Temperature weighted histogram analysis method, replica exchange, and transition paths

We analyzed the data from a replica exchange molecular dynamics simulation using the weighted histogram analysis method to combine data from all of the temperature replicas (T-WHAM) to obtain the room-temperature potential of mean force of the G-peptide (the C-terminal beta-hairpin of the B1 domain of protein G) in regions of conformational space not sampled at room temperature. We were able to determine the potential of mean force in the transition region between a minor alpha-helical population and the major beta-hairpin population and identify a possible transition path between them along which the peptide retains a significant amount of secondary structure. This observation provides new insights into a possible mechanism of formation of beta-sheet secondary structures in proteins. We developed a novel Bayesian statistical uncertainty estimation method for any quantity derived from WHAM and used it to validate the calculated potential of mean force. The feasibility of estimating regions of the potential of mean force with unfavorable free energy at room temperature by T-WHAM analysis of replica exchange simulations was further tested on a system that can be solved analytically and presented some of the same challenges found in more complex chemical systems.     

Coulombic Basis for Relative Hydrogen-Bonding Basicities and Conformational Energies of Tertiary Amine Oxides and Phosphine Oxides

The structures, energies, and natural atomic charges of 2-dimethylaminophenol oxide, 2-Me₂N-(O)C₆H₄OH, and 2-dimethylphosphinylphenol, 2-Me₂P(O)C₆H₄OH, in three different conformations were computed at the ab initio MP2/6-31G* level. Computed natural charges indicate distributions of electron density in amine oxides and phosphine oxides that are quite different from what is normally assumed on the basis of the formal charges in the usual representations of these compounds. The charges on nitrogen and phosphorus in these compounds are typically computed to be approximately zero on nitrogen and +2 on phosphorus, and the oxygen is considerably more negative in the phosphine oxide than in the amino oxide. Electronegativity differences thus play a larger role and formal charges a smaller one in determining atomic charges in these compounds than is generally believed. Despite the more negative oxygen in phosphine oxides, amine oxides are computed to be considerably more basic when participating in hydrogen bonding. Calculations treating the computed natural charges on these six conformations as point charges for classical approximations of the coulombic energies support the idea that the quantum mechanically computed relative energies are largely determined by coulombic interactions.     

Second-order epi-derivatives of integral functionals

Epi-derivatives have many applications in optimization as approached through nonsmooth analysis. In particular, second-order epi-derivatives can be used to obtain optimality conditions and carry out sensitivity analysis. Therefore the existence of second-order epi-derivatives for various classes of functions is a topic of considerable interest. A broad class of composite functions on ⁿ called fully amenable functions (which include general penalty functions composed withC ² mappings, possibly under a constraint qualification) are now known to be twice epi-differentiable. Integral functionals appear widely in problems in infinite-dimensional optimization, yet to date, only integral functionals defined by convex integrands have been shown to be twice epi-differentiable, provided that the integrands are twice epi-differentiable. Here it is shown that integral functionals are twice epi-differentiable even without convexity, provided only that their defining integrands are twice epi-differentiable and satisfy a uniform lower boundedness condition. In particular, integral functionals defined by fully amenable integrands are twice epi-differentiable under mild conditions on the behavior of the integrands.This work was supported in part by the National Science Foundation under grant DMS-9200303.     

Iron(II) and zinc(II) monohelical binaphthyl salen complexes

A new chiral binaphthyl salen ligand with rigid polyaromatic sidearms gives monohelical complexes (Fe(II) and Zn(II)) of predetermined handedness.     

Photopolymerization of vinyl fluoride

The photopolymerization of vinyl fluoride, in the presence of peroxide, was studied in dimethyl sulfoxide (DMSO) solution and in bulk. It was found that high rates of reaction could be obtained in spite of the fact that the polymer precipitates at an early stage. By continuous supply of monomer the precipitated polymer was converted into a transparent bulk polymer.