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

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

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

Thermochemically Consistent Free Energies of Hydration for Di- and Trivalent Metal Ions

This paper uses the relationship between the standard half reduction potential, the third ionization potential, and the free energies of hydration (Δ<i>G</i>_hyd) of M²⁺ and M³⁺ ions to calculate new values of Δ<i>G</i>_hyd for M²⁺ and M³⁺ ions. The numbers are “thermochemically consistent”; i.e., all numbers agree with the applied thermochemical cycle. This enables the tabulation of many Δ<i>G</i>_hyd derived mainly from the data compiled by Marcus, but consistent with Δ<i>G</i>_hyd(H⁺) = 1100 kJ/mol and SHE = 4.44 V. The accuracy of the new values of Δ<i>G</i>_hyd(M³⁺) is by definition similar to the accuracy of the experimental hydration energy of the Δ<i>G</i>_hyd(M²⁺) used for calculation, and <i>vice versa</i>, i.e. the new data have the same accuracy or higher than previously reported. As a result, the literature values for Cr³⁺ and Au³⁺, and Pd²⁺ are substantially revised. The approach also allows the calculation of new Δ<i>G</i>_hyd for metal ions such as Mn³⁺, Ti²⁺, Ag³⁺, Ni³⁺, Cu³⁺, and Au²⁺ and the theoretically interesting but experimentally inaccessible +2 ions of lanthanides. The new numbers enable a discussion of the previously unreported trend in Δ<i>G</i>_hyd(M³⁺) for the 3d metal ions, which relates to the ligand field stabilization energies and effective nuclear charge as for the M²⁺ ions. The new tabulated values should be accurate with the applied assumptions to within 10 kJ/mol and may be of value for other thermochemical calculations, for interpretation of the aqueous trend chemistry of the metal ions, and as benchmarks for theoretical chemistry

Accuracy of theoretical catalysis from a model of iron-catalyzed ammonia synthesis

DFT is widely used to study catalytic processes but its accuracy is debated. This paper shows major variations in DFT outcome for a simple model of iron-catalyzed ammonia synthesis benchmarked against experimental and high-level quantum mechanical data

Benchmarking Density Functionals for Chemical Bonds of Gold

Gold plays a major role in nanochemistry, catalysis, and electrochemistry. Accordingly, hundreds of studies apply density functionals to study chemical bonding with gold, yet there is no systematic attempt to assess the accuracy of these methods applied to gold. This paper reports a benchmark against 51 experimental bond enthalpies of AuX systems and seven additional polyatomic and cationic molecules. Twelve density functionals were tested, covering meta functionals, hybrids with variable HF exchange, double-hybrid, dispersion-corrected, and nonhybrid GGA functionals. The defined benchmark data set probes all types of bonding to gold from very electronegative halides that force Au⁺ electronic structure, via covalently bonded systems, hard and soft Lewis acids and bases that either work against or complement the softness of gold, the Au₂ molecule probing gold’s bond with itself, and weak bonds between gold and noble gases. Zero-point vibrational corrections are relatively small for Au–X bonds, ∼ 11–12 kJ/mol except for Au–H bonds. Dispersion typically provides ∼5 kJ/mol of the total bond enthalpy but grows with system size and is 10 kJ/mol for AuXe and AuKr. HF exchange and LYP correlation produce weaker bonds to gold. Most functionals provide similar trend accuracy, though somewhat lower for M06 and M06L, but very different numerical accuracy. Notably, PBE and TPSS functionals with dispersion display the smallest numerical errors and very small mean signed errors (0–6 kJ/mol), i.e. no bias toward over- or under-binding. Errors are evenly distributed versus atomic number, suggesting that relativistic effects are treated fairly; the mean absolute error is almost halved from B3LYP (45 kJ/mol) to TPSS and PBE (23 kJ/mol, including difficult cases); 23 kJ/mol is quite respectable considering the diverse bonds to gold and the complication of relativistic effects. Thus, studies that use DFT with effective core potentials for gold chemistry, with no alternative due to computational cost, are on solid ground using TPSS-D3 or PBE-D3