Transient hydrophobic exposure in the molecular dynamics of Abeta peptide at low water concentration

Abeta is a disordered peptide central to Alzheimer's Disease. Aggregation of Abeta has been widely explored, but its molecular crowding less so. The synaptic cleft where Abeta locates only holds 60-70 water molecules along its width. We subjected Abeta40 to 100 different simulations with variable water cell size. We show that even for this disordered aggregation-prone peptide, many properties are not cell-size dependent, i.e. a small cell is easily justified. The radius of gyration, intra-peptide, and peptide-water hydrogen bonds are well-sampled by short (50 ns) time scales at any cell size. Abeta is mainly disordered with 0-30% alpha helix but undergoes consistent alpha-beta transitions up to 14% strand in 5-10% of the simulations regardless of cell size. The similar prevalence in long and short simulations indicate small diffusion barriers for structural transitions in contrast to folded globular proteins, which we suggest is a defining hallmark of intrinsically disordered proteins. Importantly, the hydrophobic surface increases significantly in small cells (confidence level 95%, two-tailed t-test), as does the variation in exposure and backbone conformations (>40% and >27% increased standard deviations). Whereas hydrophilic exposure dominates hydrophobic exposure in large cells, this tendency breaks down at low water concentration. We interpret these findings as a concentration-dependent hydrophobic effect, with the small water layer unable to keep the protein unexposed, an effect mainly caused by the layered water-water interactions, not by the peptide dynamics. The exposure correlates with radius of gyration (R2 0.35-0.50) and could be important in crowded environments, e.g. the synaptic cleft

Survival of the cheapest: How proteome cost minimization drives evolution

Darwin's theory of evolution emphasized that positive selection of functional proficiency provides the fitness that ultimately determines the structure of life, a view that has dominated biochemical thinking of enzymes as perfectly optimized for their specific functions. The 20th-century modern synthesis, structural biology, and the central dogma explained the machinery of evolution, and nearly neutral theory explained how selection competes with random fixation dynamics that produce molecular clocks essential e.g. for dating evolutionary histories. However, the quantitative proteomics revealed that fitness effects not related to functional proficiency play much larger roles on long evolutionary time scales than previously thought, with particular evidence that some universal biophysical selection pressures act via protein expression levels. This paper first summarizes recent progress in the 21st century towards recovering this universal selection pressure. Then, the paper argues that proteome cost minimization is the dominant, underlying "non-function" selection pressure controlling most of the evolution of already functionally adapted living systems. A theory of proteome cost minimization is described and argued to have consequences for understanding evolutionary trade-offs, aging, cancer, and neurodegenerative protein-misfolding diseases

Using Electronegativity and Hardness to Test Density Functional Universality

Density functional theory (DFT) is used in thousands of papers each year, yet lack of universality reduces DFT's predictive capacity, and functionals may produce energy-density imbalances. The absolute electronegativity (\chi) and hardness (\eta) directly reflect the energy-density relationship via the chemical potential dE/dN and we thus hypothesized that they probe universality. We studied \chi and \eta for atoms Z = 1-36 using 50 diverse functionals covering all major classes. Very few functionals describe both \chi and \eta well. \eta benefits from error cancelation whereas \chi is marred by error propagation from IP and EA; thus almost all standard GGA and hybrid functionals display a plateau in the MAE at 0.2-0.3 eV for \eta. In contrast, variable performance for \chi indicates problems in describing the chemical potential by DFT. The accuracy and precision of a functional is far from linearly related, yet for a universal functional we expect linearity. Popular functionals such as B3LYP, PBE, and revPBE, perform poorly for both properties. Density sensitivity calculations indicate large density-derived errors as occupation of degenerate p- and d-orbitals causes "non-universality" and large dependency on exact exchange. Thus, we argue that performance for \chi for the same systems is a hallmark of universality by probing dE/dN. With this metric, B98, B97-1, PW6B95D3, APFD are the most "universal" tested functionals. B98 and B97-1 are accurate for very diverse metal-ligand bonds, supporting that a balanced description of dE/dN and dE2/dN2, via \chi and \eta, is probably a first simple probe of universality

A base measure of precision for protein stability predictors: structural sensitivity.

BACKGROUND: Prediction of the change in fold stability (ΔΔG) of a protein upon mutation is of major importance to protein engineering and screening of disease-causing variants. Many prediction methods can use 3D structural information to predict ΔΔG. While the performance of these methods has been extensively studied, a new problem has arisen due to the abundance of crystal structures: How precise are these methods in terms of structure input used, which structure should be used, and how much does it matter? Thus, there is a need to quantify the structural sensitivity of protein stability prediction methods. RESULTS: We computed the structural sensitivity of six widely-used prediction methods by use of saturated computational mutagenesis on a diverse set of 87 structures of 25 proteins. Our results show that structural sensitivity varies massively and surprisingly falls into two very distinct groups, with methods that take detailed account of the local environment showing a sensitivity of ~ 0.6 to 0.8 kcal/mol, whereas machine-learning methods display much lower sensitivity (~ 0.1 kcal/mol). We also observe that the precision correlates with the accuracy for mutation-type-balanced data sets but not generally reported accuracy of the methods, indicating the importance of mutation-type balance in both contexts. CONCLUSIONS: The structural sensitivity of stability prediction methods varies greatly and is caused mainly by the models and less by the actual protein structural differences. As a new recommended standard, we therefore suggest that ΔΔG values are evaluated on three protein structures when available and the associated standard deviation reported, to emphasize not just the accuracy but also the precision of the method in a specific study. Our observation that machine-learning methods deemphasize structure may indicate that folded wild-type structures alone, without the folded mutant and unfolded structures, only add modest value for assessing protein stability effects, and that side-chain-sensitive methods overstate the significance of the folded wild-type structure

Chemical Bond Energies of 3d Transition Metals Studied by Density Functional Theory

Despite their vast importance to inorganic chemistry, materials science, and catalysis, the accuracy of modeling the formation or cleavage of metal–ligand (M–L) bonds depends greatly on the chosen functional and the type of bond in a way that is not systematically understood. In order to approach a state of high-accuracy DFT for rational prediction of chemistry and catalysis, such system-dependencies need to be resolved. We studied 30 different density functionals applied to a “balanced data set” of 60 experimental diatomic M–L bond energies; this data set has no bias toward any d^q configuration, metal, bond type, or ligand as all of these occur to the same extent, and we can therefore identify accuracy bottlenecks. We show that the performance of a functional is very dependent on data set choice, and we dissect these effects into system type. In addition to the use of balanced data sets, we also argue that the precision (rather than just accuracy) of a functional is of interest, measured by standard deviations of the errors. There are distinct system dependencies both in the ligand and metal series: Hydrides are best described by a very large HF exchange percentage, possibly due to self-interaction error, whereas halides are best described by very small (0–10%) HF exchange fractions, and double-bond enforcing oxides and sulfides favor 10–25% HF exchange, as is also average for the full data set. Thus, average HF requirements hide major system-dependent requirements. For late transition metals Co–Zn, HF percentage of 0–10% is favored, whereas for the early transition metals Sc–Fe hybrid functionals with 20% HF exchange or higher are commonly favored. Accordingly, B3LYP is an excellent choice for early d-block but a poor choice for late transition metals. We conclude that DFT intrinsically underestimates the bond strengths of late vs early transition metals, correlating with increased effective nuclear charge. Thus, the revised RPBE, which reduces the overbinding tendency of PBE, is mainly an advantage for the early and mid transition metals and not very much for the late transition metals, i.e. there is a metal-dependent effect of the relative performance of RPBE vs PBE, which are widely used to study adsorption energetics on metal surfaces. Overall, the best performing functionals are PW6B95, the MN15 and MN15-L functionals, and the double hybrid B2PLYP

The Influence of Selection for Protein Stability on dN/dS Estimations

Understanding the relative contributions of various evolutionary processes—purifying selection, neutral drift, and adaptation—is fundamental to evolutionary biology. A common metric to distinguish these processes is the ratio of nonsynonymous to synonymous substitutions (i.e., dN/dS) interpreted from the neutral theory as a null model. However, from biophysical considerations, mutations have non-negligible effects on the biophysical properties of proteins such as folding stability. In this work, we investigated how stability affects the rate of protein evolution in phylogenetic trees by using simulations that combine explicit protein sequences with associated stability changes. We first simulated myoglobin evolution in phylogenetic trees with a biophysically realistic approach that accounts for 3D structural information and estimates of changes in stability upon mutation. We then compared evolutionary rates inferred directly from simulation to those estimated using maximum-likelihood (ML) methods. We found that the dN/dS estimated by ML methods (ωML) is highly predictive of the per gene dN/dS inferred from the simulated phylogenetic trees. This agreement is strong in the regime of high stability where protein evolution is neutral. At low folding stabilities and under mutation-selection balance, we observe deviations from neutrality (per gene dN/dS > 1 and dN/dS 1. Altogether, we show how protein biophysics affects the dN/dS estimations and its subsequent interpretation. These results are important for improving the current approaches for detecting positive selection

Positively selected sites in cetacean myoglobins contribute to protein stability.

Since divergence ∼50 Ma ago from their terrestrial ancestors, cetaceans underwent a series of adaptations such as a ∼10–20 fold increase in myoglobin (Mb) concentration in skeletal muscle, critical for increasing oxygen storage capacity and prolonging dive time. Whereas the $O_2$-binding affinity of Mbs is not significantly different among mammals (with typical oxygenation constants of ∼0.8–1.2 $µM^{−1}$), folding stabilities of cetacean Mbs are ∼2–4 kcal/mol higher than for terrestrial Mbs. Using ancestral sequence reconstruction, maximum likelihood and Bayesian tests to describe the evolution of cetacean Mbs, and experimentally calibrated computation of stability effects of mutations, we observe accelerated evolution in cetaceans and identify seven positively selected sites in Mb. Overall, these sites contribute to Mb stabilization with a conditional probability of 0.8. We observe a correlation between Mb folding stability and protein abundance, suggesting that a selection pressure for stability acts proportionally to higher expression. We also identify a major divergence event leading to the common ancestor of whales, during which major stabilization occurred. Most of the positively selected sites that occur later act against other destabilizing mutations to maintain stability across the clade, except for the shallow divers, where late stability relaxation occurs, probably due to the shorter aerobic dive limits of these species. The three main positively selected sites 66, 5, and 35 undergo changes that favor hydrophobic folding, structural integrity, and intra-helical hydrogen bonds.Chemistry and Chemical Biolog

Structure and dynamics of γ-secretase with presenilin 2 compared to presenilin 1

Severe early-onset familial Alzheimer's disease (FAD) is caused by more than 200 different mutations in the genes coding for presenilin, the catalytic subunit of the 4-subunit protease complex γ-secretase, which cleaves the C99 fragment of the amyloid precursor protein (APP) to produce Aβ peptides. γ-Secretase exists with either of two homologues, PS1 and PS2. All cryo-electron microscopic structures and computational work has so far focused on γ-secretase with PS1, yet PS2 mutations also cause FAD. A central question is thus whether there are structural and dynamic differences between PS1 and PS2. To address this question, we use the cryo-electron microscopic data for PS1 to develop the first structural and dynamic model of PS2-γ-secretase in the catalytically relevant mature membrane-bound state at ambient temperature, equilibrated by three independent 500 ns molecular dynamics simulations. We find that the characteristic nicastrin extra-cellular domain breathing mode and major movements in the cytosolic loop between TM6 and TM7 occur in both PS2- and PS1-γ-secretase. The overall structures and conformational states are similar, suggesting similar catalytic activities. However, at the sequence level, charge-controlled membrane-anchoring is extracellular for PS1 and intracellular for PS2, which suggests different subcellular locations. The tilt angles of the TM2, TM6, TM7 and TM9 helices differ in the two forms of γ-secretase, suggesting that the two proteins have somewhat different substrate processing and channel sizes. Our MD simulations consistently indicated that PS2 retains several water molecules near the catalytic site at the bilayer, as required for catalysis. The possible reasons for the differences of PS1 and PS2 are discussed in relation to their location and function