Lipid fingerprinting of gram-positive lactobacilli by intact--matrix-assisted laser desorption/ionization mass spectrometry using a proton sponge based matrix

A method of direct lipid analysis by matrix-assisted laser desorption/ionization (MALDI) mass spectrometry (MS) in intact membranes, without prior extraction/separation steps, is described. Here, we demonstrate the efficacy of a strong base, 1,8-bis(dimethylamino)naphthalene (DMAN; proton sponge), as a novel matrix for MALDI-time-of-flight (TOF) MS analysis of whole cell bacteria. Initially, individual acidic low-molecular-weight analytes such as standard free fatty acids and phospholipids were analyzed using DMAN as matrix. Clear negative-mode MALDI-TOF MS spectra of all analytes show only deprotonated analyte signals at a low picomole limit of detection with the complete absence of matrix-related signals. These results indicate that DMAN represents a suitable matrix for MALDI-TOF MS analysis of mixtures of complex lipids as the intact membranes of microorganisms. DMAN was successfully applied to the analysis of Lactobacillus sanfranciscensis and L. plantarum microorganisms. Different components were sensitively detected in a single spot, including 16:0, 18:2, 18:3, and 21:0 free acids, glycolipids, phosphatidylglycerols (PGs) and cardiolipins. This method might be of general application, offering the advantage of quickly gaining information about lipid components of other gram-positive bacterial membranes.     

A binary matrix for background suppression in MALDI-MS of small molecules

Application of matrix-assisted laser-desorption ionization mass spectrometry (MALDI-MS) to small-molecule detection is often limited, because of high matrix background signals in the low-mass region. We report here an approach in which a mixture of two conventional MALDI matrices with different proton affinity was used to suppress the formation of matrix clusters and fragments. Specifically, when acidic α-cyano-4-hydroxycinnamic acid (CHCA) and basic 9-aminoacridine (9-AA) were used as the binary matrix, fewer background matrix peaks were observed in both positive and negative-mode detection of small molecules. In addition, the presence of CHCA substantially reduced the laser fluence needed for analyte desorption and ionization; thus better signal-to-background ratios were observed for negatively charged inositol phosphates in complex plant extracts. The mixing of MALDI matrices of different protonaffinities leads to suppression of matrix clusterformation and subsequently yields cleaner MS spectraof fewer background peaks in both positive andnegative detection of small molecules     

Direct quantitative analysis of peptides using matrix assisted laser desorption ionization

The protocol and various matrices were examined for quantification of biomolecules in both the low ca. 1200 amu and mid mass 6000–12000 amu ranges using an internal standard. Comparative studies of different matrices of MALDI quantitative analysis showed that the best accuracy and standard curve linearity were obtained for two matrices: (a) 2,5-dihydroxybenzoic acid (DHB) combined with a comatrix of fucose and 5-methoxysalicylic acid (MSA) and (b) ferulic acid/fucose. In the low mass range, the quantitative limit was in the 30 fmol range and in the mid mass range the quantitative limit was in the 250 fmol range. Linear response was observed over 2–3 decades of analyte concentration. The relative error of the standard curve slope was 1.3–1.8% with correlation coefficients of 0.996–0.998.The main problem for quantitative measurement was suppression of the signal of the less concentrated component (analyte or internal standard) by the more concentrated component. The effect was identified with saturation of the matrix by the analyte. The threshold of matrix saturation was found to be in the range of 1/(3000–5000) analyte/matrix molar ratio. To avoid matrix saturation the (analyte+internal standard) to matrix molar ratio should be below this threshold. Thus the internal standard concentration should be as low as possible.DHB/MSA/fucose and ferulic acid/fucose matrices demonstrated good accuracy and linearity for standard curves even when the internal standard had chemical properties different from the analyte. However, use of an internal standard with different chemical properties requires highly stable instrumental parameters as well as constant (analyte+internal standard)/matrix molar ratio for all samples.     

Direct quantitative analysis of peptides using matrix assisted laser desorption ionization

The protocol and various matrices were examined for quantification of biomolecules in both the low ca. 1200 amu and mid mass 6000-12000 amu ranges using an internal standard. Comparative studies of different matrices of MALDI quantitative analysis showed that the best accuracy and standard curve linearity were obtained for two matrices: (a) 2,5-dihydroxybenzoic acid (DHB) combined with a comatrix of fucose and 5-methoxysalicylic acid (MSA) and (b) ferulic acid/fucose. In the low mass range, the quantitative limit was in the 30 fmol range and in the mid mass range the quantitative limit was in the 250 fmol range. Linear response was observed over 2-3 decades of analyte concentration. The relative error of the standard curve slope was 1.3-1.8% with correlation coefficients of 0.996-0.998.The main problem for quantitative measurement was suppression of the signal of the less concentrated component (analyte or internal standard) by the more concentrated component. The effect was identified with saturation of the matrix by the analyte. The threshold of matrix saturation was found to be in the range of 1/(3000-5000) analyte/matrix molar ratio. To avoid matrix saturation the (analyte+internal standard) to matrix molar ratio should be below this threshold. Thus the internal standard concentration should be as low as possible.DHB/MSA/fucose and ferulic acid/fucose matrices demonstrated good accuracy and linearity for standard curves even when the internal standard had chemical properties different from the analyte. However, use of an internal standard with different chemical properties requires highly stable instrumental parameters as well as constant (analyte+internal standard)/matrix molar ratio for all samples.     

Parameters contributing to efficient ion generation in aerosol MALDI mass spectrometry

The Bioaerosol Mass Spectrometry (BAMS) system was developed for the real-time detection and identification of biological aerosols using laser desorption ionization. Greater differentiation of particle types is desired; consequently MALDI techniques are being investigated. The small sample size ( approximately 1 microm3), lack of substrate, and ability to simultaneously monitor both positive and negative ions provide a unique opportunity to gain new insight into the MALDI process. Several parameters known to influence MALDI molecular ion yield and formation are investigated here in the single particle phase. A comparative study of five matrices (2,6-dihydroxyacetophenone, 2,5-dihydroxybenzoic acid, alpha-cyano-4-hydroxycinnamic acid, ferulic acid, and sinapinic acid) with a single analyte (angiotensin I) is presented and reveals effects of matrix selection, matrix-to-analyte molar ratio, and aerosol particle diameter. The strongest analyte ion signal is found at a matrix-to-analyte molar ratio of 100:1. At this ratio, the matrices yielding the least and greatest analyte molecular ion formation are ferulic acid and alpha-cyano-4-hydroxycinnamic acid, respectively. Additionally, a significant positive correlation is found between aerodynamic particle diameter and analyte molecular ion yield for all matrices. SEM imaging of select aerosol particle types reveals interesting surface morphology and structure.     

New matrix of MALDI-TOF MS for analysis of small molecules

New matrix, metal-phthalocyanine (MPc), of matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS) was used for analysis of small molecules (usually <500 Da). By using MPcs as matrices, small molecular samples were moved to high mass-to-charge region where there was no interference caused by the traditional matrices. The mass of the target analyte was obtained by simple calculation.     

Ionic matrix for matrix-enhanced surface-assisted laser desorption ionization mass spectrometry imaging (ME-SALDI-MSI)

Matrix-enhanced surface-assisted laser desorption ionization mass spectrometry imaging (ME-SALDI MSI) has been previously demonstrated as a viable approach to improving MS imaging sensitivity. We describe here the employment of ionic matrices to replace conventional MALDI matrices as the coating layer with the aims of reducing analyte redistribution during sample preparation and improving matrix vacuum stability during imaging. In this study, CHCA/ANI (α-cyano-4-hydroxycinnamic acid/aniline) was deposited atop tissue samples through sublimation to eliminate redistribution of analytes of interest on the tissue surface. The resulting film was visually homogeneous under an optical microscope. Excellent vacuum stability of the ionic matrix was quantitatively compared with the conventional matrix. The subsequently improved ionization efficiency of the analytes over traditional MALDI was demonstrated. The benefits of using the ionic matrix in MS imaging were apparent in the analysis of garlic tissue sections in the ME-SALDI MSI mode.     

Mesoporous tungsten titanate as matrix for matrix-assisted laser desorption/ionization time-of-flight mass spectrometry analysis of biomolecules

In this paper, mesoporous tungsten titanate (WTiO) with different nano-pore structures was utilized as matrix for the analysis of short peptides by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS). Effect of characteristic features of mesoporous matrices on laser desorption/ionization process was investigated. Experiments showed that the ordered two-dimensional and three-dimensional mesoporous matrices were superior in performance to the non-ordered WTiO matrix. The dramatic enhancement of signal sensitivity by the ordered mesoporous matrices can be reasonably attributed to the ordered structure, which facilitated the understanding on structure-function relationship in mesoporous cavity for laser desorption process of adsorbed biomolecules. With the ordered mesoporous matrix, the short peptides are successfully detected. The presence of trace alkali metal salt effectively increased the analyte ion yields and the MALDI-TOFMS using the inorganic mesoporous matrices displayed a high salt tolerance. The developed technique also showed a satisfactory performance in peptide-mapping and amino-acid sequencing analysis.     

A binary matrix for improved detection of phosphopeptides in matrix‐assisted laser desorption/ionization mass spectrometry

Application of matrix‐assisted laser‐desorption/ionization mass spectrometry (MALDI MS) to analysis and characterization of phosphopeptides in peptide mixtures may have a limitation, because of the lower ionizing efficiency of phosphopeptides than nonphosphorylated peptides in MALDI MS. In this work, a binary matrix that consists of two conventional matrices of 3‐hydroxypicolinic acid (3‐HPA) and α‐cyano‐4‐hydroxycinnamic acid (CCA) was tested for phosphopeptide analysis. 3‐HPA and CCA were found to be hot matrices, and 3‐HPA not as good as CCA and 2,5‐dihydroxybenzoic acid (DHB) for peptide analysis. However, the presence of 3‐HPA in the CCA solution with a volume ratio of 1:1 could significantly enhance ion signals for phosphopeptides in both positive‐ion and negative‐ion detection modes compared with the use of pure CCA or DHB, the most common phosphopeptide matrices. Higher signal intensities of phosphopeptides could be obtained with lower laser power using the binary matrix. Neutral loss of the phosphate group (?80 Da) and phosphoric acid (?98 Da) from the phosphorylated‐residue‐containing peptide ions with the binary matrix was decreased compared with CCA alone. In addition, since the crystal shape prepared with the binary matrix was more homogeneous than that prepared with DHB, searching for ‘sweet’ spots can be avoided. The sensitivity to detect singly or doubly phosphorylated peptides in peptide mixtures was higher than that obtained with pure CCA and as good as that obtained using DHB. We also used the binary matrix to detect the in‐solution tryptic digest of the crude casein extracted from commercially available low fat milk sample, and found six phosphopeptides to match the digestion products of casein, based on mass‐to‐charge values and LIFT TOF‐TOF spectra. Copyright © 2009 John Wiley & Sons, Ltd.     

Characterization of humic substances by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) and laser desorption/ionization (LDI-)TOFMS have been used to characterize Suwannee River humic substances, obtained from the International Humic Substances Society (IHSS), and Armadale soil fulvic acid (ASFA). An array of MALDI matrices were tested for use with humic substances, including alpha-cyano-4-hydroxycinammic acid (CHCA), 2-(4-hydroxyphenylazo)benzoic acid (HABA), 2,5-dihydroxybenzoic acid (DHBA), sinapinic acid, dithranol and norharmane. DHBA yielded the best results, exhibiting superior ionization efficiency, low noise, broad applicability to the analytes of interest, and most importantly producing an abundance of high mass ions, the highest observed being m/z 1848. A number of sample preparation modes were investigated; the overlayer method improved sample/matrix homogeneity and hence shot-to-shot reproducibility. The choice of the matrix, mass ratio of analyte to matrix, and the sample preparation protocol, were found to be the most critical factors governing the quality of the mass spectra. Matrix suppression was greatly enhanced by ensuring good mixing of matrix and analyte in the solid phase, proper optimization of the matrix/analyte ratio, and optimizing delayed extraction to ensure complete matrix-analyte reaction in the plume before ions are moved to the flight tube. A number of common features, in particular specific ions which could not be attributed to the matrices or to contaminants, were present in the spectra of all the humic substances, regardless of origin or operational definition. Additionally, a prominent repeating pattern of peaks separated by 55, 114 and 169 Da was clearly observed in both LDI and MALDI, suggesting that the humic compounds studied here may have quasi-polymeric or oligomeric features.     

Analysis of three different types of fullerene derivatives by laser desorption/ionization time‐of‐flight mass spectrometry with new matrices

Three different types of fullerene derivatives, namely methano[60]fullerene dicarboxylate esters, [60]fulleropyrrolidines, and imino[60]fullerenes, were analyzed by matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry using trans‐4‐tert‐butyl‐4′‐nitrostilbene (TBNS), 1,8,9‐anthracenetriol (dithranol), 6‐aza‐2‐thiothymine (ATT), 2,5‐dihydroxybenzoic acid (DHB) and carbazole as matrices. Unit mass resolution (sufficient to clearly resolve isotopic peaks), high signal‐to‐noise ratio, and clean mass spectra for all analytes were acquired by the optimization of experimental parameters and choice of optimal solvent for the matrix and molar matrix‐to‐analyte ratio. The new matrix, TBNS, gave the best results in the positive‐ion mode, as it can provide higher yields of analyte molecular ions at a lower laser threshold than the other four matrices, together with a very low degree of unwanted fragmentations. In the negative‐ion mode dithranol was better than TBNS, and the other three matrices gave relatively poor mass spectra for these fullerene derivatives. Copyright © 2005 John Wiley & Sons, Ltd.     

The effect of solvent and matrix combinations on the analysis of bacteria by matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry

The ability to rapidly identify the taxonomic class of the wide variety of microorganisms involved in human and animal disease is becoming increasingly important, especially with the increasing development of resistance to the antibiotics which form the main defence against them. A number of groups have recognised the utility of matrix-assisted laser desorption/ionisation time-of-flight mass spectrometry MALDI-TOF in the analysis of these microorganisms. However, no consistent methodology has been developed which is in general use. In particular the use of different solvent extraction systems and mass spectrometric matrices can have significant effects on the quality of the data obtained. We have now studied a number of the commonly used matrices and a range of solvent systems of widely varying polarity in an attempt to devise an optimum analytical strategy for the rapid characterisation of these organisms by MALDI-TOFMS. The E. coli ATCC 9637 organisms were initially washed to remove growth medium contaminants, followed by extraction with one of a range of solvents prior to admixing with a number of different single matrices or binary and ternary combinations of these matrices. The results obtained indicate that a binary combination of 2-(4-hydroxyphenylazo)benzoic acid and 2-mercaptobenzothiazole (1:1) as matrix provides the best data after the proteinaceous material from the organism cell surface was extracted with 17% formic acid, 33% isopropyl alcohol and 50% water, (solvent 2 in this work).     

Negative-mode MALDI mass spectrometry for the analysis of pigments using tetrathiafulvalene as a matrix

Negative-mode matrix-assisted laser desorption/ionization-mass spectrometry (MALDI-MS) analysis of industrial pigments was performed using tetrathiafulvalene (TTF), an electron donating compound, as a matrix. Comparing with other matrices such as tetracyanoquinodimethane (TCNQ), dithranol, 2-hydroxy-6-nitroaniline (HNA), and harmine hydrochloride, the most abundant analyte ions were produced by the TTF as radical or deprotonated anions. In addition, fragment ions in the negative mode of operation are also found to be much less abundant than those in the positive mode of operation.     

Detection of water-soluble vitamins by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry using porphyrin matrices

The detection of water-soluble vitamins B(1), B(2), B(6), B(12) and C by matrix-assisted laser desorption/ionization (MALDI) time-of-flight mass spectrometry (TOFMS) was attempted by studying 17 porphyrin matrices. Comparative studies of porphyrin matrices, useful mass spectral window, matrix/analyte molar ratio (M/A), ultraviolet-visible absorption characteristics and quantitative results were made. Most porphyrin matrices provide a useful mass spectral window in the low-mass range. The optimal M/A increases with increasing molecular mass of the vitamin. Vitamin B(12) possesses the highest molecular mass and requires a higher M/A. The presence of hydroxyl or carboxyl groups in the porphyrin is an indicator of a useful MALDI matrix. Vitamins B(2) and B(6) were readily ionized upon irradiation with a 337 nm laser without the use of any porphyrin matrix. Improved linearity and sensitivity of the calibration curves were obtained with samples prepared with a constant M/A. The limits of detection and quantitation are at the picomole level. The results indicate that MALDI-TOFMS with porphyrin matrices is a rapid and viable technique for the detection of low molecular mass water-soluble vitamins.     

Isoliquiritigenin (4,2′,4′-trihydroxychalcone): A new matrix-assisted laser desorption/ionization matrix with outstanding properties for the analysis of neutral oligosaccharides

A novel matrix of isoliquiritigenin (ISL), a flavonoid with a chalcone structure (4,2′,4′-trihydroxychalcone), was demonstrated to be advantageous in the analysis of neutral oligosaccharides by matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOF MS). With ISL as a matrix, adequate signal for an analyte can be obtained in much lower matrix concentrations and laser intensity compared to commonly used MALDI matrices. Four different sample preparation methods were tested, and the dried droplet method exhibited the best performance on MALDI-TOF-MS analysis of oligosaccharides with ISL as a matrix. For the analysis of carbohydrates, compared with popular matrices such as 2,5-dihydroxybenzoic acid (DHB) and 2,4,6-trihydroxyacetophenone (THAP), ISL exhibited outstanding matrix properties as follows: (1) higher homogeneity of crystallization thus allowing automatic data acquisition, (2) better spectral quality in terms of resolution and signal to noise ratio (S N⁻¹), (3) better salt tolerance, (4) higher sensitivity, and (5) enough fragmentation yield to use LIFT-TOF/TOF MS to get richer structural information. In addition, reliable quantitative analysis of oligosaccharides with a good linearity over two concentration orders (1–100 pmol μL⁻¹) and good reproducibility of the signal intensity (RSD less than 15%) were achieved using this matrix. These results give a new outlook on high-speed analysis of neutral carbohydrates by MALDI-TOF MS.     

Matrix-assisted laser desorption/ionization time-of-flight mass spectrometry using an inorganic particle matrix for small molecule analysis

Fine metal or metal oxide powder as an alternative to conventional organic matrices in matrix-assisted laser desorption/ionization time-of-flight mass spectrometry (MALDI-TOFMS) has been utilized successfully for lower molecular mass analytes, poly(ethylene glycol) 200 (PEG 200) and methyl stearate. Eleven kinds of particle, Al, Mn, Mo, Si, Sn, SnO2, TiO2, W, WO3, Zn and ZnO, were evaluated. The analyte was mixed with a metal or metal oxide powder (inorganic matrix) with particle diameter of tens of micrometers and liquid dispersant, followed by application to the sample target. Using a commercial MALDI-TOFMS instrument equipped with an internal 337 nm pulsed nitrogen laser, the analytes, PEG 200 and methyl stearate, were ionized as the alkali metal ion adducted molecules [M+Na]+ or [M+K]+ when the inorganic matrices Mn, Mo, Si, Sn, TiO2, W, WO3, Zn or ZnO were used. In the case of an Al matrix, PEG 200 was ionized as [M+K]+, whereas methyl stearate was ionized as [M+H]+ and [M+Al]+. These particles have potential as the matrix for MALDI. During our examination, however, only SnO2 particles did not ionize either PEG 200 or methyl stearate. Based on our protocol, when TiO2 powder was suspended with liquid paraffin, PEG 200 and methyl stearate gave their MALDI-TOF mass spectra with the lowest background noise and highest intensity. TiO2 powder seemed to be a broad potential matrix for low molecular mass polar or non-polar analytes. The results suggested that bulk particles caused rapid heating/vaporization processes and ionized analyte molecules under irradiation with a pulsed UV laser. The present method can be readily applied to obtain the low background noise MALDI-TOF mass spectra of small-sized compounds.     

C60衍生物的MALDI-TOFMS分析

C_(60)衍生物在超导、非线性光学、催化、材料和生物活性等方面有巨大的潜在应用价值。C_(60)衍生物大多为固体,蒸汽压较低,采用需要加热才能够使样品气化电离的质谱或"硬"电离质谱方法进行测定,易造成C_(60)衍生物分解并释放出配体。近年来国内外应用基体辅助激光解吸软电离质谱法成功分析了许多不同类型的C_(60)衍生物如卤化C_(60)酰胺化C_(60)芳基化C_(60)、C_(60)部花菁、煤基C_(60)烟灰萃取产物、金属C_(60)衍生物以及C_(60)乙二胺膜等。本文报道采用MALDI-TOFMS法分析C_(60)酯衍生物和C_(60)吡咯烷衍生物的结果。     

9,10‐Diphenylanthracene as a matrix for MALDI‐MS electron transfer secondary reactions

The most common secondary‐ionization mechanism in positive ion matrix‐assisted laser desorption/ionization (MALDI) involves a proton transfer reaction to ionize the analyte. Peptides and proteins are molecules that have basic (and acidic) sites that make them susceptible to proton transfer. However, non‐polar, aprotic compounds that lack basic sites are more difficult to protonate, and creating charged forms of this type of analyte can pose a problem when conventional MALDI matrices are employed. In this case, forming a radical molecular ion through electron transfer is a viable alternative, and certain matrices may facilitate the process. In this work, we investigate the performance of a newly developed electron‐transfer secondary reaction matrix: 9,10‐diphenylanthracene (9,10‐DPA). The use of 9,10‐DPA as matrix for MALDI analysis has been tested using several model compounds. It appears to promote ionization through electron transfer in a highly efficient manner as compared to other potential matrices. Thermodynamic aspects of the observed electron transfers in secondary‐ionization reactions were also considered, as was the possibility for kinetically controlled/endothermic, electron‐transfer reactions in the MALDI plume. Copyright © 2012 John Wiley & Sons, Ltd.     

Investigation of colloidal graphite as a matrix for matrix‐assisted laser desorption/ionisation mass spectrometry of low molecular weight analytes

The analysis of low molecular weight compounds by matrix‐assisted laser desorption/ionisation mass spectrometry is problematic due to the interference and suppression of analyte ionisation by the matrices typically employed – which are themselves low molecular weight compounds. The application of colloidal graphite is demonstrated here as an easy to use matrix that can promote the ionisation of a wide range of analytes including low molecular weight organic compounds, complex natural products and inorganic complexes. Analyte ionisation with colloidal graphite is compared with traditional organic matrices along with various other sources of graphite (e.g. graphite rods and charcoal pencils). Factors such as ease of application, spectra reproducibility, spot longevity, spot‐to‐spot reproducibility and spot homogeneity (through single spot imaging) are explored. For some analytes, considerable matrix suppression effects are observed resulting in spectra completely devoid of matrix ions. We also report the observation of radical molecular ions [M^–●] in the negative ion mode, particularly with some aromatic analytes. Copyright © 2016 John Wiley & Sons, Ltd.     

The cationization of synthetic polymers in matrix‐assisted laser desorption/ionization time‐of‐flight mass spectrometry: Investigations of the salt‐to‐analyte ratio

Matrix‐assisted laser desorption/ionization (MALDI) is a soft ionization technique that when used to analyze synthetic polymer analytes often requires the addition of a metal cationization agent (herein termed the “salt”). The choice of both the matrix and the cationization agent needs to be taken into account when considering the polymer under study; different polymers have shown different affinities toward different cationization agents, and their selectivity can change as the matrix changes. Salt‐to‐analyte ratio (S/A) plots are used in this work to investigate the effect of the quantity of cationization agent employed in the analysis of a poly (methylmethacrylate) (PMMA) analyte with different MALDI matrices. The point at which analyte signal stops increasing with the added cationization agent is termed the “cation saturation point,” and it was found to occur around a S/A of 1. When the analyte signal after this point remains constant, it is termed an “ideal case.” The “non‐ideal case” occurs when the analyte signal decreases after the cation saturation point. The amount of matrix present (measured as the matrix‐to‐analyte molar ratio, M/A) and the use of different counterions for the salt are also found to affect the intensity of the analyte signal. In non‐ideal cases, changes in the counterion or an increase in the M/A are found to increase the analyte signal, often converting an initially observed non‐ideal case into an ideal case. Several experiments attempting to uncover the reason for observation of the non‐ideal S/A behavior are also described.