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* Institute of Experimental Botany, Academy of Sciences of the Czech Republic, Na Pernikarce 15, 160 00 Prague 6, Czech Republic and Instituto Gulbenkian Ciência, R. Quinta Grande 6, PT-2780-156 Oeiras, Portugal
Correspondence: Address reprint requests to Laura Zonia, Institute of Experimental Botany, Academy of Sciences of the Czech Republic, Na Pernikarce 15, 160 00 Prague 6, Czech Republic. Tel.: +420-2-24310710; Fax: +420-2-33339412; E-mail: zonia{at}ueb.cas.cz.
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ABSTRACT |
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 TOP ABSTRACT INTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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INTRODUCTION |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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; Taylor and Hepler, 1997; Higashiyama et al., 2000; Feijó et al., 2001; Hepler et al., 2001).
Pollen cell biology is uniquely adapted to these complex conditions. The pollen tube is an emergent system in which order is rapidly achieved by dynamic circuits that enable optimum growth and function under variable extracellular conditions. Pollen tube growth exhibits bistability and can occur with stochastic processes during steady-state growth or with quasisinusoidal oscillatory dynamics. This observation has impelled numerous studies to identify signals that regulate growth oscillations. Oscillatory growth is correlated with oscillatory influx of Ca2+, H+, and K+ at the pollen tube apex (Pierson et al., 1996; Holdaway-Clarke et al., 1997; Messerli and Robinson, 1998; Feijó et al., 1999; Messerli et al., 1999), and with oscillations in the tip-localized free Ca2+ gradient (Pierson et al., 1994; Messerli et al., 2000). Dissipation of the intracellular free Ca2+ gradient or disruption of influx of extracellular Ca2+ inhibits pollen tube growth, demonstrating that Ca2+ ion dynamics are necessary for pollen tube growth (Pierson et al., 1994). However, correlation analyses revealed that these cation circuits are differentially phase-delayed with respect to growth oscillations (Holdaway-Clarke et al., 1997; Feijó et al., 1999; Messerli et al., 1999, 2000). These observed phase shifts indicate that the start of Ca2+, H+, and K+ cycles do not directly correlate with the start of growth cycles, and so these circuits may be passive oscillators coupled to a wider reaction network driving pollen tube growth oscillations.
Using the noninvasive self-referencing ion-specific vibrating electrode probe technology to measure current near the cell surface, our recent work identified a new dynamic circuit that involves oscillatory efflux of Cl- anion from the pollen tube apex (Zonia et al., 2001, 2002). Oscillatory Cl- efflux is the first ion signal found to be temporally coupled in phase with growth oscillations. Cell elongation during the growth pulse occurs during the subphase of the cycle with maximally increasing Cl- efflux from the apex. Cl- flux is necessary for pollen tube growth and is correlated with the cell volume or hydrostatic condition of the apical region, in that Cl- channel blockers inhibit pollen tube growth and induce cell volume increases. At 80 µM DIDS, there is a 59% increase in cell volume and 94% of pollen tubes burst near the apex within 10 min. The apical cell volume of growing pollen tubes is exquisitely sensitive to changes in the extracellular osmotic potential and hypoosmotic treatment stimulates Cl- efflux. In vertebrate cells, Cl- channels are known to be important regulators of secretory activity, osmoregulation, and membrane electrochemical potential (Chen et al., 1996; Renstrom et al., 2002). Extensive work has demonstrated that Ca2+-activated Cl- efflux channels are negatively regulated by inositol 3,4,5,6-tetrakisphosphate [Ins(3,4,5,6)P4] (Vajanaphanich et al., 1994; Ismailov et al., 1996; Barrett et al., 1998; Nilius et al., 1998; Xie et al., 1998; Yang et al., 1999; Carew et al., 2000; Ho et al., 2000, 2001; Renstrom et al., 2002). Ins(3,4,5,6)P4 has been identified in the aquatic plant Spirodela (Brearley and Hanke, 1996), and Ins(3,4,5,6)P4 1-kinase and 4- and 6-phosphatase activities have been detected in Commelina mesophyll cells (Brearley and Hanke, 2000). In pollen tubes, Ins(3,4,5,6)P4 acts in regulatory circuits that target growth, apical cell volume, and Cl- efflux oscillations. The mean growth rate after treatment with Ins(3,4,5,6)P4 was decreased by 85%, the apical cell volume increased by 54%, and normal Cl- efflux was disrupted. These effects were not mimicked by Ins(1,3,4,5)P4 or Ins(1,3,4,5,6)P5. In summary, Cl- flux was found to be an important component of regulatory circuits that control pollen tube homeostasis and polarized growth.
To fully understand the mechanics of pollen tube growth that enable sexual fertilization in higher plants, it will be essential to understand the dynamics of individual circuits within the system. The observation that Cl- efflux oscillations are coupled in phase with growth oscillations and with the physical processes driving cell elongation stimulated the investigations in this report to analyze the state and spectral properties of Cl- oscillations in pollen tube growth. The approach taken is an application of the tools of nonlinear dynamics and signal processing to characterize the behavior and solutions of Cl- oscillations in growing pollen tubes. These methods are particularly useful for this study because they characterize the system dynamics utilizing experimentally derived parameter values, which can then be used to formulate testable models. The results of these analyses suggest that Cl- signals display features that are characteristic of active oscillators that carry frequency-encoded information. In light of its direct correlation with growth oscillations, its role in hydrostatic regulation, and its potential link to inositol polyphosphate signaling cascades via Ins(3,4,5,6)P4, the Cl- oscillator may have a central role in the network of regulatory circuits that drive pollen tube growth.
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MATERIALS AND METHODS |
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Extracellular chloride flux measurements
A self-referencing ion-selective vibrating electrode probe was used to measure extracellular Cl- flux near the surface of pollen tubes. The vibrating electrode system was attached to a Nikon Eclipse TE-300 inverted microscope (Tokyo, Japan) that was housed inside a copper sheet Faraday cage. A 20x or 40x PlanApo objective under differential interference contrast was used. Microelectrodes were pulled from 1.5 mm borosilicate glass capillaries (World Precision Instruments, Sarasota, FL) with a Sutter P-98 Flaming Brown electrode puller (Sutter Instruments, Novato, CA), baked at 250°C for 8–12 h, and then vaporized with dimethyl-dichlorosilane (Sigma, St. Louis, MO) for 30 min. The capillaries were backfilled with a 15–20 µm column of 100 mM KCl, then front-loaded with a 20–25 µm column of Cl--selective liquid exchange cocktail (Fluka, Catalog nr. 24889, Milwaukee, WI). An Ag/AgCl wire electrode holder (World Precision Instruments) was inserted into the back of the electrode and established electrical contact with the bathing solution. A dry reference electrode (World Precision Instruments) was inserted into the sample bath. Signals were measured with a purpose built electrometer (Applicable Electronics, Forestdale, MA). Electrode vibration and positioning were achieved with a stepper-motor-driven three-dimensional positioner. The vibrating electrode oscillates with an excursion distance of 10 µm. A typical cycle was completed in 2.33 s; each cycle includes an adjustable settling time after each move, one measuring period at each end position of the cycle, and the excursion time. The measurement taken nearest to the cell is then subtracted by the measurement taken at the opposite end of the cycle; this represents the self-referencing correction. Cl- flux was measured by vibrating the electrode tip within 5 µm of the cell surface. Background reference values were subtracted from the µV differential recordings during data processing using Microsoft Excel. Background values of Cl- in the germination medium during the course of experiments were on the order of Cl- concentrations measured in pollen tubes using the Microquant assay kit (Merck, Darmstadt, Germany), which indicates that pollen contains a sink of Cl- ion. Data acquisition, preliminary processing, control of the 3D electrode positioner, and stepper-motor controlled fine focus of the microscope stage were performed with ASET software (Science Wares, East Falmouth, MA and Applicable Electronics). Two separate measurements that are collected for each data point in space include a local voltage in mV and the µV differential in the direction of the flux. The µV differential value measured is negative because of the negative charge on Cl- anion. The ionic flux at each data point in space is calculated with the formula:
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State and spectral analysis of chloride signals
For time domain analysis, the Cl- flux values recorded by ASET software (Science Wares and Applicable Electronics) during vibrating probe experiments were converted to absolute flux values. Phase space diagrams were computed by calculating the derivative of the flux J with respect to time (dJ/dt) and plotting against the flux value J. Calculations and plots were performed with Microsoft Excel.
For frequency domain analysis, windowed fast Fourier transforms (FFT) [f(n)g(n)] were computed for discrete signals [f(k)] of period N (Mallat, 1999):
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This is performed with N FFT procedures of size N. Direct calculation of the discrete Fourier sums is given by
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The FFT algorithm groups the direct calculations into even [fe(n)] and odd [fo(n)] frequency indexes to reduce the complexity:
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A Hanning orthonormal local cosine basis window was used:
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Information of the amplitudes computed by the windowed FFT series can be extracted and plotted as a function of the signal frequency [f] to yield a spectral analysis of the constituents of a complex signal, called a power spectrum [S(f)]. The power spectrum is the discrete Fourier transform of the covariance R(k):
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The power spectrum S(f) is plotted against the frequency (f) in Hz. Power distributions were then determined by plotting log10[S(f)] versus log10[f] and computing linear regressions. The slopes of the power distribution linear regressions are reported. Computations and plots for windowed fast Fourier transforms, power spectra, and power distributions were performed using customized transforms programmed in SigmaPlot 7.1 (SPSS Science Inc., Chicago, IL).
Inositol 3,4,5,6-tetrakisphosphate studies
Ins(3,4,5,6)P4 was synthesized by Matreya Inc. (Pleasant Gap, PA) and obtained through BioTrend Chemikalien GmbH (Köln, Germany). The experimental conditions for inositol polyphosphate studies were previously reported in detail (Zonia et al., 2002). Microinjection of Ins(3,4,5,6)P4 inhibits pollen tube growth by 85% and this effect is not mimicked by either Ins(1,3,4,5)P4 or Ins(1,3,4,5,6)P5. Extracellular addition of Ins(3,4,5,6)P4 inhibits pollen tube growth by 66%, rapidly induces increases of 54% in the pollen tube apical cell volume compared with untreated controls (which is on the order of the mean maximum volume load for cell bursting, which is a 59% volume increase, induced by the Cl- channel blocker DIDS), and disrupts normal Cl- efflux oscillations. These effects are not mimicked by either Ins(1,3,4,5)P4 or Ins(1,3,4,5,6)P5. For the studies in this report, Ins(3,4,5,6)P4 was added extracellularly to the pollen tube cultures because the integrity of the Cl- efflux signal is sensitive to mechanical perturbation. Recent work has identified sites of active membrane turnover in the pollen tube apical region that may provide a route for fluid-phase uptake of inositol polyphosphates into the cytosol (L. Zonia, unpublished). Intracellular concentrations of Ins(3,4,5,6)P4 in epithelial cells rise from 
1 µM in resting cells to 10–15 µM after cell activation (Pittet et al., 1989; Vajanaphanich et al., 1994). For the studies in this report Ins(3,4,5,6)P4 was added to the pollen tube cultures at a concentration of 20 µM.
Reagents
DIDS (4,4'-diisothiocyanatostilbene-2,2'-disulfonic acid) was from Sigma. All other chemicals were plant cell culture or reagent grade and were from Sigma or Fluka.
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RESULTS |
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DISCUSSION |
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; Rascher et al., 1998; Lüttge, 2000; Bohn et al., 2001; Hafke et al., 2001; Rascher et al., 2001; Bohn et al., 2002) and Ca2+ signaling (Allen et al., 2000, 2001). These studies demonstrate that analysis of the properties that define nonlinear control circuits can reveal important information about mechanisms of cellular signaling in plants.
State and spectral transformations of chloride signals in growing pollen tubes
Cl- flux is necessary for pollen tube growth and has an important functional role in the processes that mediate cell elongation (Zonia et al., 2002). This report has evaluated Cl- efflux signals using tools of nonlinear dynamics and signal processing to characterize the properties of the Cl- oscillator and to further assess the role of Cl- efflux oscillations during pollen tube growth. The results demonstrate that Cl- signals exhibit behaviors that are characteristic of active nonlinear harmonic oscillators.
Hypoosmotic treatment induces transitions of the limit cycle to new metastable states and modulates the frequencies of Cl- efflux oscillations (Fig. 3). Low levels of hypoosmotic treatment have been shown to cause increases in the apical cell volume (Zonia et al., 2002). Treatment with 2.5% (v/v) H2O stimulates the frequency of Cl- efflux with periods decreasing from 100 s to 50 s and 25 s (Fig. 3 D). Further hypoosmotic treatment of 10% (v/v) H2O depletes the system energy and causes a transition of the limit cycle to more negative regions of the phase space (Fig. 3, B and E). This may reflect a transient dissipation of the internal Cl- pool due to the stimulation of Cl- efflux and the decreased extracellular osmotic potential. A mechanism to adjust to more severe or prolonged hypoosmotic conditions is suggested by the observation that the system moves back to the original location in the phase space (Fig. 3, A and B) and the frequency of Cl- efflux oscillations modulates from the pretreatment period of 100 s to the more rapid period of 50 s (Fig. 3, C and F). Recent work has indicated that the phospholipid signal phosphatidic acid is induced in pollen tubes during severe hypoosmotic conditions >25–30% (v/v) H2O (L. Zonia and T. Munnik, unpublished). This result is significant for pollen tubes under severe hypoosmotic stress because activation of the phospholipase D pathway leading to increased phosphatidic acid can potentiate Cl- efflux during specific programs of cellular activation in vertebrate cells (Vajanaphanich et al., 1993; Oprins et al., 2001, 2002). Taken together, these results indicate that the Cl- oscillator can progress to new stable states and respond to increases in the intracellular hydrostatic pressure by increasing the frequency of Cl- efflux.
The Cl- channel blocker DIDS induces rapid cell volume increases that lead to cell bursting (Zonia et al., 2002). The lethal concentration of 80 µM DIDS causes the system to collapse to a fixed-point attractor near the origin (Fig. 2 A). The pollen tube shown in Fig. 2 burst within 150 s after addition of DIDS. Before cell death there was a severe depletion of energy from the system, the frequency at 0.01 Hz was obliterated, and a residual frequency emerged at 0.02 Hz (Fig. 2, B and C). It may be possible that during the rapid increase in intracellular hydrostatic pressure induced by DIDS the Cl- efflux frequency was driven from 0.01 Hz to 0.02 Hz, a response that was also observed after increases in the intracellular hydrostatic pressure induced by hypoosmotic treatment (Fig. 3).
The signal encoded in Ins(3,4,5,6)P4 has profound effects on Cl- efflux oscillations (Fig. 4). In 11 of 14 pollen tubes examined, the system moved to an attractor near the origin with a marked increase of turbulence in the trajectory (Fig. 4, B–E). The power spectra indicate that Ins(3,4,5,6)P4 inhibits the frequency of Cl- efflux oscillations, with periods increasing from the normal harmonic series of 50 and 100 s (Fig. 4 F) to periods of 100–500 s (Fig. 4 G). The periods observed (100 s, 167 s, 303 s, 500 s) represent transitions to period-tripling states and states with higher-order multiplicative increases, which may eventually lead to the onset of chaos (Fig. 4, H and I). In three of 14 pollen tubes examined, superharmonic resonance states were induced after treatment with Ins(3,4,5,6)P4 (Fig. 5). Superharmonic resonance states in nonlinear oscillators can result from the introduction of weak damping coupled with stimulatory driving of the system (Acheson, 1997). Hence, it is possible that superharmonic resonance is observed in these pollen tubes due to uptake of a suboptimal concentration of Ins(3,4,5,6)P4 that imperfectly dampens Cl- efflux oscillations, coupled with stimulatory driving of Cl- efflux oscillations by an endogenous positive feedback circuit.
The results of these perturbation studies demonstrate that the Cl- oscillator is poised to rapidly respond to both stimulatory and inhibitory feedback. Positive feedback in the form of increased intracellular hydrostatic pressure drives the system to new states with transient increases in subharmonic signal frequencies (Fig. 3). Negative feedback encoded in Ins(3,4,5,6)P4 inhibits the frequency of the Cl- signal, leading to period-tripling and multiplicative increases that may provide a route to chaos (Fig. 4). The results also indicate the existence of an internal positive feedback circuit that can drive Cl- efflux during weak damping (Fig. 5). In summary, these analyses demonstrate that the Cl- oscillator has the potential to receive input from both positive and negative feedback circuits that modulate the output frequency of the oscillator. In light of the fact that the Cl- oscillator is temporally coupled in phase with growth oscillations, and that perturbation of Cl- efflux also perturbs growth, these results suggest that the Cl- oscillator may have a central role in driving pollen tube growth.
Hypothesized reaction network regulating chloride oscillations and pollen tube growth
Pollen tube growth is a bistable system that exhibits either stochastic or quasisinusoidal dynamics. Nothing is known of the biophysical factors that determine the switch to oscillatory growth. Signals and cellular factors that are important for the fundamental mechanics of growth should be present irrespective of the system state. The observation that the Cl- signal harmonic frequencies at 0.01 and 0.02 Hz coexist with a background of noise in pollen tubes undergoing steady-state growth indicates that the Cl- oscillator signal is a component of the fundamental mechanics that drive growth (Fig. 6). These observations further suggest that the switch from stochastic to oscillatory growth may involve an increase in the biochemical or biomolecular organization of the growing pollen tube. After tobacco pollen tube growth becomes organized into sustained oscillations, the observed periods for normal growth cycle oscillations are identical with the normal harmonic frequencies of the Cl- oscillator—50 s and 100 s (Zonia et al., 2002).
A minimal reaction network that may be coupled to the Cl- oscillator during oscillatory growth is shown in Fig. 7. This network includes a sink for Cl- ions, feedback from cell volume sensors, and input from Ins(3,4,5,6)P4 and Ca2+ as two nonlinear feedback regulators of Cl- efflux.
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). The spatial coupling of influx sites along the pollen tube and efflux site at the pollen tube apex predicts that as the apical Cl- pool is depleted by cyclic efflux it can be refilled by the steady influx of Cl- in adjacent regions (Fig. 7). These dynamics induce a vectorial flux of Cl- anion traversing through the apical region of the pollen tube and promote a closed current surrounding the cell surface (Fig. 7).
Cl- channel blockers inhibit pollen tube growth and induce rapid increases in the apical cell volume (Zonia et al., 2002). Hypoosmotic treatment that induces cell volume increases also induces an increased frequency of Cl- efflux (Fig. 3). These data indicate that Cl- flux correlates with the regulation of cell volume status in the pollen tube apical region. Information about the cell volume or intracellular hydrostatic pressure may be signaled to the Cl- efflux oscillator by mechanosensitive ion channels located at the plasma membrane (Cosgrove and Hedrich, 1991). Activation of mechanosensitive channels by cell swelling or plasmolysis could also affect the membrane electrochemical potential. In this way mechanosensitive ion channels could rapidly input both positive and negative feedback signals to the Cl- oscillator and thereby function as passive integrators regulating the cell volume status (Fig. 7).
Cl- efflux is a mechanism used in both plant and vertebrate cells for regulating cell volume and hydrostatic pressure (Ward et al., 1995; Teodoro et al., 1998; Shabala et al., 2000; van der Wijk et al., 2000; Bali et al., 2001; Leonhardt et al., 2001; Okada et al., 2001; Roman et al., 2001; Wondergem et al., 2001), partly due to the capacity of anions to strongly affect the ordering and dynamics of water molecules in local domains (Kropman and Bakker, 2001; Kropman et al., 2002). Therefore, in addition to its correlation with cell volume regulation, Cl- flux through the apical region of the pollen tube may have the potential to entrain a hydrodynamic flow that provides part of the driving force for cell elongation during growth (Zonia et al., 2002).
Previous work demonstrated that Ins(3,4,5,6)P4 can act in regulatory circuits that inhibit pollen tube growth, induce cell volume increases, and disrupt Cl- efflux (Zonia et al., 2002). The present report has demonstrated that Ins(3,4,5,6)P4 inhibits the frequency of the Cl- signal and induces transitions to period-tripling and higher-order multiplicative increases that may provide a route to chaos (Fig. 4). Thus, the combined evidence indicates that Ins(3,4,5,6)P4 can act as a negative feedback regulator of Cl- efflux oscillations (Fig. 7). Possible mechanisms for generating cyclic changes in the levels of Ins(3,4,5,6)P4 could be via further phosphorylation/dephosphorylation cycles of Ins(1,4,5)P3 to one of the immediate precursors Ins(3,4,6)P3 or Ins(1,3,4,5,6)P5 (Shears, 1996; Ho et al., 2000; Irvine and Schell, 2001).
The tip-localized cytosolic Ca2+ gradient and influx of extracellular Ca2+ through channels located at the pollen tube apex are necessary for pollen tube growth (Pierson et al., 1994, 1996; Holdaway-Clarke et al., 1997; Messerli et al., 1999, 2000). Both of these circuits oscillate with the same frequency as growth but are temporally out-of-phase with respect to the start of the growth cycle. There is evidence for a role for Ca2+ during cell swelling, in that a plasma membrane Ca2+ channel is rapidly activated by hypoosmotic stress in tobacco suspension cells and in Fucus and subsequently leads to increases in cytosolic Ca2+ (Takahashi et al., 1997; Taylor et al., 1997; Goddard et al., 2000). There is also evidence for the interaction of Ca2+ and Cl-, in that anion channel activity in guard cells is stimulated by increases in cytosolic and extracellular Ca2+ (Schroeder and Hagiwara, 1989; Hedrich et al., 1990). In vertebrate secretory cells, the Cl- efflux channel that is negatively regulated by Ins(3,4,5,6)P4 is positively regulated by Ca2+ (Shears, 1996; Xie et al., 1998; Carew et al., 2000; Ho et al., 2001). Taken together, these results suggest the possibility that the nonlinear Ca2+ circuit that exists at the pollen tube apex may function at least in part as a positive feedback regulator of Cl- efflux oscillations (Fig. 7).
The hypothesized reaction network shown in Fig. 7 containing three coupled nonlinear circuits (Cl-, Ins(3,4, 5,6)P4, and Ca2) meets the theoretical requirements for the generation of limit-cycle solutions (Tyson and Light, 1973; Murray, 1993) and may define a core signaling network that has the potential to entrain a basic motive force and coordinate the cellular events driving oscillatory pollen tube growth.
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ACKNOWLEDGEMENTS |
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TOPABSTRACTINTRODUCTIONMATERIALS AND METHODSRESULTSDISCUSSIONACKNOWLEDGEMENTSREFERENCES |
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Submitted on July 14, 2002; accepted for publication September 27, 2002.
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REFERENCES |
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) and 60% (v/v) H2O (
). Note equivalent scaling of the axes in plots A and B. Power spectra (C) before treatment, and after addition of (D) 2.5% (v/v) H2O, (E) 10% (v/v) H2O, and (F) 60% (v/v) H2O. Insets in C–F show the power distributions, log10[S(f)] versus log10[f], and the linear regressions.
. The thick outline around the cell denotes the cell wall, the thin interior line denotes the plasma membrane. Details are given in the Discussion.