'Nonparametric inference in multivariate mixtures' * Biometrika (2005), 92, pp. 667 678

The left-hand side of equation (2·8), on p. 671, shouldread {₁ (1 – ₁)}^–1/2 (2₁ – 1) rather than{(1 – ₁)/₁}^1/2 (2₁ – 1). Reflecting this change,the left-hand side of equation (3·1) on the same pageshould be altered to , and the formula at the foot of p. 677 should be modified to {₁ (1– ₁)}^–1/2 (2₁ – 1) + O_p(n^–1/2). No otherformula is affected, and the left-hand side of (2·8)is still increasing in ₁. The numerical results, discussed in4, are influenced in minor ways. In the simulation study, absolutebias is reduced, and variance is either slightly increased orslightly decreased. In the real-data example, using the nonparametricapproach to analysis, mean squared error is further reduced,from 0·0011 to 0·0004. We are grateful to HiroKasahara and Katsumi Shimotsu for pointing out the error.     

Integrated likelihood functions for non-Bayesian inference

Consider a model with parameter = (, ), where is the parameterof interest, and let L(, ) denote the likelihood function. Oneapproach to likelihood inference for is to use an integratedlikelihood function, in which is eliminated from L(, ) by integratingwith respect to a density function (|). The goal of this paperis to consider the problem of selecting (|) so that the resultingintegrated likelihood function is useful for non-Bayesian likelihoodinference. The desirable properties of an integrated likelihoodfunction are analyzed and these suggest that (|) should be chosenby finding a nuisance parameter that is unrelated to and thentaking the prior density for to be independent of . Such anunrelated parameter is constructed and the resulting integratedlikelihood is shown to be closely related to the modified profilelikelihood.     

Monte Carlo Estimation for Nonlinear Non-Gaussian State Space Models

We develop a proposal or importance density for state spacemodels with a nonlinear non-Gaussian observation vector y p(y¦)and an unobserved linear Gaussian signal vector p(). The proposaldensity is obtained from the Laplace approximation of the smoothingdensity p(¦y). We present efficient algorithms to calculatethe mode of p(¦y) and to sample from the proposal density.The samples can be used for importance sampling and Markov chainMonte Carlo methods. The new results allow the application ofthese methods to state space models where the observation densityp(y¦) is not log-concave. Additional results are presentedthat lead to computationally efficient implementations. We illustratethe methods for the stochastic volatility model with leverage.     

The Meaning of Matric Potential

The commonly used equation, = P - + , which describes thepartitioning of plant water potential, , into components ofhydrostatic pressure, P, osmotic pressure, , and matric potential,, is misleading. The term , which is supposed to show the influenceof a solid phase on , is zero if a consistent definition ofpressure is used in the standard thermodynamic derivation. However,it can be usefully defined by = + _D, where _D is the osmoticpressure of the equilibrium dialysate of the system. The practicaland theoretical significance of this definition is discussed.     

Analysis of Pressure-Volume Curves of Leaves of Rosa hybrida cv. Sonia

By analysing the relationship between inverse water potential(^–1), and relative water content (RWC) measured on leavesof roses (Rosa hybrida cv. Sonia), grown soilless, it was foundthat a non-linear (NL) model was better suited than a linearmodel to reproduce values observed in the non-turgid region.To explain this apparent curvature, it is assumed that a reductionof the non-osmotic water fraction (A_p) takes place when decreases.Osmotic potentials () measured on fresh and frozen leaf discstend to support this hypothesis. A method for exploiting PVcurves, which takes into account the variation of A_p, is described.It delivers values for the turgor pressure (_p), the relativeosmotic water content, and the mean bulk volumetric elasticitycoefficient, lower than those given by the linear model. Onthe other hand, it gives higher estimates for A_p and for . Whenapplying the traditional model to obtain estimates for waterrelations characteristics of rose leaves, and comparing resultsfrom two distinct salinity treatments (electrical conductivitiesof 1·8 mS cm^–1 and 3·8 mS cm^–1, respectively),one deduces a significant reduction of at turgor-loss in thehigh salinity treatment. The NL method is, in addition, ablesimultaneously to reveal a reduction of and a significant increasein _p at RWC=100% this proves that soilless–grown roseplants are able to osmoregulate when subjected to a constantand relatively high degree of salinity. Key words: Apoplastic water, non-linear regression, pressure-volume curves, tissue-water relations     

Genotypic Differences in Leaf Water Relations between Brassica juncea and B. napus

Various kinds of measurement of tissue water status were madeseveral times during water stress and recovery in Brassica juncea(cv Canadian Black) and B napus (cv Drakkar) Unstressed plantsof the two species had similar leaf water potentials (_w), solute(_s) and turgor potentials (_p) Values of relative water content(RWC) and the slope of the linear relationship between _p andRWC (_p/RWC) were greater in B napus than in B juncea Statistical correlations of pooled data for the watered andstressed treatments differentiated the relationships among RWC,_w and its components in the two species The major statisticaldifference was that _p/RWC was related to RWC in B napus andto _w and _s in B juncea A decline in _p/RWC with decreasing _sin B juncea may be a mechanism for maintaining _p at low soilwater potentials through maintenance of more elastic cell walls. Brassica juncea, Brassica napus, osmotic adjustment, tissue elasticity, water relations     

Derivation of Pressure-Volume Curves by a Non-Linear Regression Procedure and Determination of Apoplastic Water

Data from pressure-volume (PV) analysis may be submitted totransformation I [i.e. leaf water potential (₁) versus inverserelative water content (1/R)] or to transformation II (i.e.1/₁ versus R). This may cause an essential distortion of theerror structure especially in transformation II due to the relativelylarge range which is to be covered by the 1/₁ ratio. Similarly,logarithmic transformation of leaf turgor potential (_P) whenderiving the sensitivity factor of elasticity (ß)by linear regression from values of In _p and 1/R may distortthe error structure. In order to investigate the magnitude ofthe distortion effect on parameters derived from PV analysisby regression a non-linear regression procedure was comparedwith the common linear procedure when calculating _p from ßin the turgid region and leaf osmotic potential (_P) in boththe turgid and non-turgid region. As test plants we used fieldgrown species of spring barley (Hordeum distichum L., cvs Gunnarand Alis). The results show that transformations and applicationof linear regression procedures distort the error structureof _p more than the error structure of _', which was only slightlyaffected. However, we recommend the use of the non-linear procedurein both cases. Furthermore, from PV analysis, obtained by thermocouple hygrometryon living and killed leaf tissue, respectively, we derived themathematical basis for calculating the apoplastic water fraction(R_a). R_a was 0.15 at R= 1 and decreased with dehydration. The equations describing the relation between and R and between_p and R were extended to take into account the apoplastic waterfraction. Key words: Apoplastic water, distortion errors, non-linear regression, pressure-volume curves     

An Error in the Calibration of Xylem-water Potential against Leaf-water Potential

An error occurs in the calibration of xylem pressure potential() against leaf-water potential () when the calibration is madeusing plant material in which the water stress has been inducedartificially after excision. The impostion of water stress afterexcision affects the determination more than it affects , consequentlythe relationship between these two indices of water stress isaltered. Care should be exercised to ensure that identical proceduresare adopted during . calibrations and during susbsequent fieldmeasurements of with the pressure-chamber apparatus.     

Alternative Methods of Analysing Water Potential Isotherms: Some Cautions and Clarifications: I. THE IMPACT OF NON-IDEALITY AND OF SOME EXPERIMENTAL ERRORS

In recent years alternative ways have been proposed to transformmeasurements of leaf water potential, , and relative water content,R^*, in order to derive values of osmotic pressure at full turgidityin leaves and shoots, ^o(when 0). Two types of transformationsare usually considered: 1/ versus R^* and versus 1/R^*, and linearregression is used to fit the data in the region where turgoris thought to be zero. It appears that when ^o is estimated bylinear extrapolation of 1/Psi; versus R^* then apoplastic watermight not influence the accuracy of ^o but when the versus \/R^*transformation is used apoplastic water causes an underestimateof ^o. We examine the accuracy of the estimate of ^o obtainedfrom the two transformations when there are random errors in, systematic errors in , and when the osmotic solutions arenon-ideal. The 1/ versus R^* transformation generally producesthe best estimate of ⁰ by linear extrapolation.     

Effects of Priming and Endosperm Integrity on Seed Germination Rates of Tomato Genotypes: II. GERMINATION AT REDUCED WATER POTENTIAL

Seed germination rates (GR =inverse of time to germination)are sensitive to genetic, environmental, and physiological factors.We have compared the GR of tomato (Lycopersicon esculentum Mill.)seeds of cultivar T5 to those of rapidly germinating L. esculentumgenotypes PI 341988 and PI 120256 over a range of water potential(). The influence of seed priming treatments and removal ofthe endosperm/testa cap enclosing the radicle tip on germinationat reduced were also assessed. Germination time-courses atdifferent 's were analysed according to a model that identifieda base, or minimum, allowing germination of a specific percentage(g) of the seed population (_b(g)), and a ‘hydrotime constant’(_H) indicating the rate of progress toward germination per MPa.h.The distribution of _b(g) determined by probit analysis was characterizedby a mean base (_b) and the standard deviation in _b among seeds(_b). The three derived parameters, _b, _b) and _H, were sufficientto predict the time-courses of germination of intact seeds atany . A normalized time-scale for comparing germination responsesto reduced is introduced. The time to germination at any (t_g())can be normalized to be equivalent to that observed in water(t_g(0)) according to the equation t_g(0)=[l–(/_b(g))]t_g().PI 341988 seeds were more tolerant of reduced and had a morerapid GR than T5 seeds due to both a lower _b and a smaller _H.The rapid germination of PI 120256, on the other hand, couldbe attributed entirely to a smaller _H. Seed priming (6 d in–1.2 MPa polyethylene glycol 8000 solution at 20 ?C followedby drying) increased GR at all >_b(g), but did not lower theminimum allowing germination; i.e. priming reduced _H withoutlowering _b. Removing the endosperm/testa cap (cut seeds) markedlyincreased GR and lowered the mean required to inhibit germinationby 0.7 to 0.9 MPa. However, this resulted primarily from downwardadjustment in _b during the incubation of cut seeds at low inthe test solutions. The difference in _b between intact and cutseeds incubated at high was much less (0.l MPa), indicatingthat at the time of radicle protrusion, the endosperm had weakenedto the point where it constituted only a small mechanical barrier.In the intact seed, endosperm weakening and the downward adjustmentin embryo _b ceased at < –0.6 MPa, while the reductionin _H associated with priming proceeded down to at least –1.2MPa. Based on these data and on the pressure required to pushthe embryos from the seeds at various times after imbibition,it appears that the primary effect of priming was to shortenthe time required for final endosperm weakening to occur. However,as priming increased GR even in cut seeds, priming effects onthe embryo may control the rate of endosperm weakening. Key words: tomato, Lycopersicon esculentum Mill., water potential, germination rate, seed priming, genetic variation     

Sialylation of n-alkyllactosides, galactosides and glucosides by sialyltransferases from rat liver Golgi vesicles

nAlkyl - and -lactosides, galactosides and glucosides with differentalkyl chain lengths (C₂, C₈, C₁₄, and C₂₀) were synthesizedand used as acceptors for sialyltransferases from rat liverGolgi vesicles. The -galactosides, -glucosides, and both - and-lactosides, were sialylated. Keeping the acceptor concentrationconstant, sialylation rates reached a maximum for the n-octyl- and -lactosides, n-Octyl -galactoside and noctyl -glucoside,respectively. noctyl -glucoside, respectivwly. n-Octyl -galactosideand n-octyl -glucoside were not sialylated. The reaction productswere characterized by TLC. With n-octyl lactoside and galactosideas acceptors, two major sialylation products were formed. Thjeycould be separated by preparative TLC, and their structureswere identified as 2–3 and 2–6 sialylated acceptors,respectively, by a combination of periodated oxidation, NaBD₄reduction,permethylation and subsequent analysis by fast atombombardment mass spectrometry (FAB-MS). The structure of thesingle product obtained from n-ictyl -glucoside was determinedto be the 2–6 sialylated glucoside. Competition experimentswith n-octyl lactoside and lactosylceramide and gangliosideGal1-3GalNAc1-4(NeuAc2–3)Gal1–4Glcbeeta1–1Cer(GM1) as acceptors for sialyltransferases suggested that SAT-I[NeuAc2–3Gal1–4Glc1-1Cer (GM3) synthase] was atleast in least in part responsible for the 2–3 sialylationof n-octyl lactoside. alkylgalactosides alkylglucosides alkyllactosides neoglycolipids sialytransferases     

Water Relations of Potato Leaves. II. Pressure--Volume Analysis and Inferences About the Constancy of the Apoplastic Fraction

Water relations characteristics of potato (Solanum tuberosumL. cv. Bintje) leaves were determined from pressure—volumeanalysis using a pressure chamber. Turgor was 077 MPa and thebulk volumetric modulus of elasticity 81 MPa at full turgidity;turgor loss occurred when water potential () had declined to–087 MPa at a relative water content (RWC) of 0912;the apoplastic water fraction (A) was 0235. As is usually found,there was a linear relation between 1/ and RWC beyond turgorloss. This finding supports the assumptions of the constancyof A during leaf dehydration. Beyond turgor loss the difference between and [measured afterfreezing and thawing (_d)] was about 01 MPa. This differencedid not increase as the leaf water content decreased. This resultcontradicts the constancy of A. It was concluded from calculations with a simple model of leafdehydration that analysis of the relation between and _d providesmore insight in the changes in the apoplastic fraction thanthe relation between 1/ and RWC. Research on the size of theapoplastic fraction and its changes with water potential wouldcomplement current understanding of leaf water relations. Solanum tuberosum, L., water potential, pressure chamber, osmotic potential, pressure potential, relative water content, apoplast, symplast     

Wilting of Leaves in Vicia faba L.

Wilting of leaves of Vicia faba L., which occurs when the pressurepotential (_p) is zero, and the leaf-water potential () at wiltingboth depend entirely upon the solute potential at incipientplasmolysis (_so) and not on soil-water status. Wilting in V.faba is acropetal; this is consistent with the hypothesis thatthere is a gradient of decreasing _so up the plant and that wateris transferred from the lower to the upper leaves, hasteningthe overall water loss from the lower leaves to the point when_p is zero. The gradient in _so up the plant is of the order of3–8 bar. It is proposed that wilting when _p>0 (i.e. > _so) shouldbe ‘apparent wilting’ and that when _p0 (i.e. _so),‘true wilting’.     

Water-Relations Parameters of the Phloem. Determinations of Volumetric Elastic Modulus and Membrane Conductivity using an Applied Force Method and Shrinkage and Swelling of Tissues in Solutions at Differing Osmotic Pressure

Water-relations parameters were measured on sections of secondaryphloem from red oak (Quercus borealis michx. f.) and white ash(Fraxinus americana var. biltmoreana [Beadle] J. Wright) usinga linear displacement transducer. Changes in tissue thicknessin response to changes in the osmotic pressure of the bathingsolution were used to calculate the volumetric elastic modulusplus osmotic pressure (_v + ) of the tissue, and an applied forcemethod was used to estimate the time constant for water equilibration(T). The hydraulic conductivity of the cell membranes (L_p) wascalculated utilizing _v + and r values. The time-dependent behaviour of the tissue was much more complexthan originally expected. A correction for a time-dependentprocess that we call ‘drift’ was required to obtainnumbers for _v + . Furthermore, _v + was calculated on two assumptionsin order to relate changes in tissue dimensions to sieve elementparameters. In the first case, a lower limit for _v + of thesieve elements was determined by attributing all changes intissue dimensions to these cells. For red oak the average _v+ on this assumption is 72 bars. Assuming that all cell typeswere equally responsible for the changes in tissue dimensionsresulted in an _v + value of 192 bars for oak. If _v + and rare the same for all cells in the tissue, L_p for the sieve elementsof oak is 9.6 x 10^–8 cm s^–1 bar^–1. Exudationfrom the sieve elements of white ash during excision of thephloem led to artificially high values of _v + for that species. Quercus borealis michx. f., Fraxinus americana var, biltmoreana (Beadle) J. Wright, red oak, white ash, water relations, phloem, volumetric elastic modulus, membrane hydraulic conductivity     

The Derivation of the Cell Wall Elasticity Function from the Cell Turgor Potential

An equation is derived expressing average turgor pressure ofa leaf (_p) as a function of relative water content (RWC). Basedon this derivation, the relationships of the bulk elastic modulus(_v) and both RWC and _p, are formulated and discussed. The bulkelastic modulus (_v) becomes zero for _p = 0, that is at the turgorloss point for the leaf. At full water saturation the valueof ev is proportional to the water saturation turgor potential_p(max). The factor relating _P and _v (structure coefficient ,Burstrom, Uhrstr?m and Olausson, 1970) changes only very littlefor values of _p, which are not too close to zero. An exampleis given for the calculation from experimental data of the turgorpressure function, the structure coefficient function, and the_v function. Key words: Cell wall, Turgor pressure, Bulk elastic modulus     

A Transient Stimulation of Net Photosynthesis of Rye Leaves by {alpha}-Hydroxy-2-pyridinemethanesulphonic Acid ({alpha}-HPMS) due to Inhibition of Photorespiratory CO2 Release

The effects of -hydroxy-2-pyridinemethanesulphonic acid (-HPMS)upon net photosynthesis (P_n, the CO₂ compensation point (),post-lower illumination burst of CO₂ (PLIB) and post-lower temperatureburst of CO₂ (PLTB) in detached rye (Secale cereale L.) leaveswere investigated. At low concentrations ( 0.5 mol m^–3),-HPMS initially stimulated P_n and decreased the magnitude ofboth PLIB and PLTB. The decreased at all concentrations of-HPMS (0.05–5.0 mol m^–3. The effects of -HPMS onP_n and were time-dependent and, after a few minutes, the P_nwas inhibited while values increased considerably. At a higherconcentration (5.0 mol m ^–3), the transient effects of-HPMS were shorter () or not observed at all (P_n. Both PLIBand PLTB, when expressed in relation to P_n, increased at higherlevels of this compound. Similar data with respect to the effectsof -HPMS on PLIB and PLTB were found for leaves of dandelion(Taraxacum officinale L.). The results suggest that -HPMS may stimulate P_n by inhibitingphotorespiration, as originally suggested by Zelitch (1966),but only at low concentrations and over a short time span. Thedecrease of PLIB and PLTB values at low -HPMS levels is consistentwith these processes being a residual activity of the glycolatepathway. Key words: CO₂ compensation point, -hydroxy-2-pyridinemethanesulphonic acid, photorespiration, photosynthesis     

Molecular dynamics simulations of oligosaccharides and their conformation in the crystal structure of lectin-carbohydrate complex: importance of the torsion angle {psi} for the orientation of {alpha}1,6-arm

The conformation of the heptasaccharide Man-1,6-(Man-1,3)(Xyl-ß1,2)-Man-ß,4-GlcNAc₂-ß1,4-(L-Fuc-1,3)-GlcNAc₁,the carbohydrate moiety of Erythrina corallodendron lectin (EcorL),the hexasaccharide Man-1,6-(Man-1,3) (GlcNAc-ß1,4)-Man-ß1,4-GlcNAc-ß1,4-GlcNAcand their disaccharide fragments have been studied by moleculardynamics (MD) simulations for 1000 ps with different initialconformations. In the isolated heptasaccharide, the most frequentlyaccessed conformation during MD has a value of 180° aroundMan-1,6-Man linkage. This conformation is stabilized by theformation of a hydrogen bond between the carbonyl oxygen ofGlcNAc₂ with the O3/O4 hydroxyls of the 1,6-linked mannose residue.The conformation of the heptasaccharide found in the crystalstructure of the EcorL-lactose complex (Shaanan et al., Science,254, 862, 1991), that has a value of 76° around Man-1,6-Manlinkage, is accessed, although less frequently, during MD ofthe isolated oligosaccharide. The ,, = 58°,–134°,–60°conformation around Man-₁,6-Man fragment observed in the crystalstructure of the Lathyrus ochnrs lectin complexed with a biantennaryoctasaccharide (Table I in Homans,S.W., Glycobiology, 3, 551,1993) has also been accessed in the present MD simulations.These values for the 1,6-linkage, which are observed in theprotein-carbohydrate crystal structures and are accessed inthe MD simulations, though occasionally, have not been predictedfrom NMR studies. Furthermore, these different values of leadto significantly different orientations of the 1,6-arm for thesame value of . This contrasts with the earlier predictionsthat only different values of can bring about significant changesin the orientation of the ₁,6-arm. The MD simulations also showthat the effects of bisecting GlcNAc or ß1,2-xyloseare very similar on the ₁,3-arm and slightly different on the₁,6-arm. bisecting GlcNAc carbohydrates glycoprotein lectinsaccharide complex     

Hydrophobic mannosides act as acceptors for trypanosome {alpha}-mannosyltransferases

A series of hydrophobic mannosides were synthesized and testedfor their ability to act as acceptor substrates for mannosyltransferasesin a Trypanosoma brucei cell-free system. The thiooctyl -mannosidesand octyl -mannosides all accepted single mannose residues in-linkage, as judged by thin layer chromatography of the productsbefore and after jack bean -mannosidase digestion. The mannosylationreactions were inhibited by amphomycin, suggesting that theimmediate donor was dolicholphosphate-mannose (Dol-P-Man) inall cases. The transferred -mannose residues were shown to beboth 1-2 and 1-6 linked by Aspergillus phoenicis -mannosidaseand acetolysis treatments, respectively. These data suggestthat the compounds can act as acceptor substrates for the Dol-P-Mandependent 1-2 and 1-6 mannosyltransferases of the GPI biosyntheticpathway and/or the dolichol-cycle of protein N-glycosylation.One of the compounds, Man1-6Man1-O-(CH₂)₇CH₃, inhibited endogenousGPI biosynthesis in the cell-free system, suggesting that itcould be a substrate for the trypanosome Dol-P-Man:Man₂GlcN-Pl1-2 mannosyltransferase. dolichol glycosylphosphatidylinositol mannosyltransferase trypanosome     

Pumpkin (Cucurbita sp.) seed globulin III. Comparison of subunit structures among seed globulins of various Cucurbita species and characterization of peptide components

Various Cucurbita seed globulins showed patterns similar toone another on SDS-gel electrophoresis, and ß bandsfor unreduced globulins and , ', and ' bands for reduced ones.On gel electrophoresis in 6 M urea, reduced globulin gave twoacidic and two basic bands. These corresponded to and ' chainsand ₁ and ₂ chains, respectively, identified by two-dimensionalurea-SDS gel electrophoresis. The compositions of the and ßsubunits were proposed. (Received September 8, 1977; )     

Isolation of Subunits of Coupling Factor 1 from Maize and Spinach Chloroplasts and Properties of Combinations of Subunits with ATPase Activity

Subunits (, ß, ) and mixtures of subunits ( ß, , ß , ß ) were isolated without denaturationfrom a chloroform extract of chloroplast coupling factor 1 (CF₁)from maize (Zea mays var. Ushiku 5-4) and from spinach by fastprotein liquid chromatography (FPLC), on an anion-exchange columnof Mono-Q in the presence of n-octylglucoside (OG) and on achromatofocusing column of Mono-P. The ß -subunitcomplex (CF¹ ß ) was the minimum unit required forATPase activity, as was confirmed by the reconstituted complexof ß and subunits. An subunit isolated from maizeinhibited the ATPase activity of CF₁ ß from bothmaize and spinach. CF₁ ß was found to contain anOG-dependent Mg²⁺-ATPase. The ATPase activity of CF₁ ß required divalent cations, such as Mg²⁺ or Mn²⁺, for its expressionin the presence of OG; its optimum pH was 8.0 and it was markedlyinhibited by NaN₃. The enzyme hydrolyzed ATP in prefernece toGTP but not CTP, UTP, ADP, AMP or pNPP. Lineweaver-Burk plotsof its activity were curvilinear in the range of 0.6–0.7mM ATP.Mg²⁺. ¹Present address: Department of Biology, School of Education,Waseda University, Shinjuku-ku, Tokyo, 160 Japan. (Received February 15, 1989; Accepted April 20, 1989)