Outer Splitting Research Articles

Neighboring aliphatic/aromatic side chain interactions between residues 9 and 10 in gramicidin channels.

The interactions between an aliphatic or phenyl side chain and an indole ring in a phospholipid environment were investigated by synthesizing and characterizing gramicidins in which Trp(9) was ring-labeled and D-Leu(10) was replaced by D-Val, D-Ala, or D-Phe. All three analogues form conducting channels, with conductances that are lower than that of gramicidin A (gA) channels. The channel lifetimes vary by less than 50% from that of gA channels. Circular dichroism spectra and size-exclusion chromatography show that the conformation of each analogue in dimyristoylphosphatidylcholine (DMPC) vesicles is similar to the right-handed beta(6.3)-helical conformation that is observed for gA. (2)H NMR spectra of oriented samples in DMPC show large changes for the Trp(9) ring when residue 10 is modified, suggesting a steric interaction between D-Leu(10) and Trp(9), in agreement with previous acylation studies (R. E. Koeppe II et al. (1995) Biochemistry 34, 9299-9307). The outer quadrupolar splitting for Trp(9) is unchanged with D-Phe(10), at approximately 153 kHz, but increases by approximately 25 kHz with D-Val(10) and decreases by approximately 10 kHz with D-Ala(10). With D-Ala(10) or D-Val(10), the outer resonance splits into two in a temperature-dependent manner. The NMR spectra indicate that the side chain torsion angles chi1 and chi2 for Trp(9) change when residue 10 is substituted. The changes in chi1 are small, in all cases less than 10 degrees, as is Deltachi2 when D-Ala(10) is introduced, but with D-Val(10) and D-Phe(10) Deltachi2 is at least 25 degrees. We conclude that D-Leu(10) helps to stabilize an optimal orientation of Trp(9) in gA channels in lipid bilayers and that changes in Trp orientation alter channel conductance and lifetime without affecting the basic channel fold.

Two-stage iterative methods for consistent Hermitian positive semidefinite systems

We study stationary and nonstationary two-stage iterative methods for the solution of consistent and singular linear systems Ax= b, where A is a Hermitian positive semidefinite matrix. When the outer splitting is P-regular and inner splitting is convergent, we prove the convergence of stationary two-stage iterative methods with inner iteration number q being a positive even number; conditions are given to ensure the convergence of stationary iterative methods for any positive inner iteration number q. Also, we present some theoretical results on the convergence of nonstationary two-stage methods. A comparison theorem is obtained for Hermitian positive semidefinite matrix and some applications to it are discussed. Moreover, we obtain a monotonicity result on the stationary two-stage iterative methods.

Interaction of Bee Venom Melittin with Zwitterionic and Negatively Charged Phospholipid Bilayers: A Spin-Label Electron Spin Resonance Study

Electron spin resonance (ESR) spectroscopy was used to study the penetration and interaction of bee venom melittin with dimyristoylphosphatidylcholine (DMPC) and ditetradecylphosphatidylglycerol (DTPG) bilayer membranes. Melittin is a surface-active, amphipathic peptide and serves as a useful model for a variety of membrane interactions, including those of presequences and signal peptides, as well as the charged subdomain of the cardiac regulatory protein phospholamban. Derivatives of phosphatidylcholine and phosphatidylglycerol spin-labeled at various positions along the sn-2 acyl chain were used to establish the chain flexibility gradient for the two membranes in the presence and absence of melittin. Negatively charged DTPG bilayer membranes showed a higher capacity for binding melittin without bilayer disruption than did membranes formed by the zwitterionic DMPC, demonstrating the electrostatic neutralization of bound melittin by DTPG. The temperature dependence of the ESR spectra showed that the gel-to-liquid crystalline phase transition is eliminated by binding melittin to DTPG bilayers, whereas a very broad transition remains in the case of DMPC bilayers. None of the spin labels used showed a two-component spectrum characteristic of a specific restriction of their chain motion by melittin, but the outer hyperfine splittings and effective chain order parameters were increased for all labels upon binding melittin. This indicates a reduced flexibility of the lipid chains induced by a surface orientation of the bound melittin. Whereas the characteristic shape of the chain flexibility gradient was maintained upon melittin addition to DMPC bilayers, the chain flexibility profile in DTPG bilayers was much more strongly perturbed. It was found that the steepest change in segmental flexibility was shifted toward the bilayer interior when melittin was bound to DTPG membranes, indicating a greater depth of penetration than in DMPC membranes. pH titration of stearic acid labeled at the C-5 position, used as a probe of interfacial interactions, showed net downward shifts in interfacial pK of 0.8 and 1.2 pH units contributed from the positive charge of melittin, outweighing upward shifts from interfacial dehydration, when melittin was bound to DTPG and DMPC, respectively. The perturbation of the outer hyperfine splitting was used to determine the interactions of melittin with spin-labeled lipids of different polar headgroups in DTPG and DMPC. Anionic lipids (phosphatidylserine, phosphatidylglycerol, and stearic acid) and zwitterionic lipids (phosphatidylethanolamine and phosphatidylcholine) had the largest outer splittings in the presence of melittin. Neutral lipids (protonated stearic acid and diacylglycerol) displayed the largest increase in outer splitting on binding melittin, which was attributed to a change in the vertical location of these lipids in the bilayer. Both effects were more pronounced in DTPG than in DMPC.

H-Splittings and two-stage iterative methods

Convergence of two-stage iterative methods for the solution of linear systems is studied. Convergence of the non-stationary method is shown if the number of inner iterations becomes sufficiently large. TheR 1-factor of the two-stage method is related to the spectral radius of the iteration matrix of the outer splitting. Convergence is further studied for splittings ofH-matrices. These matrices are not necessarily monotone. Conditions on the splittings are given so that the two-stage method is convergent for any number of inner iterations.

Nonequilibrium electronic polarization of the solvent in photoionization

The energetics of photoionization in condensed phases includes a significant contribution from nonequilibrium processes arising from dielectric dispersion of the solvent at the prevailing photon energy. The solvent is polarized by the varying electric field caused by the change of ionic valence as a result of photoionization. This ionic field varies in a time interval determined by the frequency of incident radiation. The following contributions from nonequilibrium processes to the energetics of photoionization are calculated for transparent and absorbing solvents: electronic polarization, London dispersion, and Born repulsion energies for a discrete model of coordinated solvent molecules in the inner-sphere solvation shell of anions and cations; electronic polarization of the outer-sphere region for a continuous medium model. The losses resulting from the rapid variation of the ionic field for an absorbing solvent are calculated for the inner- and outer-sphere regions, respectively, from a discrete model and a continuous medium. Damping of the ionic field resulting from solvent absorption is negligible. The theory is applied to aqueous solutions in the 7–10.4 eV range of photon energies by using dielectric data from reflectance spectroscopy of liquid water. Experimental dispersion spectra for photoelectron emission have the shape predicted by theory and display all the extrema at the photon energies of the calculated curves. The very pronounced effect of ionic strength on the balance between inner- and outer-sphere contributions predicted by theory (inner–outer sphere splitting) is fully confirmed by experiment. Dispersion spectra of inorganic ions in the range of each of the two absorption bands of liquid water (maxima at ∼8.2 and 10.0 eV) therefore exhibit a double maximum for normal dispersion and a double minimum for anomalous dispersion (12 extrema between 7.2 and 10.4 eV). Specific effect of the nature of anions is evident above 9.0 eV in inner–outer sphere splitting. The present study provides a way of probing the response of liquids and solutions to the rapidly varying intense ionic field resulting from the process of photoionization.

Characterization of Recursively Enumerable Sets with Supersets Effectively Isomorphic to all Recursively Enumerable Sets

We show that the lattice of supersets of a recursively enumerable (r.e.) set $A$ is effectively isomorphic to the lattice of all r.e. sets if and only if the complement $\bar A$ of $A$ is infinite and $\{ e|{W_e} \cap \bar A\;{\text {finite}}\}\;{\leqslant _{1}}\emptyset ''$ (i.e. $\bar A$ is $\text {semilow}_{1.5}$). It is obvious that the condition “$\bar {A}\; \text {semilow}_{1.5}$” is necessary. For the other direction a certain uniform splitting property (the "outer splitting property") is derived from $\text {semilow}_{1.5}$ and this property is used in an extension of Soare’s automorphism machinery for the construction of the effective isomorphism. Since this automorphism machinery is quite complicated we give a simplified proof of Soare’s Extension Theorem before we add new features to this argument.

Characterization of recursively enumerable sets with supersets effectively isomorphic to all recursively enumerable sets

We show that the lattice of supersets of a recursively enumerable (r.e.) set $A$ is effectively isomorphic to the lattice of all r.e. sets if and only if the complement $\bar A$ of $A$ is infinite and $\{ e|{W_e} \cap \bar A\;{\text {finite}}\}\;{\leqslant _{1}}\emptyset ''$ (i.e. $\bar A$ is $\text {semilow}_{1.5}$). It is obvious that the condition “$\bar {A}\; \text {semilow}_{1.5}$” is necessary. For the other direction a certain uniform splitting property (the "outer splitting property") is derived from $\text {semilow}_{1.5}$ and this property is used in an extension of Soare’s automorphism machinery for the construction of the effective isomorphism. Since this automorphism machinery is quite complicated we give a simplified proof of Soare’s Extension Theorem before we add new features to this argument.

Distinct states of lipid mobility in bovine rod outer segment membranes Resolution of spin label results

Freely diffusable lipid spin labels in bovine rod outer segment disc membranes display an apparent two-component ESR spectrum. One component is markedly more immobilized than that found in fluid lipid bilayers, and is attributed to lipid interacting directly with rhodopsin. For the 14-doxyl stearic acid spin label this more immobilized component has an outer splitting of 59 G at 0°C, with a considerable temperature dependence, the effective outer splitting decreasing to 54 G at 24°C. Spin label lipid chains covalently attached to rhodopsin can also display a two-component spectrum in rod outer segment membranes. In unbleached, non-delipidated membranes the 16-doxyl stearoyl maleimide label shows an immobilized component which has an outer splitting of 59 G at 0°C and a considerable temperature dependence. This component which is not resolved at high temperatures (24–35°C), is attributed to the lipid chains interacting directly with the monomeric protein, as with the diffusable labels. In contrast, in rod outer segment membranes which have been either delipidated or extensively bleached, a strongly immobilized component is observed with the 16-doxyl maleimide label at all temperatures. This immobilized component has an outer splitting of 62–64 G at 0°C, with very little temperature dependence (61–62 G at 35°C), and is attributed to protein aggregation.

Simulation of the EPR spectra of the cholestane spin probe under conditions of slow axial rotation. Application to gel phase dipalmitoyl phosphatidyl choline

Simulations have been made of the EPR spectra of the cholestane spin probe undergoing anisotropic rotation about its long molecular axis in macroscopically unoriented samples such as multilayer dispersions of lipids. The simulations were performed using the stochastic Liouville method with the correlation time for rotation around the long axis, τ ∥, as a variable, while the correlation time for rotation of the long axis, τ ⊥, was maintained fixed at 3 × 10 −7 sec. Empirical correlation time calibrations are introduced based on the outer splitting of the spectra, A max (valid throughout the range τ ∥ = 2 × 10 −9to 7.5 × 10 −8sec), and also on effective line height ratios of the motionally-averaged spectrum (valid for τ ∥ < 10 −9sec). The results of the simulations have been applied to the spectrum of the cholestane spin label in aqueous bilayers of dipalmitoyl phosphatidylcholine in the gel phase, below the fluid phase transition. It is found that the rate of long-axis rotation increases from that corresponding to correlation times > 10 −8 sec at 5°C to values corresponding to approximately 1–2 × 10 −9 sec at temperature > 20°C, while still in the gel phase and then to values ≲ 10 −10 sec above the main gel-fluid phase transition. In the latter case there is also appreciable motion of the long axis itself.

Observation of Divalent Dysprosium in CaF2 by Paramagnetic Resonance

The paramagnetic resonance spectra of Dy2+ in the cubic field of CaF2 were investigated at liquid-helium temperatures at frequencies of 9 to 27 kMc/sec. The nonmagnetic ground doublet (E) is strongly perturbed by two adjacent triplet states (T1 and T2) and transitions within the E state are made allowed. The T1 triplet state which is separated by 4.9 cm—1 from the ground state doublet has a g value along the [001] direction of 9.66±0.02 for the outer splitting. The observed splittings of the E and T1 states are in good agreement with the calculated values using the reported ratio of the cubic field parameters.

Paramagnetic Resonance of Trivalent Manganese in Rutile (TiO2)

An analysis has been made of the paramagnetic resonance spectrum of ${\mathrm{Mn}}^{3+}$, $3{d}^{4}$, in rutile. The spectrum at 4.2\ifmmode^\circ\else\textdegree\fi{}K can be fitted to a spin Hamiltonian with $S=2$; ${g}_{z}=1.99(\ifmmode\pm\else\textpm\fi{}0.01)$; ${g}_{\mathrm{xy}}=2.00(\ifmmode\pm\else\textpm\fi{}0.02)$; $D=\ensuremath{-}3.4$ ${\mathrm{cm}}^{\ensuremath{-}1}$(\ifmmode\pm\else\textpm\fi{}0.1); $|E|=0.116$ ${\mathrm{cm}}^{\ensuremath{-}1}$(\ifmmode\pm\else\textpm\fi{}0.001); $a=0.13$ ${\mathrm{cm}}^{\ensuremath{-}1}$(\ifmmode\pm\else\textpm\fi{}0.02); $|{A}_{x}|=84.5(\ifmmode\pm\else\textpm\fi{}2.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$; $|{A}_{z}|=52.8(\ifmmode\pm\else\textpm\fi{}0.5)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$; $|{A}_{c}|=80.6(\ifmmode\pm\else\textpm\fi{}1.0)\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}4}$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The quartic term $a$, previously observed only in the $3{d}^{5}$ group has now also been detected for $3{d}^{4}$. The value of $a$ for ${\mathrm{Mn}}^{3+}$ exceeds that for ${\mathrm{Mn}}^{2+}$ and ${\mathrm{Fe}}^{3+}$ systems ($3{d}^{5}$) by factors of 60 and 4, respectively. The constants $g$, $D$, and $A$ are in good agreement with theory. From the hyperfine splitting data a value of 3.2 ${\mathrm{a}.\mathrm{u}.}^{\ensuremath{-}3}$ was obtained for $〈{r}^{\ensuremath{-}3}〉$; this is about 30% below that calculated for the free ${\mathrm{Mn}}^{3+}$ ion. The $S$-electron contribution to the hfs, $\ensuremath{\kappa}$, was derived to be +0.52. ${\mathrm{Mn}}^{3+}$ has large zero-field splittings (the outer splitting is 412 kMc/sec), fairly long relaxation times, and narrow resonance lines and may be an appropriate material for masers operating at submillimeter wavelengths.