Reconfiguration graphs of shortest paths

For a graph $G$ and$a,b\in V\left(G\right)$, the shortest path reconfiguration graph of $G$ with respect to $a$ and$b$ is denoted by $S(G,a,b)$. The vertex set of $S(G,a,b)$ is the set of all shortest paths between $a$ and$b$ in $G$. Two vertices in $V\left(S(G,a,b)\right)$ are adjacent, if their corresponding paths in $G$ differ by exactly one vertex. This paper examines the properties of shortest path graphs. Results include establishing classes of graphs that appear as shortest path graphs, decompositions and sums involving shortest path graphs, and the complete classification of shortest path graphs with girth 5 or greater. We include an infinite family of well structured examples, showing that the shortest path graph of a grid graph is an induced subgraph of a lattice.     

Synthesis and structural analysis of Bis(2-hydroxyphenyl) phenylamine, PhN(o-C6H4OH)2: Comparison with Tris(2-hydroxyphenyl)amine N(o-C6H4OH)3

The molecular structures of N(o-C₆H₄OH)₃, PhN(o-C₆H₄OH)₂, andp-TolN(o-C₆H₄OMe)₂ have been determined by X-ray diffraction, thereby indicating several structural differences. For example, whereas the nitrogen in N(o-C₆H₄OH)₃ is pyramidal with Σ_C–N–C = 348.3^∘, the nitrogen atoms in PhN(o-C₆H₄OH)₂ andp-TolN(o-C₆H₄OMe)₂ are trigonal planar with Σ_C–N–C = 359.9^∘ and Σ_C–N–C = 360.0^∘, respectively. The phenyl andp-tolyl groups of PhN(o-C₆H₄OH)₂ andp-TolN(o-C₆H₄OMe)₂ lie close to the trigonal plane, while theo-C₆H₄OH ando-C₆H₄OMe groups are almost orthogonal to this plane. The coplanar and orthogonal orientations of the aryl groups of PhN(o-C₆H₄OH)₂ andp-TolN(o-C₆H₄OMe)₂ are in marked contrast to those of the phenyl groups within Ph₃N, which exhibit dihedral angles in the range 38–52^∘ and approximateD₃ symmetry. The observed structures of PhN(o-C₆H₄OH)₂ andp-TolN(o-C₆H₄OMe)₂ may be rationalized in terms of maximizing delocalization of the nitrogen lone pair into the phenyl andp-tolyl groups, while minimizing unfavorable overlap with theo-C₆H₄OH ando-C₆H₄OMe groups due to the presence of π-donatingortho-substituents; the orthogonal orientation of theo-C₆H₄OH ando-C₆H₄OMe groups is also one that minimizes unfavorable steric interactions between theortho-substituents.     

Solvation dynamics of Hoechst 33258 in water: an equilibrium and nonequilibrium molecular dynamics study

Integrated within an appropriate theoretical framework, molecular dynamics (MD) simulations are a powerful tool to complement experimental studies of solvation dynamics. Together, experiment, theory, and simulation have provided substantial insight into the dynamic behavior of polar solvents. MD investigations of solvation dynamics are especially valuable when applied to the heterogeneous environments found in biological systems, where the calculated response of the environment to the electrostatic perturbation of the probe molecule can easily be decomposed by component (e.g., aqueous solvent, biomolecule, ions), greatly aiding the molecular-level interpretation of experiments. A comprehensive equilibrium and nonequilibrium MD study of the solvation dynamics of the fluorescent dye Hoechst 33258 (H33258) in aqueous solution is presented. Many fluorescent probes employed in experimental studies of solvation dynamics in biological systems, such as the DNA minor groove binder H33258, have inherently more conformational flexibility than prototypical fused-ring chromophores. The role of solute flexibility was investigated by developing a fully flexible force-field for the H33258 molecule and by simulating its solvation response. While the timescales for the total solvation response calculated using both rigid (0.16 and 1.3 ps) and flexible (0.17 and 1.4 ps) models of the probe closely matched the experimentally measured solvation response (0.2 and 1.2 ps), there were subtle differences in the response profiles, including the presence of significant oscillations for the flexible probe. A decomposition of the total response of the flexible probe revealed that the aqueous solvent was responsible for the overall decay, while the oscillations result from fluctuations in the electrostatic terms in the solute intramolecular potential energy. A comparison of equilibrium and nonequilibrium approaches for the calculation of the solvation response confirmed that the solvation dynamics of H33258 in water is well-described by linear response theory for both rigid and flexible models of the probe.     

Two-dimensionally well-ordered multilayer structures in thin films of a brush polypeptide

In this study, we report the first production of two-dimensionally well-ordered molecular multilayers (i.e., with a well-defined molecular lamellar structure) based on the antiparallel beta-sheet chain conformation in thin films of a brush polypeptide, poly(S-n-hexadecyl-dl-homocysteine) (PHHC), through the use of a simple spin-coating process and the quantitative structural and property analysis of the thin films using a grazing incidence X-ray scattering technique combined with Fourier transform infrared spectroscopy and differential scanning calorimetry. These analyses provide detailed information about the structure and molecular conformation of the self-assembled lamellae in the PHHC thin film, which is not easily obtained using conventional techniques. Moreover, we used the in situ measurements carried out at various temperatures and the data analyses to establish mechanisms for the evolution of the self-assembled lamellar structures in the film and for their melting. In addition, we propose molecular structure models of the PHHC polymer molecules in the thin film at various temperatures.     

Syntheses and DNA photocleavage by mono- and bis-phenothiazinium-piperazinexylene intercalators

Chromophore systems consisting of one (compound 5) or two (compound 6) phenothiazine rings covalently attached to a bis-piperazinexylene chain were synthesized and evaluated as DNA photocleaving agents. In the presence of DNA, the compounds were shown to monointercalate in their deaggregated forms and to strongly absorb red wavelengths of light. Reactions containing micromolar concentrations of compound produced robust photocleavage of plasmid DNA under near-physiological conditions of temperature and pH (22 °C and pH 7.0). Phenothiazines 5 and 6 increased the T_m of calf thymus DNA by 17 and 19 °C, indicating that significant levels of duplex stabilization were produced.     

Infrared-vacuum ultraviolet pulsed field ionization-photoelectron study of C2H4(+) using a high-resolution infrared laser

The infrared (IR)-vacuum ultraviolet (VUV)-pulsed field ionization-photoelectron (IR-VUV-PFI-PE) spectrum for C2H4(X1A(g), v11 = 1, N'(Ka'Kc') = 3(03)) in the VUV range of 83,000-84,800 cm(-1) obtained using a single mode infrared laser revealed 24 rotationally resolved vibrational bands for the ion C2H4(+)(X2B(3u)) ground state. The frequencies and symmetry of the vibrational bands thus determined, together with the anharmonic frequency predictions calculated at the CCSD(T)/aug-cc-pVQZ level, have allowed the unambiguous assignment of these vibrational bands. These bands are mostly combination bands. The measured frequencies of these bands yield the fundamental frequencies for v8+ = 1103 +/- 10 cm(-1) and v10+ = 813 +/- 10 cm(-1) of C2H4(+)(X2B(3u)), which have not been determined previously. The present IR-VUV-PFI-PE study also provides truly rovibrationally selected and resolved state-to-state cross sections for the photoionization transitions C2H4(X1A(g); v11, N'(Ka'Kc')) --> C2H4(+)(X2B(3u); vi+, N+(Ka+Kc+)), where N'(Ka'Kc') denotes the rotational level of C2H4(X1A(g); v11), and vi+ and N+(Ka+Kc+) represent the vibrational and rotational states of the cation.     

An ab initio and density functional theory study of the structure and bonding of sulfur ylides

Sulfur ylides are useful synthetic intermediates that are formed from the interaction between singlet carbenes and sulfur-containing molecules. Partial double-bond character frequently has been proposed as a key contributor to the stability of sulfur ylides. Calculations at the B3LYP, MP2, and CCSD(T) levels of theory employing various basis sets have been performed on the sulfur ylides H(2)S-CH(2) and (CH(3))(2)S-CH(2) in order to investigate the structure and bonding of these systems. The following general properties of sulfur ylides were observed from the computational studies: C-S bond distances that are close in length to that of a typical C-S double bond, high charge transfer from the sulfide to the carbene, and large torsional rotation barriers. Analysis of the sulfur ylide charge distribution indicates that the unusually short C-S bond distance can be attributed in part to the electrostatic attraction between highly oppositely charged carbon and sulfur atoms. Furthermore, n --> sigma* stabilization arising from donation of electron density from the carbon lone pair orbital into S-H or S-C antibonding orbitals leads to larger than expected torsional barriers. Finally, natural resonance theory analysis indicates that the bond order of the sulfur ylides H(2)S-CH(2) and (CH(3))(2)S-CH(2) is 1.4-1.5, intermediate between a single and double bond.     

Structure-activity relationships in cholapod anion carriers: enhanced transmembrane chloride transport through substituent tuning

Chloride transport by a series of steroid-based "cholapod" receptors/carriers was studied in vesicles. The principal method involved preincorporation of the cholapods in the vesicle membranes, and the use of lucigenin fluorescence quenching to detect inward-transported Cl-. The results showed a partial correlation between anion affinity and transport activity, in that changes at the steroidal 7 and 12 positions affected both properties in concert. However, changes at the steroidal 3-position yielded irregular effects. Among the new steroids investigated the bis-p-nitrophenylthiourea 3 showed unprecedented activity, giving measurable transport through membranes with a transporter/lipid ratio of 1:250 000 (an average of <2 transporter molecules per vesicle). Increasing transporter lipophilicity had no effect, and positively charged steroids had low activity. The p-nitrophenyl monourea 25 showed modest but significant activity. Measurements using a second method, requiring the addition of transporters to preformed vesicle suspensions, implied that transporter delivery was problematic in some cases. A series of measurements employing membranes of different thicknesses provided further evidence that the cholapods act as mobile anion carriers.     

Continuous dependence results for inhomogeneous ill-posed problems in Banach space

We apply semigroup theory and other operator-theoretic methods to prove Hölder-continuous dependence on modeling for the inhomogeneous ill-posed Cauchy problem in Banach space. The inhomogeneous ill-posed Cauchy problem is given by , u(0)=χ, 0?t<T; where −A is the infinitesimal generator of a holomorphic semigroup on a Banach space X, χ∈X, and . For a suitable function f, the approximate problem is given by , v(0)=χ. Under certain stabilizing conditions, we prove that for a related norm, where and M are computable constants independent of β, 0<β<1, and ω(t) is a harmonic function. These results extend earlier work of Ames and Hughes on the homogeneous ill-posed problem.     

Catalytic cracking of alkylcyclohexanes: Modeling the reaction pathways and mechanisms

The cracking reaction pathways and mechanisms of ethylcyclohexane and 1-cyclohexyloctane with a rare earth Y (REY) catalyst were studied. Experiments at 500°C indicated that the dominant reactions were ring opening with subsequent secondary cracking, cracking in the alkyl side chain, isomerization, and hydrogen transfer. A kinetic model of the catalytic cracking of 1-cyclohexyloctane was developed using a novel mechanism-based lumping scheme that exploits the chemical similarities within reaction families. The formal application of 17 reaction family matrices, which correspond to 13 reaction family classes, to the matrix representations of the reactants and derived products generated the model. The reaction family concept was further exploited to constrain the kinetics within each reaction family to follow a quantitative structure/reactivity Polanyi relationship. Ultimately, nine Polanyi relationship parameters and three coking/deactivation parameters were determined by optimizing the model fit to the experimental data. The resulting model correlations were excellent, as the overall parity between experimental and model values was y_Model=−0.000470+0.986y_Exp with a correlation coefficient of 0.971. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 545–560, 1997.