Second supplementary list of genotypes of hybrid necrosis of wheat varieties

Male sterile “lines” are being made carrying either Ne ₁ ^sor Ne ₂ ^sin homozygous condition. The “lines” will be used to determine the necrosis genotype of wheat varieties and at the same time to trace genes restoring fertility in cytoplasmic sterile “lines”. It is suggested that hybrid necrosis could be used in hybrid seed production. The article is concluded with a list of 100 varieties and selections of which the genotype for hybrid necrosis is given.

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Samenvatting De methode wordt beschreven om een groot aantal tarwerassen en-selecties met behulp van mannelijke steriele toetslijnen op hun genotype voor bastaard-necrose te onderzoeken. Deze methode wordt tegelijkertijd gebruikt om fertiliteit herstellende genen op te sporen. De mogelijkheid wordt geopperd, dat bastaard-necrose te benutten zou zijn bij de productie van hybride-tarwezaad. Het artikel wordt besloten met een aanvullende lijst van 100 tarwerassen en-selecties, waarbij het genotype voor bastaard-necrose is vermeld.

     

Gas exchange,chlorophyll fluorescence,and osmotic adjustment in two mango cultivars under drought stress

The responses of photosynthetic gas exchange, chlorophyll fluorescence, content of pigments, main osmolytes, and malondialdehyde (MDA) to water-withholding for 15 days and re-hydration in seedlings of two mango cultivars (Mangifera indica L. var. “Choke Anand’ and var. “Khieo Sawoei”) under 50% sunlight and full sunlight were investigated. For both cultivars, the water-witholding resulted in progressively decreases in leaf relative water content, net photosynthesis (P _n), stomatal conductance (g _s), and increases in the conversion of xanthophyll cycle pigments estimated by an index of leaf spectral reflectance (ΔPRI), carotenoid to chlorophyll ratio, non-photochemical quenching (NPQ), the contents of malondialdehyde (MDA) and compatible solutes (total soluble sugar and proline). The effect of the water stress was more pronounced in full sunlight than 50% sunlight. The maximum photochemistry efficiency measured at dawn was fairly constant during the period of the treatment for both cultivars under both light regimes. The water stress caused less pronounced inhibition of photosynthesis in “Choke Anand” than in “Khieo Sawoei” cultivar under both light regimes. After re-hydration, the recovery was relatively quicker in “Choke Anand” than in “Khieo Sawoei” cultivar. Both cultivars in both 50% and full sunlight showed complete recovery in photochemistry after 5 days of re-watering but photosynthesis did not show a complete recovery as indicated by gas exchange rates. As the results of lower NPQ, ΔPRI and osmotic adjustment in the cultivar “Khieo Sawoei” compared to the cultivar “Choke Anand”, the former cultivar was less tolerant to drought than the latter. Our study further showed that partial shading (e.g., 50% of sunlight) significantly alleviated the harmful effect of drought stress on mango cultivars but in fact stomata of seedlings grown in partial shade was more responsive to water deficit than in full light.     

Limitation of coffee leaf photosynthesis by stomatal conductance and light availability under different shade levels

In agroforestry systems, the effect of shade trees on coffee net photosynthesis (A _n) has been the object of debates among coffee scientists. In this study, we undertook over 600 coffee A _n “spot” measurements under four different artificial shade levels (100, 72, 45 and 19% of full solar irradiance) and analyzed limitations to A _n by low light availability (photon flux density, PFD) and stomatal conductance (g _s). These gas exchange measurements were carried out during two consecutive coffee growing seasons in a commercial plantation in the Orosi valley of Costa Rica. Levels of A _n were related to PFD and g _s in order to calculate envelope functions which were used to establish PFD or g _s limitations to A _n. Under the growing conditions of the present trial, mean leaf A _n remained stable for growth irradiance (GI) as low as 45% of full sun and decreased by ~20% at 19% GI. Limitation to A _n due to g _s was strong in full sun and decreasing with increasing shade levels. On the other hand, limitation due to PFD remained at a similar level for all shade treatments. These different evolutions of limitations of A _n by PFD and g _s in response to shade explain the absence of a decrease in coffee leaf A _n with a shade level up to 55%. Consequently, these results confirm that Arabica coffee is a shade-adapted plant with leaves that can maintain a high photosynthetic performance under low light availability.     

Transport of hemicellulose monomers in the xylose-fermenting yeastCandida shehatae

Summary Cells ofCandida shehatae repressed by growth in glucose- or D-xylose-medium produced a facilitated diffusion system that transported glucose (K _s±2 mM,V _max±2.3 mmoles g⁻¹ h⁻¹),d-xylose (K _s±125 mM,V _max±22.5 mmoles g⁻¹ h⁻¹) and D-mannose, but neither D-galactose norl-arabinose. Cells derepressed by starvation formed several sugar-proton symports. One proton symport accumulated 3-0-methylglucose about 400-fold and transported glucose (K _s±0.12 mM,V _max ± 3.2 mmoles g⁻¹ h⁻¹) andd-mannose, a second proton symport transportedd-xylose (K _s± 1.0 mM,V _max 1.4 mmoles g⁻¹ h⁻¹) andd-galactose, whilel-arabinose apparently used a third proton symport. The stoicheiometry was one proton for each molecule of glucose or D-xylose transported. Substrates of one sugar proton symport inhibited non-competitively the transport of substrates of the other symports. Starvation, while inducing the sugar-proton symports, silenced the facilitated diffusion system with respect to glucose transport but not with respect to the transport of D-xylose, facilitated diffusion functioning simultaneously with thed-xylose-proton symport.     

The response of stomatal conductance to seasonal drought in tropical forests

Stomata regulate CO₂ uptake for photosynthesis and water loss through transpiration. The approaches used to represent stomatal conductance (g_s) in models vary. In particular, current understanding of drivers of the variation in a key parameter in those models, the slope parameter (i.e. a measure of intrinsic plant water‐use‐efficiency), is still limited, particularly in the tropics. Here we collected diurnal measurements of leaf gas exchange and leaf water potential (Ψ_leaf), and a suite of plant traits from the upper canopy of 15 tropical trees in two contrasting Panamanian forests throughout the dry season of the 2016 El Niño. The plant traits included wood density, leaf‐mass‐per‐area (LMA), leaf carboxylation capacity (V_c,max), leaf water content, the degree of isohydry, and predawn Ψ_leaf. We first investigated how the choice of four commonly used leaf‐level g_s models with and without the inclusion of Ψ_leaf as an additional predictor variable influence the ability to predict g_s, and then explored the abiotic (i.e. month, site‐month interaction) and biotic (i.e. tree‐species‐specific characteristics) drivers of slope parameter variation. Our results show that the inclusion of Ψ_leaf did not improve model performance and that the models that represent the response of g_s to vapor pressure deficit performed better than corresponding models that respond to relative humidity. Within each g_s model, we found large variation in the slope parameter, and this variation was attributable to the biotic driver, rather than abiotic drivers. We further investigated potential relationships between the slope parameter and the six available plant traits mentioned above, and found that only one trait, LMA, had a significant correlation with the slope parameter (R² = 0.66, n = 15), highlighting a potential path towards improved model parameterization. This study advances understanding of g_s dynamics over seasonal drought, and identifies a practical, trait‐based approach to improve modeling of carbon and water exchange in tropical forests.     

Photosynthesis Inhibition During Gas Exchange Oscillations in ABA-Treated Helianthus annuus: Relative Role of Stomatal Patchiness and Leaf Carboxylation Capacity

Environmental factors that induce spatial heterogeneity of stomatal conductance, g _s, called stomatal patchiness, also reduce the photochemical capacity of CO₂ fixation, yet current methods cannot distinguish between the relative effect of stomatal patchiness and biochemical limitations on photosynthetic capacity. We evaluate effects of stomatal patchiness and the biochemical capacity of CO₂ fixation on the sensitivity of net photosynthetic rate (P _N) to stomatal conductance (g _s), θ (θ = δP _N/g _s). A qualitative model shows that stomatal patchiness increases the sensitivity θ while reduced biochemical capacity of CO₂ fixation lowers θ. We used this feature to distinguish between stomatal patchiness and mesophyll impairments in the photochemistry of CO₂ fixation. We compared gas exchange of sunflower (Helianthus annuus L.) plants grown in a growth chamber and fed abscisic acid, ABA (10⁻⁵ M), for 10 d with control plants (-ABA). P _N and g _s oscillated more frequently in ABA-treated than in control plants when the leaves were placed into the leaf chamber and exposed to a dry atmosphere. When compared with the initial CO₂ response measured at the beginning of the treatment (day zero), both ABA and control leaves showed reduced P _N at particular sub-stomatal CO₂ concentration (c _i) during the oscillations. A lower reduction of P _N at particular g _s indicated overestimation of c _i due to stomatal patchiness and/or omitted cuticular conductance, g _c. The initial period of damp oscillation was characterised by inhibition of chloroplast processes while stomatal patchiness prevailed at the steady state of gas exchange. The sensitivity θ remained at the original pre-treatment values at high g _s in both ABA and control plants. At low g _s, θ decreased in ABA-treated plants indicating an ABA-induced impairment of chloroplast processes. In control plants, g _c neglected in the calculation of g _s was the likely reason for apparent depression of photosynthesis at low g _s. This revised version was published online in August 2006 with corrections to the Cover Date.     

Kinematics of nonstationary locomotion in the centipede <Emphasis Type="Italic">Scolopendra cingulata</Emphasis>: A single instant change of speed

The spatiotemporal parameters of leg movement in Scolopendra instantly changing the locomotion speed from V ₁ to V ₂ ≠ V ₁ are investigated. It is shown that (i) the principle of “in trail” leg placement is kept upon a change of speed; (ii) the continuity of the metachronal coordination is not disturbed; but (iii) for some time after changing speed the set of ipsilateral legs comprises (a) head-proximal legs creating a new trackway of steps with pace ℓ₂, and (b) distal legs still using the old trackway with pace ℓ₁. The two groups differ in kinematic parameters. Group (a) works in the stationary mode corresponding to speed V ₂, while group (b) works in a transitory mode. Consecutively, with a metachronal wave propagating backwards along the body but immobile relative to the ground, more and more legs from group (b) switch to the new stationary mode.     

Analysis of the exponential decay model of the neuron showing frequency threshold effects

The exponential decay model of a neuron has been analyzed using the “random walk” approach of stochastic processes and an “absorbing barrier” solution is obtained forg ^T (s)—the Laplace transform of the output pulse interval density function. An expression for the mean output frequency is derived from this and a variety of input-output curves plotted which show frequency threshold effects in single neurons. Our results are compared with those of other authors obtained by computer simulation techniques, and the significance of these results discussed with reference to the possible behavior of networks constructed of such neuron units.     

Temperature and irradiance impacts on the growth,pigmentation and photosystem II quantum yields of <Emphasis Type="Italic">Haematococcus pluvialis</Emphasis> (Chlorophyceae)

The microalga Haematococcus pluvialis Flotow has been the subject of a number of studies concerned with maximizing astaxanthin production for use in animal feeds and for human consumption. Several of these studies have specifically attempted to ascertain the optimal temperature and irradiance combination for growth of H. pluvialis, but there has been a great deal of disagreement between laboratories. “Ideal” levels of temperature and irradiance have been reported to range from 14 to 28°C and 30 to 200 μmol photons m⁻² s⁻¹. The objective of the present study was to simultaneously explore temperature and irradiance effects for a single strain of H. pluvialis (UTEX 2505) across an experimental region that encompassed the reported “optimal” combinations of these factors for multiple strains. To this end, a two-dimensional experimental design based on response surface methodology (RSM) was created. Maximum growth rates for UTEX 2505 were achieved at 27°C and 260 μmol photons m⁻² s⁻¹, while maximum quantum yield for stable charge separation at PSII (F_v/F_m) was achieved at 27°C and 80 μmol photons m⁻² s⁻¹. Maximum pigment concentrations correlated closely with maximum F_v/F_m. Numeric optimization of growth rate and F_v/F_m produced an optimal combination of 27°C and 250 μmol photons m⁻² s⁻¹. Polynomial models of the various response surfaces were validated with multiple points and were found to be very useful for predicting several H. pluvialis UTEX 2505 responses across the entire two-dimensional experimental design space.     

Apparent responses of stomata to transpiration and humidity in a hybrid poplar canopy

It has been proposed that the stomatal response to humidity relies on sensing of the transpiration rate itself rather than relative humidity or the saturation deficit per se. We used independent measurements of stomatal conductance (g_s), transpiration (E), and leaf-to-air vapour pressure difference (V) in a hybrid poplar canopy to evaluate relationships between g_s and E and between g_s and V. Relationships between E, V and total vapour phase conductance or crown conductance (g_c) were also assessed. Conductance measurements were made on exposed and partially shaded branches over a wide range of incident solar radiation. In exposed branches, g_s appeared to decline linearly with increasing E and increasing V at both high and low irradiance. However, in a partially shaded branch, a bimodal relationship between g_s and E was observed in which g_s continued to decrease after E had reached a maximum value and begun to decrease. The relationship between g_s and V for this branch was linear. Plots of g_c against E always yielded bimodal or somewhat variable relationships, whereas plots of g_c against V were invariably linear. It was not possible to derive a unique relationship between conductance and E or V because prevailing radiation partially determined the operating range for conductance. Normalization of data by radiation served to linearize responses observed within the same day or type of day, but even after normalization, data collected on partly cloudy days could not be used to predict stomatal behaviour on clear days and vice versa. An additional unidentified factor was thus also involved in determining operating ranges of conductance on days with different overall radiation regimes. We suggest that the simplest mechanism to account for the observed humidity responses is stomatal sensing of the epidermal or cuticular transpiration rate rather than the bulk leaf or stomatal transpiration rate.     

Association between contrasting methane emissions of two rice (<Emphasis Type="Italic">Oryza sativa</Emphasis> L.) cultivars from the irrigated agroecosystem of northeast India and their growth and photosynthetic characteristics

Over two consecutive years in the North Bank Plain Zone of Assam, India, during the spring growing season (February–June) of- 2006 and 2007 we examined effects of morpho-physiological characteristics of rice (Oryza sativa L.) plants in relation to methane (CH₄) emission from paddy fields. Traditional cultivar “Agni” and modern improved cultivar “Ranjit” were grown in light textured loamy soil under irrigation. A higher seasonal integrated methane flux (E _sif) was recorded from “Agni” compared to “Ranjit”. Both cultivars exhibited an emission peak during active vegetative growth and a second peak at panicle initiation. Leaf and tiller number, leaf area, length, and volume of root were greater in “Agni”, but grain yield and yield-related parameters such as increased photosynthate partitioning to panicles at the expense of roots were greater in “Ranjit”. “Ranjit” also photosynthesed faster than “Agni” during panicle development but slower than “Agni” at tillering. In both the years, a higher soil organic carbon content was recorded in plots of “Agni”. Our results suggest that in “Agni” enhanced diversion of photosynthate to roots resulted in more substrate being available to methanogenic bacteria in the rhizosphere. Additionally, the more extensive vegetative growth of this cultivar may enhance methane transport from the soil to the above-ground atmosphere.     

Nerves in the endodermal canals of hydromedusae and their role in swimming inhibition

N eoturris breviconis (Anthomedusae) has a nerve plexus in the walls of its endodermal canals. The plexus is distinct from the ectodermal nerve plexuses supplying the radial and circular muscles in the ectoderm and no connections have been observed between them. Stimulation of the endodermal plexus evokes electrical events recorded extracellularly as “E” potentials. These propagate through all areas where the plexus has been shown by immunohistology to exist and nowhere else. When Neoturris is ingesting food, trains of “E” potentials propagate down the radial canals to the margin and cause inhibition of swimming. This response is distinct from the inhibition of swimming associated with contractions of the radial muscles but both may play a part in feeding and involve chemoreceptors. Preliminary observations suggest that the “E” system occurs in other medusae including Aglantha digitale (Trachymedusae) where the conduction pathway was previously thought to be an excitable epithelium.     

Carbon fixation and carbonic anhydrase activity in Haslea ostrearia (Bacillariophyceae) in relation to growth irradiance

The metabolic pathway of primary carbon fixation was studied in a peculiar pennate marine diatom, Haslea ostrearia (Bory) Simonsen, which synthesizes and accumulates a blue pigment known as “marennine”. Cells were cultured in a semi-continuous mode under saturating [350 μmol(photon) m⁻² s⁻¹] or non-saturating [25 μmol(photon) m⁻² s⁻¹] irradiance producing “blue” (BC) and “green” (GC) cells, characterized by high and low marennine accumulation, respectively. Growth, pigment contents (chlorophyll a and marennine), ¹⁴C accumulation in the metabolites, and the carbonic anhydrase (CA) activity of the cells were determined during the exponential growth phase. Growth rate and marennine content were closely linked to irradiance during growth: higher irradiance increased both growth rate and marennine content. On the other hand, the Chl a concentration was lower under saturating irradiance. The distribution between the Calvin-Benson (C₃) and β-carboxylation (C₄) pathways was very different depending on the irradiance during growth. Metabolites of the C₃ cycle contained about 70 % of the total fixed radioactivity after 60 s of incorporation into cells cultured under the non-saturating irradiance (GC), but only 47 % under saturating irradiance (BC). At the same time, carbon fixation by β-carboxylation was 24 % in GC versus about 41 % in BC, becoming equal to that in the C₃ fixation pathway in the latter. Internal CA activity remained constant, but the periplasmic CA activity was higher under low than high irradiance.     

Photosynthetic CO2 uptake byZea mays leaves as influenced by unilateral irradiation of adaxial and abaxial leaf surfaces

A study was made on the effect of increasing photon fluence rate (I) at a unilateral irradiation of adaxial (normal leaf position) and abaxial (inverse leaf position) blade surface of maize leaves of various insertion levels on net photosynthetic CO₂ uptake (P _n ) by the leaves, as well as the contribution of individual surfaces toP _n of the leaves, and the significance of, or relationship between the stomatal (g _s ) and intracellular (gm) conductances at the CO₂ transport.P _n of leaves of various age according to their insertion level was unaffected by the direction of incident irradiation. Upon irradiation of the leaves in normal and inverse position the contribution of the adaxial and abaxial surfaces toP _n ,g _s and g_m was different. On irradiating the leaves in normal position, the contribution of the irradiated adaxial surface to the characteristics mentioned made on the average 55% of total values, the contribution of the abaxial surface irradiated in inverse position made on the average 70% inP _n andg _m , and 80% ing _s . At lowerI’s g _m was higher thang _s both in irradiated and non-irradiated surfaces. The ratio ofg _s to g_m gradually got square with increasingI. In the irradiated adaxial surface the equilibrium (g _s /g _m = 1.0) took place at the highestI’s, in the irradiated abaxial surface between 500 to 1000 μmol m⁻² s⁻¹. The significance of the ratiog _m in the CO₂ transport through the individual surfaces is discussed.     

Control of transpiration from the upper canopy of a tropical forest: the role of stomatal, boundary layer and hydraulic architecture components

Concurrent, independent measurements of stomatal conductance (g_s), transpiration (E) and microenvironmental variables were used to characterize control of crown transpiration in four tree species growing in a moist, lowland tropical forest. Access to the upper forest canopy was provided by a construction crane equipped with a gondola. Estimates of boundary layer conductance (g_b) obtained with two independent methods permitted control of E to be partitioned quantitatively between g_s and g_b using a dimensionless decoupling coefficient (Ω) ranging from zero to 1. A combination of high g_s (c. 300–600 mmol m^?2 s^?1) and low wind speed, and therefore relatively low g_b (c. 100–800 mmol m^?2 s^?1), strongly decoupled E from control by stomata in all four species (Ω= 0.7–0.9). Photosynthetic water-use efficiency was predicted to increase rather than decrease with increasing g_s because g_b was relatively low and internal conductance to CO₂ transfer was relatively high. Responses of g_s to humidity were apparent only when the leaf surface, and not the bulk air, was used as the reference point for determination of external vapour pressure. However, independent measurements of crown conductance (g_c), a total vapour phase conductance that included stomatal and boundary layer components, revealed a clear decline in g_c with increasing leaf-to-bulk air vapour pressure difference (V_a because the external reference points for determination of g_c and V_a were compatible. The relationships between g_c and V_c and between g_s and V_s appeared to be distinct for each species. However, when g_s and g_c were normalized by the branch-specific ratio of leaf area to sapwood area (LA/SA), a morphological index of potential transpirational demand relative to water transport capacity, a common relationship between conductance and evaporative demand for all four species emerged. Taken together, these results implied that, at a given combination of LA/SA and evaporative demand scaled to the appropriate reference point, the vapour phase conductance and therefore transpiration rates on a leaf area basis were identical in all four contrasting species studied.     

Is stomatal conductance optimized over both time and space in plant crowns? A field test in grapevine (Vitis vinifera)

Crown carbon gain is maximized for a given total water loss if stomatal conductance (g_s) varies such that the marginal carbon product of water (?A/?E) remains invariant both over time and among leaves in a plant crown, provided the curvature of assimilation rate (A) versus transpiration rate (E) is negative. We tested this prediction across distinct crown positions in situ for the first time by parameterizing a biophysical model across 14 positions in four grapevine crowns (Vitis vinifera), computing optimal patterns of g_s and E over a day and comparing these to the observed patterns. Observed water use was higher than optimal for leaves in the crown interior, but lower than optimal in most other positions. Crown carbon gain was 18% lower under measured g_s than under optimal g_s. Positive curvature occurred in 39.6% of cases due to low boundary layer conductance (g_bw), and optimal g_s was zero in 11% of cases because ?A/?E was below the target value at all g_s. Some conclusions changed if we assumed infinite g_bw, but optimal and measured E still diverged systematically in time and space. We conclude that the theory's spatial dimension and assumption of positive curvature require further experimental testing.     

A method for measuring the settling velocity distribution of large biotic particles

A simple method for measuring the settling velocity (V _s) distribution of pollen and spores 30–100 μm in diameter is detailed and evaluated. The method is called the ‘settling tower' and consists in taking sequential pictures of particles falling under gravity in calm air. The scene is illuminated by a cold light source, while a camera takes 15 pictures per second. Between 20,000 and 100,000 images are analysed to obtain the distribution of V _s for a given set of particles. The method was validated using two standard particles with mean diameters of 68 and 108 μm, respectively, as well as Lycopodium spores, with a mean diameter of 35 μm. For each set of particles, the theoretical V _s distribution was estimated from the particle diameter distribution and the volumetric mass using a non-Stokian law, as the Reynolds numbers of the particles were large. The mean V _s was measured with the ‘settling tower' with less than 12% error, while the standard deviation of the V _s distribution was estimated with less than 51% error. The maximum error on the mean V _s was 12% for the Lycopodium spores and less than 2% for the two larger particles. The mean V _s of Lycopodium spores was 4.2 cm s⁻¹, and its standard deviation was 0.7 cm s⁻¹. The reason for the small overestimation of V _s for Lycopodium spores by the ‘settling tower' method is discussed. Preliminary measurements shows that, the ‘settling tower' could be of great practical interest for measuring the distribution of V _s of maize pollen as well as other types of pollen or spores.     

Effect of leaf age and position on light-saturated CO<Subscript>2</Subscript> assimilation rate,photosynthetic capacity,and stomatal conductance in rubber trees

Shoots of the tropical latex-producing tree Hevea brasiliensis (rubber tree) grow according to a periodic pattern, producing four to five whorls of leaves per year. All leaves in the same whorl were considered to be in the same leaf-age class, in order to assess the evolution of photosynthesis with leaf age in three clones of rubber trees, in a plantation in eastern Thailand. Light-saturated CO₂ assimilation rate (A _max) decreased more with leaf age than did photosynthetic capacity (maximal rate of carboxylation, V _cmax , and maximum rate of electron transport, J _max), which was estimated by fitting a biochemical photosynthesis model to the CO₂-response curves. Nitrogen-use efficiency (A _max/N_a, N_a is nitrogen content per leaf area) decreased also with leaf age, whereas J _max and V _cmax did not correlate with N _a. Although measurements were performed during the rainy season, the leaf gas exchange parameter that showed the best correlation with A _max was stomatal conductance (g _s). An asymptotic function was fitted to the A _max-g _s relationship, with R ² = 0.85. A _max, V _cmax, J _max and g _s varied more among different whorls in the same clone than among different clones in the same whorl. We concluded that leaf whorl was an appropriate parameter to characterize leaves for the purpose of modelling canopy photosynthesis in field-grown rubber trees, and that stomatal conductance was the most important variable explaining changes in A _max with leaf age in rubber trees.     

Analysis of a mathematical model for the growth of tumors

 In this paper we study a recently proposed model for the growth of a nonnecrotic, vascularized tumor. The model is in the form of a free-boundary problem whereby the tumor grows (or shrinks) due to cell proliferation or death according to the level of a diffusing nutrient concentration. The tumor is assumed to be spherically symmetric, and its boundary is an unknown function r=s(t). We concentrate on the case where at the boundary of the tumor the birth rate of cells exceeds their death rate, a necessary condition for the existence of a unique stationary solution with radius r=R ₀ (which depends on the various parameters of the problem). Denoting by c the quotient of the diffusion time scale to the tumor doubling time scale, so that c is small, we rigorously prove that (i) lim inf _t→∞ s(t)>0, i.e. once engendered, tumors persist in time. Indeed, we further show that (ii) If c is sufficiently small then s(t)→R ₀ exponentially fast as t→∞, i.e. the steady state solution is globally asymptotically stable. Further, (iii) If c is not “sufficiently small” but is smaller than some constant γ determined explicitly by the parameters of the problem, then lim sup _t→∞ s(t)<∞; if however c is “somewhat” larger than γ then generally s(t) does not remain bounded and, in fact, s(t)→∞ exponentially fast as t→∞. Received: 25 February 1998 / Revised version: 30 April 1998     

pH-Induced Molten Globule State of <Emphasis Type="Italic">Rhizopus niveus</Emphasis> Lipase is More Resistant Against Thermal and Chemical Denaturation Than Its Native State

Here, we have characterized four pH-dependent states: alkaline state, “B” (pH 9.0), native state, “N” (pH 7.4), acid-induced state, “A” (pH 2.2) and molten globule state, “MG” (pH 1.8) of Rhizopus niveus lipase (RNL) by CD, tryptophanyl fluorescence, ANS binding, DLS, and enzyme activity assay. This “MG” state lacks catalytic activity and tertiary structure but it has native-like significant secondary structure. The “R _h” of all the four states of RNL obtained from DLS study suggests that the molecular compactness of the protein increases as the pH of solution decreases. Kinetic analysis of RNL shows that it has maximum catalytic efficiency at state “B” which is 15-fold higher than state “N.” The CD and tryptophanyl fluorescence studies of RNL on GuHCl and temperature-induced unfolding reveal that the “MG” state is more stable than the other states. The DSC endotherms of RNL obtained at pH 9.0, 7.4, and 2.2 were with two transitions, while at pH 1.8 it showed only a single transition.