Population cycles caused by selection by density dependent competitive interactions

Several animal species have cyclic population dynamics with phase-related cycles in life history traits such as body mass, reproductive rate, and pre-reproductive period. Although many mechanisms have been proposed there is no agreement on the cause of these cycles, and no population equation that deduces both the abundance and the life history cycles from basic ecological constraints has been formulated. Here I deduce a population dynamic equation from the selection pressure of density dependent competitive interactions in order to explain the cyclic dynamics in abundance and life history traits. The model can explain cycles by evolutionary changes in the genotype or by plastic responses in the phenotype. It treats the population dynamic growth rate as an initial condition, and its density independent fundament is Fisher’s (1930, The Genetical Theory of Natural Selection, Oxford: Clarendon) fundamental theorem of natural selection that predicts a hyper-geometrical increase in abundance. The predicted periods coincide with the cyclic dynamics of Lepidoptera, and the Calder hypothesis, which suggests that the period of population cycles is proportional to the 1/4 power of body mass, follows from first principles of the proposed density dependent ecology.     

Physio-chemical mathematical theory for transitions in cellular metabolism: An aspect of carcinogenesis

It is pointed out that the non-monotonic character of the chemical reaction rate expressions, together with the relative magnitude of the diffusivity constants, is likely to engender a multiplicity of locally stable steady-state solutions to the system of reaction-diffusion equations for the concentration distributions of molecular species through the volume of a living cell. A transition in cellular metabolism, i.e., the dynamical evolution from an initial locally stable steady-state solution for the concentration distributions to another distinct locally stable steady-state solution, can be induced by an etiologic agent which modifies the rate expressions significantly during an interval of time. Global inequality analysis is employed to derive a condition on the modified rate expressions that is sufficient to guarantee the occurrence of such a transition in cellular metabolism. The possibility of a transition induced by a chemical carcinogen is investigated by applying the latter sufficient condition, and it is found that the statistical frequency of carcinogenesis should depend essentially on the magnitude of the grouping (T ^{2 − α} D ^α) for a total doseD of carcinogen administered to an animal at a uniform rate (D/T) over a time interval of durationT, where α is a certain positive number less than 1. This theoretical result is shown to be supported by the available experimental evidence.     

The diversity of Linnaean communities: a way of detecting invertebrate groups at risk of extinction

Summary As ecologists use changes in the relative abundances of species to detect environmental stress in ecological communities, it is possible to do the same for higher taxa (‘Linnaean communities’) by examining the distribution of species between genera. Using an adaptation of Simpson’s diversity index (D), we predict that, like ecological communities, mature Linnaean communities have D values >0.8 and developing and relictual communities have D values <0.8. We show that D values for seven Australian weevil taxa, three indicated to be mature (Amycterini, Aterpini, Leptopiina), two relictual (Nemonychidae, Belinae) and two actively radiating groups (Gonipterini, Cyphicerina), are as predicted. Apparently subdivision of niche space has the same statistical effects in stressed Linnaean communities as it does in ecological communities, with firstly the loss of species in genera with intermediate numbers of species followed by the loss of monotypic genera. Clearly therefore, the protection of monotypic genera in Linnaean communities with low D values should be the highest conservation priority as these are at the highest risk of extinction, while monotypic genera in high-D communities are not at such high risk. Similarly, the geographical distribution of monotypic genera in Linnaean communities with low D values, rather than that of rare species (most of which will be in genera with many species), may constitute a useful way of identifying areas of conservation concern. CSIRO’s right to retain a nonexclusive, royalty-free licence in and to any copyright is acknowledged.     

S.A.M., the Italian Martian Simulation Chamber

The Martian Environment Simulator (SAM “Simulatore di Ambiente Marziano”) is a interdisciplinary project of Astrobiology done at University of Padua. The research is aimed to the study of the survival of the microorganisms exposed to the “extreme” planetary environment. The facility has been designed in order to simulate Mars’ environmental conditions in terms of atmospheric pressure, temperature cycles and UV radiation dose. The bacterial cells, contained into dedicated capsules, will be exposed to thermal cycles simulating diurnal and seasonal Martian cycles. The metabolism of the different biological samples will be analysed at different phases of the experiment, to study their survival and eventual activity of protein synthesis (mortality, mutations and capability of DNA reparing). We describe the experimental facility and provide the perspectives of the biological experiments we will perform in order to provide hints on the possibility of life on Mars either autochthonous or imported from Earth. Presented at: National Workshop on Astrobiology: Search for Life in the Solar System, Capri, Italy, 26 to 28 October, 2005.     

Mathematical models for cellular systems. The von foerster equation. Part II

This is the continuation of Part I, which was published in the September, 1965, issue of theBulletin. The birth rate, α(t), is now assumed to be a linear functional of the age density,n. This gives a simple model of self-replenishing stem cell compartments, and leads to a necessary condition for the existence of a steady state. Some examples are presented to illustrate the formalism. They include: (a) An equivivant population with life spanD and no losses from death or migration. The total number of cells is multiplied by 2 in each time intervalD. As a special case, frequently realized in practice, the population may be increasing exponentially with time (“log-phase” of growth). (b) A compartment with “random” emigration of cells and gamma distribution of life spans. (c) An oversimplified version of L. G. Lajtha’s model describing stem cell kinetics. In section IV a simple case in which the loss function depends explicitly onn is discussed very briefly. This work was performed under the auspices of the U.S. Atomic Energy Commission.     

Evolutionary and dynamic stability in continuous population games

 Asymptotic stability under the replicator dynamics over a continuum of pure strategies is shown to crucially depend on the choice of topology over the space of mixed population strategies, namely probability measures over the real line. Thus, Strong Uninvadability, proved by Bomze (1990) to be a sufficient condition for asymptotic stability under the topology of variational distance between probability measures, implies convergence to fixation over a pure strategy x ^* only when starting from a population strategy which assigns to x ^* a probability sufficiently close to one. It does not imply convergence to x ^* when starting from a distribution of small deviations from x ^* , regardless of how small these deviations are. It is, therefore, suggested that when a metric space of pure strategies is involved, another topology, hence another stability condition, may prove more relevant to the process of natural selection. Concentrating on the case of a one dimensional continuous quantitative trait, we resort to the natural Maximum Shift Topology in which an ɛ-vicinity of the fixation on a pure strategy x ^* consists of all mixed population strategies with support which includes x ^* and is in the ɛ-neighborhood of x ^* . Under this topology, a relatively simple necessary and sufficient condition for replicator asymptotic stability, namely Continuous Replicator Stability (CRSS), is demonstrated. This condition is closely related to the static stability condition of Neighbor Invadability (Apaloo 1997), and slightly stronger than the condition of Continuous Stability (Eshel and Motro 1981). Received: 9 July 2002 / Revised version: 12 November 2002 / Published online: 19 March 2003 Key words or phrases: CSS – ESS – NIS – Strong uninvadability – Weak topology – Replicator dynamics – Long-term evolution – Continuous population games – Continuous replicator stability – Asymptotic stability     

Soil potassium mobility and uptake by corn under differential soil moisture regimes

This study examined the effects of soil moisture on soil K mobility, dynamics of soil K, soil K fixation, plant growth and K uptake. A pot experiment, with and without corn (Zea maysL.), was conducted over a 16-d duration using a Yolo silt loam treated with two soil moisture regimes, i.e. constant moisture vs. wetting–drying (W–D) cycles. Soil K dynamics were determined using both ion exchange resin and direct extraction of soil solution. Soil K mobility increased significantly with soil moisture content (θ_v) and there was a positive curvilinear relationship between θ_v and effective diffusion coefficient (D_e), suggesting that more K⁺ can diffuse to the plant roots at sufficient soil moistures. Increase in D_e could be attributed to the decrease of impedance factor. During W–D cycles, soil solution K concentration increased as soil solution volume decreased, but soil solution K and NH₄ ⁺-extractable K pools decreased. In the constant moisture regime, available K pools decreased over the 16-d duration, but to a lesser extent than in W–D regime. The W–D cycles significantly enhanced K fixation and reduced available K pools in the soil in contrast to the constant moisture regime. Potassium fixation by the soil showed a biphasic pattern under the W–D regime, with a rapid fixation within the first 2 d after re-wetting, followed by a slower fixation. In the soil with constant moisture, K fixation was rapid during the first 8 h after wetting the soil, and then proceeded so slowly that no significant K fixation was observed after 4 d. The W–D cycles decreased root and shoot growth and K uptake by corn compared to constant moisture condition. Our results support the hypothesis that W–D cycles enhance soil K fixation, reduce soil K mobility and plant growth, and therefore reduce plant K⁺ uptake. This revised version was published online in June 2006 with corrections to the Cover Date.     

A simple model of the relationship between asymmetry and developmental stability

The relationship between developmental stability and morphological asymmetry is derived under the standard view that structures on each side of an individual develop independently and are normally distributed. I use developmental variance of sizes of parts, V_D, as the converse of developmental stability, and assume that V_D follows a gamma distribution. Repeatability of asymmetry, a measure of how informative asymmetry is about V_D, is quite insensitive to the variance in V_D, for example only reaching 20% when the coefficient of variation of V_D is 100%. The coefficient of variation of asymmetry, CV_FA, also increases very slowly with increasing population variation in V_D. CV_FA values from empirical data are sometimes over 100%, implying that developmental stability is sometimes more variable than any previously studied type of trait. This result suggests that alternatives to this model may be needed.     

Essential roles of dopamine D4 receptors and the type 1 adenylyl cyclase in photic control of cyclic AMP in photoreceptor cells

Light and dopamine regulate many physiological functions in the vertebrate retina. Light exposure decreases cyclic AMP formation in photoreceptor cells. Dopamine D₄ receptor (D₄R) activation promotes light adaptation and suppresses the light‐sensitive pool of cyclic AMP in photoreceptor cells. The key signaling pathways involved in regulating cyclic AMP in photoreceptor cells have not been identified. In the present study, we show that the light‐ and D₄R‐signaling pathways converge on the type 1 Ca²⁺/calmodulin‐stimulated adenylyl cyclase (AC1) to regulate cyclic AMP synthesis in photoreceptor cells. In addition, we present evidence that D₄R activation tonically regulates the expression of AC1 in photoreceptors. In retinas of mice with targeted deletion of the gene (Adcy1) encoding AC1, cyclic AMP levels and Ca²⁺/calmodulin‐stimulated adenylyl cyclase activity are markedly reduced, and cyclic AMP accumulation is unaffected by either light or D₄R activation. Similarly, in mice with disruption of the gene (Drd4) encoding D₄R, cyclic AMP levels in the dark‐adapted retina are significantly lower compared to wild‐type retina and are unresponsive to light. These changes in Drd4?/? mice were accompanied by significantly lower Adcy1 mRNA levels in photoreceptor cells and lower Ca²⁺/calmodulin‐stimulated adenylyl cyclase activity in retinal membranes compared with wild‐type controls. Reduced levels of Adcy1 mRNA were also observed in retinas of wild‐type mice treated chronically with a D₄R antagonist, L‐745870. Thus, activation of D₄R is required for normal expression of AC1 and for the regulation of its catalytic activity by light. These observations illustrate a novel mechanism for cross‐talk between dopamine and photic signaling pathways regulating cyclic AMP in photoreceptor cells.     

Turing instabilities in general systems

We present necessary and sufficient conditions on the stability matrix of a general n(≥2)-dimensional reaction-diffusion system which guarantee that its uniform steady state can undergo a Turing bifurcation. The necessary (kinetic) condition, requiring that the system be composed of an unstable (or activator) and a stable (or inhibitor) subsystem, and the sufficient condition of sufficiently rapid inhibitor diffusion relative to the activator subsystem are established in three theorems which form the core of our results. Given the possibility that the unstable (activator) subsystem involves several species (dimensions), we present a classification of the analytically deduced Turing bifurcations into p (1 ≤p≤ (n− 1)) different classes. For n = 3 dimensions we illustrate numerically that two types of steady Turing pattern arise in one spatial dimension in a generic reaction-diffusion system. The results confirm the validity of an earlier conjecture [12] and they also characterise the class of so-called strongly stable matrices for which only necessary conditions have been known before [23, 24]. One of the main consequences of the present work is that biological morphogens, which have so far been expected to be single chemical species [1–9], may instead be composed of two or more interacting species forming an unstable subsystem. Received: 21 September 1999 / Revised version: 21 June 2000 / Published online: 24 November 2000     

A new isoflavone glycoside from <Emphasis Type="Italic">Trifolium pratense</Emphasis> L.

The isoflavonoid composition of red clover (Trifolium pratense L.) has been studied. The following compounds have been detected: cyclopolyol (+)-pinitol, not found in clover before; known isoflavones formononetin, prunetin, genistein, and prunetin-4′-O-β-D-glucopyranoside; isoflavone monogalactosides formononetin-7-O-β-D-galactopyranoside, inermin-3-O-β-D-galactopyranoside, and genistein-7-O-β-D-galactopyranoside; and a novel compound, prunetin-4′-α-D-glucopyranoside. The structures of these compounds have been proven by UV, IR, 1H NMR, 13C NMR, mass, and circular dichroism spectra. (+)-Pinitol is known to possess biological activity.     

Mitochondrial Gene Rearrangements and Partial Genome Duplications Detected by Multigene Asymmetric Compositional Bias Analysis

Asymmetric compositional and mutation bias between the two strands occurs in mitochondrial genomes, and an asymmetric mechanism of mtDNA replication is a potential source of this bias. Some evidence indicates that during replication the heavy strand is subject to a gradient of time spent in a single-stranded state (D _ssH) and a gradient of mutational damage. The nucleotide composition bias among genes varies with D _ssH. Consequently, partial genome duplications (PGD) will alter the skew for genes located downstream of the duplication, relatively to nascent light strand synthesis, and in the same way, gene rearrangements (GRr) will affect genes by changing their skews. We examined cases where there had been PGD or GRr and determined whether this left a trace in the form of unusual patterns of base composition. We compared the skew of genes differently located on the mtDNA genome of previously published whole mtDNA genomes from amphibians, a group that shows considerable levels of both GRr and PGD. After observing a significant correlation between AT and GC skew with D _ssH at fourfold redundant sites, we ran our analysis and detected 31.3% of the species with GRr and/or PGD. By comparing the nucleotide composition at fourfold redundant sites in normal and “abnormal” species, we found that A/C variation occurs and is associated with GRr/PGD. These results show that by analyzing the nucleotide skews of only three genes, it may be possible to predict some mitochondrial GRr and/or PGD without knowing the complete mtDNA genome sequence. [Reviewing Editor: Dr. David Pollock]     

Fagopyritol B1, O-α-D-galactopyranosyl-(1→2)-D-chiro-inositol, a galactosyl cyclitol in maturing buckwheat seeds associated with desiccation tolerance

O-α-D-Galactopyranosyl-(1→2)-D-chiro-inositol, herein named fagopyritol B1, was identified as a major soluble carbohydrate (40% of total) in buckwheat (Fagopyrum esculentum Moench, Polygonaceae) embryos. Analysis of hydrolysis products of purified compounds and of the crude extract led to the conclusion that buckwheat embryos have five α-galactosyl D-chiro-inositols: fagopyritol A1 and fagopyritol B1 (mono-galactosyl D-chiro-inositol isomers), fagopyritol A2 and fagopyritol B2 (di-galactosyl D-chiro-inositol isomers), and fagopyritol B3 (tri-galactosyl D-chiro-inositol). Other soluble carbohydrates analyzed by high-resolution gas chromatography included sucrose (42% of total), D-chiro-inositol, myo-inositol, galactinol, raffinose and stachyose (1% of total), but no reducing sugars. All fagopyritols were readily hydrolyzed by α-galactosidase (EC 3.2.1.22) from green coffee bean, demonstrating α-galactosyl linkage. Retention time of fagopyritol B1 was identical to the retention time of O-α-D-galactopyranosyl-(1→2)-D-chiro-inositol from soybean (Glycine max (L.) Merrill, Leguminosae), suggesting that the α-ga-lactosyl linkage is to the 2-position of D-chiro-inositol. Accumulation of fagopyritol B1 was associated with acquisition of desiccation tolerance during seed development and maturation in planta, and loss of fagopyritol B1 correlated with loss of desiccation tolerance during germination. Embryos of seeds grown at 18 °C, a condition that favors enhanced seed vigor and storability, had a sucrose-to-fagopyritol B1 ratio of 0.8 compared to a ratio of 2.46 for seeds grown at 25 °C. We propose that fagopyritol B1 facilitates desiccation tolerance and storability of buckwheat seeds. Received: 21 May 1997 / Accepted: 5 June 1997     

Condition cycles in juvenile Pagrus auratus

Nutritional condition was measured in juvenile snapper Pagrus auratus (<200 mm fork length) using three indices: relative condition index (I_c), hepatosomatic index (I_H) and digesto-somatic index (I_D). In a laboratory starvation experiment, all three indices declined substantially over a 24-day period, but I_H was most sensitive. In wild snapper I_c and I_H showed no diel cycles. I_D for 0+ snapper showed a strong diel cycle consistent with continuous feeding during daylight hours and lack of feeding during the night. I_D for 1+ snapper showed no diel cycle. Subsequent analyses were restricted to daytime samples for I_H and morning samples for I_D to minimize the confounding effect of time of day. I_c, I_H and I_D were monitored at one site at approximately bi-monthly intervals over a period of 3.25 years. All three indices varied significantly, but only I_D and I_H displayed seasonal cycles. I_D peaked in late summer-autumn and dropped to a minimum in winter, due to seasonal fluctuations in the feeding rate that probably reflected variations in metabolic and growth rates. I_H peaked in autumn-winter and declined to a minimum in summer, thus lagging 4–6 months behind I_D. I_H varied significantly among four sampling sites for all five combinations of sampling periods and year classes, whereas I_c varied significantly among sites for only one of the five combinations. The Kawau Bay site, which supported the highest density of snapper, had the highest I_H for all except one of the combinations. This suggests that juvenile snapper aggregate selectively at sites that provide optimal feeding conditions. However, no relationship was found between I_H and growth rate, indicating that better nutritional condition may not translate into faster growth.     

Fine mapping of the region on wheat chromosome 7D controlling grain weight

We report the fine mapping of the previously described quantitative trait loci (QTL) for grain weight QTgw.ipk-7D associated with microsatellite marker Xgwm1002-7D by using introgression lines (ILs) carrying introgressions of the synthetic wheat W-7984 in the genetic background of the German winter wheat variety ‘Prinz’. The BC₄F₃ ILs had a 10% increased thousand grain weight compared to the control group and the recurrent parent ‘Prinz’, and 84.7% of the phenotypic variance could be explained by the segregation of marker Xgwm1002-7D, suggesting the presence of a gene modulating grain weight, which was preliminarily designated gw1. It was possible to delimit the QTL QTgw.ipk-7D to the interval Xgwm295–Xgwm1002, which is located in the most telomeric bin 7DS4-0.61-1.00 in the physical map of wheat chromosome arm 7DS. Furthermore, our data suggest the presence of a novel plant height-reducing locus Rht on chromosome arm 7DS of ‘Prinz’. Larger grain and increased plant height may reflect the pleiotropic action of one gene or may be caused by two linked genes. In general, our data support the concept of using nearly isogenic ILs for validating and dissecting QTLs into single Mendelian genes and open the gateway for map-based cloning of a grain-weight QTL in wheat.     

Interactions in a tritrophic acarine predator-prey metapopulation system IV: effects of host plant condition on Tetranychus urticae (Acari: Tetranychidae)

Feeding by spider mites can cause severe injury to a host plant and lead to a decreasing per capita growth rate and an increasing per capita emigration rate. Such density-dependent responses to local conditions are important in a metapopulation context because they allow the herbivores to colonize new host plants and thereby prolong the time until regional (metapopulation) extinction. In order to include density-dependent responses of the two-spotted spider mite (Tetranychus urticae) in a realistic metapopulation model, a series of greenhouse experiments was conducted with the purpose to quantify how the condition of bean plants (Phaseolus vulgaris) influences the demographic parameters of T. urticae. Plant age per se reduced the growth rate of the spider mites only slightly, whereas the growth rate declined significantly as the plants were injured by the mites. The relationships between plant condition (expressed by the plant injury index D) and the birth and loss (death + emigration) rates of the mites were quantified so as to predict population growth as a function of D. Maximum per capita growth rate (r) was estimated to be c. 0.21 day⁻¹. The growth rate is expected to be negative when D exceeds 0.8. When mites were allowed to emigrate to neighbouring plants via bridges, the per capita emigration rate increased almost exponentially with D. The proportion of eggs in the population decreased with D while the numerical ratio between immatures to adults and the sex ratio did not change with D. Overall, immatures and adults constituted 74% and 26%, respectively, of the active mites and c. 46% of the adults were males. The bridges that connected a donor plant with the surrounding recipient plants were responsible for the majority of the emigrations from donor plants. Most mites stopped after having crossed a single bridge, but a few crossed two bridges while none crossed three bridges within 24 h. The significance of the results for biological control is discussed. This revised version was published online in July 2006 with corrections to the Cover Date.     

Oligonucleotides containing a peptide internucleotide linkage. A novel class of modified oligonucleotides

Oligonucleotide analogues containing one or a few glycine, L-, and D-alanine residues instead of phosphodiester internucleotide linkages were synthesized (C3′-NH-C(O)-CH(X)-NH-C(O)-C4′, where X = H, (S)-CH₃, and (R)-CH₃. The stability of the duplexes of modified oligonucleotides with their wild-type complements was studied. The incorporation of glycine and L-alanine residues into internucleotide linkages was shown to noticeably decrease the stability of modified duplexes as compared to that of native ones (ΔT _m∼−2°C per modification), whereas analogues containing D-alanine linkers form duplexes with increased stability (ΔT _m∼+2°C per modification).     

Relationship between indoor and outdoor airborne fungal spores, pollen, and (1→3)-β-D-glucan in homes without visible mold growth

In this exploratory study, indoor and outdoor airborne fungal spores, pollen, and (1→3)-β-D-glucan levels were determined through long-term sampling (24-h) using a Button Personal Inhalable Aerosol Sampler. The air samples were collected in five Cincinnati area homes that had no visible mold growth. The total count of fungal spores and pollen in the collected samples was conducted under the microscope and Limulus Amebocyte Lysate (LAL) chromogenic assay method was utilized for the determination of the (1→3)-β-D-glucan concentration. For the combined number concentration of fungal spores and pollen, the indoor and outdoor geometric mean values were 573 and 6,435 m⁻³, respectively, with a geometric mean of the Indoor/Outdoor (I/O) ratio of .09. The geometric means of indoor and outdoor (1→3)-β-D-glucan concentrations were .92 and 6.44 ng m⁻³, respectively, with a geometric mean of the I/O ratio equal to .14. The I/O ratio of (1→3)-β-D-glucan concentration was found to be marginally greater than that calculated based on the combined number concentration of fungal spores and pollen. This suggests that (1→3)-β-D-glucan data are affected not only by intact spores and pollen grains but also by the airborne fragments of fungi, pollen, and plant material, which are ignored by traditional enumeration methodologies. Since the (1→3)-β-D-glucan level may elucidate the total exposure to fungal spores, pollen, and fungal fragments, its I/O ratio may be used as a risk marker for mold and pollen exposure in indoor environments.     

Cloned transgenic heart-healthy pork?

Here I comment on the production and uses of swine that express a humanized fat-1 gene. The gene product is a fatty acid desaturase that converts ω-6 fatty acids to ω-3 fatty acids. Omega-3 fatty acids have been implicated as being important for reproductive success, maintaining a healthy cardiovascular system, sustaining a functional immune system, and even preventing depression and cancer. The descendants of these hfat-1 transgenic swine will be very useful as models of the human condition, and if they are permitted to enter the food chain, they may improve human health.     

Mechanosensitive ion channels in chara: influence of water channel inhibitors, HgCl2 and ZnCl2, on generation of receptor potential

Characean internodal cells generate receptor potential (ΔE _m) in response to mechanical stimuli. Upon a long-lasting stimulus, the cells generated ΔE _m at the moment of both compression and decompression, and the amplitude of ΔE _m at the moment of decompression, (ΔE _m)_E, was larger than that at compression. The long-lasting stimulus caused a membrane deformation (ΔD _m) having two components, a rapid one, (ΔD _m)_rapid, at the moment of compression and a slower one, (ΔD _m)_slow, during the long-lasting compression. We assumed that (ΔD _m)_slow might have some causal relation with the larger ΔE _m at (ΔE _m)_E. We treated internodal cells with either HgCl₂ or ZnCl₂, water channel inhibitors, to decrease (ΔD _m)_slow. Both inhibitors attenuated (ΔD _m)_slow during compression. Cells treated with HgCl₂ generated smaller (ΔE _m)_E compared to nontreated cells. On the other hand, cells treated with ZnCl₂ never attenuated (ΔE _m)_E but, rather, amplified it. Thus, the amplitude of (ΔD _m)_slow did not always show tight correlation with the amplitude of (ΔE _m)_E. Furthermore, when a constant deformation was applied to an internodal cell in a medium with higher or lower osmotic value, a cell having higher turgor always showed a larger (ΔE _m)_E. Thus, we concluded that changes in tension at the membrane may be the most important factor to induce activation of mechanosensitive Ca²⁺ channel.