Atomic Latin squares of order eleven

A Latin square is pan-Hamiltonian if the permutation which defines row i relative to row j consists of a single cycle for every i j. A Latin square is atomic if all of its conjugates are pan-Hamiltonian. We give a complete enumeration of atomic squares for order 11, the smallest order for which there are examples distinct from the cyclic group. We find that there are seven main classes, including the three that were previously known. A perfect 1-factorization of a graph is a decomposition of that graph into matchings such that the union of any two matchings is a Hamiltonian cycle. Each pan-Hamiltonian Latin square of order n describes a perfect 1-factorization of Kn,n, and vice versa. Perfect 1-factorizations of Kn,n can be constructed from a perfect 1-factorization of Kn+1. Six of the seven main classes of atomic squares of order 11 can be obtained in this way. For each atomic square of order 11, we find the largest set of Mutually Orthogonal Latin Squares (MOLS) involving that square. We discuss algorithms for counting orthogonal mates, and discover the number of orthogonal mates possessed by the cyclic squares of orders up to 11 and by Parker's famous turn-square. We find that the number of atomic orthogonal mates possessed by a Latin square is not a main class invariant. We also define a new sort of Latin square, called a pairing square, which is mapped to its transpose by an involution acting on the symbols. We show that pairing squares are often orthogonal mates for symmetric Latin squares. Finally, we discover connections between our atomic squares and Franklin's diagonally cyclic self-orthogonal squares, and we correct a theorem of Longyear which uses tactical representations to identify self-orthogonal Latin squares in the same main class as a given Latin square.

Hydrochemistry, mineralogy and sulphur isotope geochemistry of acid mine drainage at the Mt Morgan mine environment, Queensland, Australia

Mineralogical, hydrochemical and S isotope data were used to constrain hydrogeochemical processes that produce acid mine drainage from sulfidic waste at the historic Mount Morgan Au–Cu mine, and the factors controlling the concentration of SO4 and environmentally hazardous metals in the nearby Dee River in Queensland, Australia. Some highly contaminated acid waters, with metal contents up to hundreds of orders of magnitude greater than the Australia–New Zealand environmental standards, by-pass the water management system at the site and drain into the adjacent Dee River. Mine drainage precipitates at Mt. Morgan were classified into 4 major groups and were identified as hydrous sulfates and hydroxides of Fe and Al with various contents of other metals. These minerals contain adsorbed or mineralogically bound metals that are released into the water system after rainfall events. Sulfate in open pit water and collection sumps generally has a narrow range of S isotope compositions (δ34S = 1.8–3.7‰) that is comparable to the orebody sulfides and makes S isotopes useful for tracing SO4 back to its source. The higher δ34S values for No. 2 Mill Diesel sump may be attributed to a difference in the source. Dissolved SO4 in the river above the mine influence and 20 km downstream show distinctive heavier isotope compositions (δ34S = 5.4–6.8‰). The Dee River downstream of the mine is enriched in 34S (δ34S = 2.8–5.4‰) compared with mine drainage possibly as a result of bacterial SO4 reduction in the weir pools, and in the water bodies within the river channel. The SO4 and metals attenuate downstream by a combination of dilution with the receiving waters, SO4 reduction, and the precipitation of Fe and Al sulfates and hydroxides. It is suggested here that in subtropical Queensland, with distinct wet and dry seasons, temporary reducing environments in the river play an important role in S isotope systematics

On the relationship between the critical temperature and the London penetration depth in layered organic superconductors

We present an analysis of previously published measurements of the London penetration depth of layered organic superconductors. The predictions of the BCS theory of superconductivity are shown to disagree with the measured zero temperature, in plane, London penetration depth by up to two orders of magnitude. We find that fluctuations in the phase of the superconducting order parameter do not determine the superconducting critical temperature as the critical temperature predicted for a Kosterlitz–Thouless transition is more than an order of magnitude greater than is found experimentally for some materials. This places constraints on theories of superconductivity in these materials.

Validity of (-)-[H-3]-CGP 12177A as a radioligand for the 'putative beta(4)-adrenoceptor' in rat atrium

1 We have recently suggested the existence in the heart of a 'putative beta(4)-adrenoceptor' based on the cardiostimulant effects of non-conventional partial agonists, compounds that cause cardiostimulant effects at greater concentrations than those required to block beta(1)- and Bz-adrenoceptors. We sought to obtain further evidence by establishing and validating a radioligand binding assay for this receptor with (-)-[H-3]-CGP 12177A ((-)-4-(3-tertiarybutylamino-2-hydroxypropoxy) benzimidazol-2-one) in rat atrium. We investigated (-)-[H-3]-CGP 12177A for this purpose for two reasons, because it is a nonconventional partial agonist and also because it is a hydrophilic radioligand. 2 Increasing concentrations of(-)-[H-3]-CGP 12177A, in the absence or presence of 20 mu M (-)-CGP 12177A to define non-specific binding, resulted in a biphasic saturation isotherm. Low concentrations bound to beta(1)- and beta(2)-adrenoceptors (pK(D) 9.4+/-0.1, B-max 26.9+/-3.1 fmol mg(-1) protein) and higher concentrations bound to the 'putative beta(4)-adrenoceptor' (pK(D) 7.5+/-0.1, B-max 47.7+/-4.9 fmol mg(-1) protein). In other experiments designed to exclude beta(1)- and beta(2)-adrenoceptors, (-)-[H-3]-CGP 12177A (1-200 nM) binding in the presence of 500 nM (-)-propranolol was also saturable (pK(D) 7.6+/-0.1, B-max 50.8+/-7.4 fmol mg(-1) protein). 3 The non-conventional partial agonists (-)-CGP 12177A (pK(i) 7.3+/-0.2), (+/-)-cyanopindolol (pK(i) 7.6+/-0.2), (-)-pindolol (pK(i) 6.6+/-0.1) and (+)-carazolol (pk(i), 7.2+/-0.2) and the antagonist (-)-bupranolol (pK(i) 6.6+/-0.2), all competed for (-)-[H-3]-CGP 12177A binding in the presence of 500 nM (-)-propranolol at the 'putative beta(4)-adrenoceptor', with affinities closely similar to potencies and affinities determined in organ bath studies. 4 The catecholamines competed with (-)-[H-3]-CGP 12177A at the 'putative beta(4)-adrenoceptor' in a stereoselective manner, (-)-noradrenaline (pK(iH) 6.3 +/- 0.3, pK(i), 3.5 +/- 0.1), (-)-adrenaline (pK(iH) 6.5 +/- 0.2, pK(iL) 2.9 +/- 0.1), (-)-isoprenaline (pK(iH) 6.2 +/- 0.5, pK(iL) 3.3 +/- 0.1), (+)-isoprenaline (pK(i) < 1.7), (-)-R0363 ((-)-(1-(3,4-dimethoxyphenethylamino)-3-(3,4-dihydroxyphenoxy)-2-propranol)oxalate, pK(i) 5.5 +/- 0.1). 5 The inclusion of guanosine 5-triphosphate (GTP 0.1 mM) had no effect on binding of (-)-CGP 12177A or (-)-isoprenaline to the 'putative beta(4)-adrenoceptor'. In competition binding studies, (-)-CGP 12177A competed with (-)-[H-3]-CGP 12177A for one receptor state in the absence (pK(i) 7.3 +/- 0.2) or presence of GTP (pK(i) 7.3 +/- 0.2). (-)-Isoprenaline competed with (-)-[H-3]-CGP 12177A for two states in the absence (pK(iH) 6.6 +/- 0.3, pK(iL) 3.5 +/- 0.1; % H 25 +/- 7) or presence of GTP (pK(iH) 6.2 +/- 0.5, pK(iL) 3.4 +/- 0.1; % H 37 +/- 6). In contrast, at beta(1)-adrenoceptors, GTP stabilized the low affinity state of the receptor for (-)-isoprenaline. 6 The specificity of binding to the 'putative beta(4)-adrenoceptor' was tested with compounds active at other receptors. High concentrations of the beta(4)-adrenoceptor agonists, BRL 37344 ((RR + SS)[4-[2-[[2-(3-chlorophenyl)-2-hydroxy -ethyl]amino]propyl]phenoxy]acetic acid, 6 mu M), SR 58611A (ethyl((7S)-7-[(2R)-2-(3-chlorophenyl)-2-hydroxyethylamino]-5,6,7,8-tetrahydronaphtyl-2-yloxy) acetate hydrochloride, 6 mu M), ZD 2079 ((+/-)-1-phenyl-2-(2-4-carboxymethylphenoxy)-ethylamino)ethan-1-ol, 60 mu M), CL 316243 (disodium (R,R)-5-[2-[2-(3-chlorophenyl)-2-hydroxyethyl-amino]propyl]- 1,3-benzodioxole-2,2-dicarboxylate, 60 mu M) and antagonist SR 59230A (3-(2-ethylphenoxy)-1-[(1S)-1,2,3,4-tetrahydronaphth-1-ylamino]-2S-2-propanol oxalate, 6 mu M) caused less than 22% inhibition of (-)-[H-3]-CGP 12177A binding in the presence of 500 nM (-)-propranolol. Histamine (1 mM), atropine (1 mu M), phentolamine (10 mu M), 5-HT(100 mu M) and the 5-HT4 receptor antagonist SE 207710 ((1-butyl-4-piperidinyl)-methyl 8-amino-7-iodo-1 ,4-benzodioxan-5-carboxylate, 10 nM) caused less than 26% inhibition of binding. 7 Non-conventional partial agonists, the antagonist (-)-bupranolol and catecholamines all competed for (-)-[H-3]-CGP 12177A binding in the absence of (-)-propranolol at beta(1)-adrenoceptors, with affinities (pK(i)) ranging from 1.6-3.6 log orders greater than at the 'putative beta(4)-adrenoceptor'. 8 We have established and validated a radioligand binding assay in rat atrium for the 'putative beta(4)-adrenoceptor' which is distinct from beta(1)-, beta(2)- and beta(3)-adrenoceptors. The stereoselective interaction with the catecholamines provides further support for the classification of the receptor as 'putative beta(4)-adrenoceptor'.

Sensitive detection of sodium in a flame using parametric four-wave mixing and seeded parametric four-wave mixing

Two-photon resonant parametric four-wave mixing and a newly developed variant called seeded parametric four-wave mixing are used to detect trace quantities of sodium in a flame. Both techniques are simple, requiring only a single laser to generate a signal beam at a different wavelength which propagates collinearly with the pump beam, allowing efficient signal recovery. A comparison of the two techniques reveals that seeded parametric four-wave mixing is more than two orders of magnitude more sensitive than parametric four-wave mixing, with an estimated detection sensitivity of 5 x 10(9) atoms/cm(3). Seeded parametric four-wave mixing is achieved by cascading two parametric four-wave mixing media such that one of the parametric fields generated in the first high-density medium is then used to seed the same four-wave mixing process in a second medium in order to increase the four-wave mixing gain. The behavior of this seeded parametric four-wave mixing is described using semiclassical perturbation theory. A simplified small-signal theory is found to model most of the data satisfactorily. However, an anomalous saturationlike behavior is observed in the large signal regime. The full perturbation treatment, which includes the competition between two different four-wave mixing processes coupled via the signal field, accounts for this apparently anomalous behavior.

Complexes of 1-thia-4,7,10-triazacyclododecane ([12]aneN(3)S) - Synthesis, structure and stability constants

The 12-membered macrocyclic ligand 1-thia-4,7, 10-triazacyclododecane ([12]aneN(3)S) has been synthesised, although upon crystallization from acetonitrile a product in which carbon dioxide had added to one secondary amine in the macrocyclic ring (H[12]aneN(3)SCO(2). H2O) was isolated and subsequently characterised by X-ray crystallography. The protonation constants for [12]aneN(3)S and stability constants with Zn(II), Pb(II), Cd(II) and Cu(II) have been determined either potentiometrically or spectrophotometrically in aqueous solution, and compared with those measured or reported for the ligands 1-oxa-4,7,10-triazacyclododecane ([12]aneN(3)O) and 1,4,7,10-tetraazacyclododecane ([12]aneN(4)). The magnitudes of the stability constants are consistent with trends observed previously for macrocyclic ligands as secondary amine donors are replaced with oxygen and thioether donors although the stability constant for the [Hg([12]aneN(4))](2+) complex has been estimated from an NMR experiment to be at least three orders of magnitude larger than reported previously. Zinc(II), mercury(II), lead(II), copper(II) and nickel(II) complexes of [12]aneN(3)S have been isolated and characterised by X-ray crystallography. In the case of copper(II), two complexes [Cu([12]aneN(3)S)(H2O)](ClO4)(2) and [Cu-2([12]aneN(3)S)(2)(OH)(2)](ClO4)(2) were isolated, depending on the conditions employed. Molecular mechanics calculations have been employed to investigate the relative metal ion size preferences of the [3333], asym-[2424] and sym-[2424] conformation isomers. The calculations predict that the asym-[2424] conformer is most stable for M-N bond lengths in the range 2.00-2.25 Angstrom whilst for the larger metal ions the [3333] conformer is dominant. The disorder seen in the structure of the [Zn([12]aneN(3)S)(NO3)](+) complex is also explained by the calculations. (C) 1999 Elsevier Science Ltd. All rights reserved.

Molecular characterization of the toxic cyanobacterium Cylindrospermopsis raciborskii and design of a species-specific PCR

Cylindrospermopsis raciborskii is a toxic-bloom-forming cyanobacterium that is commonly found in tropical to subtropical climatic regions worldwide, but it is also recognized as a common component of cyanobacterial communities in temperate climates. Genetic profiles of C. raciborskii were examined in 19 cultured isolates originating from geographically diverse regions of Australia and represented by two distinct morphotypes. A 609-bp region of rpoC1, a DNA-dependent RNA polymerase gene, was amplified by PCR from these isolates with cyanobacterium-specific primers. Sequence analysis revealed that all isolates belonged to the same species, including morphotypes with straight or coiled trichomes. Additional rpoC1 gene sequences obtained for a range of cyanobacteria highlighted clustering of C. raciborskii with other heterocyst-producing cyanobacteria (orders Nostocales and Stigonematales). In contrast, randomly amplified polymorphic DNA and short tandemly repeated repetitive sequence profiles revealed a greater level of genetic heterogeneity among C. raciborskii isolates than did rpoC1 gene analysis, and unique band profiles were also found among each of the cyanobacterial genera examined. A PCR test targeting a region of the rpoC1 gene unique to C. raciborskii was developed for the specific identification of C. raciborskii from both purified genomic DNA and environmental samples. The PCR was evaluated with a number of cyanobacterial isolates, but a PCR-positive result was only achieved with C, raciborskii. This method provides an accurate alternative to traditional morphological identification of C. raciborskii.

Determination of the stability constants of mercury(II) complexes of mixed donor macrobicyclic encapsulating ligands

The reactions of mercury(II) with the mixed donor encapsulating ligands 3,6,16-trithia-6,11,19-triazabicyclo[6.6.6]icosane (AMN(3)S(3)sar) and 1-amino-8-methyl-6,19-dithia-3,10,13,16-tetraazabicyclo[6.6.6]icosane (AMN(4)S(2)sar) have been studied. NMR ligand-ligand competition experiments with the ligands 1,4,8,11-tetraazaeyclotetradecane ([14]aneN(4)), 1-thia-4,7,10-triazacyclododecane ([12]aneN(3)S) and ethylenediaminetetraacetic acid (EDTA) with AMN(3)S(3)sar and Hg(II) indicated that [14]aneN(4) would be an appropriate competing ligand for the, determination of the Hg(II) stability constant. Calculations indicated the ratio of concentrations of AMN3S3sar, [14]aneN(4) and Hg(II) required for the determination of the stability constant ranged from 1:1:1 to 1:5:1. Refinement of the titration curves yielded log(10)K[Hg(AMN(3)S(3)sar)](2+) = 17.7. A similar competition titration resulted in the determination of the stability constant for the AMN(4)S(2)sar system as log(10)K[Hg(AMN(4)S(2)sar)](2+) = 19.5. The observed binding constants for the mixed N/S donor systems and the hexaaza analogues sar (3,6,10,13,16,19-hexaazabicyclo [6.6.6]icosane) and diamsar (1,8-diamino-3,6,10,13,16,19 -hexazabicyclo [6.6.6] icosane (log(10)K-[Hg(diamsar)](2+) = 26.4; log(10)K[Hg(sar)](2+) = 28.1) differ by approximately ten orders of magnitude. The difference is ascribed not to a cryptate effect but to a mismatch in the Hg-N and Hg-S bond lengths in the N/S systems.

The spectra of red quasars

We measure the spectral properties of a representative sub-sample of 187 quasars, drawn from the Parkes Half-Jansky, Flat-radio-spectrum Sample (PHFS). Quasars with a wide range of rest-frame optical/UV continuum slopes are included in the analysis: their colours range over 2 < B-K < 7. We present composite spectra of red and blue sub-samples of the PHFS quasars. and tabulate their emission line properties. The median Hbeta and [0 111] emission line equivalent widths of the red quasar sub-sample are a factor of ten weaker than those of the blue quasar sub-sample. No significant differences are seen between the equivalent width distributions of the C IV, C III] and Mg 11 lines. Both the colours and the emission line equivalent widths of the red quasars can be explained by the addition of a featureless red synchrotron continuum component to an otherwise normal blue quasar spectrum. The red synchrotron component must have a spectrum at least as red as a power-law of the form F-nu proportional to nu(-2.8). The relative strengths of the blue and red components span two orders of magnitude at rest-frame 500 nm. The blue component is weaker relative to the red component in low optical luminosity sources. This suggests that the fraction of accretion energy going into optical emission from the jet is greater in low luminosity quasars. This correlation between colour and luminosity may be of use in cosmological distance scale work. This synchrotron model does not, however, fit similar to10% of the quasars, which have both red colours and high equivalent width emission lines. We hypothesise that these red, strong-lined quasars have intrinsically weak Big Blue Bumps. There is no discontinuity in spectral properties between the BL Lac objects in our sample and the other quasars. BL Lac objects appear to be the red, low equivalent width tail of a continuous distribution. The synchrotron emission component only dominates the spectrum at longer wavelengths, so existing BL Lac surveys will be biased against high redshift objects. This will affect measurements of BL Lac evolution. The blue PHFS quasars have significantly higher equivalent width C IV, Hbeta and [0 111] emission than a matched sample of optically selected QSOs.

Phoriospongin A and B: Two new nematocidal depsipeptides from the Australian marine sponges Phoriospongia sp and Callyspongia bilamellata

Bioassay-directed fractionation of two southern Australian sponges, Phoriospongia sp. and Callyspongia bilamellata, yielded two new nematocidal depsipeptides, identified as phoriospongins A (1) and B (2). The structures of the phoriospongins were determined by detailed spectroscopic analysis and comparison with the previously reported sponge depsipeptide cyclolithistide A (3), as well as ESIMS and HPLC analysis of acid hydrolysates. It is noteworthy that the unique and yet structurally related metabolites 1-3 are found in sponges spanning three taxonomic orders, Poescilosclerida, Haplosclerida, and Lithistida.

The Las Campanas/AAT Rich Cluster Survey - II. The environmental dependence of galaxy colours in clusters at z similar to 0.1

We present a photometric investigation of the variation in galaxy colour with environment in 11 X-ray-luminous clusters at 0.07 less than or equal to z less than or equal to 0.16 taken from the Las Campanas/AAT Rich Cluster Survey. We study the properties of the galaxy populations in individual clusters, and take advantage of the homogeneity of the sample to combine the clusters together to investigate weaker trends in the composite sample. We find that modal colours of galaxies lying on the colour-magnitude relation in the clusters become bluer by d(B - R)/dr(p) = -0.022 +/- 0.004 from the cluster core out to a projected radius of r(p) = 6 Mpc, further out in radius than any previous study. We also examine the variation in modal galaxy colour with local galaxy density, 2, for galaxies lying close to the colour-magnitude relation, and find that the median colour shifts bluewards by d(B - R)/d log(10)(Sigma) = -0.076 +/- 0.009 with decreasing local density across three orders of magnitude. We show that the position of the red envelope of galaxies in the colour-magnitude relation does not vary as a function of projected radius or density within the clusters, suggesting that the change in the modal colour results from an increasing fraction of bluer galaxies within the colour-magnitude relation, rather than a change in the colours of the whole population. We show that this shift in the colour-magnitude relations with projected radius and local density is greater than that expected from the changing morphological mix based on the local morphology-density relation. We therefore conclude that we are seeing a real change in the properties of galaxies on the colour-magnitude relation in the outskirts of clusters. The simplest interpretation of this result (and similar constraints in local clusters) is that an increasing fraction of galaxies in the lower density regions at large radii within clusters exhibit signatures of star formation in the recent past, signatures which are not seen in the evolved galaxies in the highest density regions.

Potential triggers for akinete differentiation in an Australian strain of the cyanobacterium Cylindrospermopsis raciborskii (AWT 205/1)

Understanding the triggers for some cyanobacteria of the Nostocales and Stigonematales orders to produce specialised reproductive cells termed akinetes, is very important to gain further insights into their ecology. By improving our understanding of their life cycle, appropriate management options may be devised to control the formation of these cells, and therefore the potential bloom inoculum which they are thought to provide, may be reduced. This study investigated the effect of chemical (phosphorus limitation), and environmental variables (temperature shock) on akinete differentiation in the freshwater cyanobacterium Cylindrospermopsis raciborskii (AWT 205/1). From the preliminary results, it is suggested that the availability of phosphorus and changes in temperature were a necessary requirement for the formation of akinetes in this particular strain of C. raciborskii. In the four phosphorus treatments investigated (0, 3, 38 and 75 mug l(-1) P), only the two higher treatments produced akinetes (approximately 220 ml(-1)). When the first akinetes were observed in the 38 and 75 mug l(-1) P treatments, filterable reactive phosphorus (FRP) concentrations in the medium were approximately 22 and 52 mug l(-1) P, respectively, indicating that there was no phosphorus limitation. In the temperature shock experiment, akinetes were observed in the 15 and 20degreesC treatments. However, akinetes were degraded (pale yellow colour, limited swelling and shrivelled edges) and in much lower concentrations, which was thought to be a result of the daily temperature shock. We suggest that the formation of akinetes in C. raciborskii (AWT 205/1) can be triggered by an initial temperature shock and that phosphorus is a necessary requirement to allow further growth and full development of akinetes.

Evaluating the efficiency of fractional integration parameter estimators

This article deals with the efficiency of fractional integration parameter estimators. This study was based on Monte Carlo experiments involving simulated stochastic processes with integration orders in the range]-1,1[. The evaluated estimation methods were classified into two groups: heuristics and semiparametric/maximum likelihood (ML). The study revealed that the comparative efficiency of the estimators, measured by the lesser mean squared error, depends on the stationary/non-stationary and persistency/anti-persistency conditions of the series. The ML estimator was shown to be superior for stationary persistent processes; the wavelet spectrum-based estimators were better for non-stationary mean reversible and invertible anti-persistent processes; the weighted periodogram-based estimator was shown to be superior for non-invertible anti-persistent processes.

Organization, evolution and transcriptional profile of hexamerin genes of the parasitic wasp Nasonia vitripennis (Hymenoptera: Pteromalidae)

Hexamerins and prophenoloxidases (PPOs) proteins are members of the arthropod-haemocyanin superfamily. In contrast to haemocyanin and PPO, hexamerins do not bind oxygen, but mainly play a role as storage proteins that supply amino acids for insect metamorphosis. We identified seven genes encoding hexamerins, three encoding PPOs, and one hexamerin pseudogene in the genome of the parasitoid wasp Nasonia vitripennis. A phylogenetic analysis of hexamerins and PPOs from this wasp and related proteins from other insect orders suggests an essentially order-specific radiation of hexamerins. Temporal and spatial transcriptional profiles of N. vitripennis hexamerins suggest that they have physiological functions other than metamorphosis, which are arguably coupled with its lifestyle.

The interaction of bothropstoxin-I (Lys49-PLA(2)) with liposome membranes

Bothropstoxin-I (BthTx-I) is a Lys49-PLA(2) from the venom of the snake Bothrops jararacussu, which permeabilizes biological and artificial membranes by a mechanism independent of lipid hydrolysis. This mechanism has been investigated by studying the interaction of nine single tryptophan BthTx-I mutants with negatively charged phospholipid membranes. Changes in the solvent exposure of the tryptophan in each mutant were evaluated comparing the rate of chemical modification (k(mod)) by bromosuccinamide with the maximum intrinsic tryptophan fluorescence emission wavelength (lambda(max)) in buffer and in the presence of 10% DMPA/90% DPPC liposomes. No changes in lambda(max). were observed, whereas k(mod) values for tryptophans at positions 7, 10, 31 and 125 were significantly reduced in the presence of lipids, suggesting that bound phospholipid decreases solvent accessibility at these positions. Since the half-lives of the fluorescence and chemical modification effects differ by at least six orders of magnitude, these results suggest that the bound phospholipid may interact with multiple locations on the protein surface over micro- to millisecond timescales. (C) 2009 Elsevier Ltd. All rights reserved.