LASSI: A lattice model for simulating phase transitions of multivalent proteins.

Many biomolecular condensates form via spontaneous phase transitions that are driven by multivalent proteins. These molecules are biological instantiations of associative polymers that conform to a so-called stickers-and-spacers architecture. The stickers are protein-protein or protein-RNA interaction motifs and / or domains that can form reversible, non-covalent crosslinks with one another. Spacers are interspersed between stickers and their preferential interactions with solvent molecules determine the cooperativity of phase transitions. Here, we report the development of an open source computational engine known as LASSI (LAttice simulation engine for Sticker and Spacer Interactions) that enables the calculation of full phase diagrams for multicomponent systems comprising of coarse-grained representations of multivalent proteins. LASSI is designed to enable computationally efficient phenomenological modeling of spontaneous phase transitions of multicomponent mixtures comprising of multivalent proteins and RNA molecules. We demonstrate the application of LASSI using simulations of linear and branched multivalent proteins. We show that dense phases are best described as droplet-spanning networks that are characterized by reversible physical crosslinks among multivalent proteins. We connect recent observations regarding correlations between apparent stoichiometry and dwell times of condensates to being proxies for the internal structural organization, specifically the convolution of internal density and extent of networking, within condensates. Finally, we demonstrate that the concept of saturation concentration thresholds does not apply to multicomponent systems where obligate heterotypic interactions drive phase transitions. This emerges from the ellipsoidal structures of phase diagrams for multicomponent systems and it has direct implications for the regulation of biomolecular condensates in vivo.

Measuring NDC80 binding reveals the molecular basis of tension-dependent kinetochore-microtubule attachments.

Proper kinetochore-microtubule attachments, mediated by the NDC80 complex, are required for error-free chromosome segregation. Erroneous attachments are corrected by the tension dependence of kinetochore-microtubule interactions. Here, we present a method, based on fluorescence lifetime imaging microscopy and Förster resonance energy transfer, to quantitatively measure the fraction of NDC80 complexes bound to microtubules at individual kinetochores in living human cells. We found that NDC80 binding is modulated in a chromosome autonomous fashion over prometaphase and metaphase, and is predominantly regulated by centromere tension. We show that this tension dependency requires phosphorylation of the N-terminal tail of Hec1, a component of the NDC80 complex, and the proper localization of Aurora B kinase, which modulates NDC80 binding. Our results lead to a mathematical model of the molecular basis of tension-dependent NDC80 binding to kinetochore microtubules in vivo.

The Role of Evolutionary Selection in the Dynamics of Protein Structure Evolution.

Homology modeling is a powerful tool for predicting a protein's structure. This approach is successful because proteins whose sequences are only 30% identical still adopt the same structure, while structure similarity rapidly deteriorates beyond the 30% threshold. By studying the divergence of protein structure as sequence evolves in real proteins and in evolutionary simulations, we show that this nonlinear sequence-structure relationship emerges as a result of selection for protein folding stability in divergent evolution. Fitness constraints prevent the emergence of unstable protein evolutionary intermediates, thereby enforcing evolutionary paths that preserve protein structure despite broad sequence divergence. However, on longer timescales, evolution is punctuated by rare events where the fitness barriers obstructing structure evolution are overcome and discovery of new structures occurs. We outline biophysical and evolutionary rationale for broad variation in protein family sizes, prevalence of compact structures among ancient proteins, and more rapid structure evolution of proteins with lower packing density.