Using quaternions to calculate RMSD

A widely used way to compare the structures of biomolecules or solid bodies is to translate and rotate one structure with respect to the other to minimize the root-mean-square deviation (RMSD). We present a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. We prove that the quaternion method is equivalent to the well-known formula due to Kabsch. We analyze the various cases that may arise, and give a complete enumeration of the special cases in terms of the arrangement of the eigenvalues of a traceless, 4 x 4 symmetric matrix. A key result here is an expression for the gradient of the RMSD as a function of model parameters. This can be useful, for example, in finding the minimum energy path of a reaction using the elastic band methods or in optimizing model parameters to best fit a target structure.     

Kinetics of the radical scavenging activity of β-carotene-related compounds

To clarify the non-enzymatic radical-scavenging activity of β-carotene-related compounds and other polyenes, we used differential scanning calorimetry to study the kinetics of radical polymerization of methyl methacrylate (MMA) by 2,2′-azobisisobutyronitrile (AIBN) or benzoyl peroxide (BPO) in the absence or presence of polyenes under nearly anaerobic conditions at 70°C, and analyzed the results with an SAR approach. The polyenes studied were all-trans retinol, retinol palmitate, calciferol, β-carotene and lycopene. Polyenes produced a small induction period. The stoichiometric factor (n) (i.e. the number of radicals trapped by each inhibitor molecule) of polyenes was close to 0. Tetraterpenes (β-carotene, lycopene) suppressed significantly more of the initial rate of polymerization (R ^inh) than did diterpenes (retinol, retinol palmitate). The inhibition rate constants (k ^inh) for the reaction of β-carotene with AIBN-or BPO-derived radicals were determined to be 1.2–1.6?×?10⁵ l?/?mol?s, similar to published values. A linear relationship between k ^inh and the kinetic chain length (KCL) for polyenes was observed; as k ^inh increased, KCL decreased. KCL also decreased significantly as the number of conjugated double bonds in the polyenes increased. Polyenes, particularly β-carotene and lycopene, acted as interceptors of growing poly-MMA radicals.     

Chemical constituents of Blumea balsamifera of Indonesia and their protein tyrosine phosphatase 1B inhibitory activity

A methanol extract of the leaves of Blumea balsamifera (L.) DC. (Asteraceae) afforded a new guaian-type sesquiterpene, epiblumeaene K (1), together with four known guaian-type sesquiterpenes (2-5), three known sesquiterpenes (6-8), and nine known flavonoids (9-17) by a combination of chromatography and preparative TLC techniques. Their structures were elucidated by extensive spectroscopic methods and comparison with the literature data. Among the isolated compounds, a known sesquiterpene, beta-caryophyllene 8R,9R-oxide (6), exhibited a significant PTP1B inhibitory activity in a dose-dependent manner, with an IC50 value of 25.8 microM (5.62 microg/mL).     

Substrate specificity of fluoroacetate dehalogenase: an insight from crystallographic analysis, fluorescence spectroscopy, and theoretical computations

The high substrate specificity of fluoroacetate dehalogenase was explored by using crystallographic analysis, fluorescence spectroscopy, and theoretical computations. A crystal structure for the Asp104Ala mutant of the enzyme from Burkholderia sp. FA1 complexed with fluoroacetate was determined at 1.2 ? resolution. The orientation and conformation of bound fluoroacetate is different from those in the crystal structure of the corresponding Asp110Asn mutant of the enzyme from Rhodopseudomonas palustris CGA009 reported recently (J. Am. Chem. Soc. 2011, 133, 7461). The fluorescence of the tryptophan residues of the wild-type and Trp150Phe mutant enzymes from Burkholderia sp. FA1 incubated with fluoroacetate and chloroacetate was measured to gain information on the environment of the tryptophan residues. The environments of the tryptophan residues were found to be different between the fluoroacetate- and chloroacetate-bound enzymes; this would come from different binding modes of these two substrates in the active site. Docking simulations and QM/MM optimizations were performed to predict favorable conformations and orientations of the substrates. The F atom of the substrate is oriented toward Arg108 in the most stable enzyme-fluoroacetate complex. This is a stable but unreactive conformation, in which the small O-C-F angle is not suitable for the S(N)2 displacement of the F(-) ion. The cleavage of the C-F bond is initiated by the conformational change of the substrate to a near attack conformation (NAC) in the active site. The second lowest energy conformation is appropriate for NAC; the C-O distance and the O-C-F angle are reasonable for the S(N) 2 reaction. The activation energy is greatly reduced in this conformation because of three hydrogen bonds between the leaving F atom and surrounding amino acid residues. Chloroacetate cannot reach the reactive conformation, due to the longer C-Cl bond; this results in an increase of the activation energy despite the weaker C-Cl bond.     

Rhodium-catalyzed enantioselective synthesis, crystal structures, and photophysical properties of helically chiral 1,1'-bitriphenylenes

The highly enantioselective synthesis of helically chiral 1,1'-bitriphenylenes has been achieved via rhodium-catalyzed double [2 + 2 + 2] cycloaddition of biaryl-linked tetraynes with 1,4-diynes (up to 93% ee). Crystal structures and photophysical properties of these helically chiral 1,1'-bitriphenylenes have also been studied.     

Synthesis of poly(ethylene glycol)‐based hydrogels and their swelling/shrinking response to molecular recognition

To synthesize the novel molecular‐ and pH‐stimulus‐responsive hydrogel, we prepared poly(ethylene glycol)‐based hydrogel containing ionic groups. We evaluated the fundamental swelling/shrinking properties of the hydrogels synthesized by various conditions. Decreasing the molecular weight of a crosslinker provided the increasing of the equilibrium swelling ratio. Also, the equilibrium swelling ratio was changed by the introduction of functional ionic monomers and its compositions. Furthermore, the swelling/shrinking behaviors of the hydrogels were affected by the environmental condition of aqueous solution, in fact the hydrogels were considerably shrunk (to one‐fifth volume) using a di‐ionic solute in the aqueous solution through the ionic interactions between the hydrogel and the solutes. Additionally, the specific shrinking to diamine compounds was also observed in response to pH change. These results clearly show the swelling/shrinking responsibility of the hydrogels toward the molecular recognitions and its pH conditions. © 2013 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2013, 51, 3153–3158     

Flame Retardancy and Kinetic Behavior of Ammonium Polyphosphate–Treated Unsaturated Polyester/Phenolic Interpenetrating Polymer Network

In this study, the flammability and kinetic behavior of flame retardant unsaturated polyester (UP)/phenolic resin were investigated. The flame retardant ammonium polyphosphate (APP) was used in this research to improve the flame resistance of a UP/phenolic resin interpenetrating polymer network (IPN). The flame resistance of UP improved from none to V-0 classification by adding phenolic resin and APP. Kinetic behavior study of UP, UP/phenolic, and APP-filled UP/phenolic IPN was carried out by the Borchardt and Daniels method. The results indicated that modification of flammable UP resin markedly improved the total heat release volume of UP and the flame retardancy of the IPN network structure was also enhanced.