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First published online December 23, 2009; 10.1104/pp.109.151266 Plant Physiology 152:470-479 (2010) © 2010 American Society of Plant Biologists
Hope for Humpty Dumpty: Systems Biology of Cellular Signaling1Biology Department, Pennsylvania State University, University Park, Pennsylvania 16802
Humpty Dumpty, a traditional English nursery rhyme: Humpty Dumpty sat on a wall, Humpty Dumpty had a great fall. All the king's horses, And all the king's men, Couldn't put Humpty together again. One definition of systems biology is the modeling of the relationships, or networks, within and/or between large-scale data sets. As scientists' knowledge of living systems has grown, it has become increasing difficult to understand relationships between all the components of a biological network by intuitive approaches alone. The value of systems biology is that it (1) helps us to organize information about complex systems; (2) reveals hidden content, or "emergent properties," of the system that would not be deduced from a study of the separate parts of the system; and (3) provides predictions of how the system would behave under conditions that have not yet been observed. Such predictions can then be used to inform and direct wet bench experiments.
There are many different types of biological networks that can be investigated using systems biology approaches. Some systems are typified by a certain type of biological molecule (e.g. all of the transcription factors that are activated by cold stress or all of the proteins that are phosphorylated by a particular kinase). Other systems are studied at a particular level of organization, such as the subcellular, cellular, tissue, organ, whole plant, or ecosystem. Systems biology can yield insights into both developmental processes, such as the classic ABC model of flower development (Weigel and Meyerowitz, 1994  ), and physiological processes, such as pathogen signaling networks (Agrawal et al., 2004). This Update focuses on the systems biology of rapid cellular signaling, using as an example abscisic acid (ABA) signaling in guard cells (Figs. 1
and 2
). Accordingly, the goal of this Update is not to review ABA regulation of stomatal movements per se but rather to use this phenomenon to illustrate some general aspects of systems biology approaches toward modeling cellular signaling cascades. Figure 2 shows a signaling network for ABA-induced stomatal closure (Li et al., 2006) that can be used as a reference point for the concepts discussed in this Update. Our knowledge of ABA signaling has progressed substantially since this figure was first published in 2006, and some of the major advances are also highlighted.
Guard cells are morphologically distinct cells that are located in pairs in the epidermes of aerial plant parts, where they define the apertures of stomatal pores, through which land plants take up carbon dioxide for photosynthesis but also, inevitably, lose water vapor (Fig. 1). Guard cells have evolved exquisite mechanisms to sense and respond to endogenous and environmental stimuli such as hormones, light, carbon dioxide concentrations, temperature, humidity, and plant water status, with the result that stomatal apertures are narrowed under water-limiting conditions and widened when conditions for photosynthesis are optimal. Appropriate guard cell function is vitally important for the survival of land plants and thus has direct implications for the production of adequate food and fuel to provision the burgeoning human population. Moreover, considering the list of stimuli to which guard cells respond, it can be anticipated that guard cell responses will both be affected by and will feed back to affect global environmental parameters such as planetary temperature and atmospheric concentrations of greenhouse gases such as water vapor and CO2 (Kirschbaum, 2004 ). Indeed, it has been predicted that stomatal closure resulting from a doubling of atmospheric CO2 concentrations would decrease water vapor loss through stomata to such an extent that continental runoff of freshwater would increase significantly (Betts et al., 2007).
In addition to the relevance of guard cells to the survival of terrestrial organisms, guard cells have also become a premier model system for the study of signaling at the cellular level, in part due to their accessibility and the availability of techniques to dynamically monitor their cellular output. Because guard cells are located in the outermost cell layer of the plant, the epidermis, the effects of a stimulus can be readily and directly monitored in real time at several different levels. First, at the subcellular level, electrophysiological techniques allow the monitoring of stimulus-induced changes in ion fluxes across the guard cell membrane. Changes in the concentrations of ions and other solutes result in osmotically driven water fluxes across the guard cell membrane that in turn cause cell swelling or shrinking, resulting in stomatal opening or stomatal closure, respectively (Fig. 1). Imaging techniques also allow monitoring of changes in the concentrations of signaling ions, particularly H+ and Ca2+, in real time. Second, responses of individual guard cells to a stimulus can be quantified by direct observation of stomatal apertures with a microscope. Third, effects of a stimulus on stomatal apertures can be monitored at the integrated whole leaf level by measurements of the rate of water vapor loss (transpiration) from the leaf. From assays such as these, we know that when plants are drought stressed and guard cells are exposed to elevated ABA levels, ABA stimulates the efflux of K+, Cl–, and malate2– from the guard cells as well as Suc efflux or metabolism under some conditions. The resultant decrease in intracellular concentrations of these major solutes drives water efflux, thus shrinking guard cell volume and narrowing stomatal apertures (Fig. 1). In addition to the above real-time measurements, the ability to isolate large populations of highly pure guard cells has enabled the determination of guard cell transcriptomes and guard cell proteomes (Leonhardt et al., 2004
To model a cellular signaling system such as ABA-induced stomatal closure, the first steps are to identify the components of the system and to define the relationships between them. In a systems biology analysis, the components of the system are depicted as nodes and their relationships with each other are depicted as edges (Fig. 2), thus resulting in the assembly of a network. Edges can be either directional, indicating a specific direction of information flow (e.g. as in a signal transduction network), or nondirectional (e.g. as in the interaction of two scaffolding proteins). Edges can either be positive, indicating activation, or negative, indicating inhibition.
Identification of the nodes of cellular signaling systems has benefited from the powerful tools of forward and reverse genetics. For example, forward genetic screens in Arabidopsis (Arabidopsis thaliana) for ABA effects on seed germination and seedling growth led to the identification of ABA-insensitive mutants such as abi1-1 (Koornneef et al., 1984
Gene identification based on forward genetic screens such as these has resulted in the identification of numerous guard cell ABA signaling components. It is interesting, however, that the majority of these mutants were initially identified by screening for a non-guard cell aspect of ABA physiology, in particular ABA inhibition of seed germination (Wang et al., 2004
Reverse genetic approaches are also potent tools in the identification of cellular signaling components. In reverse genetics, a gene is first identified to be of interest, and then the impact of the knockout of this gene on the relevant system is assessed in order to decide whether or not the gene product should be included as a node in that network. A gene may be deemed to be of interest because it has homology to a protein of relevant function in another organism. For example, certain phosphorylated lipid metabolites have been implicated as secondary messengers in guard cell ABA signaling, and candidates for the genes that encode the associated kinases were identified in the Arabidopsis genome based on homology to such kinases in mammals (Worrall et al., 2008
A gene may also be deemed to be of interest because its transcript or protein product is highly abundant or highly regulated in the cellular system of interest. For example, the Arabidopsis GORK gene is now known to encode a K+ channel protein that mediates K+ efflux during stomatal closure. gork knockouts were initially targeted for investigation because of high GORK expression levels in wild-type guard cells, coupled with the observation that the GORK protein exhibits K+ channel activity when expressed in heterologous systems (Hosy et al., 2003
Once a gene (product) has been confirmed as a node in a cellular signaling system, coexpression analysis of other transcriptomic (or proteomic) data sets can be used to identify additional candidates that coexpress with the first gene/protein both in guard cells and in other tissues or conditions and, thus, are themselves implicated as having a functional relationship with the first gene/protein (Albert and Albert, 2004
Signaling networks employ not only proteins but also ions and metabolites as secondary messengers. Fluorescent reporters of ion concentration have implicated Ca2+ and H+ ions as important secondary messengers in single cell systems such as guard cells and pollen tubes. In particular, fluorescent reporters of cytosolic Ca2+ concentration have illuminated the role of Ca2+ as a secondary messenger in guard cell ABA responses, and elevation of cytosolic pH is also an important component in guard cell ABA signaling. Only a few single-cell plant systems, such as trichomes (Schilmiller et al., 2008 After assembling information on candidate nodes, the researcher must decide what standard of proof will be required for inclusion of a node in a network. Will pharmacological evidence be considered as sufficient, or is genetic and/or biochemical information required? Is pharmacological evidence less convincing because of the known lack of specificity of pharmacological interventions? Or is pharmacological evidence actually more relevant for the study of rapid physiological responses such as stomatal closure because it is a short-term manipulation and thus less likely to have pleiotropic or developmental effects that could contribute to altering the overall cellular status or "set point" of the cell? Once a standard of proof is decided on, it obviously should be applied uniformly to all the nodes under consideration for inclusion in the network.
Once the set of nodes has been identified, the relationships between them must be formalized in order to actually draw the network. Again, there are several approaches that can yield useful information. Geneticists have long employed epistasis analysis to determine the relationship between genes/gene products, and such analyses provide one mechanism to place two proteins within the same branch of a signaling network or to determine that the proteins are functioning independently, additively, or synergistically. Epistasis analysis, however, does not determine whether proteins situated in the same path of a network are actually adjacent to each other in the pathway. In the model of Figure 2, whenever indirect evidence positioned two nodes as adjacent in a pathway but direct evidence that the two nodes physically interacted was lacking, a small black circle (representing the possibility of additional, intermediate nodes) was added.
Evidence for direct node-node interactions can be provided by various protein-protein interaction assays or by detailed biochemical analyses that determine the interrelationships between two proteins or between a protein and a cofactor or metabolite. For example, it had been observed that mutation of the ABA-activated protein kinase, OST1, impaired ABA-stimulated production of ROS in guard cells and resulted in other phenotypes that were similar to those observed when the NADPH oxidases AtrbohD and AtrbohF were knocked out (Mustilli et al., 2002
When drawing edges between two nodes, the researcher must again decide what standard of proof to apply. For example, there are a variety of methods for determining protein-protein interaction, some of which are performed in vitro, others in yeast, and others in planta (Lalonde et al., 2008 The most informative signaling networks are those with edges that indicate the direction and type of information flow; so in building a signaling network, the researcher needs to identify not only which nodes are upstream and which are downstream but also which are activating and which are inhibitory. Again, genetic and biochemical approaches yield useful information, with the caveat that directionality is not indicated by all assay methods. For example, yeast two-hybrid or coimmunoprecipitation analyses show that two proteins interact but are not sufficient to indicate which protein is upstream and which is downstream in a signaling cascade, nor do such data indicate whether the interaction is positive or negative.
There are some simplifying assumptions that can be applied to aid the process of drawing edges. One overall simplifying assumption is that of parsimony (i.e. that one should construct the simplest possible network that is in accordance with the experimental data). For example, if A is known to promote both B and C and C is known to promote the A
Once the structure of a network has been finalized, its properties can be assessed. Emergent properties are those that could not be deduced by studying individual components in isolation (Bhalla and Iyengar, 1999 ). In Figure 2, the ultimate emergent property is stomatal closure, but there are also important properties within a network that can be considered as emergent. Some general aspects of networks that can be considered as emergent properties are motifs, modules, and scale. Negative and positive feedback loops are familiar examples of motifs. For example, in the network of Figure 2, cytosolic Ca2+ elevation, which activates the Ca2+ extruding ATPase, which in turn decreases cytosolic Ca2+ levels, is an example of a negative feedback loop (Ca2+c  Ca2+ ATPase  Ca2+c), while cytosolic Ca2+ activation of the enzyme phospholipase C (PLC), leading to production of inositol 1,4,5 trisphosphate (InsP3), which stimulates Ca2+ release from intracellular stores, which elevates cytosolic Ca2+ (Ca2+c PLC InsP3 Ca2+c), is an example of a positive feedback loop. Motifs may or may not occur in modules, which are subnetworks within the main network that have high interconnectivity (numerous edges) within the module and low interconnectivity (few edges) between the module and the rest of the network.
In many types of networks, including biological networks, it has been observed that there is typically a large range in the number of edges that the nodes of the network exhibit; thus, the network cannot be described adequately by a "typical" or average number of connections. Such networks are said to be scale free (Albert et al., 2000
One major goal of systems biology is to develop models that have predictive value. Once a network has been assembled, the type of modeling that can be performed with it is dependent on the depth of knowledge that is available about the system and, particularly, on whether that knowledge is quantitative or qualitative. If detailed quantitative and kinetic information is available on the status of the nodes, then a continuous model can be developed using ordinary differential equations or partial differential equations. A good introduction to these types of models is provided by Eungdamrong and Iyengar (2004) . For guard cell biology, while available techniques readily allow the collection of quantitative information at the level of the output node (e.g. the size of the stomatal aperture or the rate of transpirational water loss over time), there are only a handful of cases in which quantitative information is available regarding the status of the internal nodes in this network. Quantitative information is available from electrophysiological measurements of ion channel activity, and from fluorescent imaging of Ca2+ elevations and oscillations in response to ABA treatment. There is some quantitative information on other aspects, such as the rates of production of ROS and some lipid metabolites, but the information is insufficient to allow a completely continuous modeling approach.
Fortunately, there are other methods of network analysis that can be applied to make predictions in the absence of detailed quantitative information. Hybrid models can be applied in which some variables are continuous and others discrete, or a fully discrete model can be utilized. In a discrete model, nodes are restricted to particular states (e.g. fully on, partly on, or off). The most reduced form of a discrete model is a Boolean model, in which nodes are characterized as either on or off depending on the status of the upstream nodes and their relationship to those nodes (Albert and Wang, 2009 To perform Boolean modeling, logic rules that define the on (active) state of each node are first defined, using the Boolean operators "and," "or," and "not." For example, when ABA activates the protein kinase OST1, the model of Figure 2 predicts that this will in turn activate the NADPH oxidases (Atrboh): since OST1 is the only input into Atrboh, Atrboh will be active (on) whenever OST1 is active. For nodes with more than one input, the rules can become more complicated. For example, as shown in Figure 2, there are four secondary messengers (InsP3, cADPR, cGMP, and InsP6) implicated in stimulating Ca2+ release from internal stores (node CIS [see Fig. 2 legend]). What is the most biologically accurate way to define the active state of node CIS? Possibilities include (InsP3 or cADPR or cGMP or InsP6), (InsP3 and cADPR and cGMP and InsP6), and various mixed combinations. The experimenter's goal is to define each rule so as to incorporate existing knowledge as well as possible. In some instances, there will be conflicting or insufficient data in the literature. Thus, building these rules requires not only logic but extensive application of the scientist's expertise. Once Boolean rules have been designated for each node, there are two more decisions to make before modeling can begin. The first decision concerns how to set the initial status of the internal nodes. When modeling an irreversible developmental process, it may be a reasonable simplification to assume that all nodes downstream of the input node are inactive (off) until the input is turned on. However, for a reversible physiological process, such as stomatal closing and opening, this assumption seems likely to be invalid, absent evidence to the contrary, and so alternative approaches are desirable. One alternative is to randomly set the initial status of the internal nodes. Thus, when ABA-induced stomatal closure was simulated using the network of Figure 2, Li and colleagues (2006) modeled 10,000 in silico stomata, with the on or off status of each internal node randomly chosen anew for each in silico stoma, in order to obtain a prediction of network behavior (although 10,000 does not cover all random combinations of the node state space, results did not differ when 100,000 stomata were modeled, indicating that a sample size of 10,000 was sufficient). Another alternative is to incorporate prior knowledge to set the initial status of the internal nodes for which such information is available, while allowing the initial status of the rest of the internal nodes to be defined randomly. For example, in the network of Figure 2, if it were known that phosphoenolpyruvate carboxylase (PEPC) was always active in malate production in the absence of ABA, then the PEPC node could always initially be set to on for the modeling process.
Once an initial status of all the internal nodes has been established, randomly or otherwise, the input node can be turned on and the propagation of the signal through the network can be assessed. The second decision involves choosing how such propagation will be modeled (Albert and Wang, 2009
In the absence of loops, synchronous modeling results in information percolating from level to level in the network, with information flowing most quickly in the shortest paths (i.e. the paths with fewest nodes). For developmental processes, this might be reasonable as a first approximation. However, for reversible physiological processes, this approximation is less likely to reflect biological reality. An alternative possibility is to perform asynchronous updating, in which the internal nodes are updated sequentially in a randomly chosen order, until every internal node has been updated once (Albert and Wang, 2009
After a number of rounds of update, the output of a Boolean network will either reach a steady state or start to cycle. In the case of the ABA network of Figure 2, outputs reached steady state within eight rounds of updates. It can be readily understood that this type of modeling requires programming for all but the simplest networks. Fortunately, Albert and colleagues (2008)
The first goal in running simulations such as those described above is to assess whether the model reflects the reality of the wild-type response of the cellular signaling system. In the case of Figure 2, the model satisfied this condition in that it did indeed predict ABA-induced stomatal closure. It has also been observed that many biological signaling systems are robust; that is, the outcome is, to some extent, resilient against perturbation. The signaling network of Figure 2 was found to be robust against random rewiring, a typical approach to evaluate robustness (Shen-Orr et al., 2002 ). Had robustness not been observed, this would have suggested that reevaluation of the network structure and Boolean rules was warranted or that insufficient information was available to apply this modeling approach.
If the model satisfies initial requirements, then one can proceed to use the model to simulate interesting conditions and make predictions regarding which of the simulated changes are most likely to affect the output. For ABA-induced stomatal closure, 65% of single node knockouts were predicted not to alter ABA-induced stomatal closure, which is also consistent with a robust system; this percentage dropped to 38% for double node knockouts (Li et al., 2006
Guard cell signaling is a rapidly advancing area of research, and it is not possible within the constraints of an Update article to cover more than a small fraction of the recent publications in the field. This section very briefly summarizes some of the new information on guard cell signaling, focusing only on information that is relevant to ABA-induced stomatal closure, and thus could be used in the future to generate a revised network for this process.
Channels and transporters for ions and other solutes are the effectors of the membrane potential and water potential changes that drive stomatal movements. In response to ABA, inhibition of H+-ATPase-based H+ extrusion and activation of Ca2+ influx channels and anion efflux channels all contribute to membrane depolarization, which activates the voltage-regulated K+ channels through which K+ efflux occurs; this solute efflux results in water efflux and stomatal closure (Fig. 1). Previously identified transport proteins of the guard cell tonoplast and plasma membrane have been described in detail in recent review articles (Pandey et al., 2007
One of the most important recent discoveries is the identification of membrane-associated and soluble ABA receptors. Membrane-associated receptors, GTGs, interact with and are regulated by the G
Further evidence for the central importance of protein de/phosphorylation in guard cell physiology comes from the latest reverse genetic studies on several types of protein kinases. Members of mitogen-activated protein kinase cascades have been implicated in the regulation of guard cell physiology as well as guard cell development (Colcombet and Hirt, 2008
These are still early days for cellular systems biology. For example, the network of Figure 2 was, at the time, the most complex network to have been modeled by Boolean modeling with asynchronous update. Yet, ensuing rapid progress in guard cell signaling has provided a number of new nodes and edges, with still more to come. Thus, we are quite some time away from having a comprehensive model of ABA-induced stomatal closure. In addition, since ABA is just one facet of the multisensory capacities of the guard cell, in order to fully predict stomatal behavior it will be necessary to integrate the ABA signaling network with those for other hormones and for light, CO2, humidity, temperature, and pathogen sensing. Nevertheless, the promise of systems biology is that the wealth of information being made available by reductionistic approaches can be synthesized to yield a greater understanding of biological systems. In other words, after decades of taking apart Humpty Dumpty to figure out his components, systems biology offers the kings' soldiers a path by which Humpty might indeed eventually be put together again.
I thank Prof. Réka Albert for helpful comments on the manuscript, and I apologize to those many authors whose work was not cited owing to space limitations. Received November 20, 2009; accepted November 27, 2009; published December 23, 2009.
1 This work was supported by the National Science Foundation and the U.S. Department of Agriculture.  The author responsible for distribution of materials integral to the findings presented in this article in accordance with the policy described in the Instructions for Authors (www.plantphysiol.org) is: Sarah M. Assmann (sma3{at}psu.edu). www.plantphysiol.org/cgi/doi/10.1104/pp.109.151266
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THE SYSTEMS OF SYSTEMS...
STOMATAL GUARD CELLS
-subunit; HATPase, H+-ATPase at the plasma membrane; InsPK, inositol polyphosphate kinase; InsP3, inositol-1,4,5-trisphosphate; InsP6, inositol hexakisphosphate; KAP, K+ efflux through rapidly activating K+ channels (AP channels) at the plasma membrane; KEV, K+ efflux from the vacuole to the cytosol; KOUT, K+ efflux through slowly activating outwardly rectifying K+ channels at the plasma membrane; NOS, nitric oxide synthase; NIA12, nitrate reductase; NO, nitric oxide; OST1, protein kinase OST1; PA, phosphatidic acid; PC, phosphatidylcholine; PEPC, phosphoenolpyruvate carboxylase; PIP2, phosphatidylinositol 4,5-bisphosphate; PLC, phospholipase C; PLD, phospholipase D; RAC1, small GTPase RAC1; RCN1, protein phosphatase 2A; ROP2, small GTPase ROP2; ROP10, small GTPase ROP10; SphK, sphingosine kinase; Sph, sphingosine; S1P, sphingosine-1-phosphate.
dasgupta/network-synthesis/