While the classical view of protein folding kinetics relies on phenomenological models, and regards folding intermediates in a structural way, the new view emphasizes the ensemble nature of protein conformations. Although folding has sometimes been regarded as a linear sequence of events, the new view sees folding as parallel microscopic multi-pathway diffusion-like processes. While the classical view invoked pathways to solve the problem of searching for the needle in the haystack, the pathway idea was then seen as conflicting with Anfinsen's experiments showing that folding is pathway-independent (Levinthal's paradox). In contrast, the new view sees no inherent paradox because it eliminates the pathway idea: folding can funnel to a single stable state by multiple routes in conformational space. The general energy landscape picture provides a conceptual framework for understanding both two-state and multi-state folding kinetics. Better tests of these ideas will come when new experiments become available for measuring not just averages of structural observables, but also correlations among their fluctuations. At that point we hope to learn much more about the real shapes of protein folding landscapes.

Membrane encapsulation is frequently used by the cell to sequester biomolecules and compartmentalize their function. Cells also concentrate molecules into phase-separated protein or protein/nucleic acid "membraneless organelles" that regulate a host of biochemical processes. Here, we use solution NMR spectroscopy to study phase-separated droplets formed from the intrinsically disordered N-terminal 236 residues of the germ-granule protein Ddx4. We show that the protein within the concentrated phase of phase-separated Ddx4, [Formula: see text], diffuses as a particle of 600-nm hydrodynamic radius dissolved in water. However, NMR spectra reveal sharp resonances with chemical shifts showing [Formula: see text] to be intrinsically disordered. Spin relaxation measurements indicate that the backbone amides of [Formula: see text] have significant mobility, explaining why high-resolution spectra are observed, but motion is reduced compared with an equivalently concentrated nonphase-separating control. Observation of a network of interchain interactions, as established by NOE spectroscopy, shows the importance of Phe and Arg interactions in driving the phase separation of Ddx4, while the salt dependence of both low- and high-concentration regions of phase diagrams establishes an important role for electrostatic interactions. The diffusion of a series of small probes and the compact but disordered 4E binding protein 2 (4E-BP2) protein in [Formula: see text] are explained by an excluded volume effect, similar to that found for globular protein solvents. No changes in structural propensities of 4E-BP2 dissolved in [Formula: see text] are observed, while changes to DNA and RNA molecules have been reported, highlighting the diverse roles that proteinaceous solvents play in dictating the properties of dissolved solutes.

General principles of protein structure, stability, and folding kinetics have recently been explored in computer simulations of simple exact lattice models. These models represent protein chains at a rudimentary level, but they involve few parameters, approximations, or implicit biases, and they allow complete explorations of conformational and sequence spaces. Such simulations have resulted in testable predictions that are sometimes unanticipated: The folding code is mainly binary and delocalized throughout the amino acid sequence. The secondary and tertiary structures of a protein are specified mainly by the sequence of polar and nonpolar monomers. More specific interactions may refine the structure, rather than dominate the folding code. Simple exact models can account for the properties that characterize protein folding: two-state cooperativity, secondary and tertiary structures, and multistage folding kinetics-fast hydrophobic collapse followed by slower annealing. These studies suggest the possibility of creating "foldable" chain molecules other than proteins. The encoding of a unique compact chain conformation may not require amino acids; it may require only the ability to synthesize specific monomer sequences in which at least one monomer type is solvent-averse.Keywords: chain collapse; hydrophobic interactions; lattice models; protein conformations; protein folding; protein stabilityWe review the principles of protein structure, stability, and folding kinetics from the perspective of simple exact models. We focus on the "folding code''-how the tertiary structure and folding pathway of a protein are encoded in its amino acid sequence. Although native proteins are specific, compact, and often remarkably symmetrical structures, ordinary synthetic polymers in solution, glasses, or melts adopt large ensembles of more expanded conformations, with little intrachain organization. With simple exact models, we ask what are the fundamental causes of the differences between proteins and other polymers-What makes proteins special?One view of protein folding assumes that the "local" interactions among the near neighbors in the amino acid sequence, the interactions that form helices and turns, are the main determinants of protein structure. This assumption implies that isolated helices form early in the protein folding pathway and then assemble into the native tertiary structure (see Fig. 1). It is the premise behind the paradigm, primary + secondary -+ tertiary structure, that seeks computer algorithms to predict secondary structures from the sequence, and then to assemble them into the tertiary native structure.Here we review a simple model of an alternative view, its basis in experimental results, and its implications. We show how the nonlocal interactions that drive collapse processes in heteropolymers can give rise to protein structure, stability, and folding kinetics. This perspective is based on evidence that the folding code is not predominantly localized in short windows of the amino acid sequence. It...

We use two simple models and the energy landscape perspective to study protein folding kinetics. A major challenge has been to use the landscape perspective to interpret experimental data, which requires ensemble averaging over the microscopic trajectories usually observed in such models. Here, because of the simplicity of the model, this can be achieved. The kinetics of protein folding falls into two classes: multiple-exponential and two-state (single-exponential) kinetics. Experiments show that two-state relaxation times have "chevron plot" dependences on denaturant and non-Arrhenius dependences on temperature. We find that HP and HP+ models can account for these behaviors. The HP model often gives bumpy landscapes with many kinetic traps and multiple-exponential behavior, whereas the HP+ model gives more smooth funnels and two-state behavior. Multiple-exponential kinetics often involves fast collapse into kinetic traps and slower barrier climbing out of the traps. Two-state kinetics often involves entropic barriers where conformational searching limits the folding speed. Transition states and activation barriers need not define a single conformation; they can involve a broad ensemble of the conformations searched on the way to the native state. We find that unfolding is not always a direct reversal of the folding process.

Liquid-liquid phase separation of charge- and/or aromatic-enriched intrinsically disordered proteins (IDPs) is critical in the biological function of membraneless organelles. Much of the physics of this recent discovery remains to be elucidated. Here, we present a theory in the random phase approximation to account for electrostatic effects in polyampholyte phase separations, yielding predictions consistent with recent experiments on the IDP Ddx4. The theory is applicable to any charge pattern and thus provides a general analytical framework for studying sequence dependence of IDP phase separation.

We study the folding dynamics of short two-dimensional self-avoiding lattice model proteins and copolymers with specific HP sequences (H, hydrophobic, P, polar) that fold to unique native structures. HH contacts are favorable. The conformational landscape is found by exhaustive enumeration using two different move sets, and time evolution is modeled by a transition matrix with the Metropolis criterion. The kinetic sequence of folding events depends strongly on both the monomer sequence and on the move set. But certain features are common to all sequences with both move sets. Beginning with open conformations, chains fold through multiple paths, are slowed by kinetic traps, and accumulate in compact nonnative conformations. Most chains must surmount energy barriers, which we identify as the transition state. Strikingly, the transition state involves a chain expansion, due to the breaking of HH contacts of compact denatured conformations. Mutations can significantly affect the energy landscape and folding dynamics, but in ways that appear too subtle to predict just from knowledge of native structures. Consistent with other models, we find that sequences with a large energy gap between the native and the next higher energy level can be stable and fold rapidly.

Random mutations under neutral or nearneutral conditions are studied by considering plausible evolutionary trajectories on ''neutral nets''-i.e., collections of sequences (genotypes) interconnected via single-point mutations encoding for the same ground-state structure (phenotype). We use simple exact lattice models for the mapping between sequence and conformational spaces. Densities of states based on model intrachain interactions are determined by exhaustive conformational enumeration. We compare results from two very different interaction schemes to ascertain robustness of the conclusions. In both models, sequences in a majority of neutral nets center around a single ''prototype sequence'' of maximum mutational stability, tolerating the largest number of neutral mutations. General analytical considerations show that these topologies by themselves lead to higher steady-state evolutionary populations at prototype sequences. On average, native thermodynamic stability increases toward a maximum at the prototype sequence, resulting in funnel-like arrangements of native stabilities in sequence space. These observations offer a unified perspective on sequence design, native stability, and mutational stability of proteins. These principles are generalizable from native stability to any measure of fitness provided that its variation with respect to mutations is essentially smooth.

Endeavoring toward a transferable, predictive coarse-grained explicit-chain model for biomolecular condensates underlain by liquid–liquid phase separation (LLPS) of proteins, we conducted multiple-chain simulations of the N-terminal intrinsically disordered region (IDR) of DEAD-box helicase Ddx4, as a test case, to assess roles of electrostatic, hydrophobic, cation–π, and aromatic interactions in amino acid sequence-dependent LLPS. We evaluated three different residue–residue interaction schemes with a shared electrostatic potential. Neither a common hydrophobicity scheme nor one augmented with arginine/lysine-aromatic cation–π interactions consistently accounted for available experimental LLPS data on the wild-type, a charge-scrambled, a phenylalanine-to-alanine (FtoA), and an arginine-to-lysine (RtoK) mutant of Ddx4 IDR. In contrast, interactions based on contact statistics among folded globular protein structures reproduce the overall experimental trend, including that the RtoK mutant has a much diminished LLPS propensity. Consistency between simulation and experiment was also found for RtoK mutants of P-granule protein LAF-1, underscoring that, to a degree, important LLPS-driving π-related interactions are embodied in classical statistical potentials. Further elucidation is necessary, however, especially of phenylalanine’s role in condensate assembly because experiments on FtoA and tyrosine-to-phenylalanine mutants suggest that LLPS-driving phenylalanine interactions are significantly weaker than posited by common statistical potentials. Protein–protein electrostatic interactions are modulated by relative permittivity, which in general depends on aqueous protein concentration. Analytical theory suggests that this dependence entails enhanced interprotein interactions in the condensed phase but more favorable protein–solvent interactions in the dilute phase. The opposing trends lead to only a modest overall impact on LLPS.