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Standard quantum chemical methods are used for accurate calculation of thermochemical properties such as enthalpies of formation, entropies and Gibbs energies of formation. Equilibrium reactions are widely investigated and experimental measurements often lead to a range of reaction Gibbs energies and equilibrium constants. It is useful to calculate these equilibrium properties from quantum chemical methods in order to address the experimental differences. Furthermore, most standard calculation methods differ in accuracy and feasibility of the system size. Hence, asystematic comparison of equilibrium properties calculated with different numerical algorithms would provide a useful reference. We select two well-known gas phase equilibrium reactions with small molecules: covalent dimer formation of NO2 (2NO(2) reversible arrow N2O4) and the synthesis of NH3 (N-2 + 3 H-2 reversible arrow 2NH(3)). We test four quantum chemical methods denoted by G3B3, CBS-APNO, W1 and CCSD(T) with aug-cc-pVXZ basis sets (X = 2, 3, and 4), to obtain thermochemical data for NO2, N2O4, and NH3. The calculated standard formation Gibbs energies Delta(f)G degrees are used to calculate standard reaction Gibbs energies Delta(r)G degrees and standard equilibrium constants K-eq for the two reactions. Standard formation enthalpies Delta H-f degrees are calculated in a more reliable way using high-level methods such as W1 and CCSD(T). Standard entropies S degrees for the molecules are calculated well within the range of experiments for all methods, however, the values of standard formation Gibbs energies Delta(f)G degrees show some dependence on the choice of the method. High-level methods perform better for the calculation of molecular energies, however, simpler methods such as G3B3 and CBS-APNO perform quite well in the calculation of total reaction energies and equilibrium constants, provided that the chemical species involved do not exhibit molecular geometries that are difficult to handle by the applied method. The temperature dependence of standard reaction Gibbs energy Delta(r)G degrees for the NH3 reaction is discussed by using the calculated standard formation Gibbs energies Delta(f)G degrees of the reaction species at 298.15 K. The corresponding equilibrium constant K-eq as a function of temperature is found to be close to experimental values.
Importance of polar solvation for cross-reactivity of antibody and its variants with steroids
(2011)
Understanding the factors determining the binding of ligands to receptors in detail is essential for rational drug design. Here, the free energies of binding of the steroids progesterone (PRG) and 5 beta-androstane-3,17-dione (SAD) to the Diels-Alderase antibody 1E9, as well as the Leu(H47)Trp/Arg(H100)Trp 1E9 double mutant (1E9dm) and the corresponding single mutants, have been estimated and decomposed using the molecular mechanics-Poisson-Boltzmann surface area (MM-PBSA) method. Also the difference in binding free energies between the PRG-1E9dm complex and the complex of PRG with the antiprogesterone antibody DB3 have been evaluated and decomposed. The steroids bind less strongly to 1E9 than to DB3, but the mutations tend to improve the steroid affinity, in quantitative agreement with experimental data. Although the complexes formed by PRG or SAD with 1E9dm and by PRG with DB3 have similar affinity, the binding mechanisms are different. Reduced Waals for SAD-1E9dm versus PRG-1E9dm or for PRG-1E9dm versus PRG-DB3 are energetically compensated by an increased solvation of polar groups, partly contrasting previous conclusions based on structural inspection. Our study illustrates that deducing binding mechanisms from structural models alone can be misleading. Therefore, taking into account solvation effects as in MM-PBSA calculations is essential to elucidate molecular recognition.