Linear models of activation cascades: analytical solutions and coarse-graining of delayed signal transduction.

Cellular signal transduction usually involves activation cascades, the sequential activation of a series of proteins following the reception of an input signal. Here, we study the classic model of weakly activated cascades and obtain analytical solutions for a variety of inputs. We show that in the special but important case of optimal gain cascades (i.e. when the deactivation rates are identical) the downstream output of the cascade can be represented exactly as a lumped nonlinear module containing an incomplete gamma function with real parameters that depend on the rates and length of the cascade, as well as parameters of the input signal. The expressions obtained can be applied to the non-identical case when the deactivation rates are random to capture the variability in the cascade outputs. We also show that cascades can be rearranged so that blocks with similar rates can be lumped and represented through our nonlinear modules. Our results can be used both to represent cascades in computational models of differential equations and to fit data efficiently, by reducing the number of equations and parameters involved. In particular, the length of the cascade appears as a real-valued parameter and can thus be fitted in the same manner as Hill coefficients. Finally, we show how the obtained nonlinear modules can be used instead of delay differential equations to model delays in signal transduction.

Compound stress response in stomatal closure: a mathematical model of ABA and ethylene interaction in guard cells.

BACKGROUND: Stomata are tiny pores in plant leaves that regulate gas and water exchange between the plant and its environment. Abscisic acid and ethylene are two well-known elicitors of stomatal closure when acting independently. However, when stomata are presented with a combination of both signals, they fail to close. RESULTS: Toshed light on this unexplained behaviour, we have collected time course measurements of stomatal aperture and hydrogen peroxide production in Arabidopsis thaliana guard cells treated with abscisic acid, ethylene, and a combination of both. Our experiments show that stomatal closure is linked to sustained high levels of hydrogen peroxide in guard cells. When treated with a combined dose of abscisic acid and ethylene, guard cells exhibit increased antioxidant activity that reduces hydrogen peroxide levels and precludes closure. We construct a simplified model of stomatal closure derived from known biochemical pathways that captures the experimentally observed behaviour. CONCLUSIONS: Our experiments and modelling results suggest a distinct role for two antioxidant mechanisms during stomatal closure: a slower, delayed response activated by a single stimulus (abscisic acid 'or' ethylene) and another more rapid 'and' mechanism that is only activated when both stimuli are present. Our model indicates that the presence of this rapid 'and' mechanism in the antioxidant response is key to explain the lack of closure under a combined stimulus.

Identification of two-component system elements downstream of AHK5 in the stomatal closure response of Arabidopsis thaliana.

To optimize water use efficiency, plants regulate stomatal closure through a complex signaling process. Hydrogen peroxide (H2O2) is produced in response to several environmental stimuli, and has been identified as a key second messenger involved in the regulation of stomatal aperture. The Arabidopsis histidine kinase 5 (AHK5) has been shown to regulate stomatal closure in response to H2O2 and other stimuli that depend on H2O2. AHK5 is a member of the two-component system (TCS) in Arabidopsis. The plant TCS comprises three different protein types: the hybrid histidine kinases (HKs), the phosphotransfer proteins (HPs) and the response regulators (RRs). Here we determined TCS elements involved in H2O2- and ethylene-dependent stomatal closure downstream of AHK5. By yeast and in planta interaction assays and functional studies, AHP1, 2 and 5 as well as the response regulators ARR4 and ARR7 were identified acting downstream of AHK5 in the ethylene and H2O2 response pathways of guard cells. Furthermore, we demonstrate that aspartate phosphorylation of ARR4 is only required for the H2O2- but not for the ethylene-induced stomatal closure response. Our data suggest the presence of a complex TCS signaling network comprising of at least AHK5, several AHPs and response regulators, which modulate stomatal closure in response to H2O2 and ethylene.

Modulation of ROS production and hormone levels by AHK5 during abiotic and biotic stress signaling.

Histidine kinases have been shown to mediate responses to endogenous and exogenous stimuli in organisms such as yeast, bacteria and plants. In the model plant Arabidopsis, histidine kinases have been shown to function in hormone signaling, and abiotic and biotic stress responses. More recently, the least characterized of the Arabidopsis histidine kinases, AHK5, was demonstrated to function in resistance toward the virulent bacterium Pseudomonas syringae pv tomato DC3000 (PstDC3000) and the necrotrophic fungus Botrytis cinerea, and as a negative regulator of tolerance toward salinity. Here, we present data which indicate that AHK5 also impacts on drought stress resistance and on the outcome of an incompatible interaction with avrRpm1-expressing PstDC3000 (PstDC3000 (avrRpm1)). We present a model which proposes a role for reactive oxygen species (ROS) and hormones in integrating abiotic and biotic stress responses via AHK5.

Arabidopsis histidine kinase 5 regulates salt sensitivity and resistance against bacterial and fungal infection.

• The ability of plants to adapt to multiple stresses imposed by the natural environment requires cross-talk and fine-tuning of stress signalling pathways. The hybrid histidine kinase Arabidopsis histidine kinase 5 (AHK5) is known to mediate stomatal responses to exogenous and endogenous signals in Arabidopsis thaliana. The purpose of this study was to determine whether the function of AHK5 in stress signalling extends beyond stomatal responses. • Plant growth responses to abiotic stresses, tissue susceptibility to bacterial and fungal pathogens, and hormone production and metabolism of reactive oxygen species were monitored in a T-DNA insertion mutant of AHK5. • The findings of this study indicate that AHK5 positively regulates salt sensitivity and contributes to resistance to the bacterium Pseudomonas syringae pv. tomato DC3000 and the fungal pathogen Botrytis cinerea. • This is the first report of a role for AHK5 in the regulation of survival following challenge by a hemi-biotrophic bacterium and a necrotrophic fungus, as well as in the growth response to salt stress. The function of AHK5 in regulating the production of hormones and redox homeostasis is discussed.

Squeeze-and-breathe evolutionary Monte Carlo optimization with local search acceleration and its application to parameter fitting.

Estimating parameters from data is a key stage of the modelling process, particularly in biological systems where many parameters need to be estimated from sparse and noisy datasets. Over the years, a variety of heuristics have been proposed to solve this complex optimization problem, with good results in some cases yet with limitations in the biological setting. In this work, we develop an algorithm for model parameter fitting that combines ideas from evolutionary algorithms, sequential Monte Carlo and direct search optimization. Our method performs well even when the order of magnitude and/or the range of the parameters is unknown. The method refines iteratively a sequence of parameter distributions through local optimization combined with partial resampling from a historical prior defined over the support of all previous iterations. We exemplify our method with biological models using both simulated and real experimental data and estimate the parameters efficiently even in the absence of a priori knowledge about the parameters.

N-3-oxo-decanoyl-L-homoserine-lactone activates auxin-induced adventitious root formation via hydrogen peroxide- and nitric oxide-dependent cyclic GMP signaling in mung bean.

N-Acyl-homoserine-lactones (AHLs) are bacterial quorum-sensing signaling molecules that regulate population density. Recent evidence demonstrates their roles in plant defense responses and root development. Hydrogen peroxide (H(2)O(2)), nitric oxide (NO), and cyclic GMP (cGMP) are essential messengers that participate in various plant physiological processes, but how these messengers modulate the plant response to N-acyl-homoserine-lactone signals remains poorly understood. Here, we show that the N-3-oxo-decanoyl-homoserine-lactone (3-O-C10-HL), in contrast to its analog with an unsubstituted branch chain at the C3 position, efficiently stimulated the formation of adventitious roots and the expression of auxin-response genes in explants of mung bean (Vigna radiata) seedlings. This response was mimicked by the exogenous application of auxin, H(2)O(2), NO, or cGMP homologs but suppressed by treatment with scavengers or inhibitors of H(2)O(2), NO, or cGMP metabolism. The 3-O-C10-HL treatment enhanced auxin basipetal transport; this effect could be reversed by treatment with H(2)O(2) or NO scavengers but not by inhibitors of cGMP synthesis. Inhibiting 3-O-C10-HL-induced H(2)O(2) or NO accumulation impaired auxin- or 3-O-C10-HL-induced cGMP synthesis; however, blocking cGMP synthesis did not affect auxin- or 3-O-C10-HL-induced H(2)O(2) or NO generation. Additionally, cGMP partially rescued the inhibitory effect of H(2)O(2) or NO scavengers on 3-O-C10-HL-induced adventitious root development and auxin-response gene expression. These results suggest that 3-O-C10-HL, unlike its analog with an unmodified branch chain at the C3 position, can accelerate auxin-dependent adventitious root formation, possibly via H(2)O(2)- and NO-dependent cGMP signaling in mung bean seedlings.

In planta conditions induce genomic changes in Pseudomonas syringae pv. phaseolicola.

The co-evolution of bacterial plant pathogens and their hosts is a complex and dynamic process. Plant resistance can impose stress on invading pathogens that can lead to, and select for, beneficial changes in the bacterial genome. The Pseudomonas syringae pv. phaseolicola (Pph) genomic island PPHGI-1 carries an effector gene, avrPphB (hopAR1), which triggers the hypersensitive reaction in bean plants carrying the R3 resistance gene. Interaction between avrPphB and R3 generates an antimicrobial environment within the plant, resulting in the excision of PPHGI-1 and its loss from the genome. The loss of PPHGI-1 leads to the generation of a Pph strain able to cause disease in the plant. In this study, we observed that lower bacterial densities inoculated into resistant bean (Phaseolus vulgaris) plants resulted in quicker PPHGI-1 loss from the population, and that loss of the island was strongly influenced by the type of plant resistance encountered by the bacteria. In addition, we found that a number of changes occurred in the bacterial genome during growth in the plant, whether or not PPHGI-1 was lost. We also present evidence that the circular PPHGI-1 episome is able to replicate autonomously when excised from the genome. These results shed more light onto the plasticity of the bacterial genome as it is influenced by in planta conditions.

Role of nitric oxide in regulating stomatal apertures.

During stomatal closure, nitric oxide (NO) operates as one of the key intermediates in the complex, abscisic acid (ABA)-mediated, guard cell signaling network that regulates this process. However, data concerning the role of NO in stomatal closure that occurs in turgid vs. dehydrated plants is limited. The data presented demonstrate that, while there is a requirement for NO during the ABA-induced stomatal closure of turgid leaves, such a requirement does not exist for ABA-enhanced stomatal closure observed to occur during conditions of rapid dehydration. The data also indicate that the ABA signaling pathway must be both functional and to some degree activated for guard cell NO signaling to occur. These observations are in line with the idea that the effects of NO in guard cells are mediated via a Ca(2+)-dependent rather than a Ca(2+)-independent ABA signaling pathway. It appears that there is a role for NO in the fine tuning of the stomatal apertures of turgid leaves that occurs in response to fluctuations in the prevailing environment.

Differential requirement for NO during ABA-induced stomatal closure in turgid and wilted leaves.

Abscisic acid (ABA)-induced stomatal closure is mediated by a complex, guard cell signalling network involving nitric oxide (NO) as a key intermediate. However, there is a lack of information concerning the role of NO in the ABA-enhanced stomatal closure seen in dehydrated plants. The data herein demonstrate that, while nitrate reductase (NR)1-mediated NO generation is required for the ABA-induced closure of stomata in turgid leaves, it is not required for ABA-enhanced stomatal closure under conditions leading to rapid dehydration. The results also show that NO signalling in the guard cells of turgid leaves requires the ABA-signalling pathway to be both capable of function and active. The alignment of this NO signalling with guard cell Ca(2+)-dependent/independent ABA signalling is discussed. The data also highlight a physiological role for NO signalling in turgid leaves and show that stomatal closure during the light-to-dark transition requires NR1-mediated NO generation and signalling.

Functional characterization of a higher plant sphingolipid Delta4-desaturase: defining the role of sphingosine and sphingosine-1-phosphate in Arabidopsis.

The role of Delta4-unsaturated sphingolipid long-chain bases such as sphingosine was investigated in Arabidopsis (Arabidopsis thaliana). Identification and functional characterization of the sole Arabidopsis ortholog of the sphingolipid Delta4-desaturase was achieved by heterologous expression in Pichia pastoris. A P. pastoris mutant disrupted in the endogenous sphingolipid Delta4-desaturase gene was unable to synthesize glucosylceramides. Synthesis of glucosylceramides was restored by the expression of Arabidopsis gene At4g04930, and these sphingolipids were shown to contain Delta4-unsaturated long-chain bases, confirming that this open reading frame encodes the sphingolipid Delta4-desaturase. At4g04930 has a very restricted expression pattern, transcripts only being detected in pollen and floral tissues. Arabidopsis insertion mutants disrupted in the sphingolipid Delta4-desaturase At4g04930 were isolated and found to be phenotypically normal. Sphingolipidomic profiling of a T-DNA insertion mutant indicated the absence of Delta4-unsaturated sphingolipids in floral tissue, also resulting in the reduced accumulation of glucosylceramides. No difference in the response to drought or water loss was observed between wild-type plants and insertion mutants disrupted in the sphingolipid Delta4-desaturase At4g04930, nor was any difference observed in stomatal closure after treatment with abscisic acid. No differences in pollen viability between wild-type plants and insertion mutants were detected. Based on these observations, it seems unlikely that Delta4-unsaturated sphingolipids and their metabolites such as sphingosine-1-phosphate play a significant role in Arabidopsis growth and development. However, Delta4-unsaturated ceramides may play a previously unrecognized role in the channeling of substrates for the synthesis of glucosylceramides.

The histidine kinase AHK5 integrates endogenous and environmental signals in Arabidopsis guard cells.

BACKGROUND: Stomatal guard cells monitor and respond to environmental and endogenous signals such that the stomatal aperture is continually optimised for water use efficiency. A key signalling molecule produced in guard cells in response to plant hormones, light, carbon dioxide and pathogen-derived signals is hydrogen peroxide (H(2)O(2)). The mechanisms by which H(2)O(2) integrates multiple signals via specific signalling pathways leading to stomatal closure is not known. PRINCIPAL FINDINGS: Here, we identify a pathway by which H(2)O(2), derived from endogenous and environmental stimuli, is sensed and transduced to effect stomatal closure. Histidine kinases (HK) are part of two-component signal transduction systems that act to integrate environmental stimuli into a cellular response via a phosphotransfer relay mechanism. There is little known about the function of the HK AHK5 in Arabidopsis thaliana. Here we report that in addition to the predicted cytoplasmic localisation of this protein, AHK5 also appears to co-localise to the plasma membrane. Although AHK5 is expressed at low levels in guard cells, we identify a unique role for AHK5 in stomatal signalling. Arabidopsis mutants lacking AHK5 show reduced stomatal closure in response to H(2)O(2), which is reversed by complementation with the wild type gene. Over-expression of AHK5 results in constitutively less stomatal closure. Abiotic stimuli that generate endogenous H(2)O(2), such as darkness, nitric oxide and the phytohormone ethylene, also show reduced stomatal closure in the ahk5 mutants. However, ABA caused closure, dark adaptation induced H(2)O(2) production and H(2)O(2) induced NO synthesis in mutants. Treatment with the bacterial pathogen associated molecular pattern (PAMP) flagellin, but not elf peptide, also exhibited reduced stomatal closure and H(2)O(2) generation in ahk5 mutants. SIGNIFICANCE: Our findings identify an integral signalling function for AHK5 that acts to integrate multiple signals via H(2)O(2) homeostasis and is independent of ABA signalling in guard cells.

Expression analysis of Arabidopsis vacuolar sorting receptor 3 reveals a putative function in guard cells.

Vacuolar sorting receptors (VSRs) are responsible for the proper targeting of soluble cargo proteins to their destination compartments. The Arabidopsis genome encodes seven VSRs. In this work, the spatio-temporal expression of one of the members of this gene family, AtVSR3, was determined by RT-PCR and promoter::reporter gene fusions. AtVSR3 was expressed specifically in guard cells. Consequently, a reverse genetics approach was taken to determine the function of AtVSR3 by using RNA interference (RNAi) technology. Plants expressing little or no AtVSR3 transcript had a compressed life cycle, bolting approximately 1 week earlier and senescing up to 2 weeks earlier than the wild-type parent line. While the development and distribution of stomata in AtVSR3 RNAi plants appeared normal, stomatal function was altered. The guard cells of mutant plants did not close in response to abscisic acid treatment, and the mean leaf temperatures of the RNAi plants were on average 0.8 degrees C lower than both wild type and another vacuolar sorting receptor mutant, atvsr1-1. Furthermore, the loss of AtVSR3 protein caused the accumulation of nitric oxide and hydrogen peroxide, signalling molecules implicated in the regulation of stomatal opening and closing. Finally, proteomics and western blot analyses of cellular proteins isolated from wild-type and AtVSR3 RNAi leaves showed that phospholipase Dgamma, which may play a role in abscisic acid signalling, accumulated to higher levels in AtVSR3 RNAi guard cells. Thus, AtVSR3 may play an important role in responses to plant stress.

Nitric oxide, stomatal closure, and abiotic stress.

Various data indicate that nitric oxide (NO) is an endogenous signal in plants that mediates responses to several stimuli. Experimental evidence in support of such signalling roles for NO has been obtained via the application of NO, usually in the form of NO donors, via the measurement of endogenous NO, and through the manipulation of endogenous NO content by chemical and genetic means. Stomatal closure, initiated by abscisic acid (ABA), is effected through a complex symphony of intracellular signalling in which NO appears to be one component. Exogenous NO induces stomatal closure, ABA triggers NO generation, removal of NO by scavengers inhibits stomatal closure in response to ABA, and ABA-induced stomatal closure is reduced in mutants that are impaired in NO generation. The data indicate that ABA-induced guard cell NO generation requires both nitric oxide synthase-like activity and, in Arabidopsis, the NIA1 isoform of nitrate reductase (NR). NO stimulates mitogen-activated protein kinase (MAPK) activity and cGMP production. Both these NO-stimulated events are required for ABA-induced stomatal closure. ABA also stimulates the generation of H2O2 in guard cells, and pharmacological and genetic data demonstrate that NO accumulation in these cells is dependent on such production. Recent data have extended this model to maize mesophyll cells where the induction of antioxidant defences by water stress and ABA required the generation of H2O2 and NO and the activation of a MAPK. Published data suggest that drought and salinity induce NO generation which activates cellular processes that afford some protection against the oxidative stress associated with these conditions. Exogenous NO can also protect cells against oxidative stress. Thus, the data suggest an emerging model of stress responses in which ABA has several ameliorative functions. These include the rapid induction of stomatal closure to reduce transpirational water loss and the activation of antioxidant defences to combat oxidative stress. These are two processes that both involve NO as a key signalling intermediate.

SLAC1 is required for plant guard cell S-type anion channel function in stomatal signalling.

Stomatal pores, formed by two surrounding guard cells in the epidermis of plant leaves, allow influx of atmospheric carbon dioxide in exchange for transpirational water loss. Stomata also restrict the entry of ozone--an important air pollutant that has an increasingly negative impact on crop yields, and thus global carbon fixation and climate change. The aperture of stomatal pores is regulated by the transport of osmotically active ions and metabolites across guard cell membranes. Despite the vital role of guard cells in controlling plant water loss, ozone sensitivity and CO2 supply, the genes encoding some of the main regulators of stomatal movements remain unknown. It has been proposed that guard cell anion channels function as important regulators of stomatal closure and are essential in mediating stomatal responses to physiological and stress stimuli. However, the genes encoding membrane proteins that mediate guard cell anion efflux have not yet been identified. Here we report the mapping and characterization of an ozone-sensitive Arabidopsis thaliana mutant, slac1. We show that SLAC1 (SLOW ANION CHANNEL-ASSOCIATED 1) is preferentially expressed in guard cells and encodes a distant homologue of fungal and bacterial dicarboxylate/malic acid transport proteins. The plasma membrane protein SLAC1 is essential for stomatal closure in response to CO2, abscisic acid, ozone, light/dark transitions, humidity change, calcium ions, hydrogen peroxide and nitric oxide. Mutations in SLAC1 impair slow (S-type) anion channel currents that are activated by cytosolic Ca2+ and abscisic acid, but do not affect rapid (R-type) anion channel currents or Ca2+ channel function. A low homology of SLAC1 to bacterial and fungal organic acid transport proteins, and the permeability of S-type anion channels to malate suggest a vital role for SLAC1 in the function of S-type anion channels.

Nitric oxide evolution and perception.

Various experimental data indicate signalling roles for nitric oxide (NO) in processes such as xylogenesis, programmed cell death, pathogen defence, flowering, stomatal closure, and gravitropism. However, it still remains unclear how NO is synthesized. Nitric oxide synthase-like activity has been measured in various plant extracts, NO can be generated from nitrite via nitrate reductase and other mechanisms of NO generation are also likely to exist. NO removal mechanisms, for example, by reaction with haemoglobins, have also been identified. NO is a gas emitted by plants, with the rate of evolution increasing under conditions such as pathogen challenge or hypoxia. However, exactly how NO evolution relates to its bioactivity in planta remains to be established. NO has both aqueous and lipid solubility, but is relatively reactive and easily oxidized to other nitrogen oxides. It reacts with superoxide to form peroxynitrite, with other cellular components such as transition metals and haem-containing proteins and with thiol groups to form S-nitrosothiols. Thus, diffusion of NO within the plant may be relatively restricted and there might exist 'NO hot-spots' depending on the sites of NO generation and the local biochemical micro-environment. Alternatively, it is possible that NO is transported as chemical precursors such as nitrite or as nitrosothiols that might function as NO reservoirs. Cellular perception of NO may occur through its reaction with biologically active molecules that could function as 'NO-sensors'. These might include either haem-containing proteins such as guanylyl cyclase which generates the second messenger cGMP or other proteins containing exposed reactive thiol groups. Protein S-nitrosylation alters protein conformation, is reversible and thus, is likely to be of biological significance.

Tools to investigate reaction oxygen species-sensitive signaling proteins.

The thiol groups ofcysteine residues on proteins are attractive oxidative targets for modification by reactive oxygen species, such as hydrogen peroxide (H2O2). Such modification can lead to important cellular signaling processes that ultimately result in modification of the physiology of the organism. To identify such proteins that are amenable to oxidative modification, different methods can be used. Here, two such approaches are described: one being the use of fluorescent thiol derivatives, and the second being the use of genetic mutants that are mutated in thiol residues. Using the model plant Arabidopsis thaliana, cell cultures, and whole plants, we describe these tools to help the reader understand the function of such thiol modifications on plant responses.

Signaling on the Stigma: Potential New Roles for ROS and NO in Plant Cell Signaling.

Reactive oxygen species (ROS) and reactive nitrogen species, particularly NO, are key components of diverse signaling networks in animals and plants. We have recently shown that epidermal cells of stigmas from a range of different angiosperms accumulate relatively large amounts of ROS, principally H(2)O(2), whereas pollen produces NO. Importantly, ROS/H(2)O(2) levels appeared reduced in stigma cells supporting developing pollen grains compared to cells without pollen grains attached. To explore a possible link between pollen NO production and reduced levels of stigmatic ROS/H(2)O(2), we supplied stigmas with NO and observed an overall reduction in levels of stigmatic ROS/H(2)O(2). These new and unexpected data suggest a potential new signaling role for ROS/H(2)O(2) and NO in pollen-stigma recognition processes.