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

TORQUE AND SQUARE-ROOT-FUNCTION

• A new view on the root-function.• Numbers used in their particular, mathematical function – as the value of a measure in a unit.• By example, a view on that multiplications (genuine multiplication) which produce new units.• The way to understand why the square-root of a negative radicand is solvable by an operational way and why we have to define the root-function new.• Altogether the first step of a restructuring of whole the numerical mathematics – a reform of the sign

Genotype-Property Patient-Phenotype Relations Suggest that Proteome Exhaustion Can Cause Amyotrophic Lateral Sclerosis

Late-onset neurodegenerative diseases remain poorly understood as search continues for the perceived pathogenic protein species. Previously, variants in Superoxide Dismutase 1 (SOD1) causing Amyotrophic Lateral Sclerosis (ALS) were found to destabilize and reduce net charge, suggesting a pathogenic aggregation mechanism. This paper reports analysis of compiled patient data and experimental and computed protein properties for variants of human SOD1, a major risk factor of ALS. Both stability and reduced net charge correlate significantly with disease, with larger significance than previously observed. Using two independent methods and two data sets, a probability < 3% (t-statistical test) is found that ALS-causing mutations share average stability with all possible 2907 SOD1 mutations. Most importantly, un-weighted patient survival times correlate strongly with the misfolded/unfolded protein copy number, expressed as an exponential function of the experimental stabilities (R2 = 0.31, p = 0.002), and this phenotype is further aggravated by charge (R2 = 0.51, p = 1.8 x 10-5). This finding suggests that disease relates to the copy number of misfolded proteins. Exhaustion of motor neurons due to expensive protein turnover of misfolded protein copies is consistent with the data but can further explain e.g. the expression-dependence of SOD1 pathogenicity, the lack of identification of a molecular toxic mode, elevated SOD1 mRNA levels in sporadic ALS, bioenergetic effects and increased resting energy expenditure in ALS patients, genetic risk factors affecting RNA metabolism, and recent findings that a SOD1 mutant becomes toxic when proteasome activity is recovered after washout of a proteasome inhibitor. Proteome exhaustion is also consistent with energy-producing mitochondria accumulating at the neuromuscular junctions where ALS often initiates. If true, this exhaustion mechanism implies a complete change of focus in treatment of ALS towards actively nursing the energy state and protein turnover of the motor neurons

Heme isomers substantially affect heme's electronic structure and function

Different vinyl orientations of heme are common in proteins and may affect heme potentials by up to 0.2 V.</p

Comment on "Density functional theory is straying from the path toward the exact functional"

Recently (Science, 355, 6320, 2017, 49-52) it was argued that density functionals stray from the path towards exactness due to errors in densities (\rho) of 14 atoms and ions computed with several recent functionals. However, this conclusion rests on very compact \rho\ of highly charged 1s2 and 1s22s2 systems, the divergence is due to one particular group's recently developed functionals, whereas other recent functionals perform well, and errors in \rho\ were not compared to actual energies E[\rho] of the same distinct, compact systems, but to general errors for diverse systems. As argued here, a true path can only be defined for E[\rho] and \rho\ for the same systems: By computing errors in E[\rho], it is shown that different functionals show remarkably linear error relationships between \rho\ and E[\rho] on well-defined but different paths towards exactness, and the ranking in Science, 355, 6320, 2017, 49-52 breaks down. For example, M06-2X, said to perform poorly, performs very well on the E,\rho\ paths defined here, and local (non-GGA) functionals rapidly increase errors in E[\rho] due to the failure to describe dynamic correlation of compact systems without the gradient. Finally, a measure of "exactness" is given by the product of errors in E[\rho] and \rho; these relationships may be more relevant focus points than a time line if one wants to estimate exactness and develop new exact functionals.Comment: 1 figure (Figure 1A, 1B, 1C) and two tables of supplementary dat

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

Energy vs. density on paths toward more exact density functionals

Recently, the progression toward more exact density functional theory has been questioned, implying a need for more formal ways to systematically measure progress, i.e. a path. Here I use the Hohenberg-Kohn theorems and the definition of normality by Burke et al. to define a path toward exactness and straying from the path by separating errors in \r{ho} and E[\r{ho}]. A consistent path toward exactness involves minimizing both errors. Second, a suitably diverse test set of trial densities \r{ho}' can be used to estimate the significance of errors in \r{ho} without knowing the exact densities which are often computationally inaccessible. To illustrate this, the systems previously studied by Medvedev et al., the first ionization energies of atoms with Z = 1 to 10, the ionization energy of water, and the bond dissociation energies of five diatomic molecules were investigated and benchmarked against CCSD(T)/aug-cc-pV5Z. A test set of four functionals of distinct designs was used: B3LYP, PBE, M06, and S-VWN. For atomic cations regardless of charge and compactness up to Z = 10, the energy effects of variations in \r{ho} are < 4 kJ/mol (chemical accuracy) defined here as normal, even though these four functionals ranked very differently in the previous test. Thus, the off-path behavior for such cations is energy-wise insignificant and in fact, indeterminate because of noise from other errors. An interesting oscillating behavior in the density sensitivity is observed vs. Z, explained by orbital occupation effects. Finally, it is shown that even large normal problems such as the Co-C bond energy of cobalamins can use simpler (e.g. PBE) trial densities to drastically speed up computation by loss of a few kJ/mol in accuracy.Comment: 5 Figures in main paper; supporting information contains 14 figures and 32 table