Sequence and length-scale dependent dynamics in biocondensates of highly charged disordered proteins

Abstract

Highly-charged intrinsically disordered proteins (IDPs) underpin biomolecular condensate formation through liquid–liquid phase separation, yet the influence of charge sequences on the dynamics within the condensate phase remains poorly understood. Using extensive molecular dynamics simulations with explicit hydrodynamics and electrostatics, we study the dynamics in IDP condensates across different length and time scales, by systematically varying the charge sequences of the constituent IDPs. Contrary to the expectation that long-range interactions are heavily screened in dense semidilute polymer solutions, we find hydrodynamics and electrostatics significantly influence the dynamics in IDP condensates and their effects are strongly coupled to the charge sequence of the constituent IDPs. For condensates of low to intermediate-κ IDPs, where κ is a measure of the charge blockiness of the charge sequence, we find hydrodynamics dominates the dynamics up to the length scale of the chain and beyond. On the sub-chain level, segmental relaxation is highly coupled to intra-chain electrostatic correlations due to local charge patterns, where sections with more charge-balanced blocks have faster relaxation. Furthermore, the viscosity in IDP condensates is significantly length-scale-dependent, with condensates of high-κ IDPs exhibiting large difference between microscopic and macroscopic viscosity. Such length-scale-dependent viscosity may be the key to understanding the experimentally observed extremely fast molecule-level dynamics in biocondensates of highly-charged IDPs. Our findings highlight the intricate relationship between charge sequences, hydrodynamics, and electrostatics in shaping the dynamics in IDP condensates at different length and time scales.

Highly-charged intrinsically disordered proteins (IDPs) underpin biomolecular condensate formation, however, the influence of charge sequences on the dynamics within the condensate phase remains underexplored. Here, the authors use molecular dynamics simulations with explicit hydrodynamics and electrostatics to study the dynamics in IDP condensates across different length and time scales by varying the charge sequences of the constituent IDPs, showing that hydrodynamic and electrostatic effects are strongly coupled to the IDP charge sequence, in contrast with the expectation of long-range interactions being heavily screened.

Introduction

Intrinsically disordered proteins (IDPs) play a crucial role in the formation of biomolecular condensates—membraneless organelles that control critical cellular processes, including cell signaling^1,2, gene regulation^3–5, and intracellular spatial organization^6,7. Notably, highly-charged IDPs, such as Ddx4⁸, TAU⁹, and FUS^10,11, are capable of undergoing liquid–liquid phase separation (LLPS) by themselves (self-coacervation), resulting in liquid-like condensate droplets serving as hubs for various biofunctions¹². These highly-charged, self-coacervated IDPs usually carry both positive and negative charged residues, where the positive-negative charge sequences are vastly different among different IDPs or among different disordered regions¹³. Over the past decade, significant advancements have been made in highlighting how charge sequences can determine the structure of IDPs (in dilute solution)^14,15 and their LLPS thermodynamics^16,17.

In a seminal work, using all-atom simulations, Das and Pappu¹⁴ found that the linear distribution of the positive and negative residues, characterized by the charge blockiness parameter κ, governs the conformational properties of a single IDP in the dilute phase. This sequence–configuration relationship is further theoretically generalized by Sawle and Ghosh¹⁸. Furthermore, since LLPS of highly-charged IDPs is driven by the inter-chain electrostatic correlations, charge sequence plays a central role in the thermodynamics of self-coacervation. For instance, by performing field-theoretical simulations, McCarty et al.¹⁹ demonstrate that IDP charge sequences determine the phase windows for LLPS, where sequences with more blocky charges facilitate self-coacervation and lead to denser IDP condensates. The significant impact of IDP charge sequences on the thermodynamics and structure of condensates has been recently explored by simulation²⁰, theory²¹, and experiments^22,23, highlighting the potential of leveraging the sequence design principle in engineering polypeptide-based biomaterials²⁴.

While charge sequence has shown its significance in the structural and thermodynamical aspects in IDP condensates, its influence on the dynamical aspect of condensates remains largely unexplored. The dynamics of IDP coacervates—including chain dynamics, IDP collective dynamics, and viscosity—are fundamental to understanding essential processes such as the spatiotemporal evolution of condensates²⁵, condensate aging²⁶, and viscoelasticity of biocondensates²⁷. Recent theoretical study based on Field-theoretical and scaling approaches has shown that the structure and dynamics of polyampholyte-like IDP condensates are strongly coupled to the IDP charge sequences²⁸. Such predictions are more applicable to systems of very long chains where fluctuations on polymer scales are small, and prefactors are inconsequential. In many experimental relevant systems where condensates are formed by moderately short chains, there still exist significant challenges in capturing the detailed sequence-dependent dynamics. The challenge arises from the need to simultaneously account for hydrodynamics, electrostatics, and polymer connectivity in the dense phase—since these condensates typically consist of 55% ~84% water, 16% ~45% IDPs, and other small ions. All the three aforementioned forces are long-range interactions, and capturing the coupling among them in the condensate phase needs extensive molecular dynamics (MD) simulations. While all-atom MD simulations can explore detailed dynamical information at the residue level^29–31, they are prohibitively costly for exploring the condensate dynamics at polymer length scale. Recently, coarse-grained MD simulations^32–34 have shown successes in elucidating the essential physics of IDP dynamics in the condensate phase, and connecting the molecular insights to macroscopic dynamics. However, these coarse-grained MD simulations exclude hydrodynamic interactions, and often do not have explicit electrostatic interactions — both interactions are expected to be important in the highly charged and hydrated IDP condensate phase.

In this work, we employ extensive coarse-grained MD simulations that incorporate hydrodynamics, electrostatics, and polymer characteristics to study charge sequence-dependent dynamics in IDP condensates across various length and time scales. We examine both the single chain and collective dynamics in condensates formed by self-coacervation of IDPs with five representative charge sequences. For both single chain and collective dynamics, we find hydrodynamic interactions can dominate the condensate dynamics up to the length scale of the size of a IDP chain, with its impact being more pronounced for condensates formed by IDPs with less blocky charges, highlighting the necessity to explicitly consider hydrodynamics in biocondensate systems. On the sub-chain length scales, segmental relaxation is highly coupled to the local charge distribution, with more charge-neutral sub-sections having faster relaxation, highlighting the importance of intra-chain electrostatic correlations even in the dense IDP phase. Furthermore, we calculate the length-scale-dependent viscosity of IDP condensates, and find that condensates formed by highly blocky IDPs show stronger length-scale dependence in the viscosity. The striking differences between microscopic and macroscopic viscosity can be important for rationalizing the remarkably rapid molecular-scale dynamics observed in biocondensates with high bulk viscosity^29,35,36. Our results highlight the intricate relationship between charge sequence, hydrodynamics, and electrostatics in shaping the dynamics in IDP condensates at different length and time scales.

Results

To study the role of different charge sequences on the dynamics in the corresponding phase-separated condensates, we consider various permutations of positively and negatively charged monomers on a modeled IDP chain with a total of 25 lysine (K) and 25 glutamate (E) residues. In this article, we focus on five typical charge sequences (sv15, sv20, sv25, sv28, sv30; see schematic illustration in Fig. 1A) that are capable of self-coacervation¹⁹, whose charge organizations can be respectively characterized by the blockiness parameter κ = 0.135, 0.272, 0.528, 0.767, 1.0, first introduced by Das and Pappu¹⁴. Here, κ = 0 corresponds to a sequence with alternating positive–negative distribution, and κ = 1.0 to fully segregated charges (all positive followed by all negative, Fig. 1A). Thus, the five sequences in this study cover a wide spectrum of representative of charge blockinesses from nearly alternative to fully segregated of positive-negative domains. We then prepare coacervates via self-coacervation of these IDPs in a large simulation box (Fig. 1B, also see details in Fig. S1 in the SI). The resulting coacervates have IDP concentrations (ranging from small to large κ) of ρ_p = 16.0%, 21.0%, 28.0%, 37%, 45.0%, respectively, consistent with the concentration range obtained in most experiments.

Fig. 1. Sequence variants of highly charged IDP and the simulation procedure for obtaining condensates compositions.

A Five modeled IDP sequences of glutamate and lysine considered in this work. The middle column shows the actual sequences, with Glu(E) residues represented in red and Lys(K) residues in blue. The left column shows the label of each sequence variant (sv15 ~sv30), and the right column gives the corresponding κ values (0.135 ~1.0) introduced previously by Das and Pappu¹⁴. B Illustrations of the procedure in obtaining IDP condensate compositions from simulating liquid-liquid phase separation of each IDP sequence with water (cyan) and ions (green), showing in the simulation snapshots.

Water, ions, IDP polymers are included in our simulations (Fig. 1B), and the long-range electrostatics are explicitly modeled. To account for hydrodynamic interactions among all the constituent components, we use the pairwise Dissipative Particle Dynamics (DPD) thermostat, which conserves local momentum and as such, the hydrodynamics are captured from nanoscale to mesoscale^37–39. Other simulation details, such as water, ion, and polymers models, DPD thermostat, and electrostatic interactions, are given in “Method” section or “Supplementary Methods” section of the SI.

The importance of hydrodynamics on IDP condensate dynamics

Since different charge sequences result in IDP condensates with different polymer-to-water ratios, we expect the corresponding dynamics in condensates to vary significantly. A central question is the role of hydrodynamics on the IDP dynamics, considering that these condensates contain approximately 55% ~84% water.

To this end, we calculate the monomer mean-squared-displacement (MSD), 〈ΔR²(t)〉, as a function of time

$$⟨\mathrm{\Delta }{R}^2\left(t\right)⟩~t^{\beta },$$ 1

where 〈…〉 denotes ensemble average, and β = 1 corresponds to normal diffusion and β < 1 indicates sub-diffusive motion. If hydrodynamics is important, the MSD in the subdiffusive regime should follow the ~t^2/3 Zimm-like dynamics; otherwise, a Rouse-like scaling of ~t^1/2 should be expected due to the screening of hydrodynamics in solutions with high-concentration of polymers^40,41.

Figure 2 A shows monomer dynamics (averaged over all beads) in condensates formed by three of the IDP sequences (sv15 ~sv25, or κ = 0.14–0.53) exhibit a clear ~t^2/3 scaling in the whole sub-diffusive regime, indicative of the Zimm-like dynamics as a result of hydrodynamics-mediated polymer interactions. Note that hydrodynamics dominates the length scales well beyond the size of the IDPs, as evidenced by the consistent ΔR²(t) ~ t^2/3 scaling above their largest (sv30) radius of gyrations (R_g) (Fig. 2A). These results show that, for condensates of most IDPs, hydrodynamics must be explicitly accounted for to capture the correct dynamics up to chain-level length scales. The inter-chain electrostatic correlations among IDPs determine the water concentration of the resulted condensates, and consequently, determine the importance of hydrodynamics. For IDPs with charge sequences sv15 ~sv25 (κ = 0.14–0.53), the corresponding condensates have 62–84% water, and hydrodynamics are not be effectively screened. In condensates of highly blocky charges (sv28 and sv30, or κ = 0.76 and 1.0), hydrodynamic interactions are partially screened due to the high concentration of the polymers (ρ_p = 37% and 45%), and the subdiffusive dynamics deviate slightly from Zimm dynamics, but still faster than Rouse dynamics (~t^1/2).

Fig. 2. Monomer-level dynamics, collective relaxations, and macroscopic rheology of IDP condensates.

A Monomer MSD of condensate each formed by self-coacervation of sv15 ~sv30 (κ = 0.135–1.0) IDPs, respectively. The ~τ^2/3 scaling is indicative of the hydrodynamics-dominated Zimm-like dynamics, while the ~τ^1/2 scaling represents Rouse-like dynamics. B Relaxation time in IDP collective dynamics as a function of wavenumber for different IDP condensates. The ~q⁻³ in the log-log plot shows the hydrodynamics-dominated regime. C IDP chain diffusion coefficients in different condensates, and the corresponding bulk viscosities obtained by using the stress relaxation function G(t) (see details in SI).

The importance of hydrodynamics is more clearly manifested in the IDP collective dynamics, as showed in Fig. 2B. Here, we access IDP collective dynamics by calculating their coherent intermediate scattering function F(q, t):

$$F\left(q,t\right)=\frac{1}{N_b}{\sum }_i^{N_b}{\sum }_j^{N_b}⟨\exp \left[i2\pi \mathit{q}\cdot \left({\mathit{r}}_i\left(t\right)-{\mathit{r}}_j\left(0\right)\right)\right]⟩,$$ 2

where q is the wavevector with its magnitude q corresponding to a length scale of 1/q, N_b is the total IDP monomers in the condensates, and r_i is the position of the ith monomers. We then obtain the q-dependent relaxation time by fitting the normalized intermediate scattering function to a stretch exponential decay as $F\left(q,t\right)/F\left(q,0\right)=\exp \left[-{\left(\frac{t}{\tau }\right)}^{\mu }\right]$. For the collective relaxation time, a τ ~ q⁻³ scaling will be expected for Zimm-like dynamics, and a τ ~ q⁻² scaling is expected for Rouse-like dynamics⁴⁰. Figure 2B clearly shows a τ ~ q⁻³ scaling. Note that the q⁻³ scaling holds for qR_g <1, highlighting that hydrodynamics have persistent impact for length scales larger than the polymer size in the IDP collective dynamics.

We note that our chain length (N = 50, the most widely used chain length in IDP simulations) is moderately short, and Zimm-to-Rouse transition in subdiffusive region is expected to appear if much longer chains are used. Nevertheless, IDPs with short to intermediate chain length (N = 10–100) are widely used in many experimental polypeptide-based biocondensates systems^24,42,43, which generally results in condensates with more than 70% of water. As such, we expect our results are representative of many experimental systems, and the hydrodynamics effects will be important for most commonly studied IDP condensate systems.

At long times, the monomer reaches the diffusive regime, and monomer diffusion is similar to chain diffusion. In Fig. 2C, we plot the chain diffusivity and the bulk viscosity for different IDP condensates. The chain diffusivity D is obtained by the center-of-mass MSD in the diffusive regime (see details in Fig. S3 in the SI), and the condensate bulk viscosity is given by:

$$\eta ={\int }_0^{\infty }G\left(t\right)dt,$$ 3

where G(t) is the stress autocorrelation function (see details in the SI). Figure 2C shows the IDP with small κ diffuse much faster, due to the lower bulk viscosity of the coacervate matrix, consistent with previous study³⁴. The importance of charge sequences on condensate viscosity will be discussed in detail in the later section “Length-scale-dependent Viscosity in IDP Condensates”.

Charge pattern-dependent segmental dynamics

So far, we have examined the IDP dynamics on the monomer and chain level for different charge sequences and highlighted the importance of the hydrodynamics. Another long-range interaction to examine is the electrostatics, which is expected to influence the local sub-chain dynamics, due to the fact that sections in IDPs can have high variations of local charge patterns in different locations of the chain. As such, it is of interest to know how the local charge patterns influence the sub-chain relaxation.

To this end, we calculate the relaxation time of a section that contains s monomers in different locations of the IDP chain. The location of a section is characterized by the difference between its center bond/monomer index (N_i) and center bond index of the whole chain (25), as illustrated in Fig. 3A. For instance, N_i − 25 = 0 means the section locates at the chain center, and more negative and positive values refers to the locations closer to chain end (Fig. 3A). To access the dynamics of a particular section with s monomers, we calculate its discrete relaxation mode at time t as

$$\mathbf{X}\left(t\right)=\frac{1}{s}{\sum }_{i=1}^s{\mathbf{r}}_i\left(t\right)\cos \left(\frac{\pi \left(i-\frac{1}{2}\right)}{s}\right).$$ 4

Subsequently, the relaxation time τ_s of the section can be obtained by fitting an exponential decay to 〈X_p(t) ⋅ X_p(0)〉.

Fig. 3. Segmental relaxation time for sub-chains with s monomers located at different locations of the IDP chain in biocondensates.

A s = 10 for different IDP condensates with salt concentration at 0.1M. B s = 5, C s = 10 in sv30-condensate with salt concentration at 0.1 M (green curve) and 0.5 M salt (pink curve). The arrow points to the corresponding positions of the section. The blue shading marks the more charge-balanced sections(faster relaxation), the yellow shading locates the more high net-charge blocks(slower relaxation). N_i − 25 means the center of the sections relative to the chain center.

Figure 3 demonstrates that, for sections with s monomers, τ_s shows significant heterogeneous relaxations in different locations of the IDP chains. The variations in relaxation time are stronger for IDPs with higher charge blockiness κ. For instance, the relaxation time of a section with length s = 10 in sv30 IDP condensate can be differ by more than 2 folds, where the variations in sv15 is about 40% (Fig. 3A). Similar trend is seen for s = 5 (Fig. 3B). Interestingly, sections with more balanced charges show faster relaxation, and uniform charged blocks exhibit slowest dynamics (Fig. 3). This intriguing pattern-dependent dynamics can be understood by the correlation blob picture in polyampholyte physics: If the sections contains more balanced positive and negative charges, the local electrostatic blobs have smaller sizes^44–46 where their rearrangement takes less time, resulting in faster relaxation.

It is somewhat surprising that electrostatic correlations still have such a strong effect on the chain dynamics in the highly densed phase. Indeed, in the Debye-Hückel approximation, electrostatic interaction is expected to be screened beyond the length scale of the Debye length $\lambda =\frac{0.3\mathrm{nm}}{\sqrt{I\left(M\right)}}$, where I is the ionic strength. Our IDP condensate systems typically contain 0.1M monovalent ions, corresponding to a nominal Debye length of λ = 0.95σ, where σ is the size of the monomer. However, our results show that the relaxation of a section of s = 10 monomers significantly depends on the charge distribution, indicating that there is still strong intra-chain electrostatic correlation well beyond the Debye length. Figure 3C further demonstrates that, even at high concentration of c = 0.5M (λ = 0.43σ), there is still strong intra-chain electrostatic correlation. The strong intra-chain electrostatic correlation is likely due to chain connectivity, which results in less screening compared to the case of small mobile ions⁴⁷. Our results also qualitatively agree with a recent study based on field-theoretical and scaling approach, where the bulk viscosity of the salt-added IDP condensates is in general predicted to increase with IDP charged blockiness for random sequences²⁸ As such, similar to the case of hydrodynamics, our results suggest that it is necessary to explicitly model the long-range electrostatic interactions to predict the correct sub-chain dynamics in IDP condensates.

Length-scale-dependent viscosity in IDP condensates

Another important property of the condensates is their viscosity. It is known that the bulk viscosity of biocondensates is, in general, orders of magnitude larger than that of the dilute aqueous phase. However, recent experiments revealed that the molecular-level dynamics in IDP condensates are considerably faster than predicted for a fluid with high bulk viscosity^29,35,36. This suggests that the viscosity at local, small length scales in biocondensates is much smaller than the bulk viscosity, i.e., biocondensate viscosity is length-scale dependent. Here, we quantitatively calculate the length-scale-dependent viscosity in IDP condensates and explore its relations with IDP charge sequences.

To this end, we calculate the q-dependent transverse-current autocorrelation function (TCAF), first introduced by Palmer⁴⁸:

$$C_T\left(q,t\right)=⟨J\left(\mathit{q},t\right)J\left(\mathit{q},0\right)⟩,$$ 5

where q is the wavevector. For an N-particle system, J(q, t) is the transverse momentum field at time t defined as

$$J\left(\mathit{q},t\right)={\sum }_{j=1}^N{\mathit{p}}_{\perp }^{\mathit{j}}\exp \left(i\mathit{q}\cdot {\mathit{x}}_{\mathit{j}}\left(\mathit{t}\right)\right),$$ 6

where ${\mathit{p}}_{\perp }^{\mathit{j}}$ is the momentum component of j particle perpendicular to the wavevector q. In practice, J(q, t) is calculated in simulation by summing the sin and cos parts of the transverse momentum fields⁴⁸:

$$J\left(q,t\right)={\sum }_{j=1}^N\widehat{{\mathit{q}}_{\perp }}\cdot {\mathit{p}}^{\mathit{j}}\left(t\right)\cos \left(\mathit{q}\cdot {\mathit{x}}_{\mathit{j}}\left(\mathit{t}\right)\right)$$ 7

and

$$J\left(k,t\right)={\sum }_{j=1}^N\widehat{{\mathit{q}}_{\perp }}\cdot {\mathit{p}}^{\mathit{j}}\left(\mathit{t}\right)\sin \left(\mathit{q}\cdot {\mathit{x}}_{\mathit{j}}\left(\mathit{t}\right)\right),$$ 8

with $\widehat{{\mathit{q}}_{\perp }}$ being the unit vector perpendicular to q. The q-dependent viscosity η(q) is then calculated by refs. ^49,50

$$\eta \left(q\right)=\frac{\rho }{q^2\mathrm{\Phi }},$$ 9

where ρ is the number density in simulation and Φ is the time integral of the normalized TCAF, C_T(q, t)/C_T(q, 0). Other details are given in the SI.

Figure 4 A shows representative normalized TCAFs for the sv30 condensates at different wavenumbers. Note that for q <2, most TCAFs show clear oscillations around zero, signaling that the selected length scales enter the viscoelastic regime. Since the wavenumber corresponding to the size of one monomer in the simulation is q₀ = 2πσ ≈ 6 (σ = 1 is the simulation length unit), Fig. 4A suggests that the viscoelastic regimes apply to length scales larger than a few monomers, which is expected for a crowded macromolecular fluid.

Fig. 4. The q-dependent transverse-current autocorrelation function (TCAF) and length-scale-dependent viscosity of IDP coacervates.

A Normalized TCAFs for sv30 condensate under some representative wavenumbers. The tails of TCAFs in small q at long-time scales are not shown for better visualization of the TCAFs in intermediate to large wavenumber. B Length-dependent viscosity of sv15~sv30 condensates as a function of wavenumber, where the wavenumber is normalized by the wavelength corresponding to the simulation length unit q₀ = 2πσ.

Figure 4B shows that the local viscosity, η(q), at a given length scale is different for different sequences, with the difference being larger at smaller q. At the bulk scale, the viscosity of sv30 condensate η(sv30) is more than 6.6 times larger than η(sv15) (Fig. 2C). Interestingly, the viscosity of the different IDP condensates appears to follow η~ρ^1.71 (See Fig. S5 for details in the SI). This exponent is very close to the scaling theory of semidilute neutral polymer solutions, which predicts an exponent of 2.0 for theta solvent condition and 1.3 for good solvent condition⁴¹. Indeed, at the bulk level, complexes formed by high concentrations of polyions containing both positive and negative charges resemble the characteristics of semidilute neutral polymer solutions⁵¹. Such a high exponent (1.71) in the viscosity-density scaling is considerately stronger than the η~c^1/2 scaling for semidilute homopolyelectrolyte solutions⁵². This result indicates that condensates formed by different-sequence IDPs should be treated differently in predicting the viscosity–concentration relation.

More importantly, the increase of viscosity with length scale is much steeper in condensates formed by high-κ IDPs, indicating their bulk viscosity is much higher than the viscosity at small length scale. Indeed, the bulk viscosity (η shown in Fig. 2C) is over 26 times larger than the local viscosity at the monomer level (η(q/q₀ = 1)) in sv30 condensate, while it is about 5 times larger in the case of sv15 condensate. Therefore, our results highlight that coacervates formed by high-κ IDPs will have significant different viscosities across length scales. We expect such difference in viscosity to be more pronounced for condensates formed by complexation of purely positive and purely negative IDPs, since the constituent polymers (polycations and polyanions) have even higher charge blockiness than sv30. Our results may explain the recent experimental findings showing that the small molecule dynamics within the highly charged biocondensates is much faster than anticipated based on the condensate bulk viscosity^29,35,36. This increased bulk viscosity with charged blockiness is again in agreement with the recent theoretical study²⁸.

Discussion

Our results reveal that charge sequences have intricate interplay with long-range interactions—hydrodynamics and electrostatics—in determining the dynamics of IDP condensates. While it is commonly assumed that long-range interactions such as hydrodynamics and electrostatics are heavily screened in dense semidilute polymer solutions, our results demonstrate that these interactions remain critical in IDP condensates and their effects are strongly coupled to the charge sequences of constituent IDPs.

In particular, due to the high water content (55–84%), hydrodynamics effects persist in both chain dynamics and collective dynamics even for length scales exceeding the size of moderately short IDP chains typically used in simulations and experiments. The subchain dynamics are strongly coupled to local charge sequence heterogeneity, where more balanced charge blocks result in much faster dynamics. Remarkably, electrostatic correlations remain influential beyond the nominal Debye screening length due to chain connectivity, which results in less screening compared to small mobile ions.

By calculating the length-scale-dependent viscosity in IDP condensates, we find that condensates formed by high-κ IDPs have large differences between microscopic and macroscopic viscosity—up to 26-fold for sv30 condensate compared to 5-fold for sv15 condensate. This length-scale dependence in viscosity provides a plausible explanation for recent experimental findings showing considerably faster small-molecule dynamics within highly charged biocondensates than anticipated based on bulk viscosity. The viscosity scaling exponent (η~c^1.71) falls between theta and good solvent predictions for neutral polymers, a regime where IDP condensates bearing both positive and negative charges display macroscopic behavior characteristic of semidilute neutral polymer solutions.

Although our study focuses on condensates formed by self-coacervation of identical IDPs, we expect these results to apply broadly to condensate systems containing different charged macromolecular species, including protein complexes, protein-RNA condensates, and polycation-polyanion complex coacervates. We anticipate that greater contrast in charge patterns among species will produce more pronounced length-scale-dependent dynamical behaviors. For example, polyelectrolyte complex coacervates formed by complexation of oppositely charged polyelectrolyte solutions should exhibit even more striking differences between microscopic and macroscopic viscosities due to their higher charge blockiness. Our findings establish charge sequence as a key regulator of condensate dynamics and highlight the necessity of explicitly modeling long-range interactions to predict the correct dynamical behavior in these biologically relevant systems.

Methods

Coarse-grained model and GCMe-DPD simulation methodology

In this study, we use extensive coarse-grained molecular dynamics simulations that explicitly incorporate hydrodynamics, electrostatics, and polymer characteristics to examine charge sequence-dependent dynamics in IDP condensates across various length and time scales. Our simulations employ the Gaussian Core Model with Smeared Electrostatic (GCMe) Interactions^53,54 combined with dissipative-particle-dynamics (DPD) thermostat to capture hydrodynamic interactions^55–57. This method, which we refer to as the Gaussian Core Model with Smeared Electrostatics and Dissipative Particle Dynamics (GCMe-DPD), enables efficient modeling of the equilibrium dynamics of highly charged sequence-dependent IDP condensates systems. Due to their theoretically tractable formula, the soft-core Gaussian potentials used in GCMe can be analytically derived respectively from Gaussian-smeared mass and charges⁵³. Compared to Lennard-Jones-based bead-spring models^58–60, the soft-core potentials are appropriate to model highly coarse-grained systems that allow particles to slightly overlap.

Simulation details

In our simulations, the IDP monomers, counterions, and solvent molecules (water) are represented as coarse-grained beads, with each bead having a Gaussian distribution in mass and charge density around their center. We set the excluded volume interactions to be the same among all species to represent good solvent quality for the polymers. All the simulations are performed using LAMMPS (Large-scale Atomic/Molecular Massively Parallel Simulator)⁶¹. For LLPS simulation (with dilute phase), we run a total time steps of 2 × 10⁶ time steps, and the second half of the simulation trajectories are used to obtain the dense phase compositions. Then we utilize the dense phase compositions as input for simulation of the condensate phase. For simulation of the condensate phase, we first run 10⁶ steps for equilibrium, and run additional long-time simulation of 2 × 10⁷ steps for data analysis where the simulation box has dimensions of 40 × 40 × 40σ³ containing a total of 160,000 IDPs, counterions, and solvent beads. All the simulations are performed under canonical ensemble (NVT) with the integration time step of Δt = 0.01τ. The energy unit is taken as the thermal energy k_BT at room temperature, and the time unit is given by $\tau =\sqrt{m{\sigma }^2/k_{B}T}$ where m is the mass of a bead assumed to be the same for all the particles. With m, σ, and k_BT being the units of mass, length, and energy, respectively, the time unit τ is also 1. Additional simulation details, including choice of interaction parameters, the simulation setup, and analysis methods, are provided in “Supplementary Methods” section in the SI.

Author contributions

Haoke Zhou: Methodology, Software, Investigation, Visualization, Writing—original draft. Zongpei Wu: Software. Lingxiang Jiang: Suggestion. Zhen-Gang Wang: Supervision, Writing— review and editing. Shensheng Chen: Conceptualization, Visualization, Supervision, Writing— review and editing, Funding acquisition.

Peer review

Peer review information

Communications Chemistry thanks Artem Rumyantsev and the other, anonymous, reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Data availability

All data are included in the article and/or in the Supplementary Information. Two binary files representing initial and final configurations of the simulation trajectories are uploaded in Figshare repository (10.6084/m9.figshare.30653600). Other source data and codes are available from the corresponding author upon request.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at 10.1038/s42004-026-01903-0.