Multiscale simulations of folded and intrinsically disordered region-containing protein condensates

Abstract

We present a multiscale simulation framework that integrates all-atom (AA) structure modeling, coarse-grained (CG) Martini 3 simulations, and AA backmapping to investigate supramolecular assembly behaviors of proteins implicated in misfolding diseases. As representative systems, we modeled the C-terminal domain of human TDP-43 (residues 274–414) and a broad region of white-tailed deer prion protein (PrP) (residues 24–233), both associated with misfolding-related pathologies and exhibiting distinct structural features. This AA-CG-AA framework enables the construction and analysis of large multiunit assemblies using two Martini 3–based CG parameter sets that differ in their treatment of nonbonded interactions, including electrostatic cutoffs and the scaling of interactions involving Na⁺ and Cl⁻ ions present in solution. The framework successfully captured key mesoscale features of early supramolecular condensation and revealed pronounced condition-dependent differences in both condensate morphology and chain dynamics. Parameter sets with longer cutoffs and rescaled ion interactions promoted more interconnected, network-like assemblies—particularly for PrP—whereas standard cutoffs yielded more dispersed systems with higher translational mobility. Mean-square displacement analysis and diffusivity estimates reflected clear differences in translational mobility consistent with varying degrees of local association. Further analysis of low-mean-square-displacement chains revealed the emergence of condensate-like subpopulations, especially in PrP, where percolation-like networks formed. Solvent-accessible surface area analyses confirmed that protein chains remained solvent exposed throughout, consistent with known fluid-like phase-condensation behavior. Follow-up AA analysis revealed persistent interchain dynamical coupling even in the absence of direct chain contacts, suggesting solvent-mediated interactions. Notably, analyses revealed an inverse relationship between protein translational mobility and Na⁺ and Cl⁻ ion contact counts, suggesting that ion association contributes to early-stage condensation. These findings demonstrate the potential of integrated CG-AA simulation strategies to probe supramolecular condensation in structurally heterogeneous protein systems and support their continued development for studying misfolding-driven assembly processes at mesoscopic scales.

Significance

Understanding factors that contribute to protein phase condensation is critical for uncovering the molecular basis of neurodegenerative diseases linked to protein misfolding. This study introduces a multiscale simulation framework combining all-atom and coarse-grained modeling to capture assembly behavior in large protein systems. Beyond identifying force-field-dependent differences in dynamics and network formation, the approach revealed solvent-mediated dynamical coupling between protein chains—even without direct contacts—highlighting a potential indirect mechanism of early confinement. These findings offer valuable insight into how coarse-grained interaction parameters and protein-specific structural features influence condensation behavior in disease-related proteins and underscore the value of multiscale strategies that integrate coarse-grained modeling with all-atom resolution to probe misfolding-associated assembly processes in complex biological systems.

Introduction

Proteins are linear polymer chains composed of amino acids connected by peptide bonds. The sequence of amino acids determines the chain folding into a hierarchical three-dimensional structure spanning from primary to quaternary levels. A protein’s hierarchical structure enables key processes such as folding, protein-protein interactions, and self-assembly of supramolecular entities, all of which play a crucial role in regulating a protein’s biological function (1). Thereby the information encoded in the amino acid sequence dictates the sequence-structure-function relationship. Another key characteristic of proteins is their ability to adopt diverse three-dimensional structures (conformations) depending on their physico-chemical environment, such as interactions occurring during ligand binding (2). Notably, proteins often contain intrinsically disordered regions (IDRs), which do not form stable secondary or tertiary structures, exhibiting instead high flexibility and adaptability. Some proteins are entirely intrinsically disordered (IDPs). Despite their lack of a fixed structure, IDPs and IDRs can perform specific biological functions, demonstrating that folded structure is not always a prerequisite for functionality (3,4,5). Unlike folded proteins, IDPs and IDRs exhibit high conformational heterogeneity and transient interactions often described as “fuzzy” (5,6). Importantly, IDPs and proteins with IDRs tend to undergo liquid-liquid phase-separation (LLPS) forming droplets of phase condensates, or coacervates—micron-size and smaller fluidic aggregates surrounded by a more diluted phase (7,8). LLPS driven by IDPs or IDRs have recently been recognized as a critical process enabling cellular organization (5,7,8,9,10).

Under conditions that are not yet fully understood, some proteins can fail to fold correctly or lose their proper conformation. These misfolded proteins often form toxic aggregates, contributing to neurodegenerative diseases such as Alzheimer disease, Parkinson disease, amyotrophic lateral sclerosis, frontotemporal dementia, transmissible spongiform encephalopathies, and several others (11). These conditions remain largely incurable, partly due to an incomplete understanding of their molecular drivers. Although β-sheet-rich amyloid fibrils have been widely studied as hallmarks of misfolding disorders (11,12), growing evidence suggests that smaller, less structured oligomers formed early in the misfolding process are key pathogenic entities (13,14). These prefibrillar or nonfibrillar assemblies are difficult to characterize due to their transient nature, heterogeneity, and low abundance relative to the native and fibrillar states (14,15). Emerging evidence also indicates that disruptions in LLPS may drive pathogenic transformations (10,16,17,18), particularly for proteins with IDRs (8,17,19,20). These insights emphasize the need to investigate a broad spectrum of protein assemblies—including amyloid fibrils, oligomeric aggregates, and liquid phase condensates—to unravel the molecular mechanisms of protein misfolding and aggregation.

All-atom (AA) molecular dynamics (MD) simulations, which employ classical force fields (FFs) to describe interactions between individual atoms, have been instrumental in studying the conformations of disease-implicated proteins (21,22). However, AA frameworks face limitations in simulating misfolding, aggregation, and fibrillization, especially for proteins predisposed to phase condensation. These processes often involve large heterogeneous systems with dynamic behaviors that exceed the timescales of conventional AA simulation methods, requiring a careful balance between detailed atomic-level resolution, computational efficiency, and biological accuracy. Alternatively, coarse-grained (CG) MD models (23,24) have gained popularity. These models represent groups of atoms as simplified units (beads), reducing computational demands (Fig. 1). A variety of CG techniques have been developed and tested recently (25,26,27). The greatest computational efficiency is obtained with describing entire residues, or even several residues, as single beads (28,29,30,31). However, such models do not distinguish between backbone and side-chain interactions (26,31). Although impressive progress has been made in parameterizing one-bead-per-residue models (25,27,30,31), predicting specific conformations arising from protein aggregation requires higher-resolution approaches (22,32). CG frameworks that represent each residue with multiple beads offer a more detailed description of both side-chain and backbone dynamics, with some FFs also being compatible with explicit solvent models (24,26). Currently, popular choices for biomolecular CG simulations with multiple beads per residue include Martini 3 (33,34,35), AWSEM-MD (Associative Memory, Water Mediated, Structure and Energy Model) (36), UNRES-MD (United-Residue) FF (37), SIRAH (the South American Initiative for a Rapid and Accurate Hamiltonian) (38,39,40), OPEP (Optimized Potential for Efficient Protein Structure Prediction) (41), SPICA (Surface Property Fitting Coarse Grained) (42,43,44,45), and PLUM (46,47) FFs (Table 1).

Figure 1.

Representation of bead systems in different force fields and their computational capability versus molecular resolution and interaction complexity.

Table 1.

Coarse-grained modeling software for studying protein aggregation and misfolding

Force field	Released	Used with MD package (compatible)	Specializes on	Advantages
Martini 1-3	2004–2021	GROMACS, NAMD, LAMMPS, Materials Studio, and others	Large systems containing lipids, membranes, proteins, nucleic acids, carbohydrates, small molecules, solvents; currently, a general-purpose FF	Versatile, extensive validation, rich library of force fields and tools
AWSEM-MD	2008	LAMMPS	Protein pathways to adopt native or misfolded conformations	Tailored for simulating folding pathways and amyloid-like aggregation
UNRES	1997	UNRES-MD, GROMACS	Protein folding, large conformational transitions, and free-energy landscape exploration	Energy-based protein structure prediction on large scale; implicit solvent; applicable to medium-size protein folding from sequence alone
SIRAH	2015	AMBER, GROMACS	Proteins, nucleic acids, simple liquid systems; fibril aggregation	Suitable for fibril aggregation, protein conformational changes
PLUM	2009	LAMMPS	Protein folding and aggregation; includes models for heterogeneous interactions	Adapted for modeling IDPs and IDRs
OPEP	1999	Own simulation code	Protein aggregation and fibrillization	Parameters optimized for amyloid fibrils
SPICA	2019	GROMACS, LAMMPS	Biomembranes, carbohydrates, lipids, protein-membrane interactions, small molecules, phase behaviors	Superior treatment of water interactions

The first version of the Martini FF was published in 2004, initially designed for simulating lipids and membranes (48). It employed four bead types based on polarity and charge state, used harmonic bonded potentials parameterized to match predictions from AA simulations, and represented nonbonded interactions with Lennard-Jones potentials, alongside an explicit solvent model. Subsequent developments introduced more diverse bead types, refined bonded parameters, and extended applications to (membrane) proteins (49) and other organic materials. Since then, Martini has become widely used for biomolecular simulations and has undergone extensive improvements (34). The latest version, Martini 3.0, released in 2021 (33), includes over 800 bead types and supports mapping up to six beads per protein residue, with a plethora of tools for model building and validation. These advancements have positioned Martini 3 as a versatile FF applicable to lipids, proteins, saccharides, nucleotides, and other materials, as well as accounting for the physicochemical environment, including pH, solution ionic strength, and lipid membrane effects. For proteins, improvements addressed limitations of secondary structure stability and enhanced the accuracy of nonbonded solvent interactions.

Despite these advances, Martini’s reliance on an elastic network (EN) model biased toward specific conformations to maintain secondary structure (50) challenges its ability to capture transitions between native and misfolded protein states. Efforts to address this are ongoing. For example, recent work (51) explicitly encoded aggregated protein states via a contact map using the Gō model, enabling the observation of oligomeric self-assembly. A different CG model, AWSEM-MD (36), uses Gō-like models to drive protein folding into native conformations, and pathways of misfolding and aggregation can also be modeled in a similar way. An extension incorporating Gō-like modeling is underway to overcome the EN-related limitations in a newer CG FF, SPICA (24). However, such approaches rely on prior knowledge of misfolded states, which is generally unavailable. This limits the ability of these models to capture the heterogeneous nature of misfolded states and early oligomeric intermediates.

Alternatively, the PLUM FF (46) has been parameterized to reproduce the probability distribution of local backbone dihedral angles, enabling proteins to explore a wide range of conformations without requiring additional structural input. This makes it well suited for studying misfolding and aggregation pathways. However, its effectiveness may vary across different proteins, aggregation scenarios, and solvent conditions, as the transferability of PLUM parameters can be limited. An interesting alternative is offered by the SIRAH FF (40), which is fitted to reproduce structural information and nonbonded interactions via bottom-up multiscale parameterization based on inputs from available AA structures and quantum-level calculations. This eliminates the need for Gō-like potentials or the enforcement of secondary structure through EN constraints. Although the bottom-up parameterization allows unbiased treatment of protein backbone conformations, it relies heavily on higher-resolution input data. This dependence reduces the FF’s flexibility for systems where the higher-resolution structure is not explicitly parameterized or unknown.

Compared with globular proteins forming well-defined native conformations, in silico modeling of IDPs and IDRs is fundamentally more demanding. In their native state under physiological conditions, IDRs can adopt multiple interconvertible conformations, all of which are highly hydrated due to their extended nature (52). This makes predictions of IDR dynamics highly sensitive to the accuracy of solvent interactions—a challenging task, even for AA MD simulations, some of which predict overly compact IDP conformations (20,53,54). Although efforts to allow spatially expanded IDP conformations may seem counterintuitive given the goal of predicting β-sheet-rich misfolded structures, significant progress is being made to improve both AA and CG FFs to better represent IDP behavior (22,23,24,25). In the realm of CG simulations, general purpose FFs compatible with explicit solvent models, such as Martini and SIRAH, have gained particular attention. Although the Martini FF was not originally calibrated to represent IDPs (34), rescaling nonbonded protein-water and protein-protein Lennard-Jones interaction parameters has produced expanded conformations for IDPs (55,56). However, simulating proteins that contain both intrinsically disordered and folded domains within a single CG framework remains a challenge. Small inaccuracies in FFs, initially designed to stabilize protein native states, may be negligible for folded domains but can lead to flawed conformations in IDPs. Notably, a modified SIRAH FF has recently demonstrated consistent predictions for both folded and intrinsically disordered domains in several peptides (57), whereas the Martini 3 FF has been successfully rescaled to represent larger multidomain proteins by adjusting nonbonded protein-protein interaction parameters (58). Calibrations of CG FFs are undergoing further developments.

The ability to adjust interaction parameters or modify simulation protocols to accurately reproduce average properties, such as protein gyration radii or LLPS phase diagrams, makes CG FFs highly valuable for simulating phase-condensation (20,25). However, simplification or omission of key atomic-level interactions, such as hydrogen bonding, salt bridges, or π-π stacking, limits the ability of CG FFs to directly predict changes in protein secondary structure or its formation within the condensed phase. One approach to address this limitation is to use CG simulations to generate a phase condensate and then perform AA simulations starting from CG outputs (20,59). Although backmapping atomic coordinates from CG data to an AA model employing well-established methods for protein structure reconstruction (23) is relatively straightforward, achieving consistent secondary structures often requires extensive production AA simulations (59,60,61). Such multiscale simulations highlight the need for special strategies to benefit from the efficiency of coarse-graining without compromising the accuracy of secondary structure predictions.

In this work, we report a multiscale integration of AA and CG simulations, referred to as the AA-CG-AA framework, to model supramolecular assembly phenomena of the TAR DNA-binding protein 43 (TDP-43) and prion protein (PrP). Each of these proteins plays a key role in misfolding-related diseases (62,63). TDP-43, an RNA-binding protein with extensive IDRs, undergoes LLPS under physiological conditions, but its aberrant aggregation is linked to amyotrophic lateral sclerosis and frontotemporal dementia (17,62). PrP is an extracellular protein containing both an IDR and a folded domain. It is normally membrane anchored unless it misfolds into infectious prions, a process central to transmissible spongiform encephalopathies in both animals and humans (63,64,65). The relevance of LLPS to PrP misfolding has been recently demonstrated (66). Accurate and efficient computational modeling methods to predict protein condensation and supramolecular confinement phenomena are critical for a better understanding of disease progression and development of targeted, structure-based therapies. We specifically focus on modeling key regions of these proteins relevant to phase separation and misfolding: the C-terminal domain (CTD) of human TDP-43 (residues 274–414, Fig. 2 A), implicated in LLPS and aggregation, and an extensive region of white-tailed deer (WTD) PrP (residues 24–233, Fig. 2 B), containing both a phase-condensation-implicated N-terminal IDR and a folded CTD central to prion conversion. Studying these structurally diverse proteins allows us to examine how simulation models capture supramolecular confinement phenomena across systems with distinct structural properties.

Figure 2.

Monomeric model structures: (A) human TDP-43 CTD (274–414) and (B) WTD PrP (24–233). The colors represent secondary structure: α-helices are shown in purple, β-strands in yellow, and random coils in gray.

Materials and methods

Monomeric structure preparation

The two systems used in this study, the human TDP-43 CTD (274–414) and the WTD PrP region (24–233), were built using the artificial-intelligence-based structure predictor AlphaFold (67). The AlphaFold tool has been trained on publicly available experimental protein structures from the Protein Data Bank for TDP-43 (entry AF-Q13148-F1-v4 based on 44 PDB structures, including 5MDI (68), 4IUF, and 6T4B) and mule deer PrP (same consensus sequence as WTD PrP, entry AF-P47852-F1-v4, based on PDB: 6FNV and 4YXH (69)). The CTD domain was concatenated from the full-length TDP-43 structure, and both the N-terminal modulatory domain (residues 1–23) and the C-terminal membrane anchor (residues 234–251) were removed from the PrP structure using Discovery Studio Visualizer v.19.1.0.1828 (70). The PROPKA (H++) server (71) was used to obtain acid dissociation constant (pKa) values to determine the protonation state of titratable residues at neutral pH of around 7.0. This resulted in all lysine and arginine residues being positively charged, glutamate and aspartate residues negatively charged, and histidine residues neutral.

Initial all-atom simulations

To obtain representative conformations of our monomeric structures, the TDP-43 CTD and WTD PrP systems were first minimized in vacuum using 10,000 steps of the steepest descent algorithm. The structures were then solvated in an AMBER 99SB-disp water box, and Na⁺ and Cl⁻ counterions were added to neutralize the systems. Solvent minimization was performed with 500 steps of the steepest descent algorithm, applying strong positional restraints on all heavy protein atoms to prevent structural distortions caused by nonequilibrated solvent. Next, each solvated system underwent seven short minimization steps using the steepest descent method, with progressively decreasing position restraints on nonhydrogen protein atoms (restraint force constants: K_posre = 1 × 10⁵, 1 × 10⁴, 1000, 100, 10, and 0 kJ mol⁻¹ nm⁻²), followed by system heating. The temperature of proteins and solvent was maintained at desired level (310 K in most cases) using Berendsen thermostat coupling (72). Subsequently, seven NVT-like MD equilibration steps were performed with the same stepwise reduction of positional restraints on nonhydrogen protein atoms, with the final step performed without restraints and with stronger bath coupling. The final equilibration step and production simulations were conducted at the temperature and pressure of 310 K and 1 atm, with isotropic pressure coupling (NPT ensemble). Bond lengths were constrained using the LINCS algorithm with a fourth-order expansion. Short-range electrostatic and van der Waals (VDW) interactions were computed with a 14-Å cutoff. Long-range electrostatic interactions were treated using particle-mesh Ewald summation with a 0.315-nm grid spacing for the fast Fourier transform and cubic interpolation. Each system underwent 50 ns of AA MD simulations with a 2-fs timestep using the GROMACS-2019.6 package (73).

Construction of 50-chain protein systems

Multiunit 50-chain solutions were constructed using GROMACS’ insert-molecules script, with molecules initially placed in random orientations by default. The starting concentrations varied depending on the structural properties of each protein. For the mostly disordered CTD of TDP-43, the initial concentration was 15.0 mg/mL, and for WTD PrP, which contains both extensive folded and IDRs, it was approximately 22.0 mg/mL. The chosen densities, slightly below those experimentally observed in phase condensates produced by LLPS (20), were intended to promote condensation phenomena within a reasonable computational timescale while ensuring that the monomers did not initially interact, with a minimum distance of at least 5 Å between the closest atoms of different chains. Additionally, since the employed scripts do not preserve amino acid numbering or allow for the separation of different chains, we used custom Bash scripts to modify the PDB files accordingly. In AA representation, 50-chain CTD TDP-43 systems included 89,950 protein atoms, and WTD PrP systems included 155,150 protein atoms.

Coarse-grained simulations in solution

For CG simulations, we used GROMACS 2019.6 software (73) with the Martini 3.0.b.3.2 (33,74) CG FF. First, the two multiunit 50-unit AA-resolution systems were converted into the CG representation using the Python-based martinize2 script (75). Mild harmonic restraints, also known as rubber bonds, were applied to the secondary structure by using the EN (50). The network was defined using lower and upper harmonic (Hookean spring) bond cutoffs at 0.3 nm and 0.8 nm, respectively, and bond strengths were maintained independent of bond length. These follow a harmonic potential with a force constant of 500 kJ mol⁻¹ nm⁻² and equilibrium distances set to the distances in the input atomistic structure. The value of 500 kJ mol⁻¹ nm⁻² was chosen based on literature recommendations (50). This maintains the overall protein fold while allowing local flexibility. The systems underwent 10,000 steps of steepest descent minimization in vacuo, using the Verlet cutoff scheme and reaction-field (RF) treatment for electrostatics. Then the systems were solvated using the Martini 3 CG explicit water model (with a 0.21 nm radius, accounting for CG waters represent four molecules) and either 100 mM or150 mM of NaCl, with counterions added for charge neutralization. To mitigate the tendency of IDRs to adopt overly compact conformations, we adjusted the Martini 3.0.b.3.2 nonbonded Lennard-Jones FF parameters following recent best practices (56,58,76). Two modified FFs were employed. In the first, FF1, protein-water interactions were scaled by 1.03, and nonbonded protein-protein interactions were scaled by 0.92, replacing the standard scaling factors of 1 in the original Martini 3.0.b.3.2 FF (56,58). The second, FF2, included these adjustments along with an additional scaling of Na⁺ and Cl^– ion interactions with all components by 1.029, instead of the standard factor of 1. The resulting systems were minimized with 100,000 steps of steepest descent algorithm using the same parameters as for in vacuo minimization, with flexible bonds and position restraints that were gradually released. This process included an initial 10-fs equilibration with restraints, during which the Berendsen thermostat was used to relax the system volume, followed by a 20-fs equilibration phase with fully released restraints, employing Berendsen pressure coupling and V-rescale temperature coupling (77). The VDW cutoff radius (rvdw) and electrostatic cutoff were set to 1.0 nm in FF1 simulations and 4.0 nm in FF2 simulations, with the temperature maintained at 310 K.

For production runs, we applied an isotropic Parrinello-Rahman barostat with a relaxation time constant for pressure coupling (τ-p) of 12 ps, along with a V-rescale thermostat. The Verlet cutoff scheme was used, and electrostatics were treated with the RF method, applying a 1.0-nm cutoff in FF1 simulations and a 4.0-nm cutoff in FF2 simulations. The relative permittivity (ε_r) was set to 15, with a RF permittivity (ε_rf) of 0. The pressure was maintained at 1 atm and the temperature at 310 K. Simulations were run with a 0.02-ps timestep, with trajectory lengths ranging up to at least 1000 ns. For both WTD PrP and TDP-43, three independent replicas using different velocity seeds were generated for each 1000-ns simulation, including FF1 with 100 and 150 mM NaCl and FF2 with 150 mM NaCl. Additionally, the FF1/100 mM NaCl systems were extended to 10,000 ns by continuing from replica 1 of the corresponding 1000-ns simulations. A summary of all systems, conditions, and durations is provided in Table S1 in the supporting material.

All-atom reconstruction and secondary structure recovery

Converting predicted CG structures back to AA resolution is required for capturing atomic-level interactions and refining secondary structures. To convert the entire 50-unit CG systems into AA representation, we used the backward-v5 script (78) available in Martini 3 (74). The generic algorithm (78) performs reverse mapping from CG to AA format for selected components, including proteins and ions present in solution. To relax the atomistic structure, the AA geometry undergoes two cycles of 500-step energy minimization, the first excluding nonbonded interactions between certain groups of molecules to prevent steric clash-induced instabilities, and the second with all interactions included. This is followed by four 500-step cycles of restrained NVT equilibration at 300 K with progressively increasing time steps of 0.2 fs, 0.5 fs, 1.0 fs, and 2.0 fs using a selected AA FF. In this work, we extensively modified the procedure. Instead of the original Charmm36 AA FF, we used AMBER99SB-disp (79), with each system solvated in AMBER99SB-disp water model. To improve the convergence of large systems, the number of minimization steps was increased to 1000, and the energy step size was reduced from 0.1 to 0.05 kJ/mol/ps. Since protein monomers in solution frequently crossed periodic boundaries during long minimization runs, periodicity corrections were applied between each of these steps. For further characterization, short approximately 2-ns AA simulations were performed on the converted AA systems.

Structural and dynamical characterization

To visualize both CG- and AA-scale predicted systems, we used UCSF Chimera molecular visualization software (80), with secondary structure information extracted through VMD (81) via our custom Python script. Solvent-accessible surface area (SASA), the radius of gyration (Rgyr), and secondary structure content for individual protein chains were calculated using built-in VMD scripts (e.g., measure sasa, measure rgyr, and the secondary structure timeline tool). SASA represents the surface area of a biomolecule that is accessible to a solvent, providing insights into protein folding and exposure of residues. Mean-square displacements (MSDs) of each chain as a function of simulation time were computed using the GROMACS msd tool. MD trajectories were unwrapped before MSD calculations. Residue contact (smallest distance) maps were also calculated in GROMACS.

To characterize dynamical behaviors, we applied our group’s original essential collective dynamics (ECD) method (82,83,84,85,86). The method quantifies dynamical coupling (correlations) between atoms or residues from AA MD trajectory data. It relies on a statistical-mechanical framework (82,85) in which the dynamics is described by generalized Langevin equations, with essential collective coordinates identified as principal eigenvectors of the covariance matrix obtained from principal component analysis of MD trajectories. In the ECD method, an AA projected image of the protein is constructed in a multidimensional space of the essential collective coordinates, with each atom represented as a point (atom-image). ECD theory demonstrates (82,85) that this projected image reflects the degree of dynamical correlation between atoms. Two atom-images located close to each other indicate strongly correlated motion of the corresponding atoms, regardless of their proximity in the protein’s tertiary structure, whereas distant atom-images correspond to relatively independent motion. This concept of projected atom-images enables calculation of several simple descriptors for dynamical coupling in a protein or supramolecular complex, without requiring exhaustive conformational sampling or equilibrium assumptions to achieve accurate predictions (82,83,84,85,86,87,88). The method has been rigorously validated against NMR data, which represent longer timescales than typically used in AA MD sampling (21,82,83,84,85), and it has been applied extensively to characterize the dynamical stability of supramolecular protein assemblies (84,86,87,88) and individual protein molecules (83,84,89). The specific equations used in these analyses, as well as further methodological details, have been reported elsewhere (82,83,84,85,86). To investigate local dynamical behavior within the predicted assemblies, trajectories of two to three protein chains, along with nearby Na⁺ and Cl⁻ ions, were extracted from short (∼2 ns) AA simulations of the full 50-unit systems, which were generated by atomistic backmapping from CG simulations. ECD pair correlation maps (84,85,86) were calculated for multiple 200-ps segments using 20 principal eigenvectors, and the pair correlation descriptors were averaged over the 2-ns AA trajectories.

Results and discussion

Structural features of multiunit TDP-43 and WTD PrP systems

Our multiscale simulation workflow—referred to here as the AA-CG-AA framework—is designed to combine AA modeling of initial structures, CG Martini 3 simulations of large-scale multimeric systems, and atomistic backmapping of predicted supramolecular assemblies, followed by more detailed AA simulations, into a single integrated pipeline. A schematic overview of the framework is shown in Fig. 3.

Figure 3.

Schematic representation of the AA-CG-AA workflow for constructing large 50-unit all-atom-resolution systems, converting them to coarse-grained form, performing CG simulations, backmapping to all-atom representation, and conducting all-atom equilibrations and production simulations followed by structural and dynamical analyses.

As contrasting test cases, we selected two proteins implicated in misfolding diseases, the mostly disordered TDP-43 CTD (274–414) and WTD PrP (24–233), which includes both folded and intrinsically disordered regions. The workflow begins with building and equilibrating monomeric AA-resolution TDP-43 CTD (274–414) and WTD PrP (24–233) structures, as described in materials and methods. Examples of representative AA structures are shown in Fig. 2. These initial models were randomly positioned to construct corresponding 50-unit multimeric systems with a minimal interchain distance of at least 5 Å. The resulting AA-resolution large-scale systems are shown in Fig. 4 A and B, and their CG counterparts are presented in Fig. 4 C and D. After the AA-CG conversion, the multimeric 50-unit CG systems were first minimized in vacuo and then solvated using the Martini 3 explicit water model with the addition of counterions to neutralize the systems and supplemented with NaCl additions. After solvation, the systems were equilibrated and then subjected to CG simulations in explicit solvent using two modified Martini 3 FFs, FF1 and FF2, as listed in Table S1 and outlined in Fig. 3. To ensure reproducibility and assess variability, three independent replicas were generated for each 1000-ns simulation using different velocity seeds (see Table S1). Unless otherwise noted, the illustrations correspond to replica 1 for each system and condition.

Figure 4.

Initial model systems consisting of 50 randomly positioned TDP-43 CTD (A and C) and WTD PrP (B and D) in all-atom representation (A and B) and Martini 3 coarse-grained representation (C and D). In (A and B), the color scheme follows Fig. 2. In (C and D), pink and yellow indicate backbone and side-chain beads, respectively.

Fig. 5 A–F shows representative snapshots of the 50-unit systems after 1000-ns Martini 3 CG simulations. Panels 5A, 5C, and 5E correspond to TDP-43 CTD at 100 mM NaCl (FF1), 150 mM NaCl (FF1), and 150 mM NaCl (FF2), respectively, whereas panels 5B, 5D, and 5F show the corresponding WTD PrP systems under the same FF and salt conditions. Visual inspection of the chain configurations suggests that simulations using FF2 with 150 mM NaCl (Fig. 5 E and F) result in more pronounced condensation of the chains compared with the corresponding FF1 simulations shown in Fig. 5 A–D, for both TDP-43 CTD and WTD PrP systems under all salt conditions. This observation is consistent with the longer nonbonded cutoff radii used in FF2, which may facilitate chain association and promote the formation of condensate networks. To assess whether similar behavior would eventually emerge under FF1 conditions, we extended the 100 mM NaCl FF1 simulations to 10,000 ns. The resulting configurations are shown in Fig. 6 A and B. The extended simulations suggest differing tendencies between the two systems: the TDP-43 CTD assembly shown in Fig. 6 A remained relatively sparse even after 10,000 ns, whereas the WTD PrP system in Fig. 6 B exhibited a more pronounced degree of condensation, with a denser and more interconnected network apparent. Following CG simulations, the resulting protein structures, as well as Na⁺ and Cl^– ions present in solution, were converted to AA representation, minimized, re-solvated with explicit water, and equilibrated. Examples of postconversion AA-resolution 50-unit structures are shown in Figs. S1 and S2 in the supporting material.

Figure 5.

Coarse-grained representation of 50-unit TDP-43 CTD (A, C, and E) and WTD PrP (B, D, and F) systems after 1000-ns Martini 3 CG simulations using FF1 (A–D) and FF2 (E and F) in explicit water with 100 mM NaCl (A and B) and 150 mM NaCl (C–F).

Figure 6.

Coarse-grained representation of 50-unit TDP-43 CTD (A) and WTD PrP (B) systems after 10,000-ns Martini 3 simulations using FF1 in explicit water with 100 mM NaCl.

To characterize the observed condensation states, we first calculated SASAs for the described systems. This metric provides a general measure of chain exposure to the surrounding solvent and serves as a proxy for the degree of molecular compaction and intermolecular association. Fig. S3 displays average SASAs per chain calculated at different simulation stages, including the initially constructed AA systems, after conversion to CG representation, after production CG simulations of 1000 ns and 10,000 ns using the two FFs and solution conditions, and after AA backmapping. As shown in Fig. S3, CG simulations resulted in approximately 30% change in average SASA values compared with the initial configurations. However, the average SASAs remained surprisingly consistent across different simulation conditions. Specifically, no statistically significant differences in SASA were observed between structures obtained from FF1 and FF2 simulations at 1000 ns under different salt concentrations, nor between FF1-predicted structures at 1000 ns and 10,000 ns. As previously noted, the data shown in Fig. S3 correspond to replica 1 for each condition. For completeness, Table S2 lists the SASA values after AA reconstruction for all additional replicas. For both TDP-43 and WTD PrP systems under all FF and salt conditions, the values across replicas 2 and 3 closely match those of replica 1, with overlapping standard deviations.

To further assess the structural organization within the multiunit systems, we next calculated the average radius of gyration (Rgyr) and secondary structure contents for protein chains. These measures provide complementary information to SASA by quantifying the overall compactness and structural evolution of each chain. Table S2 lists these data in AA-resolution systems, including the initial AA configurations and those obtained after AA conversion following FF1 and FF2 CG simulations; Rgyr values are provided for all available replicas under each condition. The Rgyr values following CG simulations and AA backmapping are remarkably consistent across different simulation durations and FFs for both proteins. For TDP-43 CTD, Rgyr is tightly clustered between 28.5 and 32.6 Å, and for WTD PrP, they range narrowly between 45.5 and 48.8 Å, regardless of whether the data originate from 1000 ns or 10,000 ns simulations, and whether FF1 or FF2 was used. Rgyr values calculated from CG-resolution structures (not included in the table) closely match their AA-resolution counterparts, with differences falling within the margins of statistical uncertainty. Consistent with the SASA results, this stability suggests that the overall chain compactness is largely insensitive to the specific simulation conditions tested. When compared with the initial AA structures, however, differences emerge. TDP-43 CTD shows a reduction in Rgyr from the initial value of 47 Å, whereas PrP exhibits an increase from 23 Å, consistent with partial expansion or unfolding of its folded domains during the CG simulation. Trends in secondary structure content, as identified after AA backmapping after CG simulations, exhibit greater variability across the simulation conditions. TDP-43’s random coil content was the most stable, remaining between 93.2% and 94.7% across the AA-converted constructs, closely matching the initial value of 90.8%. This slight difference is largely due to a moderate loss in α-helical content, which decreased from 9.2% in the initial structure to 5.1%–6.6% after CG simulations and AA conversion. In WTD PrP, the α-helical content dropped from the initial level of approximately 31.0% to 21.6%–25.6% after CG simulations and AA conversion, with helix H1 being the most affected (see Fig. 2 B for the initial secondary structure in PrP). The initial β-strand content, mostly consisting of a single antiparallel β-sheet (S1-S2), largely dissolved following CG simulations and AA backmapping. Together, these changes resulted in an increase in the random coil content from 65.2% in the initial WTD PrP structure to 74.3%–78.3% after CG simulations and AA conversion. These changes in secondary structure likely contribute to the observed increases in both Rgyr and SASA for WTD PrP following FF simulations and AA backmapping. The loss of compact structural elements—such as α-helical content and, in particular, the β-sheet—leads to a more extended and flexible conformation, resulting in greater spatial dispersion of the chain and increased solvent exposure.

Although Rgyr and secondary structure analyses provide useful insights into protein chain behavior—such as compaction in TDP-43 CTD and expansion in WTD PrP—they are insufficient to explain or quantify the apparent differences in chain condensation propensities observed between FF1 and FF2 at 1000 ns, or between early and extended stages of the FF1 simulations. These metrics primarily capture intrachain structural properties and do not account for interchain spatial organization or the dynamics underlying condensate formation. To address this, we further examined translational mobility of protein chains in our systems.

Analysis of TDP-43 and WTD PrP translational mobility in solution

To understand the behaviors underlying the visually observed differences in predicted morphologies of the 50-unit systems, we calculated and analyzed the MSDs of protein chains throughout the Martini 3 CG simulations. Unlike the static structural assessments above, this dynamic metric captures the extent of chain translational mobility and offers insight into the evolving organization of the modeled assemblies. Unless otherwise noted, the illustrations correspond to replica 1 for each system and condition.

Fig. 7 shows the MSD(t) profiles averaged over all 50 chains in TDP-43 CTD (blue) and WTD PrP (black) systems, obtained during 1000-ns Martini CG simulations using FF1 with 100 mM NaCl (dashed lines), FF1 with 150 mM NaCl (dotted lines), and FF2 with 150 mM NaCl (solid lines). The plots for the FF1 simulations show moderate sensitivity to salt concentration, with 150 mM NaCl resulting in somewhat lower MSD in comparison to 100 mM NaCl. However, FF1 simulations at both NaCl concentrations show consistently higher MSD values compared with the FF2 simulations at 150 mM NaCl, indicating greater average translational mobility of protein chains under FF1 conditions. This might suggest that shorter electrostatic cutoffs employed in FF1 result in less extensive chain-chain association; however, given the previously noted uniformity in SASA across the systems, it is more likely that variations in chain-solvent interactions are at play. The moderate reduction in MSD between the 100 mM and 150 mM NaCl FF1 simulations additionally indicates that solvent interactions indeed influence chain mobility. Taken together, these trends suggest that the observed mobility differences likely arise from subtle shifts in intermolecular interactions and local microenvironments that affect how freely chains move within the assembly.

Figure 7.

MSD(t) profiles averaged over all 50 protein chains in the TDP-43 CTD (blue) and WTD PrP (black) systems, based on 1000-ns Martini 3 coarse-grained simulations. FF1 simulations with 100 mM NaCl are shown as dashed lines, FF1 with 150 mM NaCl as dotted lines, and FF2 with 150 mM NaCl as solid lines.

To gain further insight into the potential relation of overall translational mobility differences with supramolecular condensation behaviors, we calculated and analyzed MSD(t) for a subset of chains that consistently exhibited lower-than-average displacements during the later stages of the 1000 ns simulation—specifically, after 500 ns. For illustration, in Fig. 8, the selected low-MSD chains are highlighted in the final structures at the end of the 1000-ns simulations. Fig. 9 compares the MSD(t) profiles of the selected low-MSD chains with the corresponding all-chain averages for each protein, separately for FF1 at 100 mM NaCl (panel A), FF1 at 150 mM NaCl (panel B), and FF2 at 150 mM NaCl (panel C). Consistent with the selection criterion, the average MSD(t) curves for low-MSD chains (solid lines in Fig. 9) exhibit a noticeable reduction in slope after about 500 ns for both TDP-43 CTD and WTD PrP systems under all simulation conditions. Notably, in all systems, the MSD(t) curves of selected chains approach near-plateau regions, indicating a marked slowdown in displacement over time. Similarly, chains that exhibited lower-than-average displacements after 5000 ns in the 10,000-ns FF1 simulations were identified for both TDP-43 CTD and WTD PrP. These chains are highlighted in Fig. 10 A and B, respectively, and the corresponding MSD(t) profiles are shown in Fig. 10 C. The selected chains also exhibit plateau-like MSD(t) behavior, indicating reduced translational mobility during the later stages of the simulation. Notably, in all simulations, FF2 consistently produces markedly lower MSD values than FF1, and, whether averaged over all chains or restricted to the low-MSD subsets, the MSD(t) values tend to be somewhat lower in WTD PrP compared with TDP-43 CTD.

Figure 8.

All-atom representation of the 50-unit TDP-43 CTD (A, C, and E) and WTD PrP (B, D, and F) systems after 1000 ns of Martini 3 CG simulations using FF1 (A–D) and FF2 (E and F) in explicit water with 100 mM NaCl (A and B) and 150 mM NaCl (C–F), followed by AA conversion and equilibration in explicit water using the AMBER99SB-disp all-atom force field. Green color highlights chains that showed lower-than-average MSD during the CG simulations.

Figure 9.

MSD(t) profiles for selected low-MSD chains (solid lines) and full 50-chain system averages (dashed lines) for TDP-43 CTD (blue) and WTD PrP (black) in 50-unit assemblies during 1000-ns simulations: (A and B) FF1 simulations at 100 mM and 150 mM NaCl, respectively; (C) FF2 simulations at 150 mM NaCl.

Figure 10.

Low-MSD chains and their MSD(t) profiles in 10,000 ns FF1 simulations. (A and B) All-atom representation of the 50-unit TDP-43 CTD (A) and WTD PrP (B) systems after 10,000 ns of Martini 3 CG simulations using FF1 in explicit water with 100 mM NaCl, followed by AA conversion and equilibration in explicit. Green color highlights chains that showed lower-than-average MSD during the CG simulations. (C) MSD(t) profiles for the selected low-MSD chains (solid lines) and full 50-chain system averages (dashed lines) for TDP-43 CTD (blue) and WTD PrP (black) in 50-unit assemblies during these simulations.

To further quantify chain translational mobility, we calculated average diffusivities from the MSD(t) curves. Although these values are not equivalent to true self-diffusion coefficients—as they can be influenced by finite system size and collective motion—they nevertheless provide a useful comparative measure of the relative translational mobility of protein chains under different simulation conditions. Table 2 summarizes the average diffusivities calculated from MSD(t) profiles from all simulated systems. For the 1000-ns simulation replicas, diffusivities were evaluated over two time intervals, an early window (100–200 ns) and a longer-time window (500–900 ns). Based on the 10,000-ns simulations, diffusivities were calculated in the longer-time 5000- to 9000-ns interval, which was not accessible in the shorter replicas. For each system and each replica, diffusivities are reported both as averages over all 50 chains and separately for the corresponding subsets of selected low-MSD chains. Despite some variability across replicas and salt concentrations, the all-chain average diffusivities calculated under FF1 conditions remain reasonably stable within the early-time window, spanning 0.099–0.137 nm²/ns for TDP-43 and 0.065–0.083 nm²/ns for PrP. In the longer-time 500- to 900-ns window, TDP-43 diffusivities for FF1 with both salt concentrations exhibit greater interreplica variation, spanning 0.075–0.175 nm²/ns; however, these values remain within overlapping ranges with the early window and do not exhibit systematic difference across time intervals or concentrations. For PrP, in contrast, the 500- to 900-ns window values under FF1 are either at the lower edge of the early-time range or below it. For instance, at 100 mM NaCl, replicas 1 and 3 yield 0.074 nm²/ns, closely matching the early-window value of 0.075 nm²/ns, whereas replica 2 drops to 0.046 nm²/ns, well below its early value of 0.083 nm²/ns. At 150 mM NaCl, only replica 3 shows a diffusivity of 0.067 nm²/ns within the early-time range, whereas the other two replicas provide diffusivity values of 0.056 nm²/ns and 0.054 nm²/ns below their early counterparts. In the 5000–9000 ns window (FF1, 100 mM NaCl), the all-chain diffusivities fall within the ranges defined by the earlier time intervals, for both TDP-43 and PrP. Under FF2 conditions, average diffusivities across all chains show a consistent decrease between the early and later time intervals. For TDP-43, values decline from 0.051–0.052 nm²/ns (100–200 ns) to ∼0.044 nm²/ns (500–900 ns). For PrP, the corresponding decrease is from 0.041 to 0.043 nm²/ns to 0.022–0.038 nm²/ns, with variation across replicas. When compared at the same salt concentration of 150 mM, FF2 yields consistently lower all-chain diffusivities than FF1 for both proteins and across both time intervals. For TDP-43, FF1 values span 0.099–0.101 nm²/ns (100–200 ns) and 0.075–0.120 nm²/ns (500–900 ns), whereas FF2 values remain confined to 0.051–0.052 nm²/ns and 0.044 nm²/ns, respectively. Similarly, for PrP, FF1 produces 0.065–0.081 nm²/ns in the early window and 0.054–0.067 nm²/ns in the 500- to 900-ns window, compared with the lower FF2 ranges of 0.041–0.043 nm²/ns and 0.022–0.038 nm²/ns.

Table 2.

Average diffusivities of protein chains in 50-unit TDP-43 CTD and WTD PrP systems over selected time intervals

System/Replica	Time interval, ns	Average Diffusivity, nm2/ns
		FF1 and 100 mM NaCl		FF1 and 150 mM NaCl		FF2 and 150 mM NaCl
		All chains	Low-MSD chains	All chains	Low-MSD chains	All chains	Low-MSD chains
TDP-43/1	100–200	0.107 ± 0.007	0.081 ± 0.006	0.100 ± 0.006	0.080 ± 0.008	0.052 ± 0.003	0.042 ± 0.003
TDP-43/2	100–200	0.137 ± 0.008	0.106 ± 0.008	0.101 ± 0.006	0.074 ± 0.005	0.051 ± 0.003	0.039 ± 0.003
TDP-43/3	100–200	0.108 ± 0.007	0.073 ± 0.007	0.099 ± 0.005	0.074 ± 0.007	0.051 ± 0.003	0.038 ± 0.003
TDP-43/1	500–900	0.091 ± 0.019	0.011 ± 0.010	0.075 ± 0.013	0.011 ± 0.012	0.044 ± 0.009	0.009 ± 0.008
TDP-43/2	500–900	0.172 ± 0.025	0.044 ± 0.012	0.089 ± 0.017	0.018 ± 0.014	0.044 ± 0.007	0.014 ± 0.005
TDP-43/3	500–900	0.125 ± 0.022	0.032 ± 0.013	0.120 ± 0.016	0.049 ± 0.010	0.044 ± 0.008	0.011 ± 0.005
TDP-43/1	5000–9000	0.104 ± 0.016	0.014 ± 0.012	N/A	N/A	N/A	N/A
PrP/1	100–200	0.075 ± 0.005	0.057 ± 0.010	0.080 ± 0.005	0.056 ± 0.004	0.042 ± 0.003	0.033 ± 0.002
PrP/2	100–200	0.083 ± 0.005	0.060 ± 0.005	0.065 ± 0.003	0.054 ± 0.004	0.043 ± 0.002	0.033 ± 0.002
PrP/3	100–200	0.076 ± 0.004	0.058 ± 0.005	0.081 ± 0.005	0.060 ± 0.004	0.041 ± 0.002	0.035 ± 0.002
PrP/1	500–900	0.074 ± 0.016	0.010 ± 0.006	0.056 ± 0.011	0.019 ± 0.008	0.032 ± 0.006	0.006 ± 0.004
PrP/2	500–900	0.046 ± 0.011	0.010 ± 0.009	0.054 ± 0.012	0.010 ± 0.005	0.022 ± 0.005	0.006 ± 0.003
PrP/3	500–900	0.074 ± 0.012	0.016 ± 0.007	0.067 ± 0.015	0.018 ± 0.010	0.038 ± 0.006	0.013 ± 0.004
PrP/1	5000–9000	0.067 ± 0.011	0.009 ± 0.006	N/A	N/A	N/A	N/A

Each diffusivity value represents the mean over either all 50 chains within a system or a subset of chains that consistently exhibited lower-than-average MSD after 500 ns in 1000-ns simulations and after 5000 ns in 10,000-ns simulations.

When the low-MSD subset of chains is used for the calculations, the average diffusivities in the early 100- to 200-ns window are moderately lower than their all-chain counterparts, consistent with the selection criterion. What was unexpected, however, is the dramatic decline in diffusivity for the low-MSD subset at later simulation stages. In FF1 simulations for TDP-43, average diffusivities fall from 0.073 to 0.106 nm²/ns in the early window to 0.011–0.049 nm²/ns in the 500- to 900-ns window for both salt concentrations, and further to 0.014 nm²/ns in the 5000- to 9000-ns interval under 100 mM NaCl. For PrP, the drop is even more pronounced—early-window values between 0.054 and 0.060 nm²/ns decrease to 0.010–0.019 nm²/ns in the 500- to 900-ns window for both NaCl concentrations, and to just 0.009 nm²/ns at 5000–9000 ns under 100 mM NaCl. In FF2 simulations, low-MSD chain diffusivities also show substantial decreases in the 500- to 900-ns window. For TDP-43, early-window values of 0.038–0.042 nm²/ns drop to 0.009–0.014 nm²/ns; for PrP, the decline is from 0.033 to 0.035 nm²/ns to 0.006–0.013 nm²/ns. For both FFs and at both salt concentrations, many late-stage diffusivity values lie close to or within statistical uncertainty, including several replicas in the 500- to 900-ns window, particularly for PrP, and both cases in the 5000- to 9000-ns window. Although this behavior is consistent with the plateau-like regions observed in the MSD(t) curves in Figs. 9 and 10 C, it is important to note that such features were not explicitly targeted when selecting the low-MSD chains. The only selection criterion was having consistently subaverage MSD values during the later stages of the simulations.

The discussed translational mobility data show that, under FF1 conditions, the all-chain averages remain consistent across the two salt concentrations. By contrast, FF2 yields consistently lower mobilities than FF1 at the same salt concentration, suggesting more restricted dynamics. Superimposed on this, a pronounced feature across all simulation conditions is the collapse of average diffusivities within the low-MSD chain subsets at later simulation stages, in some cases reaching the level of statistical uncertainty, which points to progressive confinement of a fraction of chains. This effect is especially marked for PrP, where reduced mobility was consistently observed across replicas. To explore the structural basis of this apparent confinement, we examined the snapshots of the low-MSD chains within the simulated assemblies (Figs. 8, 10 A, and B). In the PrP systems, most of these chains tended to form network-like configurations in both FF1 and FF2 simulations, marking the core of nascent percolation-like condensates. Only a few low-MSD PrP chains remained isolated from others in this subset. In contrast, most low-MSD TDP-43 CTD chains remained relatively dispersed throughout the simulation volume, whereas making contacts with more mobile chains. Rather than forming networks, TDP-43 chains appeared to participate in more transient, loosely organized interactions that did not result in sustained confinement. This is consistent with the higher average diffusivity values in TDP-43 systems compared with PrP systems, as evident from Table 2.

Fig. S4 shows spatial configurations sampled at the end of selected simulations: FF1 at 100 mM NaCl after 10,000 ns and FF2 at 150 mM NaCl after 1000 ns, for both TDP-43 CTD and WTD PrP systems. These particular conditions were chosen to represent the simulation regimes most indicative of protein networking behavior. The panels include multiple protein chains (with low-MSD chains highlighted) and Na⁺ and Cl⁻ ions in solution. In all systems, most protein chains, including those identified as low mobility, remain well surrounded by solvent, as expected for protein phase condensates (90). This is consistent with the overall stability of SASA across all simulations for both TDP-43 CTD and WTD PrP, indicating that solvent exposure of protein chains is maintained even in the presence of reduced translational mobility. This supports the interpretation that the observed mobility reduction is not primarily driven by direct chain-chain contacts. Rather, solvent-mediated interactions across sparse network-like assemblies contribute to limiting chain motion without requiring significant desolvation or dense packing.

Although most protein chains remain solvated, tending to produce generally sparse morphologies, occasional interchain contacts are observed. These localized interactions may serve as early precursors to deleterious oligomerization and therefore warrant closer analysis. Such analyses are best conducted at AA resolution, where both chain-chain and solvent-mediated interaction patterns can be more accurately characterized. This underscores the importance of multiscale integration, where CG outputs guide the targeted application of atomistic simulations to investigate aggregation-prone configurations.

Characterization of local dynamical chain coupling

To investigate local dynamical behavior at atomic resolution, we further analyzed the simulation systems obtained from CG trajectories under conditions expected to favor protein networking—from FF1 simulations at 100 mM NaCl after 10,000 ns and from replica 1 of the FF2 simulations at 150 mM NaCl after 1000 ns, for both TDP-43 CTD and WTD PrP. As described above, these particular conditions had developed spatial configurations consistent with network-like protein organization. For this purpose, we extracted trajectories of two to three closely positioned protein chains from ∼2-ns-long post-CG AA simulations of the full 50-unit systems. Representative snapshots are shown in Fig. 11 A–D, with the selected chains denoted as I, II, and III. To analyze the dynamical coupling among these selected chains, we calculated ECD pair correlation descriptors across the chain backbones (84,85,86) from the 2-ns AA trajectories, as outlined in materials and methods. Fig. 11 presents backbone correlation maps showing both interchain and intrachain dynamical coupling for each set of selected chains. In these maps, stronger dynamical coupling is represented by lower values of the correlation descriptor and shown by red, yellow, and green colors, whereas more independent motion corresponds to higher descriptor values and is shown in dark blue. For comparison, Fig. S5 additionally shows mean smallest distance maps for all selected chain sets.

Figure 11.

Representative structures and corresponding essential collective dynamics (ECD) backbone pair correlation maps for three interacting TDP-43 CTD chains (A and C) and two interacting CWD PrP chains (B and C) during 2-ns AA simulations following atomistic backmapping from 10,000-ns FF1 CG simulations (A and B) and 1000-ns FF2 CG simulations (C and D). Protein secondary structure color coding follows Fig. 2. Blue and green spheres represent Na⁺ and Cl^– ions in solution, respectively. In the correlation maps, stronger correlations are shown by red, yellow, and green colors, and weaker correlations are shown in dark blue. The legend bar color-codes the correlation descriptor, with lower values corresponding to stronger pair correlations (84,85,86,87,88). Roman numerals I, II, and III indicate protein chains.

Usually, the strongest intrachain dynamical coupling is observed within folded domains containing secondary structure (84,89), whereas the highest interchain coupling aligns with regions of chain contact (86,87,88). Here, notably increased intrachain correlations are observed in the α-helix-containing C-terminal regions of WTD PrP, as seen in Fig. 11 B and D. In the TDP-43 CTD systems, intrachain coupling is most pronounced in chains II and III after FF1 simulations (Fig. 11 A) and in all three chains (I, II, and III) after FF2 simulations (Fig. 11 C), each of which adopted partially collapsed configurations. This behavior is consistent with the expected dynamics of IDRs that undergo partial compaction, where restricted motion leads to stronger intrachain correlations.

In the TDP-43 system shown in Fig. 11 A, pronounced interchain coupling occurs between the C-terminal end of CTD chain III and extensive regions of chain II, as well as with the C-terminal segment of chain I. According to the corresponding distance map for this system (Fig. S5 A), TDP-43 chain III indeed exhibits contacts with the C-terminus of chain I. However, contacts between chains III and II are present but very limited in extent—much more localized than the broader region of interchain dynamical correlations observed between these chains. For the other TDP-43 system (Fig. S5 C), close contacts are observed between partially collapsed chains I and III. As expected, these contacts are accompanied by pronounced interchain coupling (Fig. 11 C); however, the region of notable correlations is broader than the area of direct contact. In addition, the N-terminal region of chain II shows dynamical coupling with both other chains, despite the absence of corresponding close contacts in the distance map. Notably, the broad TDP-43 C-terminal interaction regions observed in Fig. 11 A and B align with those identified in a recent study (61). Similarly, the two WTD PrP chains in Fig. 11 B exhibit an extensive region of dynamical coupling, whereas the corresponding contact points in Fig. S5 B are very limited. Finally, in Fig. 11 D, dynamical coupling among chains I and II extends beyond their direct contacts shown in Fig. S5 D.

A remarkable observation is the persistent interchain dynamical coupling in regions where no close contacts are detected, a pattern that appears consistently in both TDP-43 and PrP systems, regardless of the CG simulation model or duration. This suggests that interchain coupling may be mediated through solvent interactions involving both water molecules and solvated Na⁺ and Cl⁻ ions. This interpretation appears to be supported by the presence of numerous Na⁺ and Cl⁻ ions in the molecular structure snapshots shown in Fig. 11, where they are frequently located near interacting protein chains. These interactions may contribute to long-range dynamical correlations by modulating electrostatic or hydrodynamic coupling between chains, suggesting a collective, environment-sensitive mechanism of early assembly and confinement that extends beyond direct physical contacts. To explore this further, we extracted the number of chain-ion and chain-chain contacts from post-CG AA simulations.

Ion-chain and chain-chain contact numbers

To better understand the origins of the reduced mobility and dynamical coupling observed in the simulations, we extracted the number of contacts between protein chains and surrounding Na⁺ or Cl⁻ ions, as well as between neighboring protein chains, from post-CG AA backmapping. Contact counts were obtained across all systems, FFs, solvent conditions, and simulation replicas. Contacts were identified using UCSF Chimera (80), applying a maximum interatomic distance of 3.6 Å and requiring a VDW overlap of ≥ −0.4 Å. Hydrogen bond overlap reduction was set to zero, and contacts between atoms separated by four or fewer covalent bonds were excluded. Table 3 summarizes the total number of ion-chain and chain-chain contacts, summed over all 50 protein chains in each system.

Table 3.

Total number of ion-chain and chain-chain contacts in 50-unit TDP-43 CTD and WTD PrP systems, extracted after all-atom backmapping following 1000-ns and 10,000-ns coarse-grained simulations

System/Replica	Time, ns	Ion-Chain and Chain-Chain Contact Numbers in 50-unit systems
		FF1 and 100 mM NaCl		FF1 and 150 mM NaCl		FF2 and 150 mM NaCl
		Ion-Chain	Chain-Chain	Ion-Chain	Chain-Chain	Ion-Chain	Chain-Chain
TDP-43/1	1000	1202	67	1470	97	1822	106
TDP-43/2	1000	1172	2	1363	40	1825	60
TDP-43/3	1000	1101	30	1290	44	1858	154
TDP-43/1	10,000	1194	168	N/A	N/A	N/A	N/A
PrP/1	1000	809	40	1018	63	1511	83
PrP/2	1000	694	68	939	5	1373	54
PrP/3	1000	886	77	937	24	1423	35
PrP/1	10,000	994	106	N/A	N/A	N/A	N/A

The number of ion-chain contacts consistently exceeds the number of chain-chain contacts in all systems and under all conditions. Within each set of 1000-ns simulations, ion-chain contact counts increase systematically across the three conditions: lowest under FF1 with 100 mM NaCl, higher under FF1 with 150 mM NaCl, and highest under FF2 with 150 mM NaCl. This trend is observed across all three replicas for both TDP-43 and PrP systems. Across all systems, PrP tends to show lower ion-chain contact counts than TDP-43 under equivalent simulation conditions. Chain-chain contact numbers are higher in the 10,000-ns simulations compared with the corresponding 1000-ns runs for both TDP-43 and PrP systems. Among the 1000-ns simulations, only TDP-43 appears to show some difference in chain-chain contacts across the tested conditions, although there is noticeable variability between replicas. The PrP systems do not display any consistent trend in chain-chain contacts across these conditions.

To further understand the factors contributing to chain mobility trends in the simulated systems, we examined the relationship between average chain diffusivity—calculated during CG simulations as discussed previously—and the number of ion-chain or chain-chain contacts observed after post-CG atomistic backmapping of entire 50-unit systems. Fig. 12 shows the relationship between the total number of contacts and chain diffusivity from all available conditions and replicas for TDP-43 and PrP systems each. Here, we used the all-chain diffusivities calculated for the late-time windows of 500–900 ns in the 1000-ns CG simulations and 5000–9000 ns in the 10,000-ns CG simulations, as listed in Table 2. Fig. 12 A presents the average chain diffusivity as a function of the total number of ion-chain contacts for TDP-43 (blue points) and for PrP (black points). Each data point represents a unique system-replica combination. Fig. 12 B shows a similar dependence of average chain diffusivity on the total number of chain-chain contacts for the same systems and simulation conditions.

Figure 12.

Relationship between average chain diffusivity and the total ion-chain (A) and chain-chain (B) contact counts in 50-chain TDP-43 and WTD PrP systems. Contact counts were obtained after post-CG all-atom backmapping following 1000-ns or 10,000-ns CG simulations. Diffusivities were calculated over the 500- to 900-ns interval for the 1000-ns CG simulations and the 5000- to 9000-ns interval for 10,000-ns CG simulations, as reported in Table 2. Each point represents a distinct replica and simulation condition; TDP-43 is shown in blue and PrP in black. Error bars indicate the diffusivity standard error of the mean.

The data in Fig. 12 reveal clear relationships between contact counts and chain mobility for both protein systems. In Fig. 12 A, average diffusivity decreases as the number of ion-chain contacts increases for both TDP-43 and PrP systems, indicating that extensive ion-protein interactions are associated with reduced translational mobility. In Fig. 12 B, TDP-43 diffusivities also tend to decrease with increasing chain-chain contacts, suggesting that direct interchain associations contribute to reduced mobility. For PrP, however, no clear trend is observed between diffusivity and interchain contacts. Together, these results indicate that interactions with Na⁺ and Cl⁻ ions play a primary role in determining the mobility of both TDP-43 and PrP chains in solution, whereas direct interchain contacts further modulate the mobility primarily in TDP-43 and to a lesser extent in PrP. The pronounced network-like configurations observed for PrP, particularly under FF2 conditions, complement the observed inverse relationship between ion-chain contacts and diffusivity, suggesting that ion-mediated interactions may facilitate or stabilize spatial confinement among chains, even in the absence of extensive direct interchain contacts. On the other hand, TDP-43 chains exhibit a higher number of ion-chain contacts than PrP under equivalent conditions, yet they remain more mobile and show less pronounced spatial clustering. This suggests that although ion association is a strong determinant of mobility, its effects may differ depending on the protein’s sequence, degree of structural disorder, or molecular size.

Given the observed link between ion-chain contacts and chain mobility, we next turned to a more detailed analysis of ion contacts at the level of individual residues across all simulation conditions. Fig. 13 shows the per-residue ion contact counts for replica 1 across all systems and simulation conditions, and Figs. S6 and S7 display the corresponding data for all three replicas from the 1000-ns simulations. Across the TDP-43 systems, the per-residue ion contact profiles in Fig. 13 A and B reveal comparable overall distributions along the protein sequence. In both panels, the central portion of the sequence—particularly residues 340–375—exhibits consistently elevated levels of ion association. This region lies within a highly conserved low-complexity domain implicated in aggregation and phase-condensation behavior (61,91,92). A similar region of preferential ion contacts is observed across the other 1000-ns simulation replicas, as shown in Fig. S6. When comparing FF1 and FF2 simulations (Fig. 13 B), FF2 results in systematically higher ion contact counts across several regions of the TDP-43 sequence, including residues 304–320, a segment around 365–380, and the C-terminal portion beyond residue 385. Similar FF2-over-FF1 differences are also observed in the other replicas (Fig. S7).

Figure 13.

Per-residue ion contact counts in TDP-43 (A and B) and WTD PrP (C and D) systems from replica 1 simulations. Bar plots show the number of ion-residue contacts for each residue after post-CG all-atom backmapping of 50-unit systems. (A and C) Comparison of FF1 simulations at 100 mM NaCl after 1000-ns and 10,000-ns runs. (B and D) Comparison of FF1 and FF2 simulations at 150 mM NaCl (1000 ns each). Figs. S6 and S7 show the data for other replicas.

In the case of PrP, the per-residue ion contact profiles (Fig. 13 C and D) exhibit a markedly different distribution compared with TDP-43. Rather than the broad regions of pronounced ion association seen in TDP-43, PrP displays more fragmented and uneven patterns of ion interaction, with extended sequence regions showing minimal contacts. Notably, the segment spanning residues 54–90—the octapeptide repeat region—consistently exhibits low levels of ion association across all conditions. This is surprising, given that the octapeptide repeats are known to bind divalent metal ions such as Cu²⁺ and Zn²⁺ (63). In contrast, elevated ion contact counts were found in several structurally and functionally diverse subunits of PrP, including the unstructured regions 24–54 and 100–125; a portion of the globular domain spanning residues 142–178, which includes β-strand S1 and α-helix H1; residues 192–204, corresponding to the loop between α-helices H2 and H3 (LH2-H3); and the C-terminal segment beyond residue ∼220 (see Fig. 2 B). Similar to the 54–90 region, these domains are rich in polar and charged residues. The markedly reduced association of Na⁺ and Cl⁻ ions with the 54–90 segment likely reflects its physicochemical selectivity for divalent transition metal binding (93). In all regions with high ion contact propensity, the FF2 simulation shows consistently higher ion contact counts compared with the FF1 counterpart, as seen in Fig. 13 D. The described ion contact trends were consistently observed across all available replicas, with comparable patterns evident from Fig. S7.

These findings demonstrate that ion-chain contacts play a significant role in modulating protein mobility and contribute more substantially than direct chain-chain contacts to the observed confinement effects. The enhanced ion contact propensity under FF2 conditions correlates with lower chain diffusivities and supports the interpretation that electrostatic interactions with the ionic environment are key drivers of mesoscale assembly behavior. Together with the translational mobility analyses, this contact-based perspective provides additional mechanistic insight into protein condensation processes.

Conclusions

This study presents a multiscale AA-CG-AA simulation framework for investigating supramolecular assembly behaviors of proteins implicated in misfolding diseases, focusing on TDP-43 CTD (274–414) and WTD PrP (24–233), both exhibiting distinct structural features. Animated 3D renderings of the 50-unit TDP-43 CTD and WTD PrP systems are provided in Videos S1 and S2. By integrating all-atom structure modeling, CG Martini 3 simulations, and backmapping to atomistic resolution followed by AA simulations, we constructed and analyzed 50-unit systems under two modified Martini 3 FFs, FF1 and FF2. These FFs differ in their treatment of nonbonded interactions, with FF2 employing longer electrostatic and VDW cutoffs and including rescaled ion-protein interactions.

The 50-unit systems exhibited noticeable differences in condensation behavior when simulated using the two CG FFs. In particular, FF2 simulations produced more compact and interconnected assemblies, especially for WTD PrP, whereas FF1 systems appeared more dispersed at similar trajectory durations, with a greater proportion of chains remaining spatially separated. However, these morphological distinctions are not captured by global structural metrics such as SASA and radius of gyration. Both SASA and Rgyr underwent changes reflecting the structural adjustment of chains both from their isolated monomeric states and during the transition between AA and CG FFs. When compared with the initial AA structures, Rgyr moderately decreased for TDP-43 CTD, consistent with slight compaction of its largely disordered chains, whereas WTD PrP exhibited a more pronounced increase, reflecting expansion or partial unfolding of its folded domains during CG simulations. However, average SASA and Rgyr values remained relatively stable throughout subsequent simulation stages, indicating their insensitivity to the observed chain condensation.

Secondary structure analysis of the AA-converted CG-simulated systems revealed modest changes in α-helical content but a substantial loss of β-sheet structure in WTD PrP—primarily the antiparallel S1-S2 β-sheet—which did not re-form upon backmapping to AA resolution. This is consistent with the substantial increase in Rgyr observed for WTD PrP. Although several strategies exist for stabilizing secondary structure in CG simulations, including the use of Gō-like biasing toward a known folded state (51) or the application of stronger ENs to preserve the input conformation (50), these approaches are not suitable here. Presupposing a single native structure may interfere with capturing unknown intermediate states relevant to misfolding and early condensation and may suppress the chain rearrangements needed to model condensation phenomena. Instead, we employed a minimally restrictive elastic network that maintains local geometry while allowing global flexibility. Although this may permit faster loss of β-structure, it provides a more realistic framework for capturing early aggregation phenomena. However, improving β-structure stability without compromising condensation dynamics remains an important challenge in multiscale simulation approaches involving CG modeling.

Here, the use of a minimally restrictive EN preserved the sensitivity of chain dynamics to the underlying FF parameters, enabling FF-dependent differences in condensation behavior and chain translational mobility to emerge. FF1 simulations showed consistently higher average MSD(t) profiles compared with FF2 simulations across both TDP-43 CTD and WTD PrP systems, at the same salt concentrations, indicating looser, more dynamic assemblies under FF1 conditions. In contrast, the lower MSDs in FF2 suggest that this FF promotes more extensive confinement of chain motion, likely reflecting enhanced local association and network formation.

To probe the formation of hypothetical condensates within the studied multiunit systems, we identified and analyzed subsets of chains that consistently exhibited lower-than-average MSD(t) values during the later stages of both FF1 and FF2 simulations. This analysis was aimed at capturing early signatures of chain confinement potentially associated with condensation processes. The MSD(t) profiles of these selected chains showed markedly reduced displacement compared with the full ensemble, with near-plateau behaviors emerging after 500 ns in FF2 and after 5000 ns in FF1 simulations. The predicted sparse chain morphologies, together with the observed uniformity of SASA across different stages of each system’s simulation, suggest that reduced translational mobility is not primarily driven by direct chain-chain contacts, but instead may arise from solvent-mediated effects driving local microstructural organization. Most chains appear to remain solvated during the simulations, as expected for fluid-like phase condensates of proteins (90).

Using the ECD method (84,85,86,87,88) applied to AA simulations of AA-converted CG-predicted structures, we identified extensive interchain dynamical coupling even in the absence of direct structural contacts across protein chains—a pattern observed in representative TDP-43 and PrP systems. This interchain coupling appears to be mediated by solvent interactions involving water molecules and solvated Na⁺ and Cl⁻ ions, as supported by the spatial distribution of ions near interacting chains. This observation aligns with the above hypothesis of an indirect mechanism of early protein assembly and confinement, in which chain interactions emerge through solvent-mediated coupling rather than direct chain-chain contacts.

To further evaluate the physical origin of reduced chain mobility, we quantified both ion-chain and chain-chain contacts across all simulated systems using post-CG AA backmapping. The ion-chain contact numbers were consistently higher than chain-chain contact numbers under all conditions and showed a clear inverse relationship with average chain diffusivity. Simulations producing greater total ion-protein interaction counts tended to exhibit markedly lower translational mobility. In contrast, no consistent relationship was observed between chain-chain contact numbers and average diffusivity, especially in WTD PrP systems where chain confinement was most pronounced. These findings support the hypothesis that solvent-mediated interactions involving Na⁺ and Cl⁻ ions are important drivers of early-stage confinement, whereas direct protein-protein contacts play a secondary or condition-specific role. This observation is consistent with the uniformity of SASA across simulation stages, the persistence of chain solvation, and the presence of interchain dynamical coupling in the absence of physical contact—all of which point to an indirect, solvent-modulated mechanism of mesoscale organization in the modeled condensates.

To summarize, the combined AA-CG-AA simulation framework successfully captured key aspects of early-stage supramolecular condensation in two structurally distinct proteins, including FF-dependent differences in translational mobility, the emergence of restricted-mobility subpopulations, and the formation of network-like structures in WTD PrP systems. For TDP-43 CTD, longer simulations may be required to reach a comparable condensation stage, highlighting the importance of integrating efficient CG methods to access extended timescales. Although the use of 50-chain systems, as considered here, represents the edge of practical feasibility for current multiscale workflows, they remain relatively small in terms of modeling macroscopic phase behavior. Nevertheless, such systems are sufficient to probe early confinement, identify emergent structural features, and uncover mechanistic differences across FFs, protein types, or solvent conditions. Importantly, the integration of CG and AA modeling allowed us to detect solvent-mediated interchain dynamical coupling, even in the absence of direct contacts, offering new insight into early confinement mechanisms during protein assembly. These insights would not be accessible through CG or AA simulations alone, as they require bridging long-time simulations of large-scale systems with residue-level dynamical resolution.

As with any evolving modeling strategy, the present framework offers clear opportunities for refinement. Although the approach captures mesoscale signatures of early assembly, further progress will require addressing both sampling limitations and model specificity. Simulation durations, although extended to 10 μs in some cases, may still fall short of accessing slower aggregation or fibril formation events. Although CG models such as Martini 3 enable large-scale simulations, their ability to retain subtle sequence-specific interactions or secondary structure elements remains limited and offers room for refinement. In particular, achieving stable β-sheet content remains challenging. With ongoing improvements in FF refinement and the development of new structure-aware multiscale CG-AA protocols, these limitations are likely to be progressively overcome. Future studies may further expand system size to explore large-scale phase boundary formation. Although the described AA-CG-AA framework is expected to be broadly applicable to diverse systems, our results demonstrate that observed trends can differ depending on the protein’s sequence, degree of structural disorder, or molecular size. Therefore, accumulating broader data on diverse full-length proteins or large fragments will be critical for defining robust, generalizable trends across biologically relevant protein systems. In addition, the role of broader environmental conditions—including varied pH, buffer composition, and heterogeneous solution components—remains to be explored.

Data and code availability

Coordinate files (PDB format), representative snapshots from different stages of the simulations, and custom simulation scripts are available at https://github.com/doroshl/martini_protein_LLPT.

Acknowledgments

We thank the Digital Research Alliance of Canada for providing the computational resources used in this study. This research was supported by the ALS Society of Canada and Brain Canada through the 2022 Discovery Grant Program (to M.S. and H.W.), as well as by Alberta Innovates (Canada) through the Chronic Wasting Disease (CWD) Research Program (awards 222300611 and 222300803 to H.W. and M.S.). We are also grateful to K. Lindorff-Larsen for his valuable advice. Molecular visualizations were prepared using the VMD package (81), UCSF Chimera (80), and Discovery Studio Visualizer (70).

Author contributions

L.D. performed research, analyzed data, and wrote the manuscript. H.W. designed research, acquired funding, and reviewed the manuscript. M.S. designed research, acquired funding, contributed analytic tools, analyzed data, and wrote the manuscript.

Declaration of interests

The authors declare no competing interests.

Editor: Ragothaman Yennamalli.