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There is notable discrepancy between experiments and coarse-grained model studies regarding the thermodynamic driving force in polyelectrolyte complex coacervation: experiments find the free energy change to be dominated by entropy, while simulations using coarse-grained models with implicit solvent usually report a large, even dominant energetic contribution in systems with weak to intermediate electrostatic strength. Here, using coarse-grained, implicit-solvent molecular dynamics simulation combined with thermodynamic analysis, we study the potential of mean force (PMF) in the two key stages on the coacervation pathway for symmetric polyelectrolyte mixtures: polycation–polyanion complexation and polyion pair–pair condensation.We show that the temperature dependence in the dielectric constant of water gives rise to a substantial entropic contribution in the electrostatic interaction. By accounting for this electrostatic entropy, which is due to solvent reorganization, we find that under common conditions (monovalent ions, room temperature) for aqueous systems, both stages are strongly entropy-driven with negligible or even unfavorable energetic contributions, consistent with experimental results. Furthermore, for weak to intermediate electrostatic strengths, this electrostatic entropy, rather than the counterion-release entropy, is the primary entropy contribution. From the calculated PMF, we find that the supernatant phase consists predominantly of polyion pairs with vanishingly small concentration of bare polyelectrolytes, and we provide an estimate of the spinodal of the supernatant phase. Finally, we showthat prior to contact, two neutral polyion pairsweakly attract each other by mutually induced polarization, providing the initial driving force for the fusion of the pairs.

Phase separation processes are increasingly being recognized as important organizing mechanisms of biological macromolecules in cellular environments. Well-established drivers of phase separation are multi-valency and intrinsic disorder. Here, we show that globular macromolecules may condense simply based on electrostatic complementarity. More specifically, phase separation of mixtures between RNA and positively charged proteins is described from a combination of multiscale computer simulations with microscopy and spectroscopy experiments. Phase diagrams were mapped out as a function of molecular concentrations in experiment and as a function of molecular size and temperature via simulations. The resulting condensates were found to retain at least some degree of internal dynamics varying as a function of the molecular composition. The results suggest a more general principle for phase separation that is based primarily on electrostatic complementarity without invoking polymer properties as in most previous studies. Simulation results furthermore suggest that such phase separation may occur widely in heterogenous cellular environment between nucleic acid and protein components.

Adhesion and insertion of curvature-mediating proteins can induce dramatic structural changes in cell membranes, allowing them to participate in several key cellular tasks. The way proteins interact to generate curvature remains largely unclear, especially at early stages of membrane remodeling. Using a coarse-grained model of Bin/amphiphysin/Rvs domain with an N-terminal helix (N-BAR) interacting with flat membranes and vesicles, we demonstrate that at low protein surface densities, binding of N-BAR domain proteins to the membrane is followed by a linear aggregation and the formation of meshes on the surface. In this process, the proteins assemble at the base of emerging membrane buds. Our work shows that beyond a more straightforward scaffolding mechanism at high bound densities, the interplay of anisotropic interactions and the local stress imposed by the N-BAR proteins results in deep invaginations and endocytic vesicular bud-like deformations, an order of magnitude larger than the size of the individual protein. Our results imply that by virtue of this mechanism, cell membranes may achieve rapid local increases in protein concentration.

The aggregation of monomeric amyloid β protein (Aβ) peptide into oligomers and amyloid fibrils in the mammalian brain is associated with Alzheimer’s disease. Insight into the thermodynamic stability of the Aβ peptide in different polymeric states is fundamental to defining and predicting the aggregation process. Experimental determination of Aβ thermodynamic behavior is challenging due to the transient nature of Aβ oligomers and the low peptide solubility. Furthermore, quantitative calculation of a thermodynamic phase diagram for a specific peptide requires extremely long computational times. Here, using a coarse-grained protein model, molecular dynamics (MD) simulations are performed to determine an equilibrium concentration and temperature phase diagram for the amyloidogenic peptide fragment Aβ16–22. Our results reveal that the only thermodynamically stable phases are the solution phase and the macroscopic fibrillar phase, and that there also exists a hierarchy of metastable phases. The boundary line between the solution phase and fibril phase is found by calculating the temperature-dependent solubility of a macroscopic Aβ16–22 fibril consisting of an infinite number of β-sheet layers. This in silico determination of an equilibrium (solubility) phase diagram for a real amyloid-forming peptide, Aβ16–22, over the temperature range of 277–330 K agrees well with fibrillation experiments and transmission electron microscopy (TEM) measurements of the fibril morphologies formed. This in silico approach of predicting peptide solubility is also potentially useful for optimizing biopharmaceutical production and manufacturing nanofiber scaffolds for tissue engineering.

Peptide self-assembly, wherein molecule A associates with other A molecules to form fibrillar β-sheet structures, is common in nature and widely used to fabricate synthetic biomaterials. Selective coassembly of peptide pairs A and B with complementary partial charges is gaining interest due to its potential for expanding the form and function of biomaterials that can be realized. It has been hypothesized that charge-complementary peptides organize into alternating ABAB-type arrangements within assembled β-sheets, but no direct molecular-level evidence exists to support this interpretation. We report a computational and experimental approach to characterize molecular-level organization of the established peptide pair, CATCH. Discontinuous molecular dynamics simulations predict that CATCH(+) and CATCH(−) peptides coassemble but do not self-assemble. Two-layer β-sheet amyloid structures predominate, but off-pathway β-barrel oligomers are also predicted. At low concentration, transmission electron microscopy and dynamic light scattering identified nonfibrillar ∼20-nm oligomers, while at high concentrations elongated fibers predominated. Thioflavin T fluorimetry estimates rapid and near-stoichiometric coassembly of CATCH(+) and CATCH(−) at concentrations ≥100 μM. Natural abundance 13C NMR and isotope-edited Fourier transform infrared spectroscopy indicate that CATCH(+) and CATCH(−) coassemble into two-component nanofibers instead of self-sorting. However, 13C–13C dipolar recoupling solid-state NMR measurements also identify nonnegligible AA and BB interactions among a majority of AB pairs. Collectively, these results demonstrate that strictly alternating arrangements of β-strands predominate in coassembled CATCH structures, but deviations from perfect alternation occur. Off-pathway β-barrel oligomers are also suggested to occur in coassembled β-strand peptide systems.

Significance The assembly of normally soluble proteins into large fibrils, known as amyloid aggregation, is associated with a range of pathologies. Prefibrillar protein oligomers but not the grown fibers are believed to be the main toxic agents. It is unresolved if these oligomers are necessary for fibril assembly or just a dangerous byproduct. We show using computer simulations that, at physiological concentrations, amyloid formation must proceed through a two-step process including prefibrillar oligomers. We find that there is an optimal oligomeric size for amyloid nucleation and that classical nucleation theory cannot be applied to this process. Formation of oligomers and hence, fibrils, is controlled by the strength of nonspecific attractions, whose weakening may be crucial in preventing amyloid aggregation. Protein oligomers have been implicated as toxic agents in a wide range of amyloid-related diseases. However, it has remained unsolved whether the oligomers are a necessary step in the formation of amyloid fibrils or just a dangerous byproduct. Analogously, it has not been resolved if the amyloid nucleation process is a classical one-step nucleation process or a two-step process involving prenucleation clusters. We use coarse-grained computer simulations to study the effect of nonspecific attractions between peptides on the primary nucleation process underlying amyloid fibrillization. We find that, for peptides that do not attract, the classical one-step nucleation mechanism is possible but only at nonphysiologically high peptide concentrations. At low peptide concentrations, which mimic the physiologically relevant regime, attractive interpeptide interactions are essential for fibril formation. Nucleation then inevitably takes place through a two-step mechanism involving prefibrillar oligomers. We show that oligomers not only help peptides meet each other but also, create an environment that facilitates the conversion of monomers into the β -sheet–rich form characteristic of fibrils. Nucleation typically does not proceed through the most prevalent oligomers but through an oligomer size that is only observed in rare fluctuations, which is why such aggregates might be hard to capture experimentally. Finally, we find that the nucleation of amyloid fibrils cannot be described by classical nucleation theory: in the two-step mechanism, the critical nucleus size increases with increases in both concentration and interpeptide interactions, which is in direct contrast with predictions from classical nucleation theory.

Significance Specific protein–protein interactions are abundant in, and essential for, cellular life. In contrast to the well-studied docking of two already folded proteins, it has been recently established that many proteins are disordered and unfolded in the absence of their partner protein, but appear folded once bound. Must these initially disordered proteins transiently fold in isolation before binding their partners? We examine a small disordered protein and find that interactions with its (already structured) partner protein are what cause the relatively unstructured protein to fold. Thus, the requirement for one protein to fold is not an obstacle for reliable, fast association between two proteins. This result offers some explanation for the abundance of similar protein–protein interactions throughout biology. Protein–protein interactions are at the heart of regulatory and signaling processes in the cell. In many interactions, one or both proteins are disordered before association. However, this disorder in the unbound state does not prevent many of these proteins folding to a well-defined, ordered structure in the bound state. Here we examine a typical system, where a small disordered protein (PUMA, p53 upregulated modulator of apoptosis) folds to an α-helix when bound to a groove on the surface of a folded protein (MCL-1, induced myeloid leukemia cell differentiation protein). We follow the association of these proteins using rapid-mixing stopped flow, and examine how the kinetic behavior is perturbed by denaturant and carefully chosen mutations. We demonstrate the utility of methods developed for the study of monomeric protein folding, including β-Tanford values, Leffler α, Φ-value analysis, and coarse-grained simulations, and propose a self-consistent mechanism for binding. Folding of the disordered protein before binding does not appear to be required and few, if any, specific interactions are required to commit to association. The majority of PUMA folding occurs after the transition state, in the presence of MCL-1. We also examine the role of the side chains of folded MCL-1 that make up the binding groove and find that many favor equilibrium binding but, surprisingly, inhibit the association process.

Fluctuations of protein three-dimensional structures and large-scale conformational transitions are crucial for the biological function of proteins and their complexes. Experimental studies of such phenomena remain very challenging and therefore molecular modeling can be a good alternative or a valuable supporting tool for the investigation of large molecular systems and long-time events. In this minireview, we present two alternative approaches to the coarse-grained (CG) modeling of dynamic properties of protein systems. We discuss two CG representations of polypeptide chains used for Monte Carlo dynamics simulations of protein local dynamics and conformational transitions, and highly simplified structure-based elastic network models of protein flexibility. In contrast to classical all-atom molecular dynamics, the modeling strategies discussed here allow the quite accurate modeling of much larger systems and longer-time dynamic phenomena. We briefly describe the main features of these models and outline some of their applications, including modeling of near-native structure fluctuations, sampling of large regions of the protein conformational space, or possible support for the structure prediction of large proteins and their complexes.

Both the small and large subunits of the ribosome, the molecular machine that synthesizes proteins, are complexes of ribosomal RNAs (rRNAs) and a number of proteins. In bacteria, the small subunit has a single 16S rRNA whose folding is the first step in its assembly. The central domain of the 16S rRNA folds independently, driven either by Mg2+ ions or by interaction with ribosomal proteins. To provide a quantitative description of ioninduced folding of the ∼350-nucleotide rRNA, we carried out extensive coarse-grained molecular simulations spanning Mg2+ concentration between 0 and 30 mM. The Mg2+ dependence of the radius of gyration shows that globally the rRNA folds cooperatively. Surprisingly, various structural elements order at different Mg2+ concentrations, indicative of the heterogeneous assembly even within a single domain of the rRNA. Binding of Mg2+ ions is highly specific, with successive ion condensation resulting in nucleation of tertiary structures. We also predict the Mg2+-dependent protection factors, measurable in hydroxyl radical footprinting experiments, which corroborate the specificity of Mg2+-induced folding. The simulations, which agree quantitatively with several experiments on the folding of a three-way junction, show that its folding is preceded by formation of other tertiary contacts in the central junction. Our work provides a starting point in simulating the early events in the assembly of the small subunit of the ribosome.

The co‐assembly of charged nanoparticles with oppositely charged molecular ions has emerged as a promising technique in the fabrication of nanoparticle superstructures. However, the underlying mechanism behind these molecular ions in mediating the repulsion between these charged nanoparticles remains elusive. Herein, coarse‐grained molecular dynamics simulations are used to elucidate the effects of valency, shape, and size of molecular anions on their co‐assembly with gold nanoparticles coated with positively charged ligands. The findings suggest that the valency, shape, and size of molecular anions significantly influence the repulsion and aggregating dynamics among these positively charged nanoparticles. Moreover, the free energy calculations reveal that ring‐shaped molecular anions with higher valences and larger sizes are more effective at reducing the repulsion between these gold nanoparticles and thus enhance the stability of the aggregate. This study contributes to a better understanding of the critical roles of valence, shape, and size of ions in mediating the electrostatic co‐assembly of nanoparticles with oppositely charged ions, and it also guides the future design of DNA templates and DNA origami in co‐assembly with oppositely charged nanoparticles. The effects of valency, shape, and size of molecular anions on their co‐assembly with gold nanoparticles covered with positively charged ligands are investigated using coarse‐grained molecular dynamics simulations. The results indicate that the valency, shape, and size of molecular anions have a considerable effect on the repulsion and aggregating dynamics of these positively charged nanoparticles.