the above discussion, a model considering LLPS and oligomer formation is proposed (Figure 5). The LLPS of TDP-43 peptides enabled formation of condensates with high peptide concentrations. Peptides in the condensates formed a porous small-world network structure dominated by sparse peptide connections. There were peptides with high peptide connections that functioned as joints or hubs of a network, linking a large portion of the condensate components within the network. Importantly, peptides in the condensates can be in distinct states depending on interpeptide residue contacts. Peptides in the low residue contact state facilitated dynamic and fluid-like properties of the condensates. In contrast, peptides in the high residue contact state were intertwined with sufficient intermolecular interactions to form relatively stable oligomers, which can further aggregate into fibrils through the liquid-to-solid transition. Thus, the heterogeneous internal structure of the condensates enabled formation of oligomers, offering new insights into the relationship between LLPS and amyloid aggregation of neurodegenerative disease-related proteins.

Figure 5.

Schematic plot of LLPS and oligomer formation within the condensates.

LLPS and Oligomers Formation in the Condensates.

Oligomers and condensates are interconnected with each other, with the rigorous relationship or distinction remains elusive to date. Experimentally, toxic oligomers have been observed to accumulate in prolonged incubation of tau condensates, suggesting the possibility of oligomer formation inside the condensates.³⁷ Physically, the condensates are micro-sized supermolecules with a porous network structure stabilized by weak and nonspecific interactions, as reflected by the fluid-like and highly dynamic features of the condensates. In contrast, oligomers usually refer to low-molecular-weight assemblies stabilized by extensive interpeptide interactions. Strong interpeptide interactions enable oligomers to be relatively long-lived and stable enough to be separated/isolated with various experimental methods, such as centrifugation and sodium dodecyl-sulfate polyacrylamide gel electrophoresis (SDS-PAGE).¹³ The secondary structure of peptides forming oligomers can be significantly changed by interpeptide interactions compared with monomers. Inspired by the characteristics, interpeptide interactions were utilized to identify oligomers formed inside the condensates with the cutoff values determined by probability distributions.

Based on our analysis, peptides in the condensates are heterogenous that can be divided into two states, namely the low and high residue contact states, with distinct contributions to the condensate structure and oligomer formation. Specifically, peptides with low residue contacts usually entailed strong connections with other peptides, serving as the joint of the network structure. In contrast, peptides with high residue contacts formed oligomers with intertwined conformations that can survive for relatively long periods. As peptides forming oligomers had a low connection with other peptides in the condensates, they were less constricted by the network structure and can easily diffuse inside the condensates or exchange with the dilute phase. Oligomers released to the dilute solution can interact with cell membranes, initiating a series of downstream events leading to neuronal or tissue death. Thus, heterogeneity of the condensates enabled oligomer formation and pointed to a possible link between LLPS and neurodegenerative diseases.

The phase separation behaviors and condensate properties of TDP-43 have significant physiological and pathological implications. The dynamic properties of the TDP-43 condensates, encoded by weak and transient interpeptide interactions, enabled reversibility of the droplets under environmental stimuli such as stresses, playing a protective role in cellular response to various stimuli. Loss of the dynamic properties, as in the case of mutation G335D with enhanced helix-to-helix contacts, led to downstream solidification of the condensates, a pathological hallmark of neurodegenerative diseases. Weak interactions between peptides in the condensates and the porous internal structures benefited recruitment, binding, and processing of RNA. The different LLPS propensities of TDP-43 mutations could alter the condensate structures, resulting in the binding with different and specific RNA regions across the transcriptome, thus affecting its RNA processing function.¹ On the other hand, the extended conformation of peptides in the condensates facilitated the liquid-to-solid transition (Figure 2F). Similarly, tau proteins in the condensates were found to be extended to promote formation of irreversible aggregates, as revealed by single-molecule Förster resonance energy transfer experiments.³⁸ Importantly, existence of peptides with high intermolecular contacts was also indicated in the condensates of stress granules, where a stable and dense core was found by super-resolution microscopy and identified to be stabilized by strong protein-protein interactions.³⁹ Together, the dynamics and structure of the TDP-43 condensates may provide rich molecular insights into the functional and pathological roles of TDP-43.

In summary, we have developed a new data-driven bottom-up coarse-grained DMD model to investigate oligomer formation within the condensates of TDP-43 LCD. Through bottom-up training of atomistic interaction information and data-driven implementation of a large set of high-resolution experimental data, the new model accurately reproduced interaction details and effectively avoided artificial overpacking. The structural properties of the condensates and oligomer formation inside the condensates were revealed with the new coarse-grained model. The condensates of TDP-43 LCD were found to be a dynamic and fluid-like molecular assembly with internal peptides associating and dissociating with surrounding peptides. The condensates provide a distinct environment for amyloid nucleation as peptides in the condensates were more extended than these in the dilute phase due to their interactions with other peptides. Moreover, the condensates formed a small-world dynamic network. The network was dominated by nodes with low connectivity or valences and edges with weak inter-peptide contacts. On the other hand, there were also nodes with high connectivity or peptides in contact with many other peptides, as well as inter-peptide interactions with a large number of contacts. Importantly, peptides in the high residue contact state were intertwined and relatively stable to form oligomers, which are dynamic and populated in the early aggregation stage. Oligomers formed in the condensates adopted diverse conformations, including the compact structures with collapsed peptides as well as extended structures with flexible linkers and branches. The oligomers were likely fibrillization intermediates, corresponding to the loci for nucleated conformational conversion into fibril seeds with high-order and in-register aligned b-sheet structures. Taken together, our coarse-grained DMD simulations offered crucial new insights into the molecular structures of the condensates and oligomer formation inside the condensates formed by TDP-43 LCD, facilitating elucidation of the pathophysiological origins of neurological disorders such as ALS and FTLD. Due to its general nature and transferability, the coarse-grained model developed in the current study can be extended to studies of a wide range of biomolecules, providing a versatile tool for elucidating phase separations that are universal in biological systems.

Materials and Methods

Details of discrete molecular dynamics (DMD), atomistic DMD simulations, construction of the coarse-grained model using iterative Boltzmann inversion method, overpacking penalty of coarse-grained beads, slab simulation setups using the coarse-grained DMD model can be found in the Supporting Information.

Supplementary Material

The Supporting Information is available free of charge online.

Data Availability Statement

The computer simulation set up and data are available via link: https://zenodo.org/records/11189714.