The use of two-way linear mixed models in multitreatment meta-analysis.

Meta-analysis summarizes the results of a series of trials. When more than two treatments are included in the trials and when the set of treatments tested differs between trials, the combination of results across trials requires some care. Several methods have been proposed for this purpose, which feature under different labels, such as network meta-analysis or mixed treatment comparisons. Two types of linear mixed model can be used for meta-analysis. The one expresses the expected outcome of treatments as a contrast to a baseline treatment. The other uses a classical two-way linear predictor with main effects for treatment and trial. In this article, we compare both types of model and explore under which conditions they give equivalent results. We illustrate practical advantages of the two-way model using two published datasets. In particular, it is shown that between-trial heterogeneity as well as inconsistency between different types of trial is straightforward to account for.

The schumann resonance: a global tropical thermometer.

The Schumann resonance, a global electromagnetic phenomenon, is shown to be a sensitive measure of temperature fluctuations in the tropical atmosphere. The link between Schumann resonance and temperature is lightning flash rate, which increases nonlinearly with temperature in the interaction between deep convection and ice microphysics.

Sprites, ELF Transients, and Positive Ground Strokes.

In two summertime mesoscale convective systems (MCSs), mesospheric optical sprite phenomena were often coincident with both large-amplitude positive cloud-to-ground lightning and transient Schumann resonance excitations of the entire Earth-ionosphere cavity. These observations, together with earlier studies of MCS electrification, suggest that sprites are triggered when the rapid removal of large quantities of positive charge from an areally extensive charge layer stresses the mesosphere to dielectric breakdown.

Probing single secretory vesicles with capillary electrophoresis.

Secretory vesicles obtained from the atrial gland of the gastropod mollusk Aplysia californica were chemically analyzed individually with a combination of optical trapping, capillary electrophoresis separation, and a laser-induced fluorescence detection. With the use of optical trapping, a single vesicle that had attoliters (10(-18) liters) of volume was introduced into the tapered inlet of a separation capillary. Once the vesicle was injected, it was lysed, and its components were fluorescently labeled with naphthalene-2, 3-dicarboxaldehyde before separation. The resultant electropherograms indicated distinct variations in the contents of single vesicles.

Biomimetic reliability strategies for self-healing vascular networks in engineering materials.

Self-healing via a vascular network is an active research topic, with several recent publications reporting the application and optimization of these systems. This work represents the first consideration of the probable failure modes of a self-healing system as a driver for network design. The critical failure modes of a proposed self-healing system based on a vascular network were identified via a failure modes, effects and criticality analysis and compared to those of the human circulatory system. A range of engineering and biomimetic design concepts to address these critical failure modes is suggested with minimum system mass the overall design driver for high-performance systems. Plant vasculature has been mimicked to propose a segregated network to address the risk of fluid leakage. This approach could allow a network to be segregated into six separate paths with a system mass penalty of only approximately 25%. Fluid flow interconnections that mimic the anastomoses of animal vasculatures can be used within a segregated network to balance the risk of failure by leakage and blockage. These biomimetic approaches define a design space that considers the existing published literature in the context of system reliability.

193 nm Laser photoionization and photodissociation for isomer differentiation in Fourier-transform mass spectrometry.

Energetic (6.4 eV) multiphoton ionization (MPI) or photodissociation, effected interchangeably in a Fourier-transform mass spectrometer, can differentiate isomers that yield similar electron ionization spectra. Selectivity is shown for isomers of C7H8, C7H9N, C7H7F, C8H10, but not of C6H3Cl{3} and C14H10. The contrasting MPI fragmentations and ionization efficiencies, as well as high sensitivities, are of substantial analytical utility. The high ionization efficiency makes possible high resolution MPI spectra, such as 470,000 (FWHH) for the molecular ion of anthracene, from a single laser pulse.

High resolution and tandem fourier-transform mass spectrometry with californium-252 plasma desorption.

For ions formed by plasma desorption (PD) in a Fourier-transform mass spectrometer, high resolution measurements are demonstrated, such as 65,000 (FWHH) for the protonated molecularion of gramicidin S (MW 1140.7). Resolution is substantially improved by delaying measurements until a significant ion concentration has built up in the cell, and by collisionally deactivating the orbital kinetic energy of the ions. This also makes the ions available for subsequent dissociation steps, so that tandem mass spectrometry can be demonstrated for PD ions. With this for larger ions, collisionally activated dissociation (CAD) is effected with > 85% efficiency. The CAD spectra of (M + Na)(+) and of fragment ions from the PD of gramicidin S provide structurally useful information.

Dissociation of heme-globin complexes by blackbody infrared radiative dissociation: molecular specificity in the gas phase?

The temperature dependence of the unimolecular kinetics for dissociation of the heme group from holo-myoglobin (Mb) and holo-hemoglobin alpha-chain (Hb-alpha) was investigated with blackbody infrared radiative dissociation (BIRD). The rate constant for dissociation of the 9 + charge state of Mb formed by electrospray ionization from a "pseudo-native" solution is 60% lower than that of Hb-alpha at each of the temperatures investigated. In solutions of pH 5.5-8.0, the thermal dissociation rate for Mb is also lower than that of HB-alpha (Hargrove, M. S. et al. J. Biol. Chem.1994, 269, 4207-4214). Thus, Mb is thermally more stable with respect to heme loss than Hb-alpha both in the gas phase and in solution. The Arrhenius activation parameters for both dissociation processes are indistinguishable within the current experimental error (activation energy 0.9 eV and pre-exponential factor of 10(8-10) s(-1)). The 9+ to 12+ charge states of Mb have similar Arrhenius parameters when these ions are formed from pseudo-native solutions. In contrast, the activation energies and pre-exponential factors decrease from 0.8 to 0.3 eV and 10(7) to 10(2) s(-1), respectively, for the 9 + to 12 + charge states formed from acidified solutions in which at least 50% of the secondary structure is lost. These results demonstrate that gas-phase Mb ions retain clear memory of the composition of the solution from which they are formed and that these differences can be probed by BIRD.

Gas-phase reactions of hydrated alkaline earth metal ions, M2+ (H2O)n (M = Mg, Ca, Sr, Ba and n = 4-7), with benzene.

Gas-phase reactions of hydrated divalent alkaline earth metal ions and benzene were investigated by electrospray ionization Fourier-transform mass spectrometry. Rate constants for solvent-exchange reactions were determined as a function of hydration extent for Mg2+, Ca2+, Sr2+, and Ba2+ clusters containing four to seven water molecules each. All of the strontium and barium clusters react quickly with benzene. Barium reacts slightly faster than the corresponding strontium cluster with the same number of water molecules attached. For calcium, clusters with four and five water molecules react quickly, whereas those with six and seven water molecules do not. Magnesium with four water molecules reacts quickly, but not when five through seven water molecules are attached. The slow reactivity observed for some of these clusters indicates that the cation-pi interaction between the metal ion and benzene is partially screened by the surrounding water molecules. The reactivity of magnesium with seven water molecules is intermediate that of the hexa- and pentahydrate and the tetrahydrate. This result is consistent with the seventh water molecule being in the outer shell and much more weakly bound. The unusual trend in reactivity observed for magnesium may be due to the presence of mixed shell structures observed previously. These results are the first to provide information about the relative importance of cation-pi interactions in divalent metal ions as a function of metal hydration extent. Such studies should also provide a model and some insight into the relative binding affinities of divalent metal ions to aromatic residues on peptides and proteins.

Modeling the maximum charge state of arginine-containing Peptide ions formed by electrospray ionization.

A model for the gas-phase proton transfer reactivity of multiply protonated molecules is used to quantitatively account for the maximum charge states of a series of arginine-containing peptide ions measured by Downard and Biemann (Int. J. Mass Spectrom. Ion Processes 1995, 148, 191-202). We find that our calculations account exactly for the maximum charge state for 7 of the 10 peptides and are off by one charge for the remaining 3. These calculations clearly predict the trend in maximum charge states for these peptides and provide further evidence that the maximum charge state of ions formed by electrospray ionization is determined by their gas-phase proton transfer reactivity.

Efficiency of collisionally-activated dissociation and 193-nm photodissociation of peptide ions in fourier transform mass spectrometry.

For tandem mass spectrometry, the Fourier transform instrument exhibits advantages for the use of collisionally-activated dissociation (CAD). The CAD energy deposited in larger ions can be greatly increased by extending the collision time to as much as 120 s, and the efficiency of trapping and measuring CAD product ions is many times greater than that found for triple-quadrupole or magnetic sector instruments, although the increased pressure from the collision gas is an offsetting disadvantage. A novel system that uses the same laser for photodesorption of ions and their subsequent photodissociation can produce complete dissociation of larger oligopeptide ions and unusually abundant fragment ions. In comparison to CAD, much more internal energy can be deposited in the primary ions using 193-nm photons, sufficient to dissociate peptide ions of m/z > 2000. Mass spectra closely resembling ion photodissociation spectra can also be obtained by' neutral photodissociation (193-nm laser irradiation of the sample) followed by ion photodesorption.

Blackbody infrared radiative dissociation of oligonucleotide anions.

The dissociation kinetics of a series of doubly deprotonated oligonucleotide 7-mers [d(A)7(2-), d(AATTAAT)2-, d(TTAATTA)2-, and d(CCGGCCG)2-] were measured using blackbody infrared radiative dissociation in a Fourier-transform mass spectrometer. The oligonucleotides dissociate first by cleavage at the glycosidic bond leading to the loss of a neutral nucleobase, followed by cleavage at the adjacent (5') phosphodiester bond to produce structurally informative a-base and w type ions. From the temperature dependence of the unimolecular dissociation rate constants, Arrhenius activation parameters in the zero-pressure limit are obtained for the loss of base. The measured Arrhenius parameters are dependent on the identity of the nucleobase. The process involving the loss of an adenine base from the dianions, d(A)7(2-), d(AATTAAT)2-, and d(TTAATTA)2- has an average activation energy (Ea) of approximately 1.0 eV and a preexponential factor (A) of 10(10) s-1. Both guanine and cytosine base loss occurs for d(CCGGCCG)2-. The average Arrhenius parameters for the loss of cytosine and guanine are Ea = 1.32 +/- 0.03 eV and A = 10(13.3 +/- 0.3) s-1. No loss of thymine was observed for mixed adenine-thymine oligonucleotides. Neither base loss nor any other fragmentation reactions occur for d(T)7(2-) over a 600 s reaction delay at 207 degrees C, a temperature close to the upper limit accessible with our instrument. The Arrhenius parameters indicate that the preferred cleavage sites for mixed oligonucleotides of similar mass-to-charge ratio will be strongly dependent on the internal energy of the precursor ions. At low internal energies (effective temperatures below 475 K), loss of adenine and subsequent cleavage of the adjacent phosphoester bonds will dominate, whereas at higher energies, preferential cleavage at C and G residues will occur. The magnitude of the A factors < or = 10(13) s-1 measured for the loss of the three nucleobases (A, G, and C) is indicative of an entropically neutral or disfavored process as the rate limiting step for this reaction.

Effects of solvent on the maximum charge state and charge state distribution of protein ions produced by electrospray ionization.

The effects of solvent composition on both the maximum charge states and charge state distributions of analyte ions formed by electrospray ionization were investigated using a quadrupole mass spectrometer. The charge state distributions of cytochrome c and myoglobin, formed from 47%/50%/3% water/solvent/acetic acid solutions, shift to lower charge (higher m/z) when the 50% solvent fraction is changed from water to methanol, to acetonitrile, to isopropanol. This is also the order of increasing gas-phase basicities of these solvents, although other physical properties of these solvents may also play a role. The effect is relatively small for these solvents, possibly due to their limited concentration inside the electrospray interface. In contrast, the addition of even small amounts of diethylamine (<0.4%) results in dramatic shifts to lower charge, presumably due to preferential proton transfer from the higher charge state ions to diethylamine. These results clearly show that the maximum charge states and charge state distributions of ions formed by electrospray ionization are influenced by solvents that are more volatile than water. Addition of even small amounts of two solvents that are less volatile than water, ethylene glycol and 2-methoxyethanol, also results in preferential deprotonation of higher charge state ions of small peptides, but these solvents actually produce an enhancement in the higher charge state ions for both cytochrome c and myoglobin. For instruments that have capabilities that improve with lower m/z, this effect could be taken advantage of to improve the performance of an analysis.

On the maximum charge state and proton transfer reactivity of peptide and protein ions formed by electrospray ionization.

A relatively simple model for calculation of the energetics of gas-phase proton transfer reactions and the maximum charge state of multiply protonated ions formed by electrospray ionization is presented. This model is based on estimates of the intrinsic proton transfer reactivity of sites of protonation and point charge Coulomb interactions. From this model, apparent gas-phase basicities (GB(app)) of multiply protonated ions are calculated. Comparison of this value to the gas-phase basicity of the solvent from which an ion is formed enables a maximum charge state to be calculated. For 13 commonly electrosprayed proteins, our calculated maximum charge states are within an average of 6% of the experimental values reported in the literature. This indicates that the maximum charge state for proteins is determined by their gas-phase reactivity. Similar results are observed for peptides with many basic residues. For peptides with few basic residues, we find that the maximum charge state is better correlated to the charge state in solution. For low charge state ions, we find that the most basic sites Arg, Lys, and His are preferentially protonated. A significant fraction of the less basic residues Pro, Trp, and Gln are protonated in high charge state ions. The calculated GB(app) of individual protonation sites varies dramatically in the high charge state ions. From these values, we calculate a reduced cross section for proton transfer reactivity that is significantly lower than the Langevin collision frequency when the GB(app) of the ion is approximately equal to the GB of the neutral base.

Hydration of gas-phase ions formed by electrospray ionization.

The hydration of gas-phase ions produced by electrospray ionization was investigated. Evidence that the hydrated ions are formed by two mechanisms is presented. First, solvent condensation during the expansion inside the electrospray source clearly occurs. Second, some solvent evaporation from more extensively solvated ions or droplets is apparent. To the extent that these highly solvated ions have solution-phase structures, then the final isolated gas-phase structure of the ion will be determined by the solvent evaporation process. This process was investigated for hydrated gramicidin S in a Fourier-transform mass spectrometer. Unimolecular dissociation rate constants of isolated gramicidin S ions with between 2 and 14 associated water molecules were measured. These rate constants increased from 16 to 230 s-1 with increasing hydration, with smaller values corresponding to magic numbers.

Dissociation energetics and mechanisms of leucine enkephalin (M + H)+ and (2M + X)+ ions (X = H, Li, Na, K, and Rb) measured by blackbody infrared radiative dissociation.

The dissociation kinetics of protonated leucine enkephalin and its proton and alkali metal bound dimers were investigated by blackbody infrared radiative dissociation in a Fourier-transform mass spectrometer. From the temperature dependence of the unimolecular dissociation rate constants, Arrhenius activation parameters in the zero-pressure limit are obtained. Protonated leucine enkephalin dissociates to form b(4) and (M-H(2)O)(+) ions with an average activation energy (E(a)) of 1.1 eV and an A factor of 10(10.5) s(-1). The value of the A factor indicates that these dissociation processes are rearrangements. The b(4) ions subsequently dissociate to form a(4) ions via a process with a relatively high activation energy (1.3 eV), but one that is entropically favored. For the cationized dimers, the thermal stability decreases with increasing cation size, consistent with a simple electrostatic interaction in these noncovalent ion-molecule complexes. The E(a) and A factors are indistinguishable within experimental error with values of approximately 1.5 eV and 10(17) s(-1), respectively. Although not conclusive, results from master equation modeling indicate that all these BIRD processes, except for b(4) --> a(4), are in the rapid energy exchange limit. In this limit, the internal energy of the precursor ion population is given by a Boltzmann distribution and information about the energetics and dynamics of the reaction are obtained directly from the measured Arrhenius parameters.

Surface-induced dissociation of peptide ions in Fourier-transform mass spectrometry.

Peptide molecular ion species up to m/z 3055 introduced into a Fourier-transform mass spectrometer can be made to undergo extensive fragmentation by electrically floating the ion cell. The proportion of ions dissociated increases with increasing voltage, with 48 eV producing the highest absolute abundance of fragment ions above m/z 200. At this energy, spectra closely resemble those from photodissociation at 193 nm, indicating an internal energy deposition of 6-7 eV; change of product abundances with kinetic energy resembles a conventional breakdown curve. The precursor ions apparently are electrostatically attracted to strike screen wires across the ion cell entrance, producing daughter ions of low kinetic energy.

Dissociation energies of deoxyribose nucleotide dimer anions measured using blackbody infrared radiative dissociation.

The dissociation kinetics of deprotonated deoxyribose nucleotide dimers were measured using blackbody infrared radiative dissociation. Experiments were performed with noncovalently bound dimers of phosphate, adenosine (dAMP), cytosine (dCMP), guanosine (dGMP), thymidine (dTMP), and the mixed dimers dAMP.dTMP and dGMP.dCMP. The nucleotide dimers fragment through two parallel pathways, resulting in formation of the individual nucleotide or nucleotide + HPO3 ion. Master equation modeling of this kinetic data was used to determine threshold dissociation energies. The dissociation energy of (dGMP.dCMP-H)- is much higher than that for the other nucleotide dimers. This indicates that there is a strong interaction between the nucleobases in this dimer, consistent with the existence of Watson-Crick hydrogen bonding between the base pairs. Molecular mechanics simulations indicate that Watson-Crick hydrogen bonding occurs in the lowest energy structures of (dGMP.dCMP-H)-, but not in (dAMP.dTMP-H)-. The trend in gas phase dissociation energies is similar to the trend in binding energies measured in nonaqueous solutions within experimental error. Finally, the acidity ordering of the nucleotides is determined to be dTMP < dGMP < dCMP < dAMP, where dAMP has the highest acidity (largest delta Gacid).

Proton transfer reactivity of large multiply charged ions.

Charge-charge interactions dramatically influence the dissociation and proton transfer reactivity of large multiply protonated ions. In combination with tandem mass spectrometry, proton transfer reactions have been used to determine the charge state of an ion and to increase the effective mass resolution of electrospray ionization mass spectra. A model for the proton transfer reactivity of multiply protonated ions, in which protons are assigned to specific sites in an ion based on the intrinsic reactivity of the site and the sum of point-charge Coulomb interactions between charges, is discussed. In combination with experimentally measured rates of proton transfer to bases of known gas-phase basicity, information about the intramolecular electrostatic interactions, gas-phase ion conformation and maximum charge state of an ion produced by electrospray ionization can be obtained.

Binding energies of the proton-bound amino Acid dimers gly.gly, ala.ala, gly.ala, and lys.lys measured by blackbody infrared radiative dissociation.

Arrhenius activation energies in the zero-pressure limit for dissociation of gas-phase proton-bound homodimers of N,N-dimethylacetamide (N,N-DMA), glycine, alanine, and lysine and the heterodimer alanine.glycine were measured using blackbody infrared radiative dissociation (BIRD). In combination with master equation modeling of the kinetic data, binding energies of these dimers were determined. A value of 1.25 +/- 0.05 eV is obtained for N,N-DMA and is in excellent agreement with that reported in the literature. The value obtained from the truncated Boltzmann model is significantly higher, indicating that the assumptions of this model do not apply to these ions. This is due to the competitive rates of photon emission and dissociation for these relatively large ions. The binding energies of the amino acid dimers are ~1.15 +/- 0.05 eV and are indistinguishable despite the difference in their gas-phase basicity and structure. The threshold dissociation energies can be accurately modeled using a range of dissociation parameters and absorption/emission rates. However, the absolute values of the dissociation rates depend more strongly on the absorption/emission rates. For N,N-DMA and glycine, an accurate fit was obtained using frequencies and transition dipole moments calculated at the ab initio RHF/2-31G* and MP2/2-31G* level, respectively. In order to obtain a similar accuracy using values obtained from AM1 semiempirical calculations, it was necessary to multiply the transition dipole moments by a factor of 3. These results demonstrate that in combination with master equation modeling, BIRD can be used to obtain accurate threshold dissociation energies of relatively small ions of biological interest.