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Proteins and nucleic acids can phase-separate in the cell to form concentrated biomolecular condensates 1 – 4 . The functions of condensates span many length scales: they modulate interactions and chemical reactions at the molecular scale 5 , organize biochemical processes at the mesoscale 6 and compartmentalize cells 4 . Understanding the underlying mechanisms of these processes will require detailed knowledge of the rich dynamics across these scales 7 . The mesoscopic dynamics of biomolecular condensates have been extensively characterized 8 , but their behaviour at the molecular scale has remained more elusive. Here, as an example of biomolecular phase separation, we study complex coacervates of two highly and oppositely charged disordered human proteins 9 . Their dense phase is 1,000 times more concentrated than the dilute phase, and the resulting percolated interaction network 10 leads to a bulk viscosity 300 times greater than that of water. However, single-molecule spectroscopy optimized for measurements within individual droplets reveals that at the molecular scale, the disordered proteins remain exceedingly dynamic, with their chain configurations interconverting on submicrosecond timescales. Massive all-atom molecular dynamics simulations reproduce the experimental observations and explain this apparent discrepancy: the underlying interactions between individual charged side chains are short-lived and exchange on a pico- to nanosecond timescale. Our results indicate that, despite the high macroscopic viscosity of phase-separated systems, local biomolecular rearrangements required for efficient reactions at the molecular scale can remain rapid. Two highly charged disordered human proteins phase-separate into viscous complex coacervates while retaining their rapid conformational dynamics through pico- to nanosecond exchange of short-lived side-chain interactions.

Proteins that undergo liquid–liquid phase separation (LLPS) have been shown to play a critical role in many physiological functions through formation of condensed liquid-like assemblies that function as membraneless organelles within biological systems. To understand how different proteins may contribute differently to these assemblies and their functions, it is important to understand the molecular driving forces of phase separation and characterize their phase boundaries and material properties. Experimental studies have shown that intrinsically disordered regions of these proteins are a major driving force, as many of them undergo LLPS in isolation. Previous work on polymer solution phase behavior suggests a potential correspondence between intramolecular and intermolecular interactions that can be leveraged to discover relationships between single-molecule properties and phase boundaries. Here, we take advantage of a recently developed coarse-grained framework to calculate the θ temperature Tθ , the Boyle temperature TB , and the critical temperature Tc for 20 diverse protein sequences, and we show that these three properties are highly correlated. We also highlight that these correlations are not specific to our model or simulation methodology by comparing between different pairwise potentials and with data from other work. We, therefore, suggest that smaller simulations or experiments to determine Tθ or TB can provide useful insights into the corresponding phase behavior.

The recent availability of long equilibrium simulations of protein folding in atomistic detail for more than 10 proteins allows us to identify the key interactions driving folding. We find that the collective fraction of native amino acid contacts, Q , captures remarkably well the transition states for all the proteins with a folding free energy barrier. Going beyond this global picture, we devise two different measures to quantify the importance of individual interresidue contacts in the folding mechanism: (i) the log-ratio of lifetimes of contacts during folding transition paths and in the unfolded state and (ii) a Bayesian measure of how predictive the formation of each contact is for being on a transition path. Both of these measures indicate that native, or near-native, contacts are important for determining mechanism, as might be expected. More remarkably, however, we found that for almost all the proteins, with the designed protein α ₃D being a notable exception, nonnative contacts play no significant part in determining folding mechanisms.

Membraneless organelles important to intracellular compartmentalization have recently been shown to comprise assemblies of proteins which undergo liquid-liquid phase separation (LLPS). However, many proteins involved in this phase separation are at least partially disordered. The molecular mechanism and the sequence determinants of this process are challenging to determine experimentally owing to the disordered nature of the assemblies, motivating the use of theoretical and simulation methods. This work advances a computational framework for conducting simulations of LLPS with residue-level detail, and allows for the determination of phase diagrams and coexistence densities of proteins in the two phases. The model includes a short-range contact potential as well as a simplified treatment of electrostatic energy. Interaction parameters are optimized against experimentally determined radius of gyration data for multiple unfolded or intrinsically disordered proteins (IDPs). These models are applied to two systems which undergo LLPS: the low complexity domain of the RNA-binding protein FUS and the DEAD-box helicase protein LAF-1. We develop a novel simulation method to determine thermodynamic phase diagrams as a function of the total protein concentration and temperature. We show that the model is capable of capturing qualitative changes in the phase diagram due to phosphomimetic mutations of FUS and to the presence or absence of the large folded domain in LAF-1. We also explore the effects of chain-length, or multivalency, on the phase diagram, and obtain results consistent with Flory-Huggins theory for polymers. Most importantly, the methodology presented here is flexible so that it can be easily extended to other pair potentials, be used with other enhanced sampling methods, and may incorporate additional features for biological systems of interest.

Diffusion on a low-dimensional free-energy surface is a remarkably successful model for the folding dynamics of small single-domain proteins. Complicating the interpretation of both simulations and experiments is the expectation that the effective diffusion coefficient D will in general depend on the position along the folding coordinate, and this dependence may vary for different coordinates. Here we explore the position dependence of D, its connection to protein internal friction, and the consequences for the interpretation of single-molecule experiments. We find a large decrease in D from unfolded to folded, for reaction coordinates that directly measure fluctuations in Cartesian configuration space, including those probed in single-molecule experiments. In contrast, D is almost independent of Q, the fraction of native amino acid contacts: Near the folded state, small fluctuations in position cause large fluctuations in Q, and vice versa for the unfolded state. In general, position-dependent free energies and diffusion coefficients for any two good reaction coordinates that separate reactant, product, and transition states, are related by a simple transformation, as we demonstrate. With this transformation, we obtain reaction coordinates with position-invariant D. The corresponding free-energy surfaces allow us to justify the assumptions used in estimating the speed limit for protein folding from experimental measurements of the reconfiguration time in the unfolded state, and also reveal intermediates hidden in the original free-energy projection. Lastly, we comment on the design of future single-molecule experiments that probe the position dependence of D directly.

Most foldable protein sequences adopt only a single native fold. Recent protein design studies have, however, created protein sequences which fold into different structures apon changes of environment, or single point mutation, the best characterized example being the switch between the folds of the GA and GB binding domains of streptococcal protein G. To obtain further insight into the design of sequences which can switch folds, we have used a computational model for the fitness landscape of a single fold, built from the observed sequence variation of protein homologues. We have recently shown that such coevolutionary models can be used to design novel foldable sequences. By appropriately combining two of these models to describe the joint fitness landscape of GA and GB, we are able to describe the propensity of a given sequence for each of the two folds. We have successfully tested the combined model against the known series of designed GA/GB hybrids. Using Monte Carlo simulations on this landscape, we are able to identify pathways of mutations connecting the two folds. In the absence of a requirement for domain stability, the most frequent paths go via sequences in which neither domain is stably folded, reminiscent of the propensity for certain intrinsically disordered proteins to fold into different structures according to context. Even if the folded state is required to be stable, we find that there is nonetheless still a wide range of sequences which are close to the transition region and therefore likely fold switches, consistent with recent estimates that fold switching may be more widespread than had been thought.

Highly charged intrinsically disordered proteins can form complexes with very high affinity in which both binding partners fully retain their disorder and dynamics, exemplified by the positively charged linker histone H1.0 and its chaperone, the negatively charged prothymosin α. Their interaction exhibits another surprising feature: The association/dissociation kinetics switch from slow two-state-like exchange at low protein concentrations to fast exchange at higher, physiologically relevant concentrations. Here we show that this change in mechanism can be explained by the formation of transient ternary complexes favored at high protein concentrations that accelerate the exchange between bound and unbound populations by orders of magnitude. Molecular simulations show how the extreme disorder in such polyelectrolyte complexes facilitates (i) diffusion-limited binding, (ii) transient ternary complex formation, and (iii) fast exchange of monomers by competitive substitution, which together enable rapid kinetics. Biological polyelectrolytes thus have the potential to keep regulatory networks highly responsive even for interactions with extremely high affinities. The intrinsically disordered linker histone H1.0 and prothymosin α form a complex which exhibits slow exchange between bound and unbound populations at low protein concentrations and fast exchange at high concentrations. Here authors explain this observation by the formation of transient ternary complexes favored at high protein concentrations that accelerate the exchange.

Intrinsically disordered proteins play an important role in cellular signalling, mediated by their interactions with other biomolecules. A key question concerns the nature of their binding mechanism, and whether the bound structure is induced only by proximity to the binding partner. This is difficult to answer through experiment alone because of the very heterogeneous nature of the unbound ensemble, and the probable rapid interconversion of the various unbound structures. Here we report the most extensive set of simulations on NCBD to date: we use large-scale replica exchange molecular dynamics to explore the unbound state. An important feature of the study is the use of an atomistic force field that has been parametrised against experimental data for weakly structured peptides, together with an accurate explicit water model. Neither the force field nor the starting conformations are biased towards a particular structure. The regions of NCBD that have high helical propensity in the simulations correspond closely to helices in the 'core' unbound conformation determined by NMR, although no single member of the simulated unbound ensemble closely resembles the core conformation, or either of the two known bound conformations. We have validated the results against NMR spectroscopy and SAXS measurements, obtaining reasonable agreement. The two helices which most stabilise the binding of NCBD with ACTR are formed readily; the third helix, which is less important for binding but is involved in most of the intraprotein contacts of NCBD in the bound conformation, is formed more rarely, and tends not to coexist with the other helices. These results support a mechanism by which NCBD gains the advantages of disorder, while forming binding-competent structures in the unbound state. We obtain support for this mechanism from coarse-grained simulations of NCBD with, and without, its binding partner.

Recent experiments on protein-folding dynamics have revealed strong evidence for internal friction effects. That is, observed relaxation times are not simply proportional to the solvent viscosity as might be expected if the solvent were the only source of friction. However, a molecular interpretation of this remarkable phenomenon is currently lacking. Here, we use all-atom simulations of peptide and protein folding in explicit solvent, to probe the origin of the unusual viscosity dependence. We find that an important contribution to this effect, explaining the viscosity dependence of helix formation and the folding of a helix-containing protein, is the insensitivity of torsion angle isomerization to solvent friction. The influence of this landscape roughness can, in turn, be quantitatively explained by a rate theory including memory friction. This insensitivity of local barrier crossing to solvent friction is expected to contribute to the viscosity dependence of folding rates in larger proteins. The interaction of water molecules with a protein results in a frictional force that influences protein conformational dynamics and folding, though the nature of the protein also influences the friction. Here, the authors use molecular simulations to examine the origin of this protein contribution.

For disordered proteins, the dimensions of the chain are an important property that is sensitive to environmental conditions. We have used single-molecule Förster resonance energy transfer to probe the temperature-induced chain collapse of five unfolded or intrinsically disordered proteins. Because this behavior is sensitive to the details of intrachain and chain–solvent interactions, the collapse allows us to probe the physical interactions governing the dimensions of disordered proteins. We find that each of the proteins undergoes a collapse with increasing temperature, with the most hydrophobic one, λ-repressor, undergoing a reexpansion at the highest temperatures. Although such a collapse might be expected due to the temperature dependence of the classical “hydrophobic effect,” remarkably we find that the largest collapse occurs for the most hydrophilic, charged sequences. Using a combination of theory and simulation, we show that this result can be rationalized in terms of the temperature-dependent solvation free energies of the constituent amino acids, with the solvation properties of the most hydrophilic residues playing a large part in determining the collapse.