Stomatal responses to non-local changes in PFD: evidence for long-distance hydraulic interactions

Interactions among stomata within a single areole have recently been reported, and evidence suggests that hydraulic mechanisms may be responsible for these interactions. Such interactions may play a role in patchy stomatal behaviour by coordinating stomatal behaviour within areoles. However, models suggest that longer‐distance interactions may be required to produce the large‐scale discoordination that is characteristic of stomatal patchiness. This study was undertaken to characterize long‐distance interactions between ‘artificial patches’ of stomata under varying conditions of evaporative demand and soil water stress. Gas‐exchange was monitored in two adjacent regions (‘patches’) of a wheat leaf by two independent gas mixing and analysis systems. When photon flux density (PFD) was changed in only one of these patches, stomatal conductance responded in both patches in a manner consistent with hydraulic interactions propagated by changes in xylem water potential. These data are discussed in the context of mechanisms for patchy stomatal conductance and implications for the design and analysis of gas‐exchange experiments.     

Dynamics of stomatal patches for a single surface of Xanthium strumarium L. leaves observed with fluorescence and thermal images

Fluorescence and thermal imaging were used to examine the dynamics of stomatal patches for a single surface of Xanthium strumarium L. leaves following a decrease in ambient humidity. Patches were not observed in all experiments, and in many experiments the patches were short-lived. In some experiments, however, patches persisted for many hours and showed complex temporal and spatial patterns. Rapidly sampled fluorescence images showed that the measurable variations of these patches were sufficiently slow to be captured by fluorescence images taken at 3-min intervals using a saturating flash of light. Stomatal patchiness with saturating flashes of light was not demonstrably different from that without saturating flashes of light, suggesting that the regular flashes of light did not directly cause the phenomenon. Comparison of simultaneous fluorescence and thermal images showed that the fluorescence patterns were largely the result of stomatal conductance patterns, and both thermal and fluorescence images showed patches of stomatal conductance that propagated coherently across the leaf surface. These nondispersing patches often crossed a given region of the leaf repeatedly at regular intervals, resulting in oscillations in stomatal conductance for that region. The existence of these coherently propagating structures has implications for the mechanisms that cause patchy stomatal behaviour as well as for the physiological ramifications of this phenomenon.     

Stomatal patchiness in Mediterranean evergreen sclerophylls

Midday depression of net photosynthesis and transpiration in the Mediterranean sclerophylls Arbutus unedo L. and Quercus suber L. occurs with a depression of mesophyll photosynthetic activity as indicated by calculated carboxylation efficiency (CE) and constant diurnal calculated leaf intercellular partial pressure of CO₂ (C_i). This work examines the hypothesis that this midday depression can be explained by the distribution of patches of either wide-open or closed stomata on the leaf surface, independent of a coupling mechanism between stomata and mesophyll that results in a midday depression of photosynthetic activity of the mesophyll. Pressure infiltration of four liquids differing in their surface tension was used as a method to show the occurrence of stomatal patchiness and to determine the status of stomatal aperture within the patches. Liquids were selected such that the threshold leaf conductance necessary for infiltration through the stomatal pores covered the expected diurnal range of calculated leaf conductance (g) for these species. Infiltration experiments were carried out with leaves of potted plants under simulated Mediterranean summer conditions in a growth chamber. For all four liquids, leaves of both species were found to be fully infiltratable in the morning and in the late afternoon while during the periods leading up to and away from midday the leaves showed a pronounced patchy distribution of infiltratable and non-infiltratable areas. Similar linear relationships between the amount of liquid infiltrated and g (measured by porometry prior to detachment and infiltration) for all liquids clearly revealed the existence of pneumatically isolated patches containing only wide-open or closed stomata. The good correspondence between the midday depression of CE, calculated under the assumption of no stomatal patchiness, and the diurnal changes in non-infiltratable leaf area strongly indicates that the apparent reduction in mesophyll activity results from assuming no stomatal patchiness. It is suggested that simultaneous responses of stomata and mesophyll activity reported for other species may also be attributed to the occurrence of stomatal patchiness. In Quercus coccifera L., where the lack of constant diurnal calculated C_i and major depression of measured CE at noontime indicates different stomatal behavior, non-linear and dissimilar relationships between g and the infiltratable quantities of the four liquids were found. This indicates a wide distribution of stomatal aperture on the leaf surface rather than only wide-open or closed stomata.Dedicated to Professor Otto L. Lange on the occasion of his 65th birthday     

The nature of heterogeneity in the stomatal behaviour of Phaseolus vulgaris L. primary leaves

The aim of this research was to investigate the nature of heterogeneity in stomatal conductance and, in particular, to determine whether the characteristic 'patchy' pattern of water infiltration is reflected in measurements on individual stomata. Silicone rubber replicas were made of primary leaves of glasshouse-grown Phaseolus vulgaris L. plants, and the leaves were then infiltrated with water at controlled sub-atmospheric gas pressures according to their estimated or measured stomatal conductance. Seven leaves examined in detail all showed patchy infiltration, and the mean sire of infiltrated areas was negatively correlated with the prevailing stomatal conductance. In four of the leaves, a one millimetre wide transect across the leaf was selected for further detailed study. Measurements of mean peristomatal groove distance (PGD) and stomatal frequency were made along the transect and related to the state of infiltration. Analysis of variance indicated that, in all four cases, variation in PGD among patches was highly significant, but there was no significant difference between patches of different infiltration categories. Thus, local (patch-level) variation in stomatal aperture appeared to bear no relation to the infiltration status of the patches. The dominant source of stomatal variability was between individual pores in the same locality, which accounted for 82% or more of the total variability. Taking into account variation in stomatal frequency, correlations between predicted stomatal conductance and the extent of infiltration were significant in only one out of the seven leaves studied. Possible reasons for these results are discussed. It is suggested that the infiltration method misrepresents the underlying state of the stomata as being either open or closed, when there is little evidence for this from measurements of stomatal dimensions. For these unstressed plants under relatively stable conditions, it is concluded that the 'unit of variability' in stomatal heterogeneity may rest at the individual pore ('micro') scale, rather than at the areolar patch ('macro') scale, or above.     

A fast method to detect the occurrence of nonhomogeneous distribution of stomatal aperture in heterobaric plant leaves

Summary Pressure infiltration of water into a leaf via the stomatal pores can be used to quickly determine whether all stomata are open, or as recently described for several mesophytic and xerophytic species, whether there is a non-homogeneous distribution of stomatal opening (stomatal patchiness) on the leaf surface. Information about this phenomenon is important since the commonly used algorithms for calculation of leaf conductance from water vapor exchange measurements imply homogeneously open stomata, which in the occurrence of stomatal patchiness will lead to erroneous results. Infiltration experiments in a growth chamber with leaves of the Mediterranean evergreen shrub Arbutus unedo, carried out under simulated Mediterranean summer day conditions, where the species typically exhibits a strong midday stomatal closure, revealed a temporary occurrence of stomatal patchiness during the phase of stomatal closure in the late morning and during the stomatal reopening in the afternoon. Leaves were, however, found to be fully (i.e. homogeneously) infiltratable in the morning and in the evening. At midday during maximum stomatal closure, leaves were almost non-infiltratable. During the day, the infiltrated amount of water was found to be linearly correlated with porometer measurements of leaf conductance of the same leaves, carried out with the attached leaves immediately before infiltration.     

Carbon-water balance and patchy stomatal conductance

Stomata govern carbon-water balance by simultaneously controlling photosynthesis (A) and transpiration (E). It is unclear how patchy stomatal conductance influences this control. Cowan and Farquhar showed that for a given water supply available during a fixed time interval, carbon gain is maximized by a pattern of stomatal behavior that keeps the partial derivative of A with respect to E constant. This result implies that spatially uniform stomatal conductance is optimal (provided photosynthetic performance and environmental conditions are spatially uniform), so patchy stomatal conductance should be detrimental to carbon-water balance. However, these results required that the curvature of A versus E be uniformly negative. Using mathematical arguments and computer modeling, we show that (1) this caveat is violated under some environmental conditions, (2) water-use efficiency (A/E) is nearly unaffected, and can actually be improved, by patchiness under these conditions, and (3) patchiness has most often been observed under conditions similar to these. These results imply that under many conditions, patchiness may not significantly influence carbon-water balance, consistent with recent work suggesting patchiness may be common but unobserved. Additionally, we discuss implications of these results that muddle the definition of `optimal' in the context of plant gas exchange in some situations, and extend the work of Cowan and Farquhar under conditions causing positive curvature in A versus E. Received: 15 May 1998 / Accepted: 14 October 1998     

Dynamics of patchy stomatal movements, and their contribution to steady-state and oscillating stomatal conductance calculated using gas-exchange techniques

Patchy stomatal movements were induced in leaves of Helianthus annuus L. and Xanthium strumarium L. by increasing Δw and decreasing light in a gas-exchange cuvette. The dynamics of the patchy movements were recorded and analysed using images of chlorophyll fluorescence, and the influence of heterogeneous stomatal activity on gas-exchange measurements of whole-leaf stomatal conductance was explored. Image series and gas-exchange measurements from two contrasting 100 min experiments are presented. One series of images, taken using Helianthus annuus, was characterized by strongly oscillating stomatal conductance induced by a decrease in light at high Δw. Fluorescence analysis revealed that individual patches of the leaf displayed a variety of behaviours (from static to strongly oscillating fluorescence), which, when averaged, matched the time dependence of the oscillating stomatal conductance measured by gas-exchange techniques. During the second series of images, taken using Xanthium strumarium, stomatal conductance (measured with gas exchange) declined slightly after an increase in Δw, and then maintained a steady state. Again, some patches in this leaf showed highly dynamic q_NP, although on the whole q_NP varied without any obvious pattern or frequency. When all patch activity in this series was averaged, it paralleled the steady whole-leaf stomatal conductance determined by gas-exchange measurements. It is clear from this work that coordinated patchy stomatal movements can contribute significantly to the dynamics of whole-leaf stomatal conductance, and, in contrast, that dynamic but uncoordinated patchy movements can average to produce a steady gas-exchange trace.     

Patch occupancy of North American mammals: is patchiness in the eye of the beholder?

Aim Intraspecific variation in patch occupancy often is related to physical features of a landscape, such as the amount and distribution of habitat. However, communities occupying patchy environments typically exhibit non‐random distributions in which local assemblages of species‐poor patches are nested subsets of assemblages occupying more species‐rich patches. Nestedness of local communities implies interspecific differences in sensitivity to patchiness. Several hypotheses have been proposed to explain interspecific variation in responses to patchiness within a community, including differences in (1) colonization ability, (2) extinction proneness, (3) tolerance to disturbance, (4) sociality and (5) level of adaptation to prevailing environmental conditions. We used data on North American mammals to compare the performance of these ‘ecological’ hypotheses and the ‘physical landscape’ hypothesis. We then compared the best of these models against models that scaled landscape structure to ecologically relevant attributes of individual species. Location North America. Methods We analysed data on prevalence (i.e. proportion of patches occupied in a network of patches) and occupancy for 137 species of non‐volant mammals and twenty networks consisting of four to seventy‐five patches. Insular and terrestrial networks exhibited significantly different mean levels of prevalence and occupancy and thus were analysed separately. Indicator variables at ordinal and family levels were included in models to correct for effects caused by phylogeny. Akaike's information criterion was used in conjunction with ordinary least squares and logistic regression to compare hypotheses. Results A patch network's physical structure, indexed using patch area and isolation, received the greatest support among models predicting the prevalence of species on insular networks. Niche breadth (diet and habitat) received the greatest support for predicting prevalence of species occupying terrestrial networks. For both insular and terrestrial systems, physical features (patch area and isolation) received greater support than any of the ecological hypotheses for predicting species occupancy of individual patches. For terrestrial systems, scaling patch area by its suitability to a focal species and by individual area requirements of the species, and scaling patch isolation by species‐specific dispersal ability and niche breadth, resulted in models of patch occupancy that were superior to models relying solely on physical landscape features. For all selected models, unexplained levels of variation were high. Main conclusions Stochasticity dominated the systems we studied, indicating that random events are probably quite important in shaping local communities. With respect to deterministic factors, our results suggest that forces affecting species prevalence and occupancy may differ between insular and terrestrial systems. Physical features of insular systems appeared to swamp ecological differences among species in determining prevalence and occupancy, whereas species with broad niches were disproportionately represented in terrestrial networks. We hypothesize that differential extinction over long time periods in highly variable networks has driven nestedness of mammalian communities on islands, whereas differential colonization over shorter time‐scales in more homogeneous networks probably governed the local structure of terrestrial communities. Our results also demonstrate that integration of a species' ecological traits with physical features of a patch network is superior to reliance on either factor separately when attempting to predict the species' probability of patch occupancy in terrestrial systems.     

The importance of scale of patchiness for selectivity in grazing herbivores

The notion that spatial scale is an important determinant of foraging selectivity and habitat utilization has only recently been recognized. We predicted and tested the effects of scale of patchiness on movements and selectivity of a large grazer in a controlled field experiment. We created random mosaics of short/high-quality and tall/low-quality grass patches in equal proportion at grid sizes of 2×2 m and 5×5 m. Subsequently, we monitored the foraging behaviour of four steers in 16 20×40 m plots over 30-min periods. As predicted on the basis of nutrient intake maximization, the animals selected the short patches, both by walking in a non-random manner and by additional selectivity for feeding stations. The tortuosity of foraging paths was similar at both scales of patchiness but selectivity was more pronounced in large patches than in small ones. In contrast, the number of bites per feeding station was not affected by patch size, suggesting that selection between and within feeding stations are essentially different processes. Mean residence time at individual feeding stations could not be successfully predicted on the basis of the marginal-value theorem: the animals stayed longer than expected, especially in the less profitable patch type. The distribution of the number of bites per feeding station suggests a constant probability to stay to feed or to move on to the next feeding station. This implies that the animals do not treat larger patches as discrete feeding stations but rather as a continuous resource. Our results have important implications for the application of optimal foraging theory in patchy environments. We conclude that selectivity in grazers is facilitated by large-scale heterogeneity, particularly by enhancing discrimination between feeding stations and larger selection units. Received: 1 March 1999 / Accepted: 14 July 1999     

Effects of patchy stomatal closure on gas exchange measurements following abscisic acid treatment

Gas exchange data and images of leaf fluorescence were collected concurrently as stomata responded to abscisic acid (ABA) application. When 10^?5kmolm^?3 ABA was applied to the transpiration stream in a short pulse, stomatal conductance (g_s), photosynthesis (A) and intercellular CO2 concentration (C_i) decreased rapidly after a short lag period and became approximately constant after 2h. There was an apparent reduction in the A versus c1 relationship as stomata closed, but the data returned to the A versus C1 curve while stomatal conductance was constant or slowly rising during the second hour after ABA treatment. Larger amounts of ABA administered during the pulse caused larger deviations from the A versus c1 relationship. When 10^?7kmolm^?3 ABA was applied continuously through the transpiration stream, gs, A and Cⁱ decreased, but there was no substantial deviation from the A versus c{ curve. Fluorescence images were patchy as stomata closed for all experiments, but became slowly more uniform during the time that gas exchange was returning to the A versus Cj curve. The distribution of con-ductance among patches was not bimodal, and larger devi-ations from the A versus ct curve had greater ranges of pixel values and more pixel values representing low values of Cj during stomatal closure than did experiments show-ing small or no deviation. Estimates of A and gs from fluo-rescence images compared favourably with measured val-ues in most cases, suggesting that the patchy distributions of fluorescence were caused by patchy distributions of stomatal conductance and that apparent reductions in the A versus ct relationship were the result of these patchy stomatai distributions and not direct effects of ABA on mesophyll functioning. The data show that stomatal patches can be temporary and that patchiness may not be reflected in gas exchange data if the range of stomatal con-ductances is not large. These observations may explain some of the discrepancies among previous studies concerning the effect of ABA on the A versus Cⁱ relationship.     

Changes in photon flux can induce stomatal patchiness

Images of chlorophyll fluorescence were used to detect the occurrence of stomatal patchiness in leaves from eight species under variable photon flux conditions. Pronounced stomatal patchiness was induced within 5–10 min after PFD was changed from intermediate (～450 μmol quanta m^?2 s^?1) to low (～150 μmol quanta m^?2 s^?1) levels. This effect was completely reversible by returning PFD to intermediate levels. The pattern of heterogeneous fluorescence for each leaf was usually similar during repeated applications of medium and low PFD. In three species, stomatal patchiness could only be induced in slightly water-stressed plants. Leaves of more severely water-stressed Xanthium strumarium plants in low air humidity exhibited oscillations in fluorescence that corresponded with oscillatory changes in leaf diffusion conductance for water vapour. Stomatal patchiness was also induced by illuminating dark-adapted leaves with low PFD (below 200–300 μmol quanta m^?2 s^?1). Infiltration of leaves with distilled water showed that heterogeneous chlorophyll fluorescence was caused by changes in stomatal apertures.     

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.     

Stomatal patchiness

Different behaviour of small groups of stomata on a single leaf blade (stomatal patchiness) is reviewed. The occurrence of stomatal patchiness depends on plant species, age, leaf position, environmental conditions,etc. The possibility of errors in conventional evaluation of stomatal and non-stomatal (biochemical) limitations of photosynthesis resulting from patchy stomatal closure is analysed. The consequences of stomatal patchiness for leaf and plant photosynthesis and water economy are discussed. A brief survey of the techniques currently used for detection and quantification of stomatal patchiness is presented.     

Short communication. Abscisic acid is not necessarily required for the induction of patchy stomatal closure

Patchy stomatal closure was observed in leaves of transgenic plants of Nicotiana plumbaginifolia producing antibodies that block the action of abscisic acid. Stomatal patchiness was induced by leaf detachment and subsequent water loss. Stomatal closure was followed by an irreversible reduction of maximal chlorophyll fluorescence. The degree of deviation from the A/ci-curve is correlated with steady-state diffusion conductance before leaf detachment. It is concluded that a heterogeneous sensitivity of stomata to abscisic acid is not directly involved in the induction of patchy stomatal closure.Keywords: Abscisic acid, chlorophyll fluorescence imaging, patchy stomatal closure, Nicotiana plumbaginifolia.      

Recurrent neural networks of integrate-and-fire cells simulating short-term memory and wrist movement tasks derived from continuous dynamic networks

Dynamic recurrent neural networks composed of units with continuous activation functions provide a powerful tool for simulating a wide range of behaviors, since the requisite interconnections can be readily derived by gradient descent methods. However, it is not clear whether more realistic integrate-and-fire cells with comparable connection weights would perform the same functions. We therefore investigated methods to convert dynamic recurrent neural networks of continuous units into networks with integrate-and-fire cells. The transforms were tested on two recurrent networks derived by backpropagation. The first simulates a short-term memory task with units that mimic neural activity observed in cortex of monkeys performing instructed delay tasks. The network utilizes recurrent connections to generate sustained activity that codes the remembered value of a transient cue. The second network simulates patterns of neural activity observed in monkeys performing a step-tracking task with flexion/extension wrist movements. This more complicated network provides a working model of the interactions between multiple spinal and supraspinal centers controlling motoneurons. Our conversion algorithm replaced each continuous unit with multiple integrate-and-fire cells that interact through delayed "synaptic potentials". Successful transformation depends on obtaining an appropriate fit between the activation function of the continuous units and the input-output relation of the spiking cells. This fit can be achieved by adapting the parameters of the synaptic potentials to replicate the input-output behavior of a standard sigmoidal activation function (shown for the short-term memory network). Alternatively, a customized activation function can be derived from the input-output relation of the spiking cells for a chosen set of parameters (demonstrated for the wrist flexion/extension network). In both cases the resulting networks of spiking cells exhibited activity that replicated the activity of corresponding continuous units. This confirms that the network solutions obtained through backpropagation apply to spiking networks and provides a useful method for deriving recurrent spiking networks performing a wide range of functions.     

Low-conductance states of K+ channels in adult mouse skeletal muscle

Single-channel currents were recorded from Ca2+-activated or ATP-sensitive K+ channels in inside-out membrane patches excised from isolated mouse toe muscles. In addition to the closed and fully open configurations, both types of channels may exhibit several intermediate low-conductance states which are clustered near multiples of elementary conductance units. The units are 1/8 or 1/6 of the channel conductance for Ca2+-activated channels and 1/4 or 1/3 for ATP-sensitive channels. Normally, low-conductance states are rare, but they occur more frequently directly after patch excision. An increased probability of low-conductance states of ATP-sensitive K+ channels was also observed in the presence and during washout of the internal channel blocker adenine. The results suggest that Ca2+-activated and ATP-sensitive K+ channels are composed of several membrane pores with strong positive cooperativity among the elementary conductance units.     

Coordinated activity of ventral tegmental neurons adapts to appetitive and aversive learning

Our understanding of how value-related information is encoded in the ventral tegmental area (VTA) is based mainly on the responses of individual putative dopamine neurons. In contrast to cortical areas, the nature of coordinated interactions between groups of VTA neurons during motivated behavior is largely unknown. These interactions can strongly affect information processing, highlighting the importance of investigating network level activity. We recorded the activity of multiple single units and local field potentials (LFP) in the VTA during a task in which rats learned to associate novel stimuli with different outcomes. We found that coordinated activity of VTA units with either putative dopamine or GABA waveforms was influenced differently by rewarding versus aversive outcomes. Specifically, after learning, stimuli paired with a rewarding outcome increased the correlation in activity levels between unit pairs whereas stimuli paired with an aversive outcome decreased the correlation. Paired single unit responses also became more redundant after learning. These response patterns flexibly tracked the reversal of contingencies, suggesting that learning is associated with changing correlations and enhanced functional connectivity between VTA neurons. Analysis of LFP recorded simultaneously with unit activity showed an increase in the power of theta oscillations when stimuli predicted reward but not an aversive outcome. With learning, a higher proportion of putative GABA units were phase locked to the theta oscillations than putative dopamine units. These patterns also adapted when task contingencies were changed. Taken together, these data demonstrate that VTA neurons organize flexibly as functional networks to support appetitive and aversive learning.     

Epithelial sodium channels: characterization by using the patch-clamp technique

The patch-clamp technique was used to resolve currents through individual Na-selective ion channels in the apical membrane of the rat cortical collecting tubule. The channels had a single unit conductance of 5 pS under control conditions (cell-attached patches, room temperature, 140 mM NaCl in the pipette). They appeared to be highly selective for Na, as K conduction through them was not measurable in inside-out patches. The channels underwent spontaneous transitions between open and closed states, both states being long-lived. At physiological temperature (37C) the conductance increased to 9 pS and the spontaneous transitions became more rapid. In the presence of amiloride on the luminal side of the membrane, the channel flickered rapidly between open and blocked states. The size of the current transitions did not change. This channel activity was observed only in rats that were fed a low-Na diet to elevate aldosterone secretion. In addition to mineralocorticoid control, the activity of the channels in inside-out patches were modulated by the pH on the cytoplasmic side of the membrane. Alkalinization from pH 6.4 to 7.4 increased the probability of channels' being open by eightfold. Changes in Ca concentration on the cytoplasmic side of the membrane did not directly affect the channels. However, addition of ionomycin, a Ca ionophore, to the bath resulted in a decrease in channel activity measured in cell-attached patches. This suggests that high cytoplasmic Ca may indirectly down-regulate Na channels in this tissue.     

A discrete fully recurrent network of max product units for associative memory and classification

This paper defines the truncated normalized max product operation for the transformation of states of a network and provides a method for solving a set of equations based on this operation. The operation serves as the transformation for the set of fully connected units in a recurrent network that otherwise might consist of linear threshold units. Component values of the state vector and outputs of the units take on the values in the set [0, 0.1,..., 0.9, 1]. The result is a much larger state space given a particular number of units and size of connection matrix than for a network based on threshold units. Since the operation defined here can form the basis of transformations in a recurrent network with a finite number of states, fixed points or cycles are possible and the network based on this operation for transformations can be used as an associative memory or pattern classifier with fixed points taking on the role of prototypes. Discrete fully recurrent networks have proven themselves to be very useful as associative memories and as classifiers. However they are often based on units that have binary states. The effect of this is that the data to be processed consisting of vectors in R(n) have to be converted to vectors in [0, 1]m with m much larger than n since binary encoding based on positional notation is not feasible. This implies a large increase in the number of components. The effect can be lessened by allowing more states for each unit in our network. The network proposed demonstrates those properties that are desirable in an associative memory very well as the simulations show.     

Ozone exposure causes a decoupling of conductance and photosynthesis: implications for the Ball-Berry stomatal conductance model

Industrialization has significantly altered atmospheric chemistry by increasing concentrations of chemicals such as nitrogen oxides (NO( x )) and volatile organic carbon, which react in the presence of sunlight to produce tropospheric ozone (O(3)). Ozone is a powerful oxidant that causes both visual and physiological damage to plants, impairing the ability of the plant to control processes like photosynthesis and transpiration. Damage to photosynthesis and stomatal conductance does not always occur at the same rate, which generates a problem when using the Ball-Berry model to predict stomatal conductance because the calculations directly rely on photosynthesis rates. The goals of this work were to develop a modeling framework to modify Ball-Berry stomatal conductance predictions independently of photosynthesis and to test the framework using experimental data. After exposure to elevated O(3) in open-top chambers, photosynthesis and stomatal conductance in tulip poplar changed at different rates through time. We were able to accurately model observed photosynthetic and stomatal conductance responses to chronic O(3) exposure in a Ball-Berry framework by adjusting stomatal conductance in addition to photosynthesis. This led to a significant improvement in the modeled ability to predict both photosynthesis and stomatal conductance responses to O(3).