Sequence-dependent material properties of biomolecular condensates and their relation to dilute phase conformations.

Material properties of phase-separated biomolecular condensates, enriched with disordered proteins, dictate many cellular functions. Contrary to the progress made in understanding the sequence-dependent phase separation of proteins, little is known about the sequence determinants of condensate material properties. Using the hydropathy scale and Martini models, we computationally decipher these relationships for charge-rich disordered protein condensates. Our computations yield dynamical, rheological, and interfacial properties of condensates that are quantitatively comparable with experimentally characterized condensates. Interestingly, we find that the material properties of model and natural proteins respond similarly to charge segregation, despite different sequence compositions. Molecular interactions within the condensates closely resemble those within the single-chain ensembles. Consequently, the material properties strongly correlate with molecular contact dynamics and single-chain structural properties. We demonstrate the potential to harness the sequence characteristics of disordered proteins for predicting and engineering the material properties of functional condensates, with insights from the dilute phase properties.

Sequence-Dependent Material Properties of Biomolecular Codensates and their Relation to Dilute Phase Conformations.

Material properties of phase-separated biomolecular assemblies, enriched with disordered proteins, dictate their ability to participate in many cellular functions. Despite the significant effort dedicated to understanding how the sequence of the disordered protein drives its phase separation to form condensates, little is known about the sequence determinants of condensate material properties. Here, we computationally decipher these relationships for charged disordered proteins using model sequences comprised of glutamic acid and lysine residues as well as naturally occurring sequences of LAF1's RGG domain and DDX4's N-terminal domain. We do so by delineating how the arrangement of oppositely charged residues within these sequences influences the dynamical, rheological, and interfacial properties of the condensed phase through equilibrium and non-equilibrium molecular simulations using the hydropathy scale and Martini models. Our computations yield material properties that are quantitatively comparable with experimentally characterized condensate systems. Interestingly, we find that the material properties of both the model and natural proteins respond similarly to the segregation of charges, despite their very different sequence compositions. Condensates of the highly charge-segregated sequences exhibit slower dynamics than the uniformly charge-patterned sequences, because of their comparatively long-lived molecular contacts between oppositely charged residues. Surprisingly, the molecular interactions within the condensate are highly similar to those within a single-chain for all sequences. Consequently, the condensate material properties of charged disordered proteins are strongly correlated with their dense phase contact dynamics and their single-chain structural properties. Our findings demonstrate the potential to harness the sequence characteristics of disordered proteins for predicting and engineering the material properties of functional condensates, with insights from the dilute phase properties.

Challenges in studying the liquid-to-solid phase transitions of proteins using computer simulations.

"Membraneless organelles," also referred to as biomolecular condensates, perform a variety of cellular functions and their dysregulation is implicated in cancer and neurodegeneration. In the last two decades, liquid-liquid phase separation (LLPS) of intrinsically disordered and multidomain proteins has emerged as a plausible mechanism underlying the formation of various biomolecular condensates. Further, the occurrence of liquid-to-solid transitions within liquid-like condensates may give rise to amyloid structures, implying a biophysical link between phase separation and protein aggregation. Despite significant advances, uncovering the microscopic details of liquid-to-solid phase transitions using experiments remains a considerable challenge and presents an exciting opportunity for the development of computational models which provide valuable, complementary insights into the underlying phenomenon. In this review, we first highlight recent biophysical studies which provide new insights into the molecular mechanisms underlying liquid-to-solid (fibril) phase transitions of folded, disordered and multi-domain proteins. Next, we summarize the range of computational models used to study protein aggregation and phase separation. Finally, we discuss recent computational approaches which attempt to capture the underlying physics of liquid-to-solid transitions along with their merits and shortcomings.

Modified Smoluchowski Rate Equations for Aggregation and Fragmentation in Finite Systems.

Protein self-assembly into supramolecular structures is important for cell biology. Theoretical methods employed to investigate protein aggregation and analogous processes include molecular dynamics simulations, stochastic models, and deterministic rate equations based on the mass-action law. In molecular dynamics simulations, the computation cost limits the system size, simulation length, and number of simulation repeats. Therefore, it is of practical interest to develop new methods for the kinetic analysis of simulations. In this work we consider the Smoluchowski rate equations modified to account for reversible aggregation in finite systems. We present several examples and argue that the modified Smoluchowski equations combined with Monte Carlo simulations of the corresponding master equation provide an effective tool for developing kinetic models of peptide aggregation in molecular dynamics simulations.

Side Chain Geometry Determines the Fibrillation Propensity of a Minimal Two-Beads-per-Residue Peptide Model.

The molecular mechanism of fibrillation is an important issue for understanding peptide aggregation. In our previous work, we demonstrated that the interchain attraction and intrachain bending stiffness control the aggregation kinetics and transient aggregate morphologies of a one-bead-per-residue implicit solvent peptide model. However, that model did not lead to fibrillation. In this work, we study the molecular origin of fibril formation using a two-beads-per-residue model, where one bead represents the backbone residue atoms and the other the side chain atoms. We show that the side chain geometry determines the fibrillation propensity that is further modulated by the modified terminal beads. This allows us to bring out the effects of side chain geometry and terminal capping on the fibrillation propensity. Our model does not assume a secondary structure and is, perhaps, the simplest bead-based chain model leading to fibrillation.

Diverse Aggregation Kinetics Predicted by a Coarse-Grained Peptide Model.

Protein and peptide aggregation is a ubiquitous phenomenon with implications in medicine, pharmaceutical industry, and materials science. An important issue in peptide aggregation is the molecular mechanism of aggregate nucleation and growth. In many experimental studies, sigmoidal kinetics curves show a clear lag phase ascribed to nucleation; however, experimental studies also show downhill kinetics curves, where the monomers decay continuously and no lag phase can be seen. In this work, we study peptide aggregation kinetics using a coarse-grained implicit solvent model introduced in our previous work. Our simulations explore the hypothesis that the interplay between interchain attraction and intrachain bending stiffness controls the aggregation kinetics and transient aggregate morphologies. Indeed, our model reproduces the aggregation modes seen in experiment: no observed aggregation, nucleated aggregation, and rapid downhill aggregation. We find that the interaction strength is the primary parameter determining the aggregation mode, whereas the stiffness is a secondary parameter modulating the transient morphologies and aggregation rates: more attractive and stiff chains aggregate more rapidly and the transient morphologies are more ordered. We also explore the effects of the initial monomer concentration and the chain length. As the concentration decreases, the aggregation mode shifts from downhill to nucleated and no-aggregation. This concentration effect is in line with an experimental observation that the transition between downhill and nucleated kinetics is concentration-dependent. We find that longer peptides can aggregate at conditions where short peptides do not aggregate at all. It supports an experimental observation that the elongation of a homopeptide, e.g., polyglutamine, can increase the aggregation propensity.

Clustering and Fibril Formation during GNNQQNY Aggregation: A Molecular Dynamics Study.

The precise kinetic pathways of peptide clustering and fibril formation are not fully understood. Here we study the initial clustering kinetics and transient cluster morphologies during aggregation of the heptapeptide fragment GNNQQNY from the yeast prion protein Sup35. We use a mid-resolution coarse-grained molecular dynamics model of Bereau and Deserno to explore the aggregation pathways from the initial random distribution of free monomers to the formation of large clusters. By increasing the system size to 72 peptides we could follow directly the molecular events leading to the formation of stable fibril-like structures. To quantify those structures we developed a new cluster helicity parameter. We found that the formation of fibril-like structures is a cooperative processes that requires a critical number of monomers, M⋆≈25, in a cluster. The terminal tyrosine residue is the structural determinant in the formation of helical fibril-like structures. This work supports and quantifies the two-step aggregation model where the initially formed amorphous clusters grow and, when they are large enough, rearrange into mature twisted structures. However, in addition to the nucleated fibrillation, growing aggregates undergo further internal reorganization, which leads to more compact structures of large aggregates.