The zigzag model of plant–microbe interactions: is it time to move on?

‘Remember that all models are wrong; the practical question is how wrong do they have to be to not be useful.’ (George E. P. Box) In 2006, Jones and Dangl proposed a simple coevolutionary model of plant–pathogen interactions, called the ‘zigzag’ model, which encompasses two branches of the plant immune system (Jones and Dangl, 2006). The first branch recognizes conserved molecules shared by many classes of microbe (pathogen-associated or microbe-associated molecular patterns, PAMPs or MAMPs), and is now called pattern-triggered immunity (PTI). The second branch recognizes and responds to virulence factors termed effectors that, in the model, serve to suppress PTI. This branch is called effector-triggered immunity (ETI). The model has captured the imagination of plant pathology researchers and students alike, and has proved to be a powerful conveyor of the principal concepts in plant–pathogen interactions. Eight years on, we take a fresh look at the model to consider how well it fits its intended purpose, and how a model framework to inspire future researchers in the field of plant–microbe interactions might develop. Models in the scientific sense are abstract representations of reality. Their purpose is to reduce the complexity of a real-world system to a manageable and understandable level. At its heart, any model simply acts as a logical machine for deducing conclusions from the restricted set of assumptions that define that model (Gunawardena, 2014). A model is, essentially, a microcosm of scientific hypothesis generation. Some models are expository, in that they are intended to clarify principles so that they can be explained simply. Expository models are not usually intended to make quantitative predictions or to generate novel insights. Examples of expository models might include diagrams that represent protein complexes inferred from a protein–protein interaction experiment or schematics of dynamic processes, such as an organism's life cycle. Other models, especially those based on physical laws or ones that are quantitative, are predictive. The aim of a predictive model is to represent complex systems in such a manner that new knowledge and understanding can be obtained by analysis of the model and not just by direct investigation of the real-world system it represents. Models of this kind include Henri–Michaelis–Menten enzyme kinetics, the Lotka–Volterra model of predator–prey interactions and the Virtual Liver(Holzhütter et al., 2012). It may not be important that an expository model is ‘wrong’ if the aim of transferring understanding is achieved. Predictive models can even achieve great utility and power when they are wrong because they are falsifiable: the assumptions that define the model can be tested experimentally and discarded if they are incorrect. Models of this kind can deliver great, and perhaps unanticipated, biological insight. As George Box pointed out, a model that has not (yet) been falsified is still likely to be wrong but, by a cycle of progressive improvement (revision of assumptions) and testing, our confidence in the model's output might be improved to the point that it is predictively useful. A quantitative, predictive model framework would be especially useful in the study of plant–microbe interactions, where so much can be measured in the context of the still-expanding influence of the many ‘omics’ methods, but the complexity of the biological system ensures that much insight is currently derived from phenomenology and guesswork. In this opinion piece we argue that the time has come for the study of plant–microbe interactions as a field to move beyond the dominant expository zigzag model of the plant immune system (Jones and Dangl, 2006) to embrace fully quantitative, predictive modelling. We want to encourage scientists in this field to adopt a diversity of model frameworks that are able to incorporate new and unexpected knowledge revealed by experiment, rather than risk moulding all interpretation into an expository model form that simply does not fit. To this end, we briefly describe a toy quantitative dynamic model that, while by no means complete or the only alternative or potentially useful model of the plant immune system, provides a basic dynamic representation of key behaviours of the plant immune system. With the advent of faster, cheaper, high-throughput ‘omics’ methods, the ability to acquire large amounts of quantitative data is transforming and accelerating research in plant science, and in plant–microbe interactions (Knief, 2014). To integrate and analyse these data in a productive way, molecular plant pathologists need not just one model, or even a single overarching model framework, but many models—predictive, quantitative, qualitative and expository—for a range of systems and interactions. Influential as the zigzag model has been, it cannot be the whole story for plant–microbe interactions. Molecular plant pathology has been relatively underserved in terms of modelling effort, particularly when compared with studies associated with similar human–microbial pathosystems. The current representation of models associated with plant pathology in the BioModels repository (http://www.ebi.ac.uk/biomodels-main/; Li et al., 2010), for example, is disappointingly sparse. This is surprising given the many natural advantages of working in this area for model validation and hypothesis generation. Plants and their pathogens, particularly microbial pathogens, are of much less ethical concern than are animal models of disease. Also, there are some well-understood pathosystems, such as Arabidopsis thaliana with Pseudomonas syringae or Hyaloperonospora arabidopsidis, that have a wide range of useful genomic resources and experimental toolkits for targeted and genome-wide knockout and RNA interference studies, and also large collections for investigation of the effects of both host and pathogen diversity. Plant pathosystems offer unparalleled opportunities for large-scale validation of biological modelling, systems biology and translation of the resulting insights into solutions to problems of food security that could potentially benefit many across the globe. Contributions of existing modelling and systems biology to plant–microbe interactions include: mathematical modelling of subcellular metabolic pathways in A. thaliana (Nägele and Weckwerth, 2013); flux-balance analysis and Boolean modelling of plant–pathogen interactions (Pinzón et al., 2010); metabolic reconstruction and modelling of nitrogen fixation (Resendis-Antonio et al., 2007); kinetic modelling of mitogen-activated protein kinase signalling in response to biotic stress (Pathak et al., 2013); and semi-quantitative models of plant signalling (Sankar et al., 2011). We have also previously proposed a quantitative framework for understanding plant–pathogen molecular interactions as changes of ‘state’ of the pathosystem (Pritchard and Birch, 2011), which is capable of integrating multiple sources of high-throughput experimental data and may also enable falsification and hypothesis generation for the complete interacting system and its interaction with the environment. Significant progress has been made in modelling (and subsequent experimental validation) of the interplay of ethylene, salicylic acid and jasmonic acid signalling pathways in PTI (e.g. Kim et al., 2014). For this discussion, we have prepared a dynamic and quantitative model of the plant immune system. This model was deposited in the BioModels database (Li et al., 2010) and assigned the identifier MODEL1408280000. The model abstracts key features of the plant–pathogen molecular interactions that feature in the zigzag model: PAMP detection and PTI; effector action to suppress PTI, with corresponding effector detection by an R protein and ETI (Figure 1, Figure S1 in Supporting Information). This model is clearly not a highly detailed, or perhaps even very accurate, representation of the plant immune system; nor are the model parameters optimized in any way to represent any biological system or reproduce experimentally acquired data. It is noted that although this model contains only nine differential equations (Figure S2) and is extremely simple in relation to the actual complexities of plant–pathogen molecular interactions, it still contains 15 reactions with 19 kinetic parameters and would require some effort to parameterize to any particular pathosystem. (a) Schematic diagram of the model plant immune system (BioModels: MODEL1408280000). The system is divided into two ‘compartments’: extracellular (external to the cell wall) and intracellular (internal to the cell wall). In the extracellular compartment the local microbial population is drawn from a remote bulk population and is also ‘destroyed’, as indicated by the arrow pointing to the empty set symbol (ϕ). The rate at which the microbe is ‘destroyed’, which may be interpreted, for example, as microbial movement or death, is enhanced by pattern-triggered immunity (PTI) and effector-triggered immunity (ETI). While local to the plant, the microbe produces two species: pathogen-associated molecular patterns (PAMP) and effector; both species can be lost (e.g. by diffusion or destruction) in the extracellular compartment. The PAMP may interact reversibly with plant pattern-recognition receptor (PRR) to produce an activated PRR* species. The effector may be internalized to the cell (translocation), where it may interact reversibly with plant R protein to produce an activated R protein* species. Within the cell compartment, if there is activated PRR*, the plant also produces callose, as a proxy for PTI activity. This is degraded within the plant cell. As a proxy for PTI, callose also increases the rate at which local microbe populations decline, and acts to reduce the rate at which effector is translocated into the cell. Activated R protein* also increases the rate at which the local microbial population is depleted, as an abstraction of ETI. (b), (c) Quantitative output of the immune system model. (b) Levels of callose and pathogen (arbitrary units) over 200 time units of simulation, for systems where the host shows: no resistance response: PTI, host shows PTI only; PTI+ETS, host shows PTI only but the pathogen suppresses PTI by effector production; PTI+ETS+ETI, host exhibits PTI and ETI, but the pathogen suppresses PTI by effector production. (c) Levels of callose and pathogen (arbitrary units) after 200 time units, when a steady state has been reached, demonstrating the influence of PTI, ETI and effector action with respect to the absence of a host immune response. The profile of steady-state pathogen levels resembles the profile of the expository zigzag model. Despite its relative simplicity, and the complete lack of parameterization to a real system, the model broadly reproduces the expected features of interaction between a host cell and an invading pathogen (Figure 1). In the absence of a host immune response, the pathogen reaches an arbitrary level of one unit, and no callose deposition occurs. If only PTI is active, callose deposition occurs and the pathogen fails to reach as high a level. If the pathogen is able to introduce an effector to suppress callose deposition, the steady-state level of pathogen is increased and the amount of callose deposition reduced. Finally, a host having both PTI and ETI systems active supports the presence of the pathogen even if it introduces a PTI-suppressing effector—but in this case the amount of callose deposition is also reduced with respect to the system in which the host does not have an active ETI response. In all cases where there is a host immune response, the pathogen briefly reaches elevated levels in the locality of the cell before this level is seen to fall (due to the action of resistance mechanisms). Each alternative scenario above leads to a different steady-state level of the pathogen as an outcome. These predictive outcomes represent falsifiable hypotheses that cannot be suggested by a purely expository model such as the zigzag. The toy model additionally overcomes several limitations of the zigzag model indicated above: the time-scale and nature of interactions is explicit in the model definition; events take place concurrently during the interaction; the results are quantitative (though due to the structure of the model, and in the absence of parameter optimization, they currently have arbitrarily values). The molecular scope of the basic assumptions of this toy model, and treatment of context, is no greater than that for the zigzag model, but it is clear how further processes (such as production of host nutrient and its effect on local pathogen levels) can be integrated into the model by the addition of further terms in the model, and how parameters might be modified to reflect the immediate history of either the plant host or pathogen. Most significantly, unlike the zigzag model, the qualitative and quantitative outcomes of interaction, i.e. ETI, ETS and PTI, are not specified directly in the model description. Instead, these outcomes are predictions of the model, which may be obtained by parameterizing the model in different ways to reflect changes in the system. There are many opportunities for improvement to the model: parameterization to reflect a ‘real’ pathosystem; dependency of pathogen propagation on host nutrient production; introduction of a panel of effector proteins (possibly with different functions, such as the promotion of pathogen growth) and corresponding R genes; competition for resources; spatial elements such as pathogen mobility and an array of host cells; integration with more complex models of PTI and signalling; environmental context and influence; and so on. Even in this simplistic form, however, it still represents a tangible basis for posing reasonable hypotheses, some of which may be answered in silico and some in vitro or in vivo, that cannot be framed at all in the context of the expository zigzag model. To investigate complex, dynamic processes we will probably always benefit from having a dynamic model for the interpretation and guidance of experiment. Models such as these can guide future research towards the most critical components of dynamic systems as we best understand them at the current moment. Any reductionist investigation of a single component of even this simple model cannot give us more than a focused, fragmentary account of the host response. Understanding and interpreting the result of a reductionist experiment may itself be dependent on the behaviour of the rest of the interacting components. The implication is clear: we need to consider the biology of the system, and dynamic modelling can be a powerful tool for achieving this goal. Dynamic, quantifiable and predictive models of host–pathogen interactions, like all models, will be wrong. They are bound to be incomplete, given our current levels of understanding, but they can form the basis for asking new questions that improve our understanding and the quality of the models themselves. Expository models such as the zigzag model have great value in conceptualizing and communicating aspects of host–pathogen interactions, but they should not form the limit of our representation or understanding. In order to understand and investigate complex dynamic processes like host–microbe interactions sufficiently well, we will need to develop dynamic models of these systems and move beyond static, expository models. Figure S1 Systems Biology Graphical Notation (SBGN, http://www.sbgn.org/) representation of the toy immune system model (BioModels accession no. MODEL1408280000 http://www.ebi.ac.uk/biomodels-main/). Figure S2 Ordinary differential equation (ODE) representation of the immune system model (BioModels accession no. MODEL1408280000 http://www.ebi.ac.uk/biomodels-main/). By convention, the terms in square brackets (e.g. [PRR]) represent a nominal concentration—or, if modelled stochastically, a count—of the entity represented within the brackets. For the simulations represented in this paper, kinetic parameters (k1, k2, etc. for each model step) were set to an arbitrary value of 0.1. In this model, time, volume and concentration were set to be dimensionless, so these parameters also have no units. Please note: The publisher is not responsible for the content or functionality of any supporting information supplied by the authors. Any queries (other than missing content) should be directed to the corresponding author for the article.