Date of Award

Winter 12-15-2022

Author's School

Graduate School of Arts and Sciences

Author's Department


Degree Name

Doctor of Philosophy (PhD)

Degree Type



Biomolecular condensates represent a new and ubiquitous class of membraneless organelles (MLOs) that are essential for healthy cellular functioning. The constituent molecules of such condensates span a vast bio-macromolecular gamut from intrinsically disordered regions and proteins (IDPs/IDRs), to RNA and RNA-binding proteins (RNPs), to polymerases and DNA etc. Apart from being part of the regular healthy cell cycle, these condensates are also implicated in many diseases, most notably progressive neurodegenerative diseases like Amyotropic Lateral Sclerosis (ALS) and Huntingtin's Disease (HD). Since the constituent molecules of these condensates span a broad range of length scales and modes of interaction, uncovering a unified framework that explains the underlying physical mechanisms for the formation of such condensates becomes important. While biological processes are decidedly out of equilibrium, equilibrium descriptions can still be useful, given the right constraints. Non-equilibrium descriptions tend to be mean-field-like, and we cannot access mechanistic details of the underlying interactions among molecules. Thus, making direct sense of the sequence encoded chemical specificity of different bio-macromolecules becomes a challenge. As such, an equilibrium mechanism for the formation of biomolecular condensates is that of phase separation coupled to percolation (PSCP). Using the physics of associative polymers as a theoretical foundation, this thesis aims to uncover the molecular mechanisms and rules for biomolecular condensates formed via PSCP.

This thesis has two overarching goals. Firstly, to develop a computational approach that allows us to investigate PSCP at the "molecular" scale. Secondly, to use that computational approach to model and understand the workings of interesting and relevant biological systems. Along the way, with help from various experimental collaborators utilizing a plethora of techniques, we test our predictions, which we use to further refine our understanding. Towards the first goal, we have developed a flexible Monte-Carlo (MC) lattice polymer simulation engine: LAttice simulation engine for sticker and spacer interactions (LaSSI). Formulated as an extension to Bond-Fluctuation Models (BFMs), LaSSI allows for both the rigorous investigation of the equilibrium statistical properties of associative polymers, and also enables investigations of the phase transitions of such systems. We show that LaSSI can be used to generate full phase diagrams, including percolation, or gel, lines. Using an example linear multivalent protein (LMVP) system, we demonstrate the validity of LaSSI, including the assessment of finite-size effects in estimating a novel order parameter for detecting phase separation. We then extend to multiple and branched components using mimics of nucleolar proteins as the example system. Apart from the full phase diagram, and percolation boundary, we also show that the concept of a saturation concentration, c_\text{sat}, breaks down for condensates formed via heterotypic interactions.

Continuing, we use LaSSI to understand the modulation of biomolecular condensates. For a broad range of condensates, only a few components, called scaffolds, are necessary to drive the formation. Such scaffolds can be considered heteropolymers comprised of interacting motifs, called stickers, connected by solubility determining regions, or spacers. Using stickers-and-spacer representation in LaSSI, and the polyphasic linkage formalism, we have uncovered some of the underlying physical principles of ligand-mediated modulation of the phase behavior of such scaffolds. For condensates that are primarily driven by heterotypically interacting scaffolds, ligands offer many different ways of modulation. On the one hand, monovalent ligands tend to only suppress phase separation whether they bind to stickers or spacers. On the other hand, divalent ligands produce a variety of effects. Ligands that interact with stickers tend to suppress the driving forces for condensation. Ligands that interact with spacers can enhance phase separation. While ligands that are bipartite, interacting with both stickers and spacers, can exhibit either suppression or enhancement, in a non-monotonic manner, depending on the asymmetry of the interaction strengths of the ligands between the stickers and spacers. Strikingly, even ligands that have minimal effects on c_\text{sat} still modulate the internal structure of the condensates. Since LaSSI allows for accessing mechanistic details behind the modulation, our results provide a set of design principles for making bespoke ligands that can affect the phase behavior or internal organization of a condensate in a prescribed manner.

Moving on, we then pivot to understanding the structural regulation of a biomolecular condensate that is actively performing a function. Using some of the mitochondrial transcriptional machinery, our collaborators have been able to generate a minimal model of such a biomolecular condensate. Our collaborators show that these condensates are capable of transcribing RNA in-vitro. Strikingly, the rates of RNA production are lower than well mixed systems, despite the increased local concentration of components. The components make heterogeneous multi-component condensates that seem to be kinetically and dynamically arrested. Using computational models that recapitulate the phase behavior of binary mixtures of the components, we then correctly predict that the condensates have spatially inhomogeneous organization of the underlying components. Furthermore, we show that the structure of the condensate is altered as more RNA is transcribed. We then predict that this disruption of the condensate structure can be mitigated by the inclusion of RNPs, which are then confirmed by in-vivo assays performed by our collaborators. Importantly, we demonstrate that the vesicular structures seen in in-vitro experiments are out of equilibrium, and dynamically arrested phases. This is then verified experimentally where the order of addition of RNA produces very different organization of the condensates.

Lastly, we investigate the subtleties of systems that undergo PSCP. While Classical Nucleation Theory (CNT) predicts that the sub-saturated regime should be comprised mostly of monomers and exponentially small populations of oligomers, the physics of associative polymers predicts that this need not be the case. Indeed, our experimental collaborators show that the FET-family of proteins forms continuous heterogeneous distributions of oligomeric species, or clusters. Strikingly, small populations of mesoscale clusters, from 100 nm to 1000 nm, exist in a truly sub-saturated regime. Such clusters are quasi-spherical, thermodynamically stable, reversible and easily exchange material with solutions. We demonstrate not only that this is a general feature of the FET-family of proteins but that there is sequence specificity for the driving forces of cluster formation. We then further show that the interactions that lead to cluster formation and condensate formation can be decoupled using appropriate chemical solutes, or amino-acid substitutions. Furthermore, the data suggest that multiple length and energy scales are required to generate such mesoscale clusters. Indeed, using LaSSI simulations we show that homopolymers are not capable of generating mesoscale clusters but can only drive condensation in an all or none fashion. Heteropolymers, or associative polymers, are able to generate mesoscale clusters where the length asymmetry and interaction strength tunes the driving forces for cluster formation. The in-vivo implications are immense since most cellular scaffold concentrations are well within this subsaturated regime. That there are multiple components within the crowded environment of the cell makes an even stronger case for studying this phenomenon deeper where we could uncover the sequence principles behind the coupling of percolation and phase separation, and what the biological function of such clusters might be. We thus find that equilibrium descriptions of biomolecular condensates still have much more to offer, and that the physics of associative polymers provides a provides a stable foundation with which we can explore the molecular details of PSCP.


English (en)

Chair and Committee

Anders Carlsson

Committee Members

Rohit V Pappu


Update embargo

Included in

Physics Commons