Mathematical foundations of the dendritic growth models

At present two growth models describe successfully the distribution of size and topological complexity in populations of dendritic trees with considerable accuracy and simplicity, the BE model (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) and the S model (Van Pelt and Verwer in Bull. Math. Biol. 48:197-211, 1986). This paper discusses the mathematical basis of these models and analyzes quantitatively the relationship between the BE model and the S model assumed in the literature by developing a new explicit equation describing the BES model (a dendritic growth model integrating the features of both preceding models; Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997). In numerous studies it is implicitly presupposed that the S model is conditionally linked to the BE model (Granato and Van Pelt in Brain Res. Dev. Brain Res. 142:223-227, 2003; Uylings and Van Pelt in Network 13:397-414, 2002; Van Pelt, Dityatev and Uylings in J. Comp. Neurol. 387:325-340, 1997; Van Pelt and Schierwagen in Math. Biosci. 188:147-155, 2004; Van Pelt and Uylings in Network. 13:261-281, 2002; Van Pelt, Van Ooyen and Uylings in Modeling Dendritic Geometry and the Development of Nerve Connections, pp 179, 2000). In this paper we prove the non-exactness of this assumption, quantify involved errors and determine the conditions under which the BE and S models can be separately used instead of the BES model, which is more exact but considerably more difficult to apply. This study leads to a novel expression describing the BE model in an analytical closed form, much more efficient than the traditional iterative equation (Van Pelt et al. in J. Comp. Neurol. 387:325-340, 1997) in many neuronal classes. Finally we propose a new algorithm in order to obtain the values of the parameters of the BE model when this growth model is matched to experimental data, and discuss its advantages and improvements over the more commonly used procedures.     

Maintenance mechanisms of the pipe model relationship and Leonardo da Vinci’s rule in the branching architecture of <Emphasis Type="Italic">Acer rufinerve</Emphasis> trees

The pipe model relationship (constancy of branch cross-sectional area/leaf area) and Leonardo da Vinci’s rule (equality of total cross-sectional area of the daughter branches and cross-sectional area of their mother branch) are empirical rules of tree branching. Effects of branch manipulation on the pipe model relationships were examined using five Acer rufinerve trees. Half the branches in each tree were untreated (control branches, CBs), and, for the others (manipulated branches, MBs), either light intensity or leaf area (both relating to photosynthetic source activity), or shoot elongation (source + sink activities), was reduced, and responses of the pipe model relationships were followed for 2 years. The pipe model relationship in MBs changed by suppression of source activity, but not by simultaneous suppression of source + sink activities. The manipulations also affected CBs in the year of manipulation and both branches in the next year. The branch diameter growth was most affected by light, followed by shoot elongation and leaf area, in that order. Because of the decussate phyllotaxis of A. rufinerve, one branching node can potentially have one main and two lateral branches. Analysis of 295 branching nodes from 13 untreated trees revealed that the da Vinci’s rule held in branching nodes having one shed branch but not in the nodes without branch shedding, indicating the necessity of natural shedding of branches for da Vinci’s rule to hold. These analyses highlight the importance of the source–sink balance and branch shedding in maintenance of these empirical rules. This article was contributed at the invitation of the Editorial Committee.     

Numerical Simulation of Unsteady Blood Flow through Capillary Networks

A numerical method is implemented for computing unsteady blood flow through a branching capillary network. The evolution of the discharge hematocrit along each capillary segment is computed by integrating in time a one-dimensional convection equation using a finite-difference method. The convection velocity is determined by the local and instantaneous effective capillary blood viscosity, while the tube to discharge hematocrit ratio is deduced from available correlations. Boundary conditions for the discharge hematocrit at divergent bifurcations arise from the partitioning law proposed by Klitzman and Johnson involving a dimensionless exponent, q≥1. When q=1, the cells are partitioned in proportion to the flow rate; as q tends to infinity, the cells are channeled into the branch with the highest flow rate. Simulations are performed for a tree-like, perfectly symmetric or randomly perturbed capillary network with m generations. When the tree involves more than a few generations, a supercritical Hopf bifurcation occurs at a critical value of q, yielding spontaneous self-sustained oscillations in the absence of external forcing. A phase diagram in the m–q plane is presented to establish conditions for unsteady flow, and the effect of various geometrical and physical parameters is examined. For a given network tree order, m, oscillations can be induced for a sufficiently high value of q by increasing the apparent intrinsic viscosity, decreasing the ratio of the vessel diameter from one generation to the next, or by decreasing the diameter of the terminal vessels. With other parameters fixed, oscillations are inhibited by increasing m. The results of the continuum model are in excellent agreement with the predictions of a discrete model where the motion of individual cells is followed from inlet to outlet.     

Fine root architecture, morphology, and biomass of different branch orders of two Chinese temperate tree species

We have limited understanding of architecture and morphology of fine root systems in large woody trees. This study investigated architecture, morphology, and biomass of different fine root branch orders of two temperate tree species from Northeastern China—Larix gmelinii Rupr and Fraxinus mandshurica Rupr —by sampling up to five fine root branch orders three times during the 2003 growing season from two soil depths (i.e., 0–10 and.10–20 cm). Branching ratio (R _b) differed with the level of branching: R _b values from the fifth to the second order of branching were approximately three in both species, but markedly higher for the first two orders of branching, reaching a value of 10.4 for L. gmelinii and 18.6 for F. mandshurica. Fine root diameter, length, SRL and root length density not only had systematic changes with root order, but also varied significantly with season and soil depth. Total biomass per order did not change systematically with branch order. Compared to the second, third and/or fourth order, the first order roots exhibited higher biomass throughout the growing season and soil depths, a pattern related to consistently higher R _b values for the first two orders of branching than the other levels of branching. Moreover, the differences in architecture and morphology across order, season, and soil depth between the two species were consistent with the morphological disparity between gymnosperms and angiosperms reported previously. The results of this study suggest that root architecture and morphology, especially those of the first order roots, should be important for understanding the complexity and multi-functionality of tree fine roots with respect to root nutrient and water uptake, and fine root dynamics in forest ecosystems.     

Effect of fungal infection on reproductive potential and survival time of <Emphasis Type="Italic">Tetranychus urticae</Emphasis> (Acari: Tetranychidae)

The effect of fungal infection on the reproductive potential of two-spotted spider mite, Tetranychus urticae, was evaluated as part of the full biocontrol potential of three entomopathogenic fungi by modeling of fecundity probability. Female mites (≤2-day-old) on leaves were exposed to the sprays of Beauveria bassiana, Paecilomyces fumosoroseus and Metarhizium anisopliae at the concentrations of 1.13 × 10³, 1.55 × 10³ and 0.95 × 10³ deposited conidia mm⁻² and then individually reared at 25°C and 12:12 L:D for oviposition. Mite mortalities 10 days after spraying were 73.1, 75.4 and 67.9% in the fungal treatments versus 15.5% in control. On average, females infected by the three fungal species survived 5.8, 6.2 and 6.3 days, and laid 3.1, 4.0 and 4.0 eggs per capita, respectively. These were 3–4 fold lower than the control fecundity at 12.3. The cumulative probabilities [P(m ≤ N)] for the counts of infected and non-infected (control) females laying m eggs per capita (m ≤ N) during 10 days fit very well the equation P(m ≤ N) = 1/[1 + exp(a + bm)] (r ² ≥ 0.98), yielding a solution to the probability for the female mites to achieve a specific fecundity {P(m ≤ N)−P[m ≤ (N − 1)]}. Consequently, the infected mites had 71–78% chance to lay ≤5 eggs per capita but only 5–8% to deposit >10 eggs despite some variation among the tested fungi. In contrast, the chances for the non-infected mites to achieve the low and high fecundities were 23 and 55%. The fitted probabilities provide a full coverage of the fecundity potential of infected versus non-infected mites and are more informative than the mean fecundities.     

Density effects and self-thinning in even-aged pure stands ofEucalyptus camaldulensis Dehn

The competition density effect and changes of mean total tree weight (w) and stand density (ρ) during course of self-thinning were examined in even-aged pure stands ofEucalyptus camaldulensis Dehn. which were planted in the tropical monsoon region. The level of competition was controlled by changing the initial stand density from 625 trees ha⁻¹ to 40,000 trees ha⁻¹. Hozumi's model was used to describe thew-ρ trajectory with aging of each stand and thew-ρ relation between stands of different densities at each time. The higher density produced trees of smaller mean tree sizes. The higher the density, the sooner self-thinning began. The growth curve ofE. camaldulensis followed the logistic growth curve where both maximum size and intrinsic growth rate change with time. Mean intrinsic growth rate was maximized at initiation of growth after lag time and then gradually decreased as time progressed. Hozumi's model was considered to be the best model with wide applicability for describing and comparing the growth characteristics during the course of self-thinning among different species, especially in tropical forest plantations, in which many diverse species were used for reforestation.     

Antifungal and cytotoxic effects of cyanein derivatives

The effects of cyanein, tetrahydrocyanein and diacetyl-O-cyanein on the growth and morphology of fungi and HeLa cells were studied. The change of cyanein structure decreased its cytotoxic effect (HeLa cell) to approx. a half and the antifungal effect up to 100 times (Saccharomyces cerevisiae andEremothecium ashbyi). Cyanein caused characteristic changes in morphology ofBotrytis cinerea (“bulging effect”, branching of hyphae) andPaecilomyces viridis (branching of hyphase, yeast-like growth). Except for flexuose ofPaecilomyces viridis hyphae caused by diacetyl-O-cyanein the cyanein derivatives did not induce the above mentioned morphologic changes.     

ARCHITECTURE AND CROWN GEOMETRY IN TABEBUIA ROSEA (BIGNONIACEAE)

In the tropical tree Tabebuia rosea, seedlings form an erect unbranched stem with rhythmic growth. Three distinct and predictable geometrical stages are then recognized in crown development. Sympodial branching begins with the arrest of the terminal bud of the trunk and symmetric outgrowth of a pair of subtending lateral buds. During an intermediate phase, branching becomes asymmetric at about Order 5. At each sympodial bifurcation there is differentiation between vigorous, relatively straight main branches (leaders) and less vigorous laterals forming regular pseudomonopodial branch complexes, which collectively constitute the cup-shaped crown. Finally, dormant lateral buds in the lowest bifurcation of the trunk are released and reiterate the original crown form. Ultimately an erect, apparently monopodial tree is formed by a set of superimposed cup-shaped crowns. Crown development of Tabebuia is unique because it involves predictable ontogenic changes in branching patterns. Crowns of open-grown Tabebuia consist of relatively few, wide branch tiers, crowns of forest grown trees are tall and narrow. Analysis of the adaptive geometry of wide vs. narrow crowns through computer simulation illustrates the precise cost of mechanical support for terminal leaf rosettes at successive developmental phases and suggests that tall, erect, narrow, and multi-tiered crowns are more efficient than wide open crowns.     

Comparative morphology of acrogenous branch systems and phylogenetic considerations. II. Angiosperms

A concept for a primitive angiospermous branch system is given in order to have a starting point for the derivation of the diverse and highly differentiated branch systems observed in contemporary angiosperms. Hitherto Troll's (1964, 1969) comparative study of the synflorescences in this plant group — developed out predominantly on herbaceous plants — was the most comprehensive and sophisticated treatment dealing with branch systems. Unfortunately, the work on tropical tree architecture by Hallé et al. (1978) has no reference to the classical studies of Troll and his pupils. Thus Müller-Doblies and Weberling (1984) emphasized the high degree of terminological incompatibility between the two works. Angiosperms are seen as a monophyletic plant division. Consequently, the branch system of the first primitive angiosperms must be the starting point in the evolution of the abundant diversity of branch systems and growth forms of modern angiosperms. If it is accepted that primitive angiospermous shoots were terminated by a large flower, one may assume, that the reproductive end of the shoot was enriched by paracladia early in evolution, thereby developing a terminal inflorescence instead of a single flower. Thus the primitive shoot unit was divided into a basal vegetative region — the trophotagma, branching retardively — and the reproductive terminal region, the anthotagma, branching simultaneously. It is demonstrated through a selection of different examples, that the construction of such a system possesses the options for several modifications, enabling the evolution of the abundant diversity of branch systems which characterizes contemporary angiosperms.     

Relationship of Pruning and Growth Morphology with Hormone Ratios in Shoots of Pillar and Standard Peach Trees

Genotype and cultural management determine the shape of peach [Prunus persica (L.) Batch] tree canopies in orchards. Not well understood, however, is the relationship between terminal growth, lateral branching, and shoot hormone levels that can fundamentally affect tree canopy development. In this experiment, two peach cultivars with widely differing growth habits (Pillar, KV930479 and Standard, ‘Harrow Beauty’) were budded on ‘Lovell’ rootstock, planted in the field in 1998, and characterized for shoot morphology and hormone concentrations in 2002 and 2003 (the fourth and fifth leaf, respectively). Auxin (indole-3-acetic acid) and cytokinins (largely trans-zeatin riboside, dihydrozeatin riboside, and isopentenyladenosine) were measured in shoot tips (2002) and current-year shoots (2003) using mass spectrometry. In 2002, Pillar trees had less sylleptic branching, more upright growth, and higher auxin and auxin-to-cytokinin ratios than Standard trees. In Pillar trees in 2003, auxin concentrations and shoot growth were highest in current year shoots; in pruned trees, only auxin levels increased. Peach tree growth habits may be the result of altered hormone metabolism. Growth forms leading to superior production efficiency may be developed by selection based on specific target hormone concentrations and ratios.     

Definitions and Epidemiology of Candida Species not Susceptible to Echinocandins

Antifungal susceptibility testing of Candida against the echinocandin antifungal agents (anidulafungin [ANF], caspofungin [CSF], micafungin [MCF]) has been standardized by the Clinical and Laboratory Standards Institute (CLSI) Subcommittee on Antifungal Testing. The CLSI proposed a single set of clinical breakpoints (CBPs) for all three echinocandins and all species of Candida: susceptible, minimum inhibitory concentration (MIC) ≤ 2 μg/mL; nonsusceptible, MIC > 2 μg/mL. Subsequently, these CBPs have been shown to lack sensitivity in detecting strains of Candida with acquired resistance mechanisms associated with treatment failure. Studies using the CLSI method have defined wild-type (WT) MIC distributions and epidemiologic cutoff values (ECVs) for each echinocandin and the common species of Candida. The ECVs serve as a sensitive means of discriminating WT strains from those with acquired resistance mechanisms. WT MIC distributions revealed ECV ranges of 0.03 to 0.25 μg/mL for all major species except C. parapsilosis (1–4 μg/mL) and C. guilliermondii (4–16 μg/mL). These ECVs reliably differentiate WT strains of each species from non-WT strains containing fks mutations. These data, coupled with additional biochemical, clinical, pharmacokinetic, and pharmacodynamic considerations, have resulted in new CBPs of ≤0.25 μg/mL (susceptible), 0.5 μg/mL (intermediate), and ≥1 μg/mL (resistant) for ANF, CSF, and MCF for C. albicans, C. tropicalis, and C. krusei. For these agents and C. parapsilosis, the new CBPs are ≤2 μg/mL (susceptible), 4 μg/mL (intermediate), and ≥8 μg/mL (resistant). For C. glabrata, the CBPs for ANF and CSF are ≤0.12 μg/mL (susceptible), 0.25 μg/mL (intermediate), and ≥0.5 μg/mL (resistant), whereas those for MCF are ≤0.06 μg/mL, 0.12 μg/mL, and ≥0.25 μg/mL, respectively. Application of both ECVs and the lower species-specific CBPs for the echinocandins has proven useful in both resistance surveillance and clinical care and will serve as an important step in international harmonization of in vitro susceptibility testing of this important antifungal class.     

Stochastic continuous time neurite branching models with tree and segment dependent rates

In this paper we introduce a continuous time stochastic neurite branching model closely related to the discrete time stochastic BES-model. The discrete time BES-model is underlying current attempts to simulate cortical development, but is difficult to analyze. The new continuous time formulation facilitates analytical treatment thus allowing us to examine the structure of the model more closely. We derive explicit expressions for the time dependent probabilities p(γ,t) for finding a tree γ at time t, valid for arbitrary continuous time branching models with tree and segment dependent branching rates. We show, for the specific case of the continuous time BES-model, that as expected from our model formulation, the sums needed to evaluate expectation values of functions of the terminal segment number μ(f(n),t) do not depend on the distribution of the total branching probability over the terminal segments. In addition, we derive a system of differential equations for the probabilities p(n,t) of finding n terminal segments at time t. For the continuous BES-model, this system of differential equations gives direct numerical access to functions only depending on the number of terminal segments, and we use this to evaluate the development of the mean and standard deviation of the number of terminal segments at a time t. For comparison we discuss two cases where mean and variance of the number of terminal segments are exactly solvable. Then we discuss the numerical evaluation of the S-dependence of the solutions for the continuous time BES-model. The numerical results show clearly that higher S values, i.e. values such that more proximal terminal segments have higher branching rates than more distal terminal segments, lead to more symmetrical trees as measured by three tree symmetry indicators.     

Isoquinoline alkaloids from Mahonia aquifolium stem bark are active against Malassezia spp

Bioassay directed fractionation of crude extract fromMahonia aquifolium led to the isolation of fraction A (bisbenzylisoquinoline alkaloid complex, BBI) and a fraction of protoberberine alkaloids, where the major compounds berberine and jatrorrhizine were isolated as their iodides. The antifungal activity of the crude extract, two protoberberine alkaloids and BBI fromM. aquifolium stem bark were evaluated against six strains ofMalassezia spp. The compounds tested were generally found to possess only weak to moderate antifungal properties: the MICs for individual strains were in the range ≤50–≥1000 mg/L.     

Peroxidase activity and lignification in soybean root growth-inhibition by juglone

The changes in activities of soluble and cell wall-bound peroxidases and lignin contents in juglone-stressed soybean (Glycine max) seedlings and their relationships with root growth were investigated. Soybean seedlings (3-d-old) were cultivated in nutrient solution supplemented with 0.5 to 25 μM juglone for 24 h. Length and dry mass of roots decreased after 5 to 25 μM juglone treatments. Low juglone concentrations (≤ 1 μM) increased soluble peroxidase activity, while high concentrations (≥ 10 μM) inhibited activities of soluble and cell wall-bound peroxidases. Juglone (≤ 1 μM) did not affect lignin content but highly increased lignification after 5 to 25 μM treatments. Results indicate that lignification may be an important step in root growth reduction of juglone-stressed soybean.     

Effect of organic pollutant treatment on the growth of pea and maize seedlings

This study confirmed the considerable effect of polycyclic aromatic hydrocarbon fluoranthene (FLT; 0.01, 0.1, 1, 4 and 7 mg/l) exposure on the germination of seeds, growth and root morphology of seedlings in Zea mays and Pisum sativum. Seed germination was significantly inhibited at FLT≥0.01 mg/l in maize and at ≥1 mg/l in pea. The amount of released ethylene after 3 days of germination was significantly increased in both species at FLT≥0.1 mg/l. After 7 days of seedling cultivation a significant decrease in the dry weight of roots and shoots occurred in maize at FLT≥0.1 mg/l while in pea similar effect was observed at ≥1 mg/l. The total length of primary and lateral roots was significantly reduced by FLT≥1 mg/l in maize and by 4 and 7 mg/l in pea. The length of the non-branched part of the primary root was significantly reduced by FLT≥0.1 mg/l in maize and ≥0.01 mg/l in pea. In both species the number of lateral roots was significantly increased at FLT≤1 mg/l and inhibited at concentrations of 4 and 7 mg/l. Fluoranthene content in roots and shoots of both species positively correlated with the FLT treatment.     

rol-Gene expression in transgenic aspen (Populus tremula) plants results in accelerated growth and improved stem production index

Stem and trunk growth, axillary bud break and branching habits are extremely important parameters of wood production in forest trees. The possibility of altering tree form by transformation with genes responsible for hormone biosynthesis and/or activity is most attractive. We examined four different phenotypically selected transgenic clones of a model tree –Populus tremula– expressing rol genes from Agrobacterium rhizogenes under their native promoters. Several of the observed phenotypic modifications were correlated with rol-gene expression, including breaking of stem apical dominance which resulted in the development and branching of up to four axillary buds per explant, as compared to a lack of axillary bud break in a uidA (β-glucuronidase-encoding)-transgenic aspen line and control (non-transformed) plants. rol-Transgenic plants also exhibited a higher cumulative stem length and enhanced growth rate, and hence a higher stem production index. During their first and second years in the greenhouse, rol-transgenic aspen plants exhibited enhanced growth and delayed winter dormancy relative to non-transformed plants. Although initially rol-transgenic plants had smaller, wrinkled leaves, these changes were not observed in the 2-year-old plants, which exhibited a phenotypically true-to-type leaf shape. Received: 13 September 1998 / Accepted: 15 April 1999     

Theoretical relationship between the optimal models of the vascular tree

Two models of optimal branching structure of the vascular tree are compared. Murray’s minimum work model derived from minimum energy loss due to flow and volume in the duct system is proved to be included as a mathematical group in the authors’ model defined by the minimum volume under determinant pressure, flow and position at the terminals. The problem about heterotypical trees which are identical at the terminal conditions but different in the topological order of branch combinations are discussed, applying the results of analyses on the equivalent duct of uniform terminal pressure trees. It is proved that the minimum work tree has the least energy loss compared with its heterotypical minimum volume trees and is a better model of branching structure of the vascular tree.     

Spatial and age-dependent tree-ring growth responses of Larix gmelinii to climate in northeastern China

Tree-ring width chronologies from 276 Larix gmelinii cores taken in northeastern China were used to analyze spatial and age-dependent growth–climate response relationships. Tree radial growth from five localities showed similar patterns, while exhibiting different tree-ring growth responses to local climate. The rotated principal component analysis (RPCA) indicated that tree age, growing season moisture conditions, and ambient air temperature variations resulted from location differences (e.g., longitude, latitude, and altitude), which could explain the non-stationary spatial climate–growth relations observed. The study tested the fundamental assumption that the climate–growth of L. gmelinii was age independent after the removal of size trends and disturbance signals. The age-related climate–growth relationship might potentially improve the veracity of past climate reconstructions. Bootstrapped correlation function analyses suggested that the response of L. gmelinii radial growth to climate differed between trees ≥150 years old and <150 years old. Mean sensitivity and standard deviation for trees increased with age in the <150 years old tree class; whereas trees ≥150 years old had no significant relationship with age. These results showed that the assumption of age-independent climate–growth relationship is invalid at these sites. Physiological processes and/or hydraulic constraints dependent on tree age, together with detrending techniques could be the possible causal factors of clear age-dependent responses. These results suggested the importance of incorporating trees of all ages into the chronology to recover a detailed climatic signal in a reconstruction of L. gmelinii for this region.     

QTL analysis of leaf morphology in tetraploid Gossypium (cotton)

Molecular markers were used to map and characterize quantitative trait loci (QTLs) determining cotton leaf morphology and other traits, in 180 F₂ plants from an interspecific cross between a Gossypium hirsutum genotype carrying four morphological mutants, and a wild-type Gossypium barbadense. The prominent effects of a single region of chromosome 15, presumably the classical ”Okra-leaf” locus, were modified by QTLs on several other chromosomes affecting leaf size and shape. For most traits, each parent contained some alleles with positive effects and others with negative effects, suggesting a large potential for adapting leaf size and shape to the needs of particular production regimes. Twenty one QTLs/loci were found for the morphological traits at LOD≥3.0 and P≤0.001, among which 14 (63.6%) mapped to D-subgenome chromosomes. Forty one more possible QTLs/loci were suggested with 2.0≤LOD<3.0 and 0.001<P≤0.01. Among all of the 62 possible QTLs (found at LOD≥2.0 and P≤0.01) for the 14 morphological traits in this study, 38 (61.3%) mapped to D-subgenome chromosomes. This reinforces the findings of several other studies in suggesting that the D-subgenome of tetraploid cotton has been subject to a relatively greater rate of evolution than the A-subgenome, subsequent to polyploid formation. Received: 26 April 1999 / Accepted: 30 July 1999     

Fluctuations during growth of the plasma membrane H(+)-ATPase activity of Saccharomyces cerevisiae and Schizosaccharomyces pombe

The plasma membrane H⁺-ATPase activity was determined under various growth conditions using the yeastsSaccharomyces cerevisiae andSchizosaccharomyces pombe. Under early batch-growth conditions in a rich medium, the budding yeastS. cerevisiae ATPase specific activity increased 2-to 3-fold during exponential growth. During late exponential growth, a peak of ATPase activity, followed by a sudden decrease, was observed and termed “growth-arrest control”. The growth arrest phenomenon ofS. cerevisiae could not be related to the acidification of the culture medium or to glucose exhaustion in the medium or to variation of glucose activation of the H⁺-ATPase. Addition of ammonium to a proline minimum medium also stimulated transiently the ATPase activity ofS. cerevisiae. Specific activity of the fission yeastS. pombe ATPase did not show a similar profile and steadily increased to reach a plateau in stationary growth. Under synchronous mitotic growth conditions, the ATPase activity ofS. cerevisiae increased during the cell division cycle according to the “peak” type cycle, while that ofS. pombe was of the “step” type.