Balancing thermodynamic stability, dynamics, and kinetics in phase separation of intrinsically disordered proteins

Increasing evidence has revealed that many intrinsically disordered proteins (IDPs) can undergo liquid–liquid phase separation, resulting in the coexistence of a protein-rich phase and a dilute phase in solution.^1–4 This phase separation is recognized to play crucial roles in various essential biological processes by forming membrane-less organelles.^5–8 Despite their involvement in diverse fundamental cellular processes, these higher-order phase-separated organelles, such as P granules,⁹ Cajal bodies,¹⁰ stress granules,¹¹ and nucleoli,¹² share the common property of locally concentrating different elements as a prerequisite for specific biological functions. It is well acknowledged that the driving forces of phase separation are the multivalent attractive interactions,^13–15 which originate from the specific features of protein sequences.^5,16,17 Recently, extensive studies have established strong connections between disease-related mutations and the promotion of liquid–liquid phase separation, leading to the formation of pathological gel-like and solid-like aggregates.^18–21 These findings underline the important roles of phase separation in disease pathology. Therefore, it is imperative to delineate the fundamental physical principles of phase separation, understand the underlying interactions, and identify the external factors that impact this process.

Environmental factors such as temperature, pH, and salt concentration can significantly impact the macroscopic properties of phase separation.^5,22 Notably, intrinsically disordered proteins (IDPs), which are major players in phase separation, possess a distinct functional advantage: the high resistance to non-native environmental conditions.²³ This resilience is largely attributed to the fact that the biological functions of IDPs, mediated by their unstructured chains, are more likely to remain consistent under various conditions.²⁴ Recent experiments have revealed that IDPs in liquid-like droplets retain high degrees of conformational disorder.^25,26 For instance, Majumdar et al. developed an excimer emission fluorescence technique to measure intra-molecular distances and identified a large-scale conformational expansion during the transition from the dilute phase to the dense phase for Alzheimer’s disease-related tau protein.²⁷ These findings support the hypothesis that the highly extended structures of IDPs in condensates may also be insensitive to environmental factors. Consequently, the seemingly contradictory environment-(in)dependent macroscopic properties of the condensates and microscopic structures of proteins within them present an intriguing avenue for further investigation.

Despite the fact that IDPs remain conformationally disordered in phase-separated condensates, their translational diffusion and global motion are significantly repressed in the dense phase compared to the bulk solution. This is due to the presence of highly concentrated biomolecules, which result in high viscosity within the condensates.^25,26,28,29 Recent studies using nuclear magnetic resonance (NMR),³⁰ single-molecule F$ö$rster resonance energy transfer (smFRET),³¹ and all-atom molecular dynamics (MD) simulations^31,32 have demonstrated that IDPs are highly mobile in the condensates, with local chain motions being exceedingly dynamic, associated with rapid breaking and formation of different types of molecular interactions.³³ This highly dynamic chain property, induced by weakly formed and transient interactions, facilitates the fast exchange of binding partners, thereby enabling efficient biomolecular functions within the condensates.^34,35 Being at thermodynamic equilibrium, the thermodynamic stability of the condensate can be quantified by the upper critical solution temperature for phase separation.^36,37 Intuitively, one may expect the trade-off between thermodynamic stability and dynamics, as the driving forces in stabilizing the condensates may slow down the diffusion of molecular mobilities.³⁸ Given that liquid-like chain dynamics within the dense phase are essential for biological function,^7,39,40 there is a delicate balance between the thermodynamic stability of the condensates and the dynamics of the chains,⁴¹ likely modulated by the underlying molecular interactions. However, understanding this balance in phase separation is quite challenging.

IDPs generally cannot fold into stable structures due to their low hydrophobicity.⁴² Bioinformatic analyses have revealed that IDPs typically have high percentages of charged residues in their sequences and most are polyampholytes.⁴³ Both theoretical and experimental studies have shown that IDP sequences with fully segregated oppositely charged residues can reduce their dimensions by collapsing,^44,45 significantly impacting the thermodynamic and kinetic properties of IDP binding.^46,47 In addition, the charge distribution patterns of IDP chains play a crucial role in phase separation, particularly in the thermodynamic stability of condensates.^48–50 It has been established that there is a strong correlation between the degree of compaction of isolated IDPs and their propensity to form phase-separated condensates.^22,37,48,49 This suggests that the bipolarly charged IDPs, which are capable of forming highly compacted chains in isolated states, exhibit high thermodynamic stability in phase-separated condensates.⁴⁸ As IDPs undergo conformational expansions from collapsed structures at the free state to extended structures in the condensates during phase separation,²⁷ unraveling of highly collapsed IDP chains may slow down the phase separation process. A similar phenomenon has been observed in the folding-coupled binding of the bipolarly charged IDP Chz1 to its target histone proteins, where collapsed IDP chains acted as trapping states during the association process.^51–53 However, the interplay between the thermodynamic stability of condensates and the kinetic rates of their formation during phase separation remains largely elusive.

To address these challenges, we performed MD simulations using a simplified coarse-grained model to explore the thermodynamics, dynamics, and kinetics of phase separation induced by a bipolarly charged IDP system. Our observations revealed that the extended IDP conformational ensemble in the condensates remains highly conserved with respect to the changes in the interaction strengths and environmental conditions. We found that the global reconfiguration timescales of the IDP chains were slowed down upon condensate formation, while the local chain flexibility remained largely unchanged between the dilute and dense phases. Notably, we uncovered a non-monotonic relationship between the thermodynamic stability and formation rates of condensates in the early stage of phase separation, highlighting the delicate balance between speed and stability in this process. By focusing on elucidating the interplay among thermodynamic stability, dynamics, and kinetics in phase separation, our study provides valuable insights into the mechanistic understanding of this complex phenomenon.

Despite recent progress in all-atom MD simulations on identifying different types of interactions stabilizing the dense phase,^31,32,54 coarse-grained models offer unique advantages in reaching the necessary timescales for studying phase separation processes.⁵⁵ Various coarse-grained models have been developed, leading to significant achievements in understanding these slow and complex processes.^{37,49,56–59} Here, we employed a simplified coarse-grained model to characterize the thermodynamic stability, chain conformation, dynamic characteristics, and kinetic rates of phase separation.

We studied the phase separation of an ideal polyampholytic IDP system, which is comprised of 25 lysine (K, positively charged) and 25 glutamic acid (E, negatively charged) residues in a single chain.^45,49 Specifically, we focused on the system, where the oppositely charged residues are fully segregated in the linear sequence [Fig. 1(a)]. This IDP system was previously found to be highly compacted in the dilute phase, exhibiting a high propensity for phase separation.^48,49

Even with the coarse-grained model, obtaining well-converged thermodynamic properties for the coexistence of two phases in simulations, starting from fully dispersed and randomly placed configurations, is practically challenging. To address this issue, we employed the slab method, previously developed by Dignon et al.⁵⁶ The slab simulations were initialized with a slab-like configuration, in which the chains are densely packed in a confined space. This setup enhances the convergence of the thermodynamic simulation, facilitating accurate study of phase separation. The validity of the slab method has been demonstrated in various studies, which have investigated phase separation processes induced by different biomolecules using different models.^49,56,65 Here, we applied the slab method to conduct simulations, aiming to quantify the thermodynamic properties of phase separation and the conformational characteristics of the IDP chains.

The slab simulations proceeded as follows (Fig. S1): Initially, 200 IDP chains, each comprising 50 amino acids, were placed within a square box. Then, an NPT simulation was conducted using Berendsen pressure coupling, with the reference pressure set to 1000 bars in the xyz direction.⁶⁶ During this process, the box size was gradually decreased until the amino acid concentration reached ∼9.0M, higher than the typical concentrations observed experimentally for IDPs (approximately ranging from 1.0 to 7.0M).⁶¹ Subsequently, the box size was fixed with the dense phase appearing in a slab-like configuration. Finally, to achieve coexistence of the dilute and condensed phases, the box was stretched in the z-direction to 50 nm, and NVT simulations were performed [Fig. 1(a)]. Analyses were conducted after the system reached equilibration during the NVT simulations.

To investigate the rates of condensate formation during the phase separation process, we performed kinetic simulations using the same stretched box utilized in the thermodynamic slab simulations. Initial configurations for the kinetic simulations were generated from the thermodynamic simulations conducted at high temperatures, where only one homogeneous phase was present in the system at the end of the simulations. For each LJ interaction strength (ɛ_LJ) or environmental condition (temperature T and salt concentration C_salt) conducive to phase separation, we conducted 20 independent simulations. Each simulation was initialized from a different system configuration, and the results were analyzed by collecting and averaging all the simulation trajectories.

We used the GROMACS (version 4.5.7) software to perform MD simulations.⁶⁷ Reduced units were used throughout the simulations, except that the length is in the unit of nm. Temperature is in the energy unit (ɛ₀) by multiplying the Boltzmann constant. As the molecular weights of lysine and glutamic acid are about 146 and 147 Da, respectively, the concentration of 1M in our simulation may approximately correspond to 147 g/l in reality. The time step was set to be 0.005 τ₀, where τ₀ is the unit of time. We applied Langevin dynamics with the friction coefficient set as 1.0 $τ0−1$⁠. Non-bonded interactions were truncated at the distance of 6a ≈ 3.6 nm, and the periodic boundary conditions were used in all three dimensions. To explore the effects of interactions and environmental conditions on phase separation, we modulated the strength of the LJ potential (ɛ_LJ), temperature (T), and salt concentration (C_salt) and applied to different simulations.

During each thermodynamic simulation, the equilibration step was set to be 5 × 10⁴ τ₀, which was determined to be sufficient for achieving the thermodynamic convergence. All the kinetic simulations were performed at T = 1.75 ɛ₀, where phase separation could occur for all the interaction strengths and environmental conditions of interest. For analyzing the results, the kinetic trajectories from the first 500 τ₀ were collected, after which the number of contacts between the chains in the system changed very slowly and the system reached a steady state.

We investigated the phase separation of an ideal polyampholytic IDP system, consisting of 25 positively and 25 negatively charged residues with a bipolarly charged distribution along the linear sequence. This IDP model, akin to the KE sequences studied in previous research,⁴⁵ exhibits a diblock sequence feature with maximal opposite charge segregation [Fig. 1(a)]. Previous studies have underscored the pivotal roles of electrostatic interactions in inducing single-chain compaction and multiple-chain phase separation in this IDP system.^45,48,49 Using the slab simulation method, we identified a coexistence of low- and high-density phases for the IDPs under moderate environmental conditions with noticeable conformational differences in the IDP chains observed between the dilute and dense phases [Figs. 1(a) and 1(b)]. As the temperature increases, the trend of the coexistence of the two phases weakens [Fig. 1(c)]. The critical temperature (T*), denoting the highest temperature for phase separation to occur, was determined from the coexistence densities, with details provided in the supplementary material and previous studies.^37,56

We found that the phase separation of this IDP system can occur over a wide range of non-bonded LJ interaction strengths (ɛ_LJ) and salt concentrations (C_salt) (Figs. S2–S11). This suggests that bipolarly charged IDPs naturally possess sequences with a strong propensity for phase separation.⁵⁶ As the IDPs here are associative polymers, they can form networks characterized by interactions among oppositely charged residues.⁶⁹ We therefore estimated the extent of percolation, known as the gel fraction,⁷⁰ and found that the phase separation observed in our study is highly coupled to percolation (Fig. S12), leading to a phase-separation-coupled percolation transition.^71,72 To investigate the effects of interactions and salt concentrations on phase separation, we calculated the critical temperature (T*) as a function of ɛ_LJ at both high and low values of C_salt [Fig. 1(d)]. The critical temperature characterizes the tendency for IDPs to undergo phase separation, serving as a potential indicator for the thermodynamic stability of the condensates formed in the coexistence phases.⁵⁶ We observed monotonically positive correlations of T* with ɛ_LJ at both C_salt. A comparison of T* between these two salt concentrations revealed that strong electrostatic interactions favor phase separation. Our results suggest that strengthening the interactions, either through short-range LJ interactions or long-range electrostatic interactions, is capable of enhancing the thermodynamic stability of phase separation in IDPs and increasing the density of the condensates (Fig. S13). Previous research has established a power-law correlation between the degree of single-chain compaction, described by the average radius of gyration (R_g) and the thermodynamic stability of multi-chain phase separation (T*).^37,48,73 In our simulations, we observed that ɛ_LJ and C_salt significantly impact the compaction of the single chain, although conformational fluctuations were noted due to the energy–entropy compensation (Fig. S14). This further leads to strong correlations between R_g and T* (Fig. S15).

Interestingly, despite the apparent temperature-dependent compaction of IDPs in the free state, we observed that the distributions of R_g for IDPs in the condensates during phase separation remained consistent across temperatures [Fig. 1(e)]. Furthermore, we performed principal component analysis (PCA), which considers the spatial distribution of residues relative to the centroid of the IDP as a feature [Figs. 1(f) and 1(g)]. PC1 describes the synchronous opening (or closing) of the N- and C-terminal segments with the center of the chain almost fixed, while PC2 describes the oscillation of the short-length segments in the IDP chain (Fig. S16). Although these two PCs capture more conformational characteristics than R_g, we found that the PCA plots still reveal similar temperature-dependent and temperature-independent behaviors for IDPs at the free state and in the condensates, respectively. In addition, we noted a positive correlation of the average R_g with temperature for IDPs at the free state, implying that higher (lower) temperatures result in more extended (compacted) structures. In contrast, IDPs in the condensates appeared to be more extended than those in their free state, and these extended structures showed insensitivity to temperature [Fig. 1(h)]. Our findings are in line with previous studies using different coarse-grained models,^73–75 suggesting the general temperature-independent chain properties in the condensates.

By varying the interaction strengths and salt concentrations, we observed that the average R_g remained nearly constant for IDPs in the condensates [Fig. 1(i)]. These results suggest that the conformational ensemble of IDPs in the condensates is highly conserved and does not change with variations in interactions or environmental conditions. We further conducted a thorough analysis of intra- and inter-chain contacts for IDPs at the free state and in the condensates (Fig. S4). We observed a decreasing number of contacts within the chain itself in the free state with increasing temperature, providing an explanation for why IDPs tend to adopt more extended conformations at higher temperatures. In contrast, the number of intra-chain contacts for IDPs in the condensates remained nearly constant across different temperatures and environmental conditions. Furthermore, IDPs in the condensates exhibited fewer intra-chain contacts than those at the free state. These results suggest that IDPs are more extended in the condensates, in line with previous simulation and experimental studies.^27,76,77 Meanwhile, the number of inter-chain contacts for IDPs in the condensates decreases significantly with increasing temperature (Fig. S4). In addition, changing the interaction strengths and salt concentrations has a significant impact on altering the inter-chain contacts of IDPs in the condensates (Figs. S2–S11). Our findings revealed that the conformation ensembles of IDPs remain largely unaltered with respect to changes in interaction strengths, temperatures, and salt concentrations. Therefore, the interaction and environmental factors modulate the macroscopic thermodynamic properties of phase separation primarily through changing the microscopic underlying inter-chain interactions of IDPs, which maintain the highly conserved, albeit extended, conformational ensembles in the condensates.

To assess the liquid-like nature of the dense phase, we calculated the mean squared displacement (MSD) of the IDPs in the condensates moving along the z-direction as a function of time [Fig. 2(a)]. The linear region in the plot suggests that the dynamics of IDPs in the condensates are liquid-like, indicating fluid behavior rather than tightly formed aggregation. In addition, we observed that IDPs diffuse much faster at the free state than in the condensates. This observation, consistent with numerous previous studies,^78–80 is primarily attributed to the high viscosity present in the condensate, resulting from the multivalent interaction network induced by the multichain nature of IDPs.¹⁴ 

Recent accumulating evidence has shown that proteins in phase-separated condensates may exhibit different behaviors at various timescales.^{6,30,31,81,82} We extracted the MSD values at different timescales and examined their correlations with interaction strengths and temperatures [Figs. 2(b), 2(c), and S17]. The gaps between the MSD values at the free state and in the condensates become more significant as the observing timescales increase, indicating that the slowing effects of condensate formation on the translational diffusion of IDPs are more pronounced at longer timescales. We also calculated the diffusion coefficient for IDPs at the free state and in the condensates for different interaction strengths, temperatures, and salt concentrations using the method proposed previously (Fig. S18).³² We found that the formation of condensates can significantly decrease the diffusion coefficient of the IDP chains by about 10–20 times, close to the observations from previous studies.^28,31

Since the diffusion of the IDP at the free state is directly proportional to temperature, the slope of the MSD–T curve reflects the positive effect of temperature on facilitating chain diffusivity. Interestingly, we found that although the MSD values are smaller in the condensates than at the free state, the slopes of MSD–T curves are generally steeper, suggesting that temperature has a more profound effect on accelerating the motions of the chain in the condensates. Furthermore, we identified a negatively correlated relationship between the density of the condensate and the MSD across different temperatures (Fig. S19). These observations are likely due to the fact that increasing temperature not only increases the kinetic energy of the beads but also loosens the network of inter-chain interactions in the condensates.

We calculated the timescales of the IDP conformational dynamics, represented by the relaxation time γ_P−N of the autocorrelation function C_P−N, which focuses on the change in distance between the centroids of the positively and negatively charged residues of the IDP chain [Figs. 2(d), S17, and S20]. Our findings indicated that the conformational reconfigurations of IDPs are much slower in the condensates compared to those at the free state. This suggests that the formation of condensates can slow down both translational motions and conformational adaptations of IDPs, as widely observed in previous studies.^30,31

To investigate how interaction strengths and temperature influence the timescales of chain dynamics, we calculated γ_P−N for IDPs both at the free state and in the condensates, across different temperatures and ɛ_LJ. Strikingly, we observed distinct temperature- and interaction-dependent behaviors of γ_P−N for IDPs at the free state and in the condensates [Fig. 2(e)]. When the IDP is isolated, weakening the intra-chain interactions induces a more extended and flexible chain, thus slowing down the conformational dynamics. Although increasing temperature accelerates the motions of the beads in the IDP chain, the overall slow chain dynamics caused by more extended and flexible conformations can counterbalance the kinetic energy gained from higher temperatures, eventually resulting in a negative correlation between temperature and reconfiguration timescales for IDPs at the free state. In contrast, as demonstrated in Fig. 1, strengthening the interactions does not alter the intra-chain conformational ensembles but increases the number of inter-chain contacts in the condensates. In this regard, stronger (weaker) interactions lead to a more (less) dense phase, resulting in slower (faster) conformational dynamics of IDPs in the condensates. Inter-chain interactions within condensates have been deemed as an important factor to slowing of chain dynamics, in addition to the viscosity increase led by the density increase in the dense phase.²⁶ Furthermore, increasing temperature weakens the inter-chain interactions while maintaining highly conserved intra-chain conformations, thereby facilitating the IDP conformational dynamics in the condensates.

We further investigated the short-time chain dynamics by calculating the changes in d_P−N per time unit [δ_P−N = Δd_P−N/τ₀, Figs. 2(f), S17, and S20]. δ_P−N measures the amplitudes of chain conformational sampling rate; thus, it reflects chain flexibility. Different from the reconfiguration timescales of global chain dynamics, we observed slight enhancements in chain flexibility in the condensates compared to those at the free state. Furthermore, temperature has positive effects on enhancing chain flexibility both at the free state and in the condensates. IDPs in the condensates experience high macroscopic viscosity, which slows down the global conformational dynamics of the chain. However, our results suggest that the amplitudes of chain dynamics at short timescales are largely preserved, similar to those at the free state. These findings echo previous experiments, where IDPs maintained their chain flexibility upon phase separation or in the presence of intracellular crowders.^83,84

We observed that Qc increases abruptly at the very beginning of the phase separation process, indicating rapid formation of a significant number of inter-chain contacts within small-sized droplets at the early stages [Figs. 3(a) and 3(b)]. Subsequently, the establishment of inter-chain contacts appears to be relatively slow, possibly involving the process of droplet-coalesced condensate merging, which can be hindered by the slow thermal diffusivity of the condensates.^86–88 To compare the kinetic rates of phase separation for different interaction strengths of the IDPs, we extracted the simulation times, when certain values of Qc are reached [Fig. 3(c)]. Overall, the kinetics of phase separation are accelerated by strong electrostatic interactions, as evidenced by the increasing time to completion of Qc with increasing C_salt. In addition, we found that the time to completion of Qc is strongly dependent on the interaction strengths of IDPs at different salt concentrations. Interestingly, the effects of interaction strengths on the early stages of phase separation (time to reach Qc = 0.35 and Qc = 0.50) are non-monotonic. In particular, the rate of forming phase-separated condensates is slowest when ɛ_LJ = 0.2 ɛ₀. This phenomenon is more pronounced at a high salt concentration (C_salt = 0.3M).

Multivalent interactions occurring at the inter-chain scale have been recognized as important in facilitating the phase separation of IDPs.¹⁴ Stronger (weaker) inter-chain interactions are expected to lead to faster (slower) formation of condensates during phase separation. Consequently, the non-monotonic relationship between the kinetic rates and the interaction strengths may be attributed to intra-chain interactions. Hence, we monitored the evolution of intra-chain conformational properties, described by the average R_g of the IDP monomer and the average number of intra-chain contacts in the IDP, during phase separation [Figs. 3(e) and S21]. We observed an abrupt chain compaction associated with a significant establishment of intra-chain contacts in IDPs in the early stages of the phase separation processes. These observations are more pronounced with a larger value of ɛ_LJ, where IDPs exhibit more conformational collapse when they start to phase separate, compared to those in the condensates. To compare the timescales of intra-chain collapse and inter-chain interaction establishment, we performed simulations of IDPs at the free state, initialized from the configurations obtained from high-temperature simulations. We observed that at the free state, IDPs undergo a faster and more significant collapse compared to when they are in the presence of other chains (Fig. S22). This suggests that the compaction of IDPs at the initial stage of phase separation is weakened and slowed down by the formation of inter-chain interactions, which is a slow process in phase separation. The non-monotonic decrease-followed-by-increase behavior of R_g for the IDP chain observed in phase separation demonstrates the competition between the intra-chain and inter-chain dynamics of IDPs during the phase separation process. As shown in our thermodynamic analyses (Fig. 1), the conformational ensembles of IDPs are highly conserved in the condensates with different interaction strengths. Thus, forming the extended IDP conformations in the condensates inevitably leads to opening up of the chains during phase separation. Strong interactions of IDPs may contribute to slowing down the process, particularly when ɛ_LJ is large enough to induce highly compacted IDP conformations at the free state. Meanwhile, strong interactions of IDPs lead to high degrees of chain compaction at the free state, further resulting in high thermodynamic stability for phase separation. In this regard, there is a delicate balance between kinetic efficiency and thermodynamic stability in the formation of condensates, modulated by chain interactions and external environmental factors. Therefore, we suggest that the high thermodynamic stability of the condensate does not always imply the fast formation of phase separation and vice versa.

We performed MD simulations using a simplified coarse-grained model to study the phase separation of bipolarly charged IDPs. This IDP system, which is an ideal polyampholytic chain, features fully segregated oppositely charged residues in its linear sequence. Our investigation focused on delineating the thermodynamic stability of the condensates, the conformational properties and chain dynamics of the IDPs in the condensates, and the kinetic rate of phase separation under various interaction strengths and environmental conditions. Consistent with previous studies from theoretical, computational, and experimental aspects,^22,37,48,49 we also observed that the highly collapsed IDP structures resulting from strong chain interactions lead to highly stable phase-separated condensates. This finding implies a similarity between the inter-chain interactions stabilizing the IDP-rich condensates and the intra-chain interactions driving the compaction of IDPs.^14,71,91

Interestingly, different interaction strengths lead to different degrees of IDP chain compaction, but the extended IDP conformational ensembles within the condensates remain highly conserved (Fig. 4). Previous studies using different coarse-grained models also observed more expanded conformations of protein chains in condensates, suggesting a generic feature of protein conformational properties in phase separation.^77,92 Recently, Tesei et al. developed a data-driven coarse-grained IDP model restrained by experimental data, which also revealed that IDP chains are more expanded in the dense phase compared to the dilute phase.⁹³ By varying the net charge percentages of the IDP chains, they found that the scaling exponents ν in the relationship R_g ∝ N^ν (N is the sequential distance of residues) for IDP chains in the condensates are consistently close to 0.5. This value corresponds to the Θ-state in polymers, indicating conserved ideal-chain-like IDP conformational ensembles in the condensates. In our study, we further changed the environmental conditions (temperature and salt concentration) and found that the conformational properties of the IDPs in the condensates remain unchanged. Our findings imply that the formation of condensates may serve as a protection shield, wherein IDPs can maintain their molecular-scale conformation ensembles. Since structural characteristics are essential for exerting the correct biological function, our results suggest that forming the condensates is beneficial to proteins from the functional perspective, as protein structures in the dense phase are more resistant to the alterations of external stimuli than in the dilute phase.

Due to the high viscosity caused by multi-chain assembly, IDPs in the dense phase have been consistently characterized to exhibit the slowing down of translational diffusion and conformational dynamics, compared to when they are in the dilute phase.^78–80 Here, we observed distinct interaction- and temperature-dependent behaviors on the reconfiguration timescales of global chain dynamics for IDPs at the free state and in the condensates. This is likely due to the fact that changing the interactions or environmental conditions alters the network of multi-chain interactions, further impacting the motions and chain dynamics of IDPs in the condensates. At the free state, weak interactions and high temperature induce broad conformational distributions of IDPs, thus slowing down the reconfiguration dynamics of the global chain conformation. In contrast, due to the protective effects provided by the condensates, the conformational distributions of IDPs remain similar in dense phase under different conditions, while the reconfiguration chain dynamics of IDPs are accelerated by the weak inter-chain interactions led by the small ɛ_LJ and high temperature. Our findings highlight that the macroscopic thermodynamic properties of the condensates and global chain dynamics of the IDPs in the dense phase are intimately modulated by multiple factors, primarily through inter-chain interactions.⁸² We also observed that the fast chain sampling dynamics of isolated IDPs at short timescales are preserved in the condensates (Fig. 4). These findings are in good agreement with a recent study that the rapid breaking and forming of inter-chain contacts in the condensates were detected through a combination of single-molecule spectroscopy and all-atom MD simulations.³¹ 

We observed a non-monotonic correlation between the interaction strengths of the chains and the kinetic rates for forming condensates (Fig. 4). This result highlights the delicate balance between speed and stability in biomolecular phase separation. It is widely recognized that inter-chain interactions play a critical role in phase separation: these interactions must be strong enough to form stable condensates yet weak enough to maintain liquid-like dynamics.^7,39 Recent studies have shown that favorable environmental conditions for phase separation generally lead to fast kinetics of condensate formation.^89,94 Our kinetic study emphasizes the importance of the moderate strengths of chain interactions in promoting the formation of phase-separated condensates. The interaction strengths of IDP chains have distinct impacts on different stages of phase separation, suggesting that phase separation is a multi-step nucleation, growth, and assembly process, as widely observed in recent experiments.^89,95–101 In the early stages of phase separation, a limited number of IDP chains assemble into small clusters. When these clusters are weakly formed (e.g., under high salt concentrations in our work), the single-chain properties at the molecular level may play a significant role in the kinetic formations of these low-affinity associative complexes.⁵¹ Strong chain interactions can collapse IDPs in their free states, thus slowing down the initial formation of complexes, where chains are required to open up. Once the clusters are formed, they can grow effectively by coalescing with each other in the late stage, which is less dependent on the single-chain properties. To characterize the multi-step process of phase separation, we further calculated the evolution of the number of clusters and the fraction of free chains in the kinetic simulations (Fig. S23). We successfully observed the cluster formation, coalescence, and the merging of free chains into clusters during our simulations. These three activities can occur simultaneously and are influenced by the interaction strengths and salt concentrations. Taken together, phase separation is optimized by multiple factors through underlying molecular interactions,¹⁴ ensuring the efficient formation of stable condensates, wherein the rapid liquid-like chain dynamics involving interaction forming and breaking can occur simultaneously.

To reduce computational complexity, our study focused on an ideal polyampholytic IDP system using a simplified coarse-grained model. As a result, the findings may have limited applicability to phase-separated proteins in reality. However, proteins composed solely of positively charged lysine and negatively charged glutamic acid residues have been widely used as model systems to study phase behaviors,^37,45,48,49 yielding valuable insights into the complex process of phase separation. Recently, Devarajan et al. revealed that polyampholytic sequences exhibit material properties of condensates similar to those of natural proteins with analogous charge segregation patterns.¹⁰² Furthermore, strong correlations between the sequence patterns of charged residues and phase behaviors were observed for both polyampholytic model and natural proteins using different coarse-grained models. These studies underscore the potential of applying the results obtained from model proteins to enhance our understanding of phase separation in natural proteins. Detailed energy analysis showed that the energy contributions of electrostatic and LJ potentials to the total energy for the IDP system in our study can span a wide range depending on different interaction strengths and environmental conditions (Figs. S24 and S25). This variability suggests that our results may encompass real-world protein scenarios. Rigorous verification of our findings can be made by focusing on natural proteins using transferable coarse-grained models that carefully balance molecular interactions at the microscopic level.^56,103–105

In summary, our work uncovered the role of phase-separated condensates in preserving the conformational properties of proteins under various internal and external conditions, serving as a potential advantage for maintaining structure–function relationships of proteins in the dense phase.²³ Furthermore, the observed fast short-time chain dynamics against the slow global reconfiguration dynamics at the background in the condensates may contribute to aiding efficient biochemical reactions.^7,39,40 We demonstrated that moderate strengths of chain interactions are essential to balance speed and stability for optimizing the phase separation process. Our studies offer molecular-level insights into the interplay of thermodynamic stability, dynamics, and kinetics in phase separation, providing useful guidance for engineering biomolecular condensate.

See the supplementary material for additional materials and methods, references, and figures.

X.C. acknowledges the support from the National Natural Science Foundation of China (Grant No. 32201020), the general program of Guangdong Basic and Applied Basic Research Foundation (Grant No. 2024A1515010862), the general program (Grant No. 2023A04J0083) and the Guangzhou-HKUST(GZ) joint funding program (Grant No 2023A03J0060) of the Guangzhou Municipal Science and Technology Project. X.C. was also partly supported by the Municipal Key Laboratory Construction program of the Guangzhou Municipal Science and Technology Project (Grant No. 2023A03J0003). The authors also acknowledge the Green e Materials Laboratory (GeM) and HPC + AI Intelligence Computing Center at the Hong Kong University of Science and Technology (Guangzhou) for providing computational support.

The authors have no conflicts to disclose.

Guoqing Zhang: Data curation (lead); Formal analysis (equal); Investigation (equal); Methodology (equal); Software (equal); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal). Xiakun Chu: Conceptualization (lead); Formal analysis (lead); Funding acquisition (lead); Investigation (equal); Methodology (equal); Project administration (lead); Resources (lead); Software (equal); Supervision (lead); Validation (equal); Visualization (equal); Writing – original draft (equal); Writing – review & editing (equal).

The necessary files for setting up GROMACS (version 4.5.7) simulations and analysis programs/scripts are publicly available at https://osf.io/n5q2z/. The data that support the findings of this study are available within the article and its supplementary material and from the corresponding author upon reasonable request.