Session Y12: Physics of Emergent Protein-Complex Assemblies

Live

Intracellular biopolymer solutions, such as the cytosol and the nucleoplasm, can demix to form a wide variety of phase-separated condensates. A single intracellular compartment may in fact feature multiple coexisting condensates with distinct compositions. These observations raise the question of how reliably such complex phase behavior can be "programmed" into a biopolymer solution containing thousands of components. Here we describe a theoretical model of phase separation in which components may be shared among multiple condensates. Theoretical analysis and molecular simulations demonstrate that a large number of condensates can be programmed by tuning the intermolecular interactions and subsequently assembled by selective nucleation at heterogeneous nucleation sites. When condensates share components, the number of compositionally distinct condensates that can be reliably programmed grows superlinearly with the number of components in the mixture. As a result, we propose that biological systems may take advantage of similar combinatorial strategies to broaden the range of useful behaviors that can be achieved via phase separation.   

Live

Self-organization is essential for keeping living organism functional. Any mistake leads to severe disease such as Alzheimer. In this case, protein that are usually soluble start aggregating leading to fibril structures that are incompatible with the initial biological role of the protein. We try to understand this tendency that a wide variety of protein exhibit using a very general mechanism. Indeed, if on the one hand a surface tension energy would drive the aggregation, on the other hand, because of their ill fitting shape, proteins would need to deform to do so, which has a cost of elastic energy. Fiber like aggregate would therefore be a trade of between those two energies. Previous studies have already found that fiber like aggregate can have an energetic benefit over other shape, but here we investigate, using statistical physics tools, the thermodynamic properties of such fibers.   

Live

The combinatorial complexity of large macromolecular structures is central to many questions in biophysics, polymer physics, and other fields, yet hinders theoretical study of these objects using the standard methods of statistical physics. We approach this challenge by describing an operator formalism for classical multi-particle complexes. The framework, which is built from a Fock space of hard-core bosons, allows particles to be joined together into large complexes based on a small number of algebraically defined assembly rules. We further introduce diagrammatic techniques that make this algebra visually intuitive and facilitate analytical calculations through a connection with Wick’s theorem. These techniques can be used to study a wide range of systems, both in and out of thermal equilibrium. They also help to unify intuitive but seemingly distinct notions of coarse graining. We explore specific applications of these methods to the biophysical modeling of transcriptional regulation.   

Live

The nucleation and growth of protein aggregates are important both to understanding both the structure of the cell’s membraneless organelles and the pathogenesis of many diseases. The intrinsically stochastic nature of the aggregation process challenges our theoretical and computational abilities. To explore the mechanistic details of the stochastic aggregation process more efficiently, we explore a new approach to stochastic aggregation kinetics based on accompanying noise in averaged equations based on mathematical moment closure schemes. Stochastic moment equations cope with the large diversity of species while taking into account the stochastic fluctuations accompanying both primary and secondary nucleation as well as aggregate growth, dissociation, and fragmentation. This method of ”second stochastization” works well in the regime of moderate fluctuation often encountered in vivo where N ~ O(10² - 10³). Simulations reveal a scaling law that correlates the size of fluctuation with the total number of monomers. We believe second stochastization schemes will prove valuable for bridging the gap between experiments and theoretical modeling.   

Live

Membrane-less compartments regulate biochemical processes in living cells. These condensates exhibit a complex rheology including viscoelastic, glassy and gel-like behaviour. It has been suggested that condensate rheology plays an important role in regulating physiological but also aberrant processes such as the irreversible aggregation into fibrils. Here, we investigate how rheological properties of liquid condensates can control fibril aggregation. To address this question, we present a kinetic theory of fibril aggregation in the presence of phase-separated condensates and account for condensate rheology by a mobility that depends on the aggregate size. Our theory reveals that aggregation is strongly affected by condensate rheology. For example, for gel-like condensates giving rise to a reptation-like kinetics of fibrils, we show that aggregates are strongly enriched inside condensates and the average number of aggregates can be reduced. Our results suggest a possible physical mechanism for how living cells may control fibril aggregation by exploiting phase separation and altering the rheological properties of the liquid condensates.   

Live

Proteins bind to other proteins to form complexes with biological function. Predicting the structure of these complexes and understanding their assembly mechanisms are of fundamental importance for protein assembly, rational drug design, and the engineering of proteins as building blocks for new materials. Understanding the role of the various forces contributing to protein-protein interactions is particularly critical in this regard. Shape complementarity is one such contribution known to play a role in protein binding. Using molecular simulation, we investigated the binding of 50 protein dimers with atomic-level resolution of rigid molecular shape and a generic entropic depletion interaction to isolate the role of shape in the assembly of these dimers, and compared the assembled configurations with known native structures. Our simulations predict the yield of native contacts in thermodynamic equilibrium. We find that shape complementarity is sufficient to predict native complexes as equilibrium assemblies in six cases. We corroborate our findings by analyzing the relative importance of competing binding configurations.   

Live

Motility is critical for the survival and dispersal of bacteria, and it plays an important role during infection. Regulation of bacterial motility via chemotaxis and gene regulation is well studied. However, recent work has added a new dimension to this problem. The flagellar motor of bacteria autonomously assembles and disassembles torque-generating stator units in response to changes in the external viscous load. In Escherichia coli, up to 11 stator units drive the motor at high load while all the stator units are released at low load. We study this process by artificially manipulating the motor load using electrorotation, where a high frequency rotating electric field applies an external torque on the flagellar motor. Using this technique, we can increase or decrease the motor load at will and measure the resulting stator remodeling. We measured stator remodeling in both clockwise and counterclockwise rotating motors, and found that the motor’s response has a conserved torque dependence. We built a model that captures the observed dynamics and provides insight into the underlying molecular interactions. Torque-dependent stator remodeling takes place within tens of seconds, making it a highly responsive autonomous control mechanism.   

Live

Bending of the membrane into vesicles and viruses requires work performed by multi-protein assemblies. The ability of these protein components to nucleate and assemble on membranes can be triggered through both ATP-independent processes, and through energy-consuming reactions such as phosphorylation. Clathrin-mediated endocytosis, an essential process for internalizing transmembrane cargo across the cell membrane, provides a rich system for studying how assembly is controlled via stochastic and active forces. Using kinetic and reaction-diffusion modeling, we show how the stoichiometry of the assembly components, which can be effectively controlled via enzymatic reactions (which turn on and off interactions), can control the kinetics and success of clathrin assembly. We quantify how specific assembly components can stabilize assembly growth either through the formation of 2D interactions on the surface, or through their ability to induce or stabilize curvature and membrane bending necessary for vesicle formation. Using continuum thin-film models, we show how these proteins can create mechanical feedback that renders the membrane effectively more ‘sticky’ to subsequent protein recruitment interactions. Our models can be directly applied to studying related assembly processes such as viral budding within the cell.   

Live

The spatial organization of complex biochemical reactions is of fundamental importance in order to maintain correct regulation of cellular processes. Small structures known as foci create local high concentrations of proteins needed for DNA repair. One specific way to introduce such a heterogeneity is by the process of a phase separation where proteins with energetically favorable interactions cluster inside droplets. However it is still extremely difficult to define whether observable foci are formed as a phase separation or merely as the result of an increased number of specific binding sites. In this work we outline possible observables to differentiate between the two existing models based on tracking of single molecules. We discuss relations between the steady state behaviour and the diffusion properties on shorter time scales as a way to identify the underlying physical structure of foci.   

Live

Many proteins assemble into stable complexes or transient clusters to perform a biological function in the cytoplasm. Unlike stable complexes that can be visualized with super-resolution microscopy, the detection of transient clusters is elusive as the composition of protein assemblies vary with cellular conditions. A main challenge is to establish the physical principles that govern assembly that takes the transient nature into account. Here, we utilized the tools of statistical inference and modeling from experimental data dealing with the average abundances of various protein species. Resulting from our model, the grand canonical Monte Carlo simulations of multi-component protein-complex mixture accurately reproduce transient complex formation found by experiments. We also provide general insight into the physical principles that govern these complex assemblies.   

On Demand

Synthetic peptides are excellent candidates for the design of nanoscale materials through controlled, targeted assembly with atomistic precision due to an ability to mimic complex protein structures and properties in nature. The ability to precisely design and control structure at the molecular level plays essential roles in constructing new materials with target desired structures and properties. Herein, computationally designed peptides are used to construct a hierarchically organized fiber material with exceptional mechanical properties. The basic peptide building blocks are self-assembled into coiled-coil bundles, or ‘bundlemers’, that subsequently undergo covalent conjugation between bundlemers to form polymers. The resultant hybrid peptide-based polymers formed by concurrent physical (non-covalent) and covalent interactions of bundlemers exhibit rigid-rod structure owing to a rigidity of constituent bundlemers and direct, covalent linkages between them. The resultant rod-like polymers are subsequently employed to fabricate a higher-ordered fiber material via electrospinning, while preserving their unique rod-like characteristic. Moreover, the apparent mechanical properties of the final rod nanofibers are compared with other protein-based fiber materials.