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Towards modelling emergence in plant systems

Published online by Cambridge University Press:  10 July 2023

Melissa Tomkins*
Affiliation:
Computational and Systems Biology, John Innes Centre, Norwich, United Kingdom
*
Corresponding author: Melissa Tomkins; Email: [email protected]

Abstract

Plants are complex systems made up of many interacting components, ranging from architectural elements such as branches and roots, to entities comprising cellular processes such as metabolic pathways and gene regulatory networks. The collective behaviour of these components, along with the plant’s response to the environment, give rise to the plant as a whole. Properties that result from these interactions and cannot be attributed to individual parts alone are called emergent properties, occurring at different time and spatial scales. Deepening our understanding of plant growth and development requires computational tools capable of handling a large number of interactions and a multiscale approach connecting properties across scales. There currently exist few methods able to integrate models across scales, or models capable of predicting new emergent plant properties. This perspective explores current approaches to modelling emergent behaviour in plants, with a focus on how current and future tools can handle multiscale plant systems.

Type
Perspective
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This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (https://creativecommons.org/licenses/by/4.0), which permits unrestricted re-use, distribution and reproduction, provided the original article is properly cited.
Copyright
© The Author(s), 2023. Published by Cambridge University Press in association with The John Innes Centre

1. Introduction

What does it mean to say that plants are complex systems? Is the number of components the sole determinant of a system’s complexity? A mechanical clock, made up of many gears, cogs and springs, is a good example of a system with a large number of interacting components. The function of a clock is to keep time, carried out through the rotation of its hands, and the manner in which its components are assembled enable this designed function. To determine whether a clock is a complex system, we can consider the set of core features proposed to define complex systems, which include hierarchical organisation, feedback, nonlinearity, spontaneous order, robustness without central control, and emergence (Ladyman et al., Reference Ladyman, Lambert and Wiesner2013). When we evaluate clocks based on these features, it becomes clear that they would fail on most of these (with the possible exception of hierarchical organisation). Therefore, we can say that clocks are not complex systems.

Plants, on the other hand, do contain all of the core features of complex systems outlined above. They are decentralised systems that self-assemble their components across different temporal and spatial scales. There are many non-linear interactions, both within the plant and between the plant and its environment. Plants need to maintain homeostasis of water, gases, temperature and nutrients often within highly changeable environments, and this is achieved by buffering and feedback regulation. Although plants do have great phenotypic plasticity (Sultan, Reference Sultan2003), meaning a single genotype can result in varying phenotypes based on environmental factors such as nutrient and water availability, and stressors, many features of plant structure are remarkably consistent. Hierarchical organisation is a characteristic feature of biology, which is full of multilevel hierarchies from small molecules to macromolecules, to functional complexes, to subcellular compartments, to cells; from simple multicellular organisms to highly complex forms (Vanchurin et al., Reference Vanchurin, Wolf, Katsnelson and Koonin2022). But what about the last of the core features outlined by Ladyman et al. (Reference Ladyman, Lambert and Wiesner2013): emergence. What exactly is emergence?

Emergence describes any phenomenon of a system that cannot be predicted through the study of its individual parts, but is explainable by the collective activity of its parts (Long & Boudaoud, Reference Long and Boudaoud2019). So, returning to the clock example, whilst it is possible that there might be other configurations of the clock components that would also make the clock hands rotate, it is unlikely that they would do so in time intervals that correspond to seconds, minutes and hours. Most configurations of the clock components will likely do nothing at all. We thus have the case of a rather unique configuration with the functionality of a clock among many possible other configurations that do not have this property. Additionally, the function of a clock could be predicted using mechanics and kinematics if the configuration of all the components were known. Whilst the resulting position of the hands is a consequence of the clock components and their interactions, we wouldn’t say that the function emerges.

As modellers, we are interested in reproducible patterns and in trying to understand how these patterns arise, often with the goal of predicting them. Whereas predicting emergent properties from their components alone is impossible, prediction from knowledge of the components and their interactions is possible, at least in principle. Doing this requires definition of the ‘local rules’ that underly particular system behaviours. For example, reproducing the complex formation of microtubule structure has been achieved through the use of simulations based on simple local rules defining microtubule behaviour after collisions, in which shallow contacts favour coalignment (‘zippering’) and steeper collisions tend to result in depolymerisation (Dixit & Cyr, Reference Dixit and Cyr2004; Sambade et al., Reference Sambade, Pratap, Buschmann, Morris and Lloyd2012). Many emergent patterns and structures of plant systems, such as cell size, cell arrangement, microtubule formation, gene regulatory network (GRN) dynamics, and gradients of morphogens, have been characterised and modelled by defining the local rules that underlie them (Long & Boudaoud, Reference Long and Boudaoud2019). However, determining the local rules that result in emergent phenomena in plants is a significant undertaking for plant biologists and often requires extensive experimentation (Roeder, Reference Roeder2021).

One major challenge for plant modellers is how to link together models of different temporal and spatial scales, in order to obtain an integrated view of plant development and function. Many plant properties can be categorised as being emergent, from the shape and structure of each cell, which arise from interactions between factors across different scales, such as the plant DNA, and internal and external signals such as hormone gradients, light, the cytoskeleton, the plant wall, and space limitations from neighbouring cells (Kondorosi et al., Reference Kondorosi, Roudier and Gendreau2000). The interactions between plant cells then produce new emergent properties, such as tissue and organ formation, regulation of plant development, and response to external stresses such as nutrient or water restriction. Each spatial scale of a plant is composed of emergent properties arising from the interactions of properties from a smaller scale, each of which can also be viewed as emergent properties of the level below (Figure 1). Given this, the notion of attempting to track a single genotypic perturbation through the resulting individual plant phenotype, and potentially, up to the organisation of many such plants across a landscape displaying heterogeneity in soil type and weather patterns seems nigh on impossible.

Figure 1. The growth and form of plants are influenced by interconnected processes that occur at different temporal and spatial scales. For instance, the growth of roots is affected by local factors such as soil composition, water and nutrient availability, as well as plant properties like the location of primordia, growth rates, and root growth angle. These interactions result in the formation of the root structure, which in turn affects the transport of water and nutrients, and shapes the overall plant structure and form, including the shape of individual cells. This structure also affects photosynthesis through factors such as the availability of chloroplasts and shading. On a cellular level, processes like gene expression and metabolism have an impact on photosynthesis and cell-to-cell communication. This limited example illustrates how the emergent properties of plants arise from underlying interactions and how these properties can further impact the interactions that gave rise to them.

Creating integrated models with the ability to capture multiscale emergent properties can be simplified through the development of generalisable modelling formalisms. Many models involving complex systems or behaviours are designed to answer specific questions that cannot be addressed using more traditional techniques, rather than for the advancement of general theory. This was something highlighted over 20 years ago by Volker Grimm, which he termed as a need for a ‘paradigmatic’ rather than ‘pragmatic’ approach (Grimm, Reference Grimm1999). Such a focus of models on specific biological questions has also been proposed to be a barrier to progress in plant modelling (Louarn & Song, Reference Louarn and Song2020). The main focus in this perspective is therefore on models and formalisms able to characterise general rules for emergence in plant systems, and as such, I will be limiting its scope to the mathematical formalisms and software able to advance general theory of plant emergent properties. This is not intended to be an exhaustive review of models relating to plant emergence, as that would be far beyond the scope of a single paper, but will rather highlight some recent key studies on modelling formalisms at two scales of plant systems: plant architecture and plant cell processes. In addition, I will discuss multiscale models that have successfully linked together different existing models, highlighting the strengths and weaknesses of such approaches. Finally, the discussion will examine collaborations designed to facilitate the integration of models, as well as highlighting how a recent organism-centric perspective aimed at characterising living systems could be utilised to integrate plant components across scales, in order to both characterise existing and predict new emergent plant properties.

2. Modelling emergent properties in plants

The selection of an appropriate modelling tool depends upon the plant system of interest, the question to be addressed, and the relevant time and spatial scales. Different modelling formalisms exist aimed at representing plants at specific scales, and here, we look at those aimed firstly at representing how plant architecture both influences, and is influenced by, plant development, and secondly, the interactions between cellular processes and the plant as a whole.

2.1. Plant architecture as an emergent property

The structure and function of plants, like any living system, are closely linked. Plants construct themselves through the process of morphogenesis, driven by the interactions between plant components and processes, their environment, and their genetic code (Zahadat et al., Reference Zahadat, Hofstadler, Schmickl, Dorigo, Birattari, Blum, Christensen, Reina and Trianni2018). Additionally, plant growth and development take place in dynamic and often harsh environments, where plants exhibit remarkable adaptability in response to external factors such as resource competition, stress from pathogens, herbivores, and weather (Sultan, Reference Sultan2003). This raises questions about the balance between a plant’s predetermined genetic code and its development through interactions with its surroundings. Thus, models of plant morphogenesis must account for the interplay between the physical and biological processes driving development across scales, as well as the plant’s response to the environment.

Creating generalised models of the interplay between plant architecture and plant function requires formalisms able to simplify the wide range of complexity and diversity of plant shapes. Here, I only focus on those approaches best suited to generalised applications, and a more full description of the established mathematical paradigms for the formal representation of plant shape can be found in Pałubicki et al. (Reference Pałubicki, Kokosza and Burian2019). Models that account for plant architecture and how it impacts and is impacted by plant processes such as growth and development are known as functional-structural plant models (FSPMs) (Letort et al., Reference Letort, Sabatier, Okoma, Jaeger and de Reffye2020). FSPMs represent plant architecture as interconnected plant components and can explicitly handle spatial distribution of both environmental and biological processes (Godin & Sinoquet, Reference Godin and Sinoquet2005), allowing them to incorporate feedback-loops between plant structure, function, and the environment (Bongers, Reference Bongers2020). FSPMs allow for questions relating to the interplay between plant development and plant environment to be addressed, and are able to handle variability between individual plant components. A complete review and history of FSPMs can be found in Louarn and Song (Reference Louarn and Song2020).

One major consideration when developing an FSPM is how to represent the plant architecture. A commonly used formalism that can describe a wide range of plant features and types is an L-system. L-systems, short for Lindenmayer systems, are defined through a rewriting language able to generate complex patterns through repeated application of a set of production rules to a starting string (Lindenmayer, Reference Lindenmayer1968). Each L-system consists of an alphabet of symbols, a set of production rules, and the initial string. L-systems are powerful tools for generating complex patterns that exhibit self-similarity and fractal properties, and have been used to model the growth of branches, roots and flowers (Leitner et al., Reference Leitner, Klepsch, Knieß and Schnepf2010). Different extensions of the L-system language can allow for more dynamic integration of plant structure and function. Parametric L-systems have parameters associated with each rule, and can be updated according to a model of the plant physiological properties run in parallel. In addition, stochastic L-systems and context-sensitive L-systems choose rules based on random values and local contexts, such as developmental triggers, respectively (Green et al., Reference Green, Klomp, Rimmington, Sadedin, Green, Klomp, Rimmington and Sadedin2020). Another formalism based on a rewriting language, relational growth grammars (RGGs) were proposed to address some of the limitations of L-systems, such as their inability to represent the relationships between symbols, and that an additional step is required in order to create the geometry (Hemmerling et al., Reference Hemmerling, Kniemeyer, Lanwert, Kurth, Buck-Sorlin, Hemmerling, Kniemeyer, Lanwert, Kurth and Buck-Sorlin2008). RGGs are rewriting systems that are applied in parallel to graphs, with the nodes of the graphs being objects, such as plant organs, allowing for complete model information such as structure, geometry and internal state, to be accessible within a single representation (Hemmerling et al., Reference Hemmerling, Kniemeyer, Lanwert, Kurth, Buck-Sorlin, Hemmerling, Kniemeyer, Lanwert, Kurth and Buck-Sorlin2008). RGGs are implemented in the modelling environment GroIMP, which was recently used to quantify the increase in photosynthetic rates for bent shoots compared with upright shoots in cut-rose production, while demonstrating that there was no impact on the quality of the harvestable flowers from the plants with bent shoots (Zhang et al., Reference Zhang, van Westreenen, Evers, Anten and Marcelis2020).

Information about plant structure can also be encoded in a simple and general manner using multiscale tree graphs (MTGs) (Godin & Caraglio, Reference Godin and Caraglio1998). MTGs are built upon the concept that plants can be regarded as modular organisms composed of distinct units or modules with similar characteristics. Each module within an MTG represents a specific part or component of the plant, and by capturing the similarities among these modules, the MTG provides a structured and scalable representation of plant architecture. L-systems and MTGs have been used as the basis for different dynamic plant modelling software packages able to represent emergent plant growth and development, by incorporating plant architectural models with plant system feedbacks and environmental conditions. The Virtual Laboratory (vlab / L-studio) is a plant visualisation and simulation tool based on L-systems (Federl & Prusinkiewicz, Reference Federl and Prusinkiewicz1999; Karwowski & Prusinkiewicz, Reference Karwowski and Prusinkiewicz2004; Prusinkiewicz et al., Reference Prusinkiewicz, Karwowski, Měch and Hanan2000), recently used to study phyllotactic patterns in flower heads (Prusinkiewicz et al., Reference Prusinkiewicz, Zhang, Owens, Cieslak and Elomaa2022; Zhang et al., Reference Zhang, Cieslak, Owens, Wang, Broholm, Teeri, Elomaa and Prusinkiewicz2021). MTGs have been used in software such as OpenAlea (Pradal et al., Reference Pradal, Dufour-Kowalski, Boudon, Fournier and Godin2008; Reference Pradal, Coste, Boudon, Fournier and Godin2013; Reference Pradal, Fournier, Valduriez and Cohen-Boulakia2015) and AMAPstudio (Griffon & de Coligny, Reference Griffon and de Coligny2012) (Figure 2). One recent study using OpenAlea investigated canopy formation in grapevine, demonstrating that representing light interception and gas exchange for individual leaves, based on leaf nitrogen content and position in the canopy, more accurately reproduces the daily pattern of gas exchange for different canopy architectures of grapevines than using a single rate for the entire canopy (Prieto et al., Reference Prieto, Louarn, Perez Peña, Ojeda, Simonneau and Lebon2020).

Figure 2. Formalisms such as L-systems and MTGs allow for the generation of complex plant shapes and fields of individual plants. (a) L-systems enable the encoding of a complex structure within simple, iterative rules, as demonstrated by this monopodial tree-like structure and plant. Tree and plant rendered in Blender, using the lsystem add-on (https://github.com/krljg/lsystem). Script for defining these systems taken from code based on Prusinkiewicz and Lindenmayer (Reference Prusinkiewicz and Lindenmayer1990) (b) Interactions between the underlying rules for the structure development and environmental conditions can allow for different structures to emerge, such as for the squash (left) and bean (right) root systems generated with OpenRootSim (Postma et al., Reference Postma, Kuppe, Owen, Mellor, Griffiths, Bennett, Lynch and Watt2017), rendered in Blender. Entire fields (d) can be generated based on a single plant (c) with AMAPstudio (Griffon & de Coligny, Reference Griffon and de Coligny2012).

Whilst the software described above has focussed on the above ground parts of plants, OpenSimRoot is an example of a package designed to simulate plant root growth. Descriptions of the root simulations are held in XML files, and include information about the plant parameters, such as locations of root tips (primordia), root growth rates, direction and plasticity, as well as environmental conditions such as nutrient and water availability, and soil type (Postma et al., Reference Postma, Kuppe, Owen, Mellor, Griffiths, Bennett, Lynch and Watt2017). Different plant species can be defined by changes to these parameters, and the overall root shape emerges from the interactions between each growing root and its environment. A similar approach, although following an object oriented design can be found in CRootBox (Schnepf et al., Reference Schnepf, Leitner, Landl, Lobet, Mai, Morandage, Sheng, Zörner, Vanderborght and Vereecken2018), a C++ implementation of the MATLAB application, RootBox (Leitner et al., Reference Leitner, Klepsch, Knieß and Schnepf2010). Whilst RootBox was based on an L-system formalism, the choice of a move to an object-oriented approach for CRootBox was motivated by both technical and conceptual considerations. An object-oriented approach allows for inclusion of code reuse and encapsulation, making the code easier to read and understand. Additionally, it facilitates connection of the CRootBox root model to shoot models, allowing for the development of an integrated plant system able to represent the complex interplays and trade-offs faced by plants during their growth and development (Schnepf et al., Reference Schnepf, Leitner, Landl, Lobet, Mai, Morandage, Sheng, Zörner, Vanderborght and Vereecken2018). Integration with other models was further enabled by inclusion of Python bindings allowing coupling with other models, including soil and environmental models. CRootBox was demonstrated to successfully predict the response of a root with a known structure under different phosphate and water conditions (De Bauw et al., Reference De Bauw, Mai, Schnepf, Merckx, Smolders and Vanderborght2020).

Individual-based modelling (IBM), also known as agent-based modelling, is a computational approach that focuses on simulating the behaviour and interactions of individual entities, or agents, within a system. Each agent within an individual-based model has a set of rules, behaviours, and interactions with other agents and its environment. The model then simulates these behaviours and interactions over time, allowing the properties of the system to emerge. IBMs allow researchers to investigate complex systems in which variation between individuals influences the system dynamics. Such variation between individuals could be random, based on genetic mutation, arise due to differences in resources such as light or nutrients, or be based on the state of neighbours, such as hormones, or RNA expression.

A recent study developed an IBM representing wheat spikelet growth as the addition of individual units of either shoot, vegetative, inflorescence, or meristem blocks, which contained the initiation sites for both the vegetative and floral units (Backhaus et al., Reference Backhaus, Lister, Tomkins, Adamski, Simmonds, Macaulay, Morris, Haerty and Uauy2022) (Figure 3). The authors were testing a hypothesis based on their experimental data suggesting that this delayed transition could be attributed to the presence of opposing gradients of two specific genes, and the IBM was able to demonstrate that these assumptions were indeed sufficient to produce the previously unexplained lanceolate shape of developing wheat spikes. In the model, each newly formed meristem adheres to the same set of rules but can give rise to either a leaf, spikelet, or both based on the current gene profile of the two distinct classes. The individual variation observed among meristem agents is therefore influenced by the states of their neighbouring agents and the progression of time, as gene expression is influenced by the initiation of flowering. In this way, IBMs provide an excellent iterative tool for the testing and refining of hypotheses concerning emergent properties, in concert with experimental validation. For example, insight into the mechanisms behind experimental observations on how the light/gibberellin signalling pathway affects the properties of microtubules required to reorient growth was explored through the use of an IBM (Sambade et al., Reference Sambade, Pratap, Buschmann, Morris and Lloyd2012). In addition, the emergence of plant root structure has been simulated with an IBM (Zahadat et al., Reference Zahadat, Hofstadler, Schmickl, Dorigo, Birattari, Blum, Christensen, Reina and Trianni2018). Their Vascular Morphogenesis Controller algorithm, inspired by the distribution of common resources between the branches of plant, uses an individual-based representation of interaction between competing branches. Each branch explores its environment and produces auxin in response to light. This auxin flows towards the roots, adjusting the quality of its vessels along its way. In this way, there is positive feedback to paths that successfully transport auxin, and the system of vessel paths self-organises in a dynamic way, with nodes both being created and destroyed. Although this was a biologically inspired approach designed and tested for artificial systems, it could be applied to the development of real plant root systems, and their response to environmental stimulus, such as light and nutrients.

Figure 3. Individual-based models provide a perfect, iterative testing ground for hypotheses based on experimental data. An IBM developed in the agent-based modelling environment, Netlogo (Wilensky, Reference Wilensky1999), demonstrates how spikelet initiation depends upon the expression of two classes of genes: SEP and SVP (Backhaus et al., Reference Backhaus, Lister, Tomkins, Adamski, Simmonds, Macaulay, Morris, Haerty and Uauy2022). The model uses expression of SEP and SVP class genes to predict when meristems (red) produce leaf tissue (green) and when they switch to producing spike tissue (yellow). SVP suppresses SEP expression, with SVP expression itself starting to decrease once flowering is triggered, allowing SEP expression to increase (top-right graph). The middle and bottom graphs depict the gradients of SEP and SVP expression, respectively, from the basal to the apical spikelets. Leaf initiation rates are suppressed by SEP, whereas spikelet initiation requires SEP. The opposing gradients of these two genes result in delayed vegetative to floral transition of the basal spikelets.

One current challenge for FSPMs is integrating across the whole plant. Most current ‘virtual’ plants focus either on the functions of the shoot or the root, and do not include the interplays between these two parts of a plant that become critical when adapting to stressful conditions (Louarn & Song, Reference Louarn and Song2020). Whole plant modelling was the ambitious aim of a recent study that linked together a reactive transport model for variably saturated media (Min3P; Mayer et al., Reference Mayer, Amos, Molins and Gerard2012), a root architectural model (ArchiSimple; Pagès et al., Reference Pagès, Bécel, Boukcim, Moreau, Nguyen and Voisin2014), and a shoot FPSM implemented in GroImp (Evers & Bastiaans, Reference Evers and Bastiaans2016), to explore the impact of soil water availability on plant development (Braghiere et al., Reference Braghiere, Gérard, Evers, Pradal and Pagès2020). This was a challenging undertaking, as the models were developed in different computing languages, on different platforms, and by different teams from different disciplines. Linking together models in this way requires careful handling of parameters and variables, ensuring that variables being passed between different models represent the same plant characteristic, of timescales, and also of updates in terms of whether variables are updated synchronously or asynchronously, and whether updates are frequent enough. Their model was able to successfully predict plant–plant competition and regulation on stomatal conductance to drought when parameterised under different growing conditions, demonstrating the potential for such integrated approaches for FSPMs in the future.

2.2. Emergence of cells and their functions

“…in its complexity and functionality even the simplest, tiniest cell dwarfs everything humankind has ever been able to engineer…” (Wolkenhauer & Hofmeyr, Reference Wolkenhauer and Hofmeyr2007)

The previous section explored methods for representing the interplay between plant architecture and plant growth and development, and we now turn our attention to the emergence of the cell, and those processes resulting in its own fabrication, and its integration and response to the rest of the plant system.

Plant cells contain complex signalling networks, involving thousands of molecules, which have evolved to allow plants to respond to daily biotic and abiotic stressors (Struk et al., Reference Struk, Jacobs, Sánchez Martín-Fontecha, Gevaert, Cubas and Goormachtig2019). Defining the state of a cell requires knowledge of not only its size and shape, but also its components, intracellular reactions and interactions with the environment (Luthey-Schulten, Reference Luthey-Schulten2021), which vary over space and time. ‘Whole cell’ approaches aim to represent all, or at least, the most important of these processes and interactions within an individual cell. These approaches have been proposed to have several potential benefits, such as the integration of heterogeneous datasets, prediction and understanding of multi-network phenotypes, development of new hypotheses and identification of knowledge gaps for experimental design, and the generation of frameworks for the design of genetically modified organisms (Carrera & Covert, Reference Carrera and Covert2015). Core cellular components, such as cellulose, starches, proteins, fats and RNA, are often represented using particle-based reaction diffusion (PBRD). This requires implementation decisions based on the features of interest, the computational cost, and the available toolbox (Schöneberg et al., Reference Schöneberg, Ullrich and Noé2014). Difficulties in obtaining experimental data, combined with the challenges of simulating such systems on biologically relevant timescales necessitate decisions such as whether to use free (no boundaries) or confined particle diffusion, whether the particles are represented as points, or have specific volumes (allowing for crowding, etc.), and whether to include particle–particle interactions and potentials (Schöneberg et al., Reference Schöneberg, Ullrich and Noé2014). Examples of tools for cell simulations of this kind include E-Cell (Tomita et al., Reference Tomita, Hashimoto, Takahashi, Shimizu, Matsuzaki, Miyoshi, Saito, Tanida, Yugi and Venter1999), which has been mostly used for human and animal cells (Nishino et al., Reference Nishino, Yachie-Kinoshita, Hirayama, Soga, Suematsu and Tomita2013; Okubo et al., Reference Okubo, Sano, Naito and Tomita2013; Shimo et al., Reference Shimo, Arjunan, Machiyama, Nishino, Suematsu, Fujita, Tomita and Takahashi2015), but could be applied to plant cells and MCell (https://github.com/mcellteam/mcell). MCell uses spatially realistic 3D cellular models and specialised Monte Carlo algorithms to simulate the movements and reactions of molecules within and between cells. MCell has recently been integrated into Blender, a free and open-source 3D computer graphics software toolset, within CellBlender (Figure 4), allowing for robust and reproducible simulations and visualisations of cell models.

Figure 4. The CellBlender module for Blender can be used for the fast creation of simplified 3D cell models represent a limited number of relevant reactions. This screenshot is taken from the example model ‘Organelle’, and shows the interaction between surface and internal molecules of two organelles. At the start of the simulation, molecule A (dark blue) is located within the cell, outside of the organelles, and molecule B (light blue) is within organelle 2 (right). A molecules can be transported into organelle 2, through interactions with a surface molecule (green), where they interact with B molecules to produce C molecules (pink). C molecules can then interact with the surface molecule to be translocated into the cell. CellBlender development is supported by the NIGMS-funded (P41GM103712) National Center for Multiscale Modeling of Biological Systems (MMBioS).

While whole cell modelling has shown some success for minimal bacterial cells (Luthey-Schulten, Reference Luthey-Schulten2021), simulating all molecules and interactions within plant cells is not computationally tractable, due to the number of particles involved. For example, it has been estimated that an average Arabidopsis mesophyll cell contains about 25 billion protein molecules (Heinemann et al., Reference Heinemann, Künzler, Eubel, Braun and Hildebrandt2020). It has also been suggested that whole cell modelling could miss the point of mathematical modelling, which is not to realistically reproduce all molecular interactions, but to discover the general principles that determine experimental measurements (Wolkenhauer & Hofmeyr, Reference Wolkenhauer and Hofmeyr2007). In this regard, studying the intricate networks of molecular interactions within a cell can provide insights into the functioning of the cell as a whole. By focusing on these interconnected networks, researchers can gain a deeper understanding of the underlying principles that drive cellular functions and behaviours, rather than aiming for a comprehensive representation of every molecular detail.

Complex GRNs within a plant determine its final form and dynamic response to the external environment (Long et al., Reference Long, Brady and Benfey2008). There are countless examples of how the study of specific GRNs has improved our knowledge of plant sub-systems, including salt-response (Wu et al., Reference Wu, Goh, Azodi, Krishnamoorthi, Liu and Urano2021), and the development and physiological mechanisms that regulate floral transitions (Jaeger et al., Reference Jaeger, Pullen, Lamzin, Morris and Wigge2013; Madrid et al., Reference Madrid, Chandler and Coupland2021). GRNs aim to represent condition specific interactions of gene expression with the expression of target genes (Tripathi & Wilkins, Reference Tripathi and Wilkins2021). Representing the complete inventory of gene regulatory events in a cell would require a multitude of spatially and temporally resolved GRNs, plus all their interactions and output. The Arabidopsis genome has over 30,000 loci, meaning that a complete inventory of transcriptional regulation would have over 30,000 nodes. If each gene were controlled by 10–100 TFs, then such a network would have between $3\cdot 10^5$ and $3\cdot 10^6$ edges, excluding the contribution of miRNAs (Mejia-Guerra et al., Reference Mejia-Guerra, Pomeranz, Morohashi and Grotewold2012). Representing this number of connections is not computationally tractable, and so partial approaches or computational methods are needed to make predictions (Tripathi & Wilkins, Reference Tripathi and Wilkins2021).

One method that can be used to predict emergent properties of GRNs is through investigation of random Boolean networks (RBNs) (Socolar & Kauffman, Reference Socolar and Kauffman2003). RBNs consist of a set of nodes, each of which can be in one of two states: ‘on’ or ‘off’, represented by the Boolean values ‘true’ or ‘false’. These nodes are connected by randomly assigned links, and each node is assigned a Boolean function that determines their state in the next time step as a function of their neighbouring nodes. The Boolean functions are assigned randomly, meaning that the rules determining the behaviour of the network are unpredictable and nonlinear. As a result, RBNs can exhibit complex dynamics, including the emergence of patterns, self-organisation, and phase transitions. RBNs provide a simple yet powerful framework for studying the behaviour of complex systems, such as GRNs, and have contributed significantly to our understanding of features such as criticality (Torres-Sosa et al., Reference Torres-Sosa, Huang and Aldana2012), robustness (Siegal & Bergman, Reference Siegal and Bergman2002), and evolutionary capacitance (Bergman & Siegal, Reference Bergman and Siegal2003) all of which have been proposed to be emergent properties of GRNs.

Coupling GRNs with FSPMs can allow for integration between cellular-level processes and plant phenotypic development. Chew et al. (Reference Chew, Wenden, Flis, Mengin, Taylor, Davey, Tindal, Thomas, Ougham, Reffye, Stitt, Williams, Muetzelfeldt, Halliday and Millar2014) linked four different models—a carbon dynamic model (CDM), an FSPM describing individual leaf growth and how each leaf contributes to light capture, a photothermal model (PTM) that predicted the timing of flowering based on temperature, and a photoperiodism model (PPM), which is a gene dynamic model of the circadian clock—into a multiscale mathematical model of Arabidopsis. This multilevel model was able to make multilevel predictions, from individual plant components such as leaf biomass, to the level of processes, such as the flexibility of photosynthetic control, up to entire phenotypes, such as those shown by a developmentally misregulated transgenic line. Such an approach is therefore not only able to represent changes to emergent properties resulting from changes to individual system components, but also allows for investigation into plant function and development across scales. However, linking together different models in this way is not a simple task. Even though the models were written in the same language (MATLAB), and had been developed by the same two labs, linking them together required careful consideration of decisions such as choosing a standardised time-step, and connecting variables between models—for example, a simple ratio in one model was replaced with a more complex allocation from another model. Parameterising the combined model also requires careful handling; in order to avoid overfitting, they tried to retain the original model parameters as much as possible.

3. Discussion

“The purpose of a model is to capture the essence of a problem and to explore different solutions of it.” (Grimm, Reference Grimm1999)

The phenotype, function, and response of plants are the result of intricate interactions among cells, networks and architecture. These interactions, which occur across various temporal and spatial scales, give rise to emergent properties in a decentralised and robust complex system (Figure 5). In this perspective, I have introduced formalisms and technologies that can effectively represent these emergent properties of plants. However, the integration of plant emergent properties across scales remains a significant challenge for plant modellers, highlighting its continued importance in the field.

Figure 5. Integrated models of plant development can potentially be built using a modular approach that connects different models of underlying components, ranging from the cellular to the organ level. However, the large differences in temporal and spatial scales, underlying frameworks, and implementations complicate the linking of different modelling formalisms.

Connecting multiple models as modules across spatial and temporal scales is a non-trivial undertaking. Even models written in the same language, as in Chew et al. (Reference Chew, Wenden, Flis, Mengin, Taylor, Davey, Tindal, Thomas, Ougham, Reffye, Stitt, Williams, Muetzelfeldt, Halliday and Millar2014), require careful consideration and handling of time units, model parameters, and differences in the way the same variables are characterised in different models. One key problem is ensuring that the data used for validation of each model are quantitatively comparable, as recalibrating parameter values for models at different scales is time-consuming and would require coordination of data acquisition between researchers from different groups, and possibly even different disciplines (Chew et al., Reference Chew, Wenden, Flis, Mengin, Taylor, Davey, Tindal, Thomas, Ougham, Reffye, Stitt, Williams, Muetzelfeldt, Halliday and Millar2014). Although packages with the capability of linking together models written in different languages have been developed (Lang, Reference Lang2019), differences in model formalisms and implementations are likely to complicate such integrations. Progress in modular, multiscale model development could be assisted by standardising biological computational model formulation and communication, which is the aim of the Computational Modelling in Biology Network (COMBINE) (Hucka et al., Reference Hucka, Nickerson, Bader, Bergmann, Cooper, Demir, Garny, Golebiewski, Myers, Schreiber, Waltemath and Le Novère2015). COMBINE promotes a number of standard formats for model description and analysis, such as CellML, an XML-based format for the encoding of mathematical models, Systems Biology Graphical Notation (SBGN), Systems Biology Markup Language (SBML), and BioPAX (Demir et al., Reference Demir, Cary, Paley, Fukuda, Lemer, Vastrik, Wu, D’Eustachio, Schaefer, Luciano, Schacherer, Martinez-Flores, Hu, Jimenez-Jacinto, Joshi-Tope, Kandasamy, Lopez-Fuentes, Mi, Pichler and Bader2010), a language for the representation of biological pathways.

Some researchers have proposed that the development of integrated models starts with the development of an integrated perspective. One such proposed perspective—The Theory of Organisms (ToO)—has already shown great potential in the field of animal modelling. The fundamental principles of ToO include the definition of a default cell state, which includes proliferation with variation and motility, combined with the principle of organisation by closure of constraints (Carvalho, Reference Carvalho2022; Longo et al., Reference Longo, Montévil, Sonnenschein and Soto2015; Soto et al., Reference Soto, Longo, Miquel, Montevil, Mossio, Perret, Pocheville and Sonnenschein2016). For a model to be closed with respect to its constraints, each component must impact, and be impacted by, at least one other component (Figure 6). Constraint closure emphasises the interconnectedness and interdependencies between the various components of the model. In other words, no component within the model is isolated or independent; instead, they are linked through a network of constraints. This closure ensures that changes or perturbations in one component can propagate and affect other components, maintaining a cohesive and integrated behaviour of the model as a whole. The concept of constraint closure helps capture the complexity and dynamic nature of interactions between components, enabling a more comprehensive understanding of the system being modelled.

Figure 6. For a system to exhibit constraint closure, all of its processes (red) have to have at least one constraint (blue), and generate at least one other constraint for another process. Constraint closure allows the dynamics of the system to self-organise, and for the emergence of new properties in response to changes in conditions such as nutrient concentration, light and temperature. Figure based on Montévil and Mossio (Reference Montévil and Mossio2015).

Models developed from a ToO perspective require the ability to represent individual differences in their components, often at the level of individual cells. Both IBMs and cellular automata have proven to be successful formalisms for building ToO models. For example, an IBM study investigating mammary ductal morphogenesis revealed the influence of mechanical forces between cells and collagen fibres, with the organisation of collagen fibres impacting cell mobility and reproductive capabilities (Montévil & Soto, Reference Montévil, Soto and Mossio2023). Surprisingly, the model predicted occasional branching, a phenomenon observed in living organisms during mammary gland development, demonstrating the emergence of novel properties without explicit implementation of local rules. Cellular automata have been employed to develop ToO 2D models of single-layered cell cultures. These models have explored the effects of culture geometries on tissue growth (Carvalho, Reference Carvalho2023) and the influence of cell bioelectric properties on tumour growth (Carvalho, Reference Carvalho2022). For instance, the latter model demonstrated how the default cell state of proliferation and motility, combined with simple rules governing bioelectric properties can shape the organisation of bioelectric properties across the cell population, ultimately determining organism size and shape.

While not yet tested extensively in plant models, ToO could be applied to well-characterised plant processes occurring across scales, such as circadian rhythms, responses to external stimuli (defence, nutrient starvation, temperature), and inflorescence timing. One of the defining principles of ToO includes motility, and while plants are sessile organisms, they still exhibit motion over a wide range of sizes and time scales (Forterre, Reference Forterre2013). Through processes such as the generation of turgor pressure and osmosis, plants can grow towards light, open and close stomata, and induce rapid movements in response to stimuli such as the detection of insects.

Developing models from a multilevel perspective and investigating how emergent properties interact across scales holds great potential for understanding plant development and response, it is important to remember that modelling is not an attempt to recreate realism. It might appear that a logical next step would be to work towards a complete virtual plant system, with each property emerging from its underlying model components, but such a model system seems both unachievable and undesirable. Developing multiscale models involves trade-offs between the increase in model completeness, with a corresponding increase in complexity, and loss of precision (Fish et al., Reference Fish, Wagner and Keten2021). Therefore, model design should include consideration of whether the addition of multiscale interactions are essential to represent the features of interest. Determining the appropriate level of resolution can be achieved through a scaling-down process, starting from a coarse model designed to explain some pattern or observation of interest. If the model is either unable to reproduce the data, or fails to capture the parameters of interest, then the model can be extended step by step on a modular basis, with checks being carried out after each extension, to ensure that it still produces the same output in a similar fashion to each previous model (Grimm, Reference Grimm1999). Moreover, as with any experimental design, it is important to have a clear idea of how the model data will be collected, analysed and validated. Another important factor is the scope or range of applicability of the model. Model design should seek to establish the experimental conditions that the model should cover (and with what acceptable accuracy), which conditions might be considered desirable rather than essential, and which cases are out of scope.

Finally, some of the formalisms described here involve complex models, which have their own technical considerations. For instance, individual-based models have been described as being doubly complex, as they simulate complex systems using computer code that is itself complex (Vedder et al., Reference Vedder, Ankenbrand and Sarmento Cabral2021). Structural considerations then extend from the essential system components to the software and hardware platforms on which they are run, and to how the output is stored and communicated. The many recent advances both in image analysis and sequencing technologies have paved the way for simulation methods able to incorporate complex and detailed datasets. Quantitative modelling pipelines that start from experimental data and live imaging and allow researchers to test hypotheses across scales hold great potential for generating causative links between genotype to phenotype and beyond. Whether the chosen approach is modular, or organism-centric, understanding the interactions between emergent plant properties requires a fully integrated view of a plant system incorporating complexity across spatial and temporal scales.

Acknowledgements

I would like to gratefully acknowledge Richard J. Morris for his numerous helpful discussions and feedback on the manuscript and Franziska Hoerbst for reading the manuscript and offering advice and corrections.

Financial support

This article is part of a project (‘Plamorf’) that has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (Grant Agreement No. 810131).

Competing interest

The author declares no competing interests exist.

Authorship contribution

M.T. conceived and wrote the manuscript and prepared the figures.

Data availability statement

Data sharing is not applicable to this article as no new data were created or analysed in this study.

References

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Figure 0

Figure 1. The growth and form of plants are influenced by interconnected processes that occur at different temporal and spatial scales. For instance, the growth of roots is affected by local factors such as soil composition, water and nutrient availability, as well as plant properties like the location of primordia, growth rates, and root growth angle. These interactions result in the formation of the root structure, which in turn affects the transport of water and nutrients, and shapes the overall plant structure and form, including the shape of individual cells. This structure also affects photosynthesis through factors such as the availability of chloroplasts and shading. On a cellular level, processes like gene expression and metabolism have an impact on photosynthesis and cell-to-cell communication. This limited example illustrates how the emergent properties of plants arise from underlying interactions and how these properties can further impact the interactions that gave rise to them.

Figure 1

Figure 2. Formalisms such as L-systems and MTGs allow for the generation of complex plant shapes and fields of individual plants. (a) L-systems enable the encoding of a complex structure within simple, iterative rules, as demonstrated by this monopodial tree-like structure and plant. Tree and plant rendered in Blender, using the lsystem add-on (https://github.com/krljg/lsystem). Script for defining these systems taken from code based on Prusinkiewicz and Lindenmayer (1990) (b) Interactions between the underlying rules for the structure development and environmental conditions can allow for different structures to emerge, such as for the squash (left) and bean (right) root systems generated with OpenRootSim (Postma et al., 2017), rendered in Blender. Entire fields (d) can be generated based on a single plant (c) with AMAPstudio (Griffon & de Coligny, 2012).

Figure 2

Figure 3. Individual-based models provide a perfect, iterative testing ground for hypotheses based on experimental data. An IBM developed in the agent-based modelling environment, Netlogo (Wilensky, 1999), demonstrates how spikelet initiation depends upon the expression of two classes of genes: SEP and SVP (Backhaus et al., 2022). The model uses expression of SEP and SVP class genes to predict when meristems (red) produce leaf tissue (green) and when they switch to producing spike tissue (yellow). SVP suppresses SEP expression, with SVP expression itself starting to decrease once flowering is triggered, allowing SEP expression to increase (top-right graph). The middle and bottom graphs depict the gradients of SEP and SVP expression, respectively, from the basal to the apical spikelets. Leaf initiation rates are suppressed by SEP, whereas spikelet initiation requires SEP. The opposing gradients of these two genes result in delayed vegetative to floral transition of the basal spikelets.

Figure 3

Figure 4. The CellBlender module for Blender can be used for the fast creation of simplified 3D cell models represent a limited number of relevant reactions. This screenshot is taken from the example model ‘Organelle’, and shows the interaction between surface and internal molecules of two organelles. At the start of the simulation, molecule A (dark blue) is located within the cell, outside of the organelles, and molecule B (light blue) is within organelle 2 (right). A molecules can be transported into organelle 2, through interactions with a surface molecule (green), where they interact with B molecules to produce C molecules (pink). C molecules can then interact with the surface molecule to be translocated into the cell. CellBlender development is supported by the NIGMS-funded (P41GM103712) National Center for Multiscale Modeling of Biological Systems (MMBioS).

Figure 4

Figure 5. Integrated models of plant development can potentially be built using a modular approach that connects different models of underlying components, ranging from the cellular to the organ level. However, the large differences in temporal and spatial scales, underlying frameworks, and implementations complicate the linking of different modelling formalisms.

Figure 5

Figure 6. For a system to exhibit constraint closure, all of its processes (red) have to have at least one constraint (blue), and generate at least one other constraint for another process. Constraint closure allows the dynamics of the system to self-organise, and for the emergence of new properties in response to changes in conditions such as nutrient concentration, light and temperature. Figure based on Montévil and Mossio (2015).

Author comment: Towards modelling emergence in plant systems — R0/PR1

Comments

Submission of manuscript “Modelling of emergence in plant systems across scales” for the special collection on ‘Emergent Behaviour in Plants’

Dear Quantitative Plant Biology Editors,

I wish to submit my manuscript “Modelling of emergence in plant systems across scales” for consideration in the special collection on ‘Emergent Behaviour in Plants’ in Quantitative Plant Biology.

This review shows how an emergent perspective for plant systems across spatial and temporal scales has increased our understanding of the mechanisms behind processes including plant patterns across landscapes, plant response to pathogens, the success of invasive species, the development of plant form and function, and the interactions and networks within a cell. Furthermore, in this review I propose that a multi-scale framework integrating different complex models would constitute a valuable tool to explore how the individual model assumptions, and the interactions between the models, influence plant system level behaviour.

Many technologies currently exist for modelling plant systems, from the ecological down to the cellular level, and this review summarises the current research, discussing the considerations behind selecting each approach. As such, it will be of great interest to modellers, and quantitative plant biologists who are interested in understanding the spatio-temporal complexity of plants and plant systems.

I think that Quantitative Plant Biology would be an ideal journal for this review that would allow it to reach its target readership most effectively.

I thank you for your consideration and look forward to hearing from you.

Sincerely,

Melissa Tomkins

Corresponding Author:

Melissa S. Tomkins

Department of Computational and Systems Biology

The John Innes Centre

Norwich Research Park

Norwich NR4 7UH

Email: [email protected]

Review: Towards modelling emergence in plant systems — R0/PR2

Conflict of interest statement

Reviewer declares none.

Comments

Nice summarizing opinion paper. The author proposes that ‘understanding and predicting plant form and function requires <…> a multiscale approach able to link together emergent properties across different scales’. While I wholeheartedly agree with this statement, it is by no means a novel view. This proposition has been put forward in some shape or form in various other such works in the recent and less recent past. While this does not invalidate the current manuscript, I do feel the author does not make explicitly clear what novel approach modelling plant systems really needs right now.

Abstract

• The abstract contains too many abstract terms. Please make sure the abstract becomes more concrete and clear by shortly defining (or give examples of) ‘plant systems’, ‘components’, ‘parts’, ‘interactions’, ‘properties’.

Introduction

• Please try to be concrete and close to the subject of this study, the plant. What does it really mean that ‘plants self-organise into patterns’? A plant is a pattern? In what? Intuitively I understand what the author wants to say, but I challenge the author to write such things down with in more directly understandable terms.

• The introduction seems to communicate plant structure and functioning is the emergent property of interactions between all underlying components. Only at the end of the second paragraph, the author acknowledges the role of ‘the environment’. I propose the role of environmental influence on plant structure and functioning to be stressed from the start, as plants are so well known to be able to tailor their functioing as well as their shape to the environment they live in. They are highly plastic in that sense, and I feel this aspect is underrepresented in the introduction. Of course this plasticity has a genetic nature, so this link could be made.

Spatial patterns in the distribution of land plants

• This section focuses on the mechanisms governing distribution of plants in an area, and feels a bit disconnected from the introduction. 1) In the firsat half of the introduction, there the focus was much more on the emergence of plant functioning based on interactions between plant internal processes, rather than between individual plants given rise to specific patterns. The whole DNA paragraph does not apply to this section on spatial patterns at all. 2) The second half of the intro does treat such spatial patterns but deals with animals, and is merely meant to explain the terms emergence and self-organisation; so also this part of the introduction does not seem to link naturally to the current section on spatial patterns of land plants. I recommend the author to try to make the introduction a bit more balanced to cover both the plant as an emergent property itself, as well as the driver of higher-scale emergent properties such as plant distribution patterns.

• PDE is introduced as a abbeviation twice. Please remove the second instance (end of paragraph 1 on page 5).

Emergence of plants stucture and function

• The (Bongers 2020) reference seems to be missing from the literature list.

• The line ‘Once we reduce growth to modules and the links between them, then increasing or reducing complexity becomes a simple question of adding or removing modules’ is not completely clear. ‘Growth’ in plants is the increase in biomass and/or size, which in FSPMs is usually simulated as the increase in these traits of the modules themselves. Adding modules could also represent growth, seeing the use of modules makes growth of the whole plant a discrete process; however oftentimes adding modules relates more to development of plants rather than growth, i.e. the appearance of new organs that where not there before, like a new leaf or new side root. Please consider this and possibly reword this line.

• Expanding on my earlier remark, I feel this section does not do justice to the immense fexilibity of plants to adapt to their growth environment, shaped by surrounding plants. Plants are extremely plastic and this is often captured by such models by combining both the underlying internal rules as well as the effect of shade/nutrient depletion, etc. Please see if this aspect can be improved to make this piece more generally applicable.

Emergence of cells and their functions

• I feel ‘a complete representation of the inner workings of a cell’ is overstating it. This cannot be achieved, due to the simple fact we do not know yet of exactly all the inner workings. It will never be complete. Please tone this down.

• What I miss is a link between this section and the previous one on whole plants. In fact also a link to the section on plant distribution. Now, the three sections are basically isoloated descriptions treating 3 scale levels, but it would be very interesting to discuss the (im)possibilities and (in)sensibility of trying to make whole plants emergence from subcellular processes, or trying to make plant distributions the result of sub-plant processes. Spanning scales. This very much relates to the question what are the boudaries of the system of interest, at what level do I want to predict and thus at what level do mechanisms need to be defined. Perhaps this could be embedded in the discussion actually. The current discussion does go in this direction but mostly treat model complexity and not necessarily the number of scales crossed within a model, and whether or not that is useful at all.

Review: Towards modelling emergence in plant systems — R0/PR3

Conflict of interest statement

Reviewer declares none

Comments

This manuscript describes concepts of emergence and self organization in plants. The text describes a wide range of concepts and their application across multiple scales. There are many interesting ideas described in the manuscript, and it is potentially a good fit for QPB.

Some suggestions which would strengthen the manuscript:

The emphasis of the text appears to be on the modelling approaches used to simulate these processes. While examples are provided, they description is not particularly in depth. A detailed investigation of specific examples where these have yielded meaningful biological insights would provide the reader a greater insight into the value of such models.

A range of scales are covered ranging from cells to ecosystems. A more focused approach may be fruitful, allowing for a more detailed exploration of modelling concepts and their application in a given context. Perhaps the spatial-ecological scale as this is most clearly described.

The article’s exploration of the quantification of emergence could be strengthened for this submission to QPB. Quantitative approaches are not explored to a high degree in the text – for example statistical spatial analysis of patterns generated using models vs observed data. Quantitative network-based approached from the labs of Saket Navlakah, George Bassel and Zoran Nikoloski have applied these to the organism, tissue and cell levels, respectively. Engagement with this literature would strengthen the thesis of this manuscript.

Figure on Page 2 of the PDF- contains many concepts but it is not coherent. Ideas are placed in non-intuitive places, and linked in unexpected ways. It is not clear how the ideas are flowing based on this graphic.

Would it be possible to remake the figure in such a way that follows a clear logical flow? For example, Plant structure and plant function are separate boxes which have arrows pointing to FPSMs and Virtual Plants. It is not particularly clear what this means.

The introduction briefly explains some concepts in self organization and emergence. This is a very difficult thing to do as it is both introducing complex ideas while relying on the reader having an understanding of others (i.e. PDEs). Describing these concepts to a general plant science audience which does not rely upon them having intimate knowledge of different modelling approaches would make this more accessible.

Minor points:

Adding more references to the introduction would also be beneficial.

Text is in large blocks. Separating these into smaller paragraphs would make it easier to read.

Lack of line numbers makes it difficult to flag issues in text.

Instances where references were intended to be added but were not: “their resulting Turing patterns (refs)”

Recommendation: Towards modelling emergence in plant systems — R0/PR4

Comments

While both reviewers agree that the subject of the article is of interest, they have also indicated several major points in need of improvement. One such point is what this review -which in its subject is not novel- adds to existing work, and a clearer formulation of the directions the field should move towards in the discussion. Different parts of the paper are not always clearly or logically linked, and there is a strong focus on modeling approaches with less attention for what this has brought in terms of biological insight. We ask the author to carefully consider the reviewers suggestions to amend these issues.

Decision: Towards modelling emergence in plant systems — R0/PR5

Comments

No accompanying comment.

Author comment: Towards modelling emergence in plant systems — R1/PR6

Comments

No accompanying comment.

Review: Towards modelling emergence in plant systems — R1/PR7

Conflict of interest statement

Reviewer declares none.

Comments

This review aims to discuss emergence in plants and their ecology, and different modelling approaches to study this. Specifically, one of the listed aims is to discuss how these models may be coupled to understand emergence across scales. I would first like to say that I agree with the premise and that the aims are interesting and ambitious. I was not familiar with some of the modelling formalisms that were discussed, so it has been already a useful resource for me – and I expect it could be useful for other people too. I would therefore like to see it published once some of the issues with the current version are addressed.

Some model formalisms are discussed at much greater length than others. Often, it remains unclear how the model works, what kinds of questions it addresses, and what actually emerges (and how) from lower-level interactions. This makes it difficult to see how these models were useful in revealing such emergence. There is also little discussion on how the models could be integrated in a conceptual or practical manner, which means that the aims of the review aren’t really reached. I’m also not sure that a strong case has been made for why we should aim for this integration – could you discuss in your introduction what questions we then address, that are still open now? Finally, while a large range of models is discussed, tissue-scale cell-based models of gene expression regulation are conspicuously missing, though they are such prime examples of emergence and may have good integration possibilities.

The review may benefit from constraining the scope a bit, to tie it closer together. There seems to be an emphasis on models to do with plant physiology and metabolism. If you limit the scope to that type of models and how they could be integrated, you could establish a clearer connection between levels and discuss the questions and models in greater depth. At that point, you could choose not to discuss those cellbased models I mentioned before if that is out of scope. Choose those models which you think are particularly suited for integration into others, and leave out those that are unfeasible.

Introduction: you make a distinction between self-organisation and emergence, which is nice but not entirely clear to me. Is self-organisation a form (or subset) of emergent behaviour? Is there a distinction to be made at what level the behaviour is -- ie with self-organisation, you focus on an ordered pattern of the individual components, while emergence can be at a much higher scale?

Specific lines:

L28-31: “To combat these challenges, plants have evolved a high level of structural and functional diversity, including complex signalling networks involving 1000s of molecules, such as proteins, nucleic acids, lipids, chromatin, and low-molecular weight compounds”

What do you mean with diversity? At which level, that of species, or diversity in the kinds of compounds they produce?

L 62: “individuals” – do you mean components?

L91: why do you also need statisticians? You made the case for models (and computational biology) only, and your review only considers simulation.

L219: You switch from morphogenesis to physiological models that don’t seem to actually model development, just take into account a fixed plant structure – this is a bi tconfusing. Or do FSPMs incorporate actual growth and development? If so, please make this clearer.

L159: what are these “individual plant dynamics” and why did they matter? You risk saying “it’s important” without showing why.

L188: why is that the goal? What question would this answer?

L 222: what are examples of such biological processes? You mention a model later, so it would be helpful to know what they included as “individual leaf processes” (L 227)

L245: didn’t the FSPM already divide the plant up into modules?

L259: Please replace the explanation about Lindenmayer with an explanation of what Lsystems do; and how can they be coupled to other levels, or how are they an example of emergence?

L271: What does MTG stand for?

L280: It seems that MTGs are just a data format then, not an actual model – What makes this different from other modular approaches?

L284: Why would one use spatial density functions, versus Lsystems or MTG or FSPMs? What are the emergent properties?

L352: Wasn’t morphographx the only cell-based model? The others seemed to have branches or leaves as the basic unit.

L367: probably missing a word here.

L370: what are modules here? The subcellular components?

L394: what do/can these particles represent?

L431: I can infer how these might be integrated with higher-level modules, but it would be good to describe that explicitly

L443: I find the discussion of GRNs quite odd – especially because there are various plant models (not discussed in this review) which do an excellent job of extracting the relevant GRN module for tissue patterning, showing how pattern emerges from gene interactions and tissue dynamics. Think of Henrik Jonsson’s and Kirsten ten Tusscher’s models, just to name two. They don’t represent all regulation going on in the cell, but that is not the point.

L448: I think discussing ML is an odd choice, since I’m not sure how they show emergence in plant biology. If included, please discuss this

Review: Towards modelling emergence in plant systems — R1/PR8

Conflict of interest statement

Reviewer declares none

Comments

The review discuses the concepts of emergence and self-organization in the context of plant development and ecosystems. In this context, it highlights 1) select models and frameworks that simulate plant patterns at different scales (eco-system, individual, architectural, cellular and sub-cellular) and 2) possible paths towards achieving multiscale simulations. These are interesting, actively researched topics. Moreover, despite longstanding efforts in many modeling communities, methods to easily and rigorously link the abstractions used to model biological systems at different scales are lacking. In this sense, the review is timely, and highlights a number of recent interesting works.

While I enjoyed the overall topic of the review, it comes across as somewhat inconsistent in it’s coverage of the area, as well as the conceptual underpinnings and difficulties that must be addressed in constructing multi-scale models.

I believe that the insights into methodologies for multiscale modeling need to be refined. A focus throughout appears to be that the use of modularization (the division of a model into well-defined sub-units) and abstraction (representing reality without attempting to recreate it exactly) are important paths towards the creation of multi-scale models. As these are both well-known and broadly applied model concepts, this perspective seems to underestimate the difficulties in establishing multi-scale modeling frameworks. Similarly, I feel the many difficulties incurred in building plant models that can account for the addition and removal of modules is likewise underestimated. For instance, formalisms like L-system that allow for the modeling of branching structures via the addition and removal of modules took several decades to develop. Equivalent formalisms able to handle growing cellular structures in a straight forward and extendible manner have yet to be properly developed.

There are several other aspects of the manuscript that make the coverage of materials seem inconsistent:

1) The manuscript discusses a limited slice of related works. It is never clearly articulated what reasoning guided the inclusion vs exclusion of examples, and source material. This makes the examples presented, as well as the conclusions drawn from them, feel much less compelling.

2) The description of source material and concepts is often superficial. General approaches and formalisms are not presented clearly enough to appreciate the key features or the distinctions between them. For example, despite having worked with L-systems, IBMs (agent-based models) and MTGs I could not reconcile the description with my understanding. Also, L-systems and IBMs are general enough that almost all phenomena at the ecosystem and architectural level can be modelled – thus teasing out the distinctions and relative advantages of each requires some subtlety. Similarly, a more complete presentation of GeMMs would be very helpful. At present, it seems difficult to understand the stated advantages and disadvantages of approaches without substantial review of the cited literature (beyond what I would expect in a review).

3) There is almost no comment on the substantial work modeling emergence at the scale of cellular tissues and organs in plants (for example, see Long and Boudaoud, Emergence of robust patterns from local rules during plant development, Current Opinion in Plant Biology 2019). As modeling tissues typically requites a graph-based topology (as opposed to a branching structure), it benefits from distinct formalisms (e.g. Cellular Potts, Virtual Leaf, Cell Complexes) and has led to issues and concepts that are somewhat distinct from those occurring at other scales.

Adding additional details and discussion to the manuscript may help address these concerns. Also, better indicating the scope as well as the intended audience for the review may help address these points. If presented more as a survey of some key recent works, the manuscript would feel more internally consistent (although the rationale for which works are considered in detail would need to be expanded).

Additional comments:

1) The use of module is confusing throughout, especially with regards to the topics discussed. In some cases it is used in an architectural sense (e.g. metamer, fruit or flower) and in other cases in a functional sense.

2) Some sentences are repeated almost verbatim, which should be avoided (e.g. Lines 58-61 & 39-40; )

3) Incorporating environmental heterogeneity is repeatedly highlighted as an issue for more coarse grained models (e.g. PDEs). However, these factors are often represented via continuous maps which are quite compatible with PDE based approaches. More details is required to appreciate what specific issues are being highlighted.

4) Starting on Line 293, MorphoGraphX is discussed. As this section is mostly focused on the macroscopic/architectural level (i.e. branching structures) this feels very out of place. MGX is intended for studies at the microscopic scale. Other tools are used to quantify 2d/3d organ form at macroscopic scales (e.g. geometric morphometrics, morphospaces, persistent homology, etc..).

Recommendation: Towards modelling emergence in plant systems — R1/PR9

Comments

Dear Melissa,

Due to unavailability of the reviewers that read the first version of your manuscript, a second set of reviewers was invited to evaluate the revised version of your manuscript. As you will see in their comments very similar issues were raised as by the first reviewers. After having a look at the manuscript myself I agree that these issues have indeed not yet been resolved.

Although we appreciate your efforts in revising the manuscript, it still appears to suffer from a lack of coherence and focus for it to deliver a strong message or conclusion, and as such it will require extensive major revisions. Both reviewers have provided concrete suggestions for such a revision. As an alternative to such extensive rewriting you may choose to submit your manuscript elsewhere.

Kind regards,

Kirsten ten Tusscher

Decision: Towards modelling emergence in plant systems — R1/PR10

Comments

No accompanying comment.

Author comment: Towards modelling emergence in plant systems — R2/PR11

Comments

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Review: Towards modelling emergence in plant systems — R2/PR12

Conflict of interest statement

Reviewer declares none.

Comments

I appreciate that the author has made a lot of changes to the manuscript, and I think much has improved. The introduction reads like an introduction, and the models are better connected to each other. I think the focus on just plant- and cell level modelling also improved the review. However, there are still some general and particular things that need addressing.

The introduction states that the focus of the review is on “...formalisms that are able to characterise general rules for emergence in plant systems [..]”. But what are some of these general rules that were found with these formalisms? It would be good if this could be highlighted for each formalism; the specific models using these formalisms that are discussed seem to be addressing rather specific questions instead of general principles. Likewise, since the review focuses on emergent properties, these need to be highlighted beyond the introduction section. Right now, in section 2.1 and 2.2, the discussion of the formalisms is remains on the technical side. Please be more explicit about what emerges in the specific models that are discussed, and how the formalisms accommodate the study of this emergence.

I got confused by the last two paragraphs of section 2.2. It starts by acknowledging the usefulness of specific GRNs. It then (probably correctly) claims that simulating all possible interactions between all possible genes is unfeasible. But the problem seems not, as line 373 says, to be “limited data” but computational power (more and more transcriptomics data roll in by the day). The proposed alternative, of random Boolean networks, feels slightly old-fashioned and not very plant-specific. What about those partial approaches mentioned in line 360-362? We don’t expect all genes to be active in all tissues at all times.

My main issue is with the new section on “A theory of Organisms”, which is proposed as an alternative to the “modular” approaches of the two sections before. As far as I can tell, this theory is not a model formalism, but a philosophical perspective on the concept of (modelling) organisms in biology. The description of the theory is quite jargon-y and abstract: how should I understand variation – is it between organisms or cells within the organism? And how literal should we take motility: what biological process does it correspond to? Throughout the section it remains unclear how to put this philosophy/framework into practice when modelling plants. A final gripe I have with this section is that it contains two of the longest descriptions of models and their outcomes, and these are models of animals rather than plants. How the theory of organisms is put into practice in these animal models also remains unclear.

If this section is to stay, it needs to be much clearer how this theory of organisms actually translates to an (organismal or cellular) model, how it is different from the models in the other sections, and why we need it for plants. The final sentence, that the Theory of Organisms leads to more tractable models, needs more explanation too.

The figures are nice but could be referred to in the text more to support what is written. The legends vary a lot in detail and what they discuss about the model, this could be more consistent.

Specific comments:

L 31: spurious “of”

introduction, L71-80: I don’t really understand the distinction between a bottom-up approach and defining the local rules. What constitutes a rule? And does a bottom-up approach always have to start from the absolute bottom or necessarily include all known particles? I would consider partial approaches, that start from building blocks at one level to study emergent properties a higher level, also bottom-up (to be contrasted with top-down). Please clarify the distinction.

L148: The examples given in this section, like Zhang et al., 2020, seem pretty specific rather than generalised. Do you mean that the formalism should be general, so that it can be used to build multiple different specific models?

L186-189: How does this new representation change the kind of models that can be built with RGGs compared to L-systems?

Figure 2: The reference to the book by Prusinkiewicz and Lindenmayer lists the wrong year of publication (should be 1990 I think). Google citations often gets this wrong with older books.

It would be nice if the different elements of the figure were referred to in the text, with an explanation of how this result demonstrates emergence.

L 249: what are the traditional methods that are contrasted with IBMs here?

L250-258: It looks like a cool model, but how does the fact that the modules are Agents make a difference here, compared to the aforementioned L-systems, RGGs and MTGs (aka how do interactions between agents yield the wheat spike)?

L266-274: this is a nice description where it is more clear what the agents do and what emerges.

Figure 3: The figure is not very informative – what do SVP and SEP refer to in the top right graph; what are the sliding handles for, and what is in the two graphs? If the figure is there to demonstrate a toolbox, please provide a short explanation of the capabilities; otherwise, explain more what are the different elements in the picture and the graphs.

L 315-316: slightly redundant sentence, maybe a copy/paste error?

L320-324: why do these models have these benefits?

Figure 4: Is this figure possibly mirrored? I could not quite line up the description with the picture.

L351: I agree with this statement – but should this not be mentioned a bit earlier? And it seems to me that the model displayed in figure 4 is not a “whole-cell model” but focuses on relevant interactions, which seems both sensible and doable.

L403: Could you specify what were the emergent properties in the model/approach mentioned?

L495: “the” and “of” switched

L496: “be” → “been”

Review: Towards modelling emergence in plant systems — R2/PR13

Conflict of interest statement

Reviewer declares none.

Comments

I very much appreciate the detailed revisions undertaken by the author to address reviewer comments. These efforts have improved the manuscript substantially.

I would still encourage the author to more fully articulate the rationale for inclusion of particular models throughout, but my concern on this point has been mostly addressed at this point.

The manuscript still appears to review things more from the perspective of metabolic pathways/physiology, and it would be helpful if this was mentioned more explicitly in the introduction.

Additional comments:

1) Line 442: Here it is stated that the “Theory of Organisms” relies on proliferation with variation and motility. It’s unclear to me how this translates to plant tissues, where cells cannot move relative to each other.

Minor comments:

1) In several places, the manuscript tacitly assume emergence from chemical reactions without explicitly stating this, which leads to some confusion:

Line 61-63: “if all we could control as experimentalists was, for instance, the identity and concentration of components”. Biological experiments have a richer repertoire than the targeted application of substances in varying concentrations.

Line 71-72: “the number of particles and their interactions…”. Perhaps rephrase to “the number of molecules and potential interactions in biological systems…”.

2) Line 131: “how plant architecture forms plant development” sounds very strange to me, perhaps “shapes” would be better?

3) Line 149: “interplay between plant architecture” is ambiguous, interplay with what? On the same line, do you want to “simplify the wide range of complexity and diversity of plant shapes”, or simplify their representation (or the models reproducing them)?

4) Line 202: L-systems are a rewriting system, and hence provide a dynamic representation of both architecture as well as state values. I’m not sure what you mean by “static” in this instance.

5) Line 422: Previous models, which did not employ the “theory of organisms”, also have been extensively used to predict new emergent properties.

Recommendation: Towards modelling emergence in plant systems — R2/PR14

Comments

As you will see from the reviewers comments, despite them appreciating that the manuscript has significantly improved, they still raise some important issues. Most important among those is the extent to which matters such as models being suited for discovering and deciphering emergent properties are being explicitly highlighted in sections coming after the introduction, or the link with plant modeling to the final more philosophical and animal research oriented section.

At the same time we appreciate that you have put in considerable efforts and went through several iterations. As a solution, we propose to change the article format from review into perspective. This would target the article somewhat more as an introduction to non experts to enhance their capacity to interact with modelers and would require relatively limited rewriting.

Decision: Towards modelling emergence in plant systems — R2/PR15

Comments

No accompanying comment.

Author comment: Towards modelling emergence in plant systems — R3/PR16

Comments

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Recommendation: Towards modelling emergence in plant systems — R3/PR17

Comments

No accompanying comment.

Decision: Towards modelling emergence in plant systems — R3/PR18

Comments

No accompanying comment.