Kinetic interplay between droplet maturation and coalescence modulates shape of aged protein condensates

Abstract

Biomolecular condensates formed by the process of liquid-liquid phase separation (LLPS) play diverse roles inside cells, from spatiotemporal compartmentalisation to speeding up chemical reactions. Upon maturation, the liquid-like properties of condensates, which underpin their functions, are gradually lost, eventually giving rise to solid-like states with potential pathological implications. Enhancement of inter-protein interactions is one of the main mechanisms suggested to trigger the formation of solid-like condensates. To gain a molecular-level understanding of how the accumulation of stronger interactions among proteins inside condensates affect the kinetic and thermodynamic properties of biomolecular condensates, and their shapes over time, we develop a tailored coarse-grained model of proteins that transition from establishing weak to stronger inter-protein interactions inside condensates. Our simulations reveal that the fast accumulation of strongly binding proteins during the nucleation and growth stages of condensate formation results in aspherical solid-like condensates. In contrast, when strong inter-protein interactions appear only after the equilibrium condensate has been formed, or when they accumulate slowly over time with respect to the time needed for droplets to fuse and grow, spherical solid-like droplets emerge. By conducting atomistic potential-of-mean-force simulations of NUP-98 peptides-prone to forming inter-protein [Formula: see text]-sheets-we observe that formation of inter-peptide [Formula: see text]-sheets increases the strength of the interactions consistently with the loss of liquid-like condensate properties we observe at the coarse-grained level. Overall, our work aids in elucidating fundamental molecular, kinetic, and thermodynamic mechanisms linking the rate of change in protein interaction strength to condensate shape and maturation during ageing.

Figure 1

(A) Coarse-grained representation of intrinsically disordered proteins composed of stickers of type A (depicted as blue beads), stickers of type B (depicted as red beads), and spacers (depicted as grey beads). The model considers transient weak interactions among spacer–spacer, spacer–sticker, and homotypic sticker–sticker pairs (i.e., sticker A–sticker A and sticker B–sticker B pairs; grey curve), and strong longer-lived interactions among heterotypic sticker A–sticker B pairs (red curve). A Lennard-Jones potential of different well-depths is used to represent the associative interactions among the different types of beads: ${\epsilon }_D$ is used for interactions between weakly binding bead pairs, and ${\epsilon }_S$ for interactions between strongly binding ‘sticker A–sticker B’ bead pairs. Each bead represents a group of $\sim$ 6–8 amino acids. Each protein is composed of 39 beads: 3 blue beads, 2 red beads and 34 grey ones. The excluded volume ($\sigma$) of each segment type is the same. Results for an alternative CG representation of strong protein binding and a different protein sequence patterning to that depicted in (A) are available in the Supplementary Information. (B) Time-evolution of the protein diffusion coefficient (D) in the condensed phase for different interaction strengths ${\epsilon }_S$ (in $k_B$T) between strongly-binding protein segments (please note that ${\epsilon }_S=10{\epsilon }_D$). The horizontal black dashed line represents the kinetic threshold of our simulation timescale that distinguishes between ergodic liquid-like behaviour and ageing (transient liquid-to-solid) behaviour. Interaction strengths lower than $5.25k_{\mathrm{B}}$T between the strongly-binding segments permit liquid-like behaviour (up to ${\epsilon }_S=3.5k_{\mathrm{B}}$T and ${\epsilon }_D=0.35k_{\mathrm{B}}$T where LLPS is no longer possible), while equal or higher strengths lead to the gradual deceleration of protein mobility over time as shown by D. However, in absence of strongly-binding segments (i.e., where all beads bind to one another with uniformly weak binding strength), liquid-like behaviour can be still observed even at ${\epsilon }_D$ values of $0.66k_{\mathrm{B}}$T (empty blue triangle). Black arrows indicate the time dependent behaviour of condensates over time in the liquid-like (Top) and ageing regimes (Bottom). The time evolution snapshots of the condensate corresponds to systems with ${\epsilon }_S=5k_{\mathrm{B}}$T (Top) and ${\epsilon }_S=6.6k_{\mathrm{B}}$T (Bottom). Please note that these snapshots do not correspond to the NVT bulk systems employed to compute the diffusion coefficient in the B left panel.

Figure 2

(A) Thermal hysteresis of the condensates probed via coarse-grained protein simulations. (Top panel) Time-evolution starting from an homogeneous system where inter-protein interactions are moderate (i.e., ${\epsilon }_S=5k_{\mathrm{B}}T$; ${\epsilon }_D=0.5k_{\mathrm{B}}T$). (Bottom panel) Time evolution at the same conditions above, although starting from a matured condensate that was formed under ageing regime conditions (i.e., strong inter-protein interactions of ${\epsilon }_S=6.6k_{\mathrm{B}}T$). Note that in our model, temperature T is proportional to $\frac{1}{{\epsilon }_{D(S)}}$. (B) Number of strong interactions as a function of time within a preformed spherical condensate (${\overline{N}}_{s-s}$) normalised by the typical strong contact threshold (horizontal dashed line) that induces ageing behaviour of protein condensates at those conditions (i.e., number of strong interactions per condensate volume found at the cross-over of the blue curve with the kinetic threshold shown in Fig. 1B). Snapshots of the condensate shape as a function of time are shown. Protein segments that do not participate in strengthen contacts are depicted in grey, while those involved in clusters of stronger interactions are coloured in green. The protein interaction strength of this simulation was set to ${\epsilon }_S=6.6k_{\mathrm{B}}$T, the same set value for the condensates shown in the bottom left panel of Fig. 1B.

Figure 3

Competition between droplet coalescence time and maturation rate as a function of strong inter-protein interactions (${\epsilon }_S$) for different droplet sizes. Blue curve, termed ’border’, depicts the lapse of time before proteins enter into the ageing (kinetically-trapped) regime due to the emergence of long-lived contacts. The blue curve is a kinetic line that is defined as the intersection of the different diffusion curves and the horizontal kinetic threshold shown in Fig. 1B (Left panel). Filled squares represent the time required for two spherical tangent droplets of a given size to fuse into a single spherical condensate, while empty squares depict the (arbitrary) maximum simulated time for tangent droplets that did not achieve complete coalescence or shown strong trends of the formation of a single spherical condensate. Snapshots of the typical time-evolution of coalescing droplets in both regimes at ${\epsilon }_S=5.25k_{\mathrm{B}}$T are included for droplet sizes of 100 (liquid-like regime) and 200 proteins (ageing regime).

Figure 4

Atomistic potential-of-mean-force (PMF) dissociation curve of an 8-amino acid segment (PDB code: 6BZM) of NUP-98 protein from a $\beta$-sheet structure of 4 peptides (of the same sequence) as a function of the center of mass distance (COM) using the a99SB-disp force field. Red curve depicts the interaction strength among peptides with a well-defined folded structure, kinked $\beta$-sheet structure, while grey curve represents the interaction strength among the same segments but when they are disordered. The binding interaction strength difference between disordered and ordered peptides differs by almost an order of magnitude. The same calculations performed using the CHARM36m force field are shown in Fig. S9, where the obtained difference in binding strength between disordered and structured peptides is of the same order.