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     

Abscisic Acid and Water Relations of Rice (Oryza sativa L.): Sequential Responses to Water Stress in the Leaf

Water stress was imposed by withholding water at an early vegetativestage from plants of two rice cultivars (IR20 and 63–83)grown in pots. As stress intensified the following sequenceof responses of the leaves was observed: (i) rise in abscisicacid (ABA) content, (ii) closure of stomata, (iii) initiationof leaf rolling. In both cultivars, turgor (_p) declined linearly with total waterpotential () of the leaf. Bulk leaf ABA content increased linearlyas _p declined, and attained twice the control (unstressed) levelfollowing a reduction in _p of about 0.12 MPa. Stomatal conductance exhibited a sigmoidal relationship to _p,declining abruptly when a particular ‘critical’_p was reached (threshold response). The critical potentialsvaried considerably between experiments, but were closely correlatedwith control potentials and with the potentials at which ABAconcentration doubled relative to controls. Leaf rolling was initiated at s near to zero _p. Increases inthe ratio of adaxial to abaxial conductance were associatedwith rolling. Variations in the above responses could be accounted for byvariations in the rate of stress development, which in termsof reduction ranged from 0.38 to 0.86 MPa day^–1. Fastdrying rates resulted in: (a) reduced osmotic adjustment, (b)increased amounts of ABA in the leaf at a given level of or_p, (c) an increase in the ABA concentration present at 50 percent stomatal closure, and (d) initiation of leaf rolling ata higher . Oryza sativa L., rice, water stress, stomata, leaf rolling, abscisic acid     

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     

Osmotic Properties of Drought Stressed Periwinkle (Catharanthus roseus) Genotypes

The pressure-volume technique was employed to compare waterrelations and moisture stress-induced osmotic adjustment ofPeriwinkle (Catharanthus roseus) cv. Pink (PC), Oscillatus (REC)and White (WC). Leaf water potential (_w), osmotic potential(_s), turgor potential (_p), bulk modulus of elasticity (), boundwater (RWC_w) and leaf hydration (H), were estimated by exposingthe plants to a drying cycle during which well watered plantswere dehydrated to zero turgor, and then irrigated. Osmoticadjustment (_w ¹⁰⁰) was calculated by comparing _a at full hydration(_a ¹⁰⁰) in stressed plants after recovery, with _a ¹⁰⁰ in controlplants. Values of ₂¹⁰⁰ were 0.76, 0.33 and 0.11 MPa in cv. PC,REC and WC, respectively. Maintenance of _p at lower ₃ and relativeleaf water content (RWC) in prestressed PC was attributableto a higher alkaloid content and greater leaf cell wall elasticity.RWCW was plotted against _p to determine its contribution tohydration maintenance at lower _p. Genotype PC showed greaterRWC_w at lower _p compared with REC and WC. The present studyhas demonstrated that there are cultivar differences in alkaloidaccumulation and water relations in acclimated plants and thatthe relative ranking for drought resistance within periwinkleappeared to correspond with the changes in osmotic properties. Medicinal plant, drought resistance, alkaloids, periwinkle [Catharanthus roseus (L.) G. Don]     

Responses of Soybean Leaf Angle, Photosynthesis and Stomatal Conductance to Leaf and Soil Water Potential

The hypothesis that soil water potential (_s) is better correlatedto heliotropic leaf orientation, photosaturated photosyntheticCO₂ assimilation and stomatal conductance during periods oflimited water availability than is bulk leaf water potential(₁) was examined in greenhouse-grown soybean (Glycine max) plants,submitted to a progressive drought. Paired plants were exposedto either 1000 or 100 µmol m^–2 s^–1 photonflux densities (PFD) for 45–60 mins. The higher irradianceinduced short-term decreases in ₁, due to increased transpiration,while _l in the plant exposed to low PFD did not decrease. Thesechanges in ₁ occurred independently of changes in soil waterstatus. Concurrent to the light treatments, a single attachedleaf from each of the two plants was isolated from the restof the plant by shading, and the pulvinus of its terminal leafletwas exposed to a perpendicular PFD of 500 µmol m–²S^–1. Leaf movement of this leaflet was recorded in responseto this light, until a stable leaflet angle was achieved. Valuesof _s and _l (before and after light treatment), and photosaturatedrates of photosynthesis and stomatal conductance, were thenmeasured on these leaves. Leaflet angle and gas exchange werebetter correlated with _s (r² = 0.50, 0.50 and 0.57 for angle,photosynthesis and conductance, respectively) than with _l especiallywhen _l was the result of short-term, high-light induced changesin leaf water status (r² = 0.36, 0.32 and 0.49, for the sameparameters). Leaflet angle was also correlated with stomatalconductance (r² = 0.61) and photosynthetic rate (r² = 0.60),suggesting a close association between leaf orientation, leafmetabolism and soil water availability. Glycine max (L.) Merr. cv. Essex, soybean, heliotropism, water potential, photosynthesis, stomatal conductance, solar tracking     

An Analysis of Seed Development in Pisum sativum III. The Relationship Between the r Locus, the Water Content and the Osmotic Potential of Seed Tissues in vivo and in vitro

The water content and osmotic potential (₂) of the differentparts of the pea fruit have been measured during developmentof the seed in two lines near-isogenic except for the r locus.During the early development of both genotypes, the testa possesseda more negative ₂ than either embryo, endosperm or pod while,at stages when liquid endosperm was present, the embryo alwaysmaintained ₂, more negative than the endosperm. A clear effectof the r locus on water content and ₂ was only observed in embryotissue — wrinkled (rr) embryos possessing more water andmaintaining a more negative ₂ than round (RR) for most of thedevelopmental period studied. The more negative ₂ of wrinkledembryos correlated with their greater uptake of water in vivo. When cultured in vitro, the embryos of both genotypes showedmaximum growth (fresh or dry weight) if 10 per cent sucrosewas added to the medium (equivalent to about — 1.2 MPa).Round embryos, however, increased in weight more than wrinkledat all sucrose concentrations examined. Cultured embryos maintaineda similar or more negative ₂ than their surrounding medium;wrinkled more negative than round. Embryo culture, osmotic potential, Pisum sativum, pea, r locus, seed development, tissue culture, water content     

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     

Photosynthetic Oxygen Evolution at Low Water Potential in Leaf Discs Lacking an Epidermis

Land plants encountering low water potentials (low _w) closetheir stomata, restricting CO₂ entry and potentially photosynthesis.To determine the impact of stomatal closure, photosyntheticO₂ evolution was investigated in leaf discs from sunflower (Helianthusannuus L.) plants after removing the lower epidermis at low_w. Wounding was minimal as evidenced by O₂ evolution nearlyas rapid as that in intact discs. O₂ evolution was maximal in1 % CO₂ in the peeled discs and was markedly inhibited when_w was below –1·1 MPa. CO₂ entered readily at all_w, as demonstrated by varying the CO₂ concentration. Resultswere the same whether the epidermis was removed before or afterlow _w was imposed. Due to the lack of an epidermis and readymovement of CO₂ through the mesophyll, the loss in O₂ evolvingactivity was attributed entirely to photosynthetic metabolism.Intact leaf discs showed a similar loss in activity when measuredat a CO₂ concentration of 5 %, which supported maximum O₂ evolutionat low _w. In 1 % CO₂, however, O₂ evolution at low _w was belowthe maximum, presumably because stomatal closure restrictedCO₂ uptake. The inhibition was larger than in peeled discs at_w between –1 and –1·5 MPa but became thesame as in peeled discs at lower _w. Therefore, as photosynthesisbegan to be inhibited by metabolism at low _w, stomatal closureadded to the inhibition. As _w became more negative, the inhibitionbecame entirely metabolic.     

Effects of Low Temperature on Potential Net Photosynthesis in Two Field-grown Winter Cereals

Winter wheat and winter barley were tested for their photochemicaland osmotic potentials during the course of one growth cyclein the field. Prolonged winter conditions induced an absolutehigh in potential net photosynthesis (P_N) of winter wheat. Barleyexhibited relatively low P_N rates, which may explain the inferiorfrost hardiness of this species. Osmotic potentials () in bothspecies were quite similar, followed rather uniform trends andwere never extreme. There are doubts, however, whether the assessments truly reflected the osmotic stress on cell membranesin frost-hardened leaves. Increased deposition of cryoprotective assimilates in wheatas the cause of continued frost hardiness is discussed. Triticum aestivum, Hordeum sativum, wheat, barley, potential photosynthesis, winter hardiness     

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     

{gamma}-Amiobutyric Acid Metabolism in Plants: Part 1. Metabolism in Yeasts

The metabolism of -aminobutyric acid (AB) by two yeasts, Saccharomycescerevisiae and Torulopsis utilis, was investigated. Both yeastsgrew well upon AB as a sole source of nitrogen (N), and thelag phase for Torulopsis was shorter than when provided the N-source. The metabolism of AB by Torulopsis, whichwas associated with an increased O₂ uptake, was adaptive incharacter. The enzyme whose formation was induced by the supplyof AB was a transaminase, which was apparently specific forAB as the amino donor. Small amounts of transaminase were presentin unadapted, -grown cells. The optimum pH, equilibrium constant, Michaelis' constant, and coenzyme requirementwere investigated for the transamination reaction involving-ketoglutaric acid (KG) as amino group acceptor. Succinic semi-aldehyde(SSA) was a product of this transamination reaction.The possibility;that some AB was converted into SSA by a direct oxidative deaminationremained unconfirmed. The further conversion of SSA into succinic acid was establishedusing intact. cells for both yeasts. This oxidation processwas shown to be linked to the reduction of pyridine nucleotidesvising extracts of Saccharomyces as a source of SSA dehydrogenase.Dehydrogenase activity could be ascribed to two separate enzymes,one linked to DPN, and the other utilizing TPN and requiringMg⁺⁺ as an activator. The properties of the former enzyme, whichwas more important quantitatively, were investigated and comparedwith those described in the literature for an aldehyde dehydrogenaseof baker's yeast and for SSA dehydro-genases of Pseudomonas.Torulopsis extracts could catalyse the reduction of SSA to -hydroxybutyricacid (OHB); the OHB dehydrogenase involved required TPNH asa coenzyme. Certain other properties of this enzyme are recorded. The possibility is discussed that AB and SSA act as intermediatesin a metabolic pathway that may form a by-pass of the KG-succinatestage of the tricarboxylic acid cycle.     

Water Relations of Sitka Spruce Seedlings After Root Damage

Sitka spruce[Picea sitchensis(Bong.) Carr] seedlings were subjectedto varying degrees of root damage in a growth room, rangingfrom careful transplanting to exposure of the root system toair for up to 3 h. After replanting, transpiration (E), leafwater potential (₁) and growth of the shoot and root were measuredand observations made on plant survival. Some plants in the root exposure treatments died 20–85days after planting. In plants which eventually died, E wasdepressed directly after treatment, but ₁ showed a variableresponse. In some plants ₁ decreased from —8·0x 10⁵ to —30 x 10⁵ Pa after only 10 days but in othersthere was little change in ₁ for 50 days. In spite of the maintenanceof a high water potential in some of the latter plants for longperiods, no root or shoot growth occurred. In plants which lived, the root damage reduced root and shootgrowth relative to untreated controls, and most treatments stronglydepressed E but had little or no effect on ₁. The changes of E and ₁ in treated plants suggest that the suppressionof E was often independent of ₁ although water stress eventuallydeveloped in some of the severely treated plants. Sitka spruce, Picea sitchensis (Bong.)Carr, water relations, root damage, transpiration, leaf water potential     

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     

Competition for Light in a Plant Monoculture Modelled as a Spatial Stochastic Process

In a glasshouse experiment closely spaced plants were regularlysub-irrigated with nutrient solution and it was assumed thatcompetition between individuals was for light. Interaction betweenneighbours is modelled as a spatial process in relation to differencesin plant height. The influence one plant has on another is calculatedas the ratio of the angle ß between their apices,and an angle which represents the intensity of competitionin the population as a whole. When ß < suppressionis considered to occur, i.e. tall plants suppress short plantsbut not vice versa, competition is one-sided. The status ofeach plant within the population is calculated by multiplicationof its individual plant neighbour interaction terms where ß< . This need not be restricted to nearest neighbours. Plantswith status = 1 are free from competition, those with status= 0 are totally suppressed. It is acknowledged that other processes than that modelled ascompetition may result in variation in relative growth rates.To account for this plant status is used to modify a relativegrowth rate drawn from a population of mean µ and standarddeviation . Plants for which status µ is less than anestimated are considered to die. Parameter values were estimatedfor a sequence of fortnightly harvests of glasshouse grown Tagetespatula. There was a decrease in µ and , increased andplants came to compete with their second nearest neighboursas well as their nearest as the community developed. The greatest was at an intermediate stage, suggesting that more frequentassessments of the competition process are required at somestages than at others. Model parameters fitted to one data setwere used in a Monte Carlo testing procedure with a second,independent data set. The importance of this technique is stressedbecause plants in a single community are not independent realizationof the competition process. Simulations with the model reproducedboth bimodality in the frequency distributions of plant sizeand an even spatial distribution of large or surviving plants,features which have been observed in a range of plant monocultures.To achieve these features it was essential that plant interactionbe modelled as a one-sided process. Tagetes patula L., competition, light, monoculture, growth model     

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     

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     

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 Theory of Diffusion of Solutes in Pollen; Theory, Design and Experimental Procedure

The theory of diffusion of solutes in pollen is developed andused to derive formulae from which the mean diffusion coefficient() can be determined. A mathematical relation ß_PGC t = ln (C₀/C_f) is developedby employing Fick's law. In this relation is the average diffusion coefficient, ß_PGC is a constantcharacteristic of the pollen, the ‘Pollen Grain Constant’,C₀ and C_f are the initial and final concentration differencesbetween the solution of the solute and the pollen grain andt is the time of diffusion in seconds. A diffusion apparatushas been designed and made. The design is simple to operateand an experimental procedure is described to determine theß_PGC using dilute potassium chloride solutions. Knowingthe pollen grain constant, the method to determine diffusioncoefficient () with any other solute is explained. Diffusion, design, pollen, solutes, theory