Session S06: Biomolecular Phase Separation I - Interactions, Thermodynamics and Mechanics

A Molecular View of Liquid-Liquid Phase Separation of Disordered Proteins

Demixing of protein solutions is a well-known phenomenon that has gained renewed interest due to its role in forming membraneless organelles, especially in the context of intrinsically disordered proteins (IDPs). The molecular driving forces underlying the dense "protein-rich" phase formation are only beginning to be probed. The amino acid composition and the specific arrangement of these in the sequence are expected to play an important role. We have recently developed a computational framework to elucidate the sequence determinants of protein liquid-liquid phase separation (LLPS) and apply it to many different IDPs of interest using coarse-grained molecular dynamics simulations. We demonstrate the effects of sequence and patterning on phase separation as well as the relationship between single chain compaction and phase separation. We further delve into the molecular driving forces underlying phase separation using atomic-resolution molecular dynamics simulations to highlight the contributions of different interaction modes to association of IDP fragments, to provide a mechanistic understanding of their role in driving LLPS.   

Liquid state theory study of the microstructure and phase behavior of protein condensates

Protein condensates formed by liquid-liquid phase separation of intrinsically disordered proteins or proteins with low complexity domains are found to be ubiquitous in cells. It is believed that these condensates typically are in a homogeneous isotropic liquid state. However, their internal microstructures, which presumably are sequence-dependent, are incompletely understood. Here, we use polymer integral equation theory (PRISM), which describes globally disordered structural correlations over a wide range of length scales in melts and solutions, to study the internal organization of protein condensates. Using an associating polymer/sticker-spacer minimal model, PRISM theory allows the effect of the sequence, condensate packing fraction, sticker fraction, and the strength and range of sticker-sticker interactions on microstructural correlations to be investigated. Based on computing the spinodal curve, we also study the sequence-specificity of the competition between macro- and micro-phase separation. Example calculations will be presented motivated by their direct or generic biological relevance. The structural results are also germane to constructing theories of dynamics, viscoelasticity, and kinetic arrest in condensates.   

Phase separation vs aggregation behavior for model disordered proteins

Liquid-liquid phase separation (LLPS) is widely utilized by the cell to organize and regulate various biochemical processes. In this talk, we present how sequence distribution, sticker fraction and chain length impact the formation of finite-size aggregates which can preempt macroscopic phase separation for some sequences. We demonstrate that a normalized sequence charge decoration (SCD) parameter establishes a "soft" predictive criterion for distinguishing when a model protein undergoes macroscopic phase separation vs finite aggregation. Furthermore, this order parameter was found to be strongly correlated to the critical density for phase separation, highlighting an unambiguous connection between sequence distribution and condensed phase density. Results obtained from an analysis of the order parameter reveals that at sufficiently long chain lengths, the vast majority of sequences are likely to phase separate. Our results suggest classical LLPS should be the primary phase transition for disordered proteins when short-ranged attractive interactions dominate and hints at a possible reason behind recent findings of widespread phase separation throughout living cells.   

Nucleation in multicomponent liquid mixtures

Phase separation of multicomponent liquid mixtures plays an integral part in many processes ranging from industry to cellular biology. While the nucleation of two-phase systems is well understood, it remains relatively unexplored how nucleation proceeds in multiphase systems, such as intracellular condensates. Here, we investigate the nucleation of a new droplet inside a multiphase system. To estimate the critical droplet size and the energy barrier, we used the string method, which can efficiently find transition pathways in highly dimensional energy landscapes. The results of the string method are consistent with the classical nucleation theory for both homogeneous and heterogeneous nucleation, where droplets nucleate inside one of the phases and at the interface of two phases, respectively. The heterogeneous nucleation results in lower energy barriers when the nucleating phase partially wets the preexisting two phases. These results provide the guiding principles for the analysis of nucleation in multiphase systems, which can proceed in several steps.   

Thermodynamic stability and critical points in multicomponent mixtures with structured interactions

It is increasingly recognized that the phase behavior of mixtures with many components plays an important role in biology. But while the thermodynamics of mixtures with random interactions is well understood, functional mixtures often contain a large number of components that interact through a smaller number of features, leading to a structured interaction matrix. Here we consider such solutions with non-random interactions, characterized in terms of a pairwise interaction matrix of variable rank. We derive mean-field conditions for thermodynamic stability and critical behavior that only depend on the distribution of the components in the lower-dimensional space of features, thus strongly reducing the complexity of the problem. This representation in feature space also suggests a principled way for coarse-graining multicomponent mixtures as binary mixtures while preserving the system’s location with respect to the spinodal and critical manifold. More generally, the framework we develop offers an instructive perspective on multicomponent mixtures and might help to elucidate principles of intracellular phase behavior.   

Material properties of Rubisco-EPYC1 condensates in an algal pyrenoid model

The photosynthetic alga Chlamydomonas reinhardtii contains a liquid-like membraneless organelle called the pyrenoid which concentrates carbon dioxide for more efficient carbon capture. The matrix of the pyrenoid is packed with the carbon-fixing enzyme Rubisco and a linker protein Essential Pyrenoid Component 1 (EPYC1) which serves as molecular glue. We developed a coarse-grained model for interacting Rubisco and EPYC1, with bonding properties derived from experiments, to understand the dynamics and material properties of Rubisco-EPYC1 condensates. We study how condensate properties such as surface tension and viscosity depend on the microscopic variables such as the number of binding sites on each EPYC1 molecule, bond strengths, and the lengths of the linkers between the sites, as well as on the stoichiometry between EPYC1 and Rubisco. We consider how cells can regulate pyrenoid properties, formation, and dissolution via modifications to EPYC1.   

Sequence and stoichiometry dependence of surface properties of biomolecular condensates

Cells organize many of their internal processes in space and time using condensates formed by liquid-liquid phase separation (LLPS) of biopolymers. Unlike conventional phase separation, biopolymer LLPS typically involves specific, heterotypic interactions between residues or domains, and the stoichiometry and specific sequences of these domains are biologically tunable parameters. Furthermore, LLPS is necessarily accompanied by the emergence of surface tension, which influences the dynamics, permeability, and internal structure of condensates. How does polymer sequence and stoichiometry influence condensate surface structure and surface tension? Using MD simulations, we discovered that the sequence and stoichiometry of heterotypic interaction domains determine the interface entropy, which in turn strongly influences the surface properties of the condensates, suggesting a mechanism of biological regulation.   

Withdrawn

A living biological cell has multiple macromolecules that occupy 30-40% of the total volume, or more. This phenomenon is known as macromolecular crowding.  Crowding conditions can be mimicked in vitro using colloidal suspensions of artificial crowders, a common choice being spherical polysucrose (Ficoll) nanoparticles. Despite many studies where Ficoll is considered as providing a hard-sphere-like excluded volume interaction, the structure of Ficoll has not yet been elucidated.

We carried out nuclear magnetic resonance spectroscopy studies on diffusion and relaxation of Ficoll 400 (molecular mass 400 kD) as well as water as a function of Ficoll 400 concentration. These studies provide strong evidence that Ficoll 400 is highly porous. The form factor obtained from small angle neutron scattering experiments reveal that the Ficoll 400 particle is closer to a diffusive blob or indeed a Gaussian polymer. The osmotic compressibility, extracted from the structure factor, is much smaller than Carnahan-Starling model for hard spheres, implying a system with soft inter-particle repulsion. Finally, measurements of suspension viscosity help to quantify the softness of Ficoll 400.   

On the interplay between phase separation and aggregation

Interactions among proteins in living cells can lead to both coexisting phases as well as aggregates of different sizes. Both processes play an important role in the spatial organization of cells and the regulation of biological function as well as dysfunction. A key challenge is to better understand the interplay between aggregation and phase separation. Here, we investigate how phase coexistence influences aggregation equilibrium and how, in turn, aggregation affects the properties of coexisting phases. To this end, we propose a theory for a multicomponent mixture that contains aggregates of different sizes. Aggregates can nucleate, grow, shrink, and phase separate from the solvent. At thermodynamic equilibrium, we find that the size distributions of aggregates are significantly different between the dilute and the dense phase. Strikingly, we show that the aggregation equilibrium differs from the stationary state of the same system where phase separation is suppressed. Moreover, we find a gelation transition of the dense phase that coexists with a dilute phase mainly composed of small aggregates. We then study the aggregation kinetics of coexisting phases initially composed of monomers. We show that the formation of aggregates affects the size of the dense phase and its composition. Our findings show that aggregation kinetics can strongly affect the properties of coexisting phases and are consistent with recent experimental observations of densification and volume changes of protein droplets.    

Dynamics of intrinsically disordered proteins and their droplet-like aggregates

The  intrinsically disordered proteins (IDPs) may aggregate and form multiprotein droplets that act as membraneless organelles. Theoretical understanding of the formation and dynamics of such droplets requires using coarse-grained molecular dynamics models. We describe a novel model (constructed with Lukasz Mioduszewski) that is a generalization of the so-called Go-like model, originally designed for structured proteins, and based on the concept of contact interactions between amino acids. In the case of the IDPs, the contacts are derived primarily from an instantaneous shape of the backbone and not from the geometry of a single reference state (such as the native state). The metastable proteinaceous droplets may arise within the two-fluid coexistence region that is bounded by the binodal and spinodal lines. We present novel theoretical methods to derive these lines. As an illustration, we discuss phase diagrams for systems of elastins and polyglutamines.   

Phase behavior and kinetics in systems with random interactions

I investigate properties of systems with random interactions. Such systems were initially proposed by Sear and Cuesta to understand phase behavior in biology, and usually solved in the mean-field regime. In this talk, I will revisit this model using theory and computer simulations. I will show that in the limit of a large number of components, the partition function is factorizable, and that this factorization remains valid for temperatures above a demixing temperature. However, these systems tend to exhibit particularly slow dynamics. In addition, I confirm the prediction of Jacobs and Frenkel: the transition temperature is intimately linked to extreme values of the interaction distribution. In this context, I will discuss the suitability of such models for biological systems.   

Computational design of amino-acid sequence variations that modulate the liquid-liquid phase separation of intrinsically disordered proteins

Liquid-liquid phase separation (LLPS) is an important mechanism that contributes to intracellular organization via the formation of biomolecular condensates. From a theoretical and computational perspective, the development of accurate and transferable coarse-grained models that allow us to elucidate the molecular mechanisms driving condensate formation in the cytoplasm and nucleoplasm with attainable computational cost is highly desirable.  We recently developed a multiscale coarse-grained model, termed ‘Mpipi‘ [1] that predicts phase diagrams of proteins in excellent quantitative agreement with experiments [2]. Mpipi provides a balanced parametrization of interaction strengths between different types of amino acids, accounting for the dominant role of π-based interactions. Here, we combine Mpipi with a genetic algorithm [3] to rationally design amino acid sequence mutations with desired LLPS properties. We propose a set of experimentally-testable amino-acid sequence variations of intrinsically disordered proteins that can either promote or inhibit their phase separation.

[1] Joseph, Reinhardt et al., Physics driven coarse-grained model for biomolecular phase separation with near-quantitative accuracy, Nat. Comput. Sci., 2021 (in press).

[2] Bremer et al, Deciphering how naturally occurring sequence features impact the phase behaviors of disordered prion-like domains, bioRxiv, 2021.

[3] Lichtinger et al, Targeted modulation of protein liquid–liquid phase separation by evolution of amino-acid sequence, Plos CompBiol, 2021