A computational framework for cortical microtubule dynamics in realistically shaped plant cells

Microtubule simulations in plant biology: A field coming to maturity

The plant cortical microtubule array is an important determinant of cell wall structure and, therefore, plant morphology and physiology. The array consists of dynamic microtubules interacting through frequent collisions. Since the discovery by Dixit and Cyr (2004) that the outcome of such collisions depends on the collision angle, computer simulations have been indispensable in studying array behaviour. Over the last decade, the available simulation tools have drastically improved: multiple high-quality simulation platforms exist with specific strengths and applications. Here, we review how these platforms differ on the critical aspects of microtubule nucleation, flexibility, and local orienting cues; and how such differences affect array behaviour. Building upon concepts and control parameters from theoretical models of collective microtubule behaviour, we conclude that all these factors matter in the debate about what is most important for orienting the array: local cues like mechanical stresses or global cues deriving from the cell geometry.

A Stochastic Model of Cortical Microtubule Anchoring and Mechanics Provides Regulatory Control of Microtubule Shape

The organization of cortical microtubule arrays play an important role in the development of plant cells. Until recently, the direct mechanical influence of cell geometry on the constrained microtubule (MT) trajectories have been largely ignored in computational models. Modelling MTs as thin elastic rods constrained on a surface, a previous study examined the deflection of MTs using a fixed number of segments and uniform segment lengths between MT anchors. It is known that the resulting MT curves converge to geodesics as the anchor spacing approaches zero. In the case of long MTs on a cylinder, buckling has been found for transverse trajectories. There is a clear interplay between two factors in the problem of deflection: curvature of the membrane and the lengths of MT segments. Here, we examine the latter in detail, in the backdrop of a circular cylinder. In reality, the number of segments are not predetermined and their lengths are not uniform. We present a minimal, realistic model treating the anchor spacing as a stochastic process and examine the net effect on deflection. We find that, by tuning the ratio of growth speed to anchoring rate, it is possible to mitigate MT deflection and even prevent buckling for lengths significantly larger than the previously-derived critical buckling length. We suggest that this mediation of deflection by anchoring might provide cells with a means of preventing arrays from deflecting away from the transverse orientation.

Probing stress-regulated ordering of the plant cortical microtubule array via a computational approach

BACKGROUND

Morphological properties of tissues and organs rely on cell growth. The growth of plant cells is determined by properties of a tough outer cell wall that deforms anisotropically in response to high turgor pressure. Cortical microtubules bias the mechanical anisotropy of a cell wall by affecting the trajectories of cellulose synthases in the wall that polymerize cellulose microfibrils. The microtubule cytoskeleton is often oriented in one direction at cellular length-scales to regulate growth direction, but the means by which cellular-scale microtubule patterns emerge has not been well understood. Correlations between the microtubule orientation and tensile forces in the cell wall have often been observed. However, the plausibility of stress as a determining factor for microtubule patterning has not been directly evaluated to date.

RESULTS

Here, we simulated how different attributes of tensile forces in the cell wall can orient and pattern the microtubule array in the cortex. We implemented a discrete model with transient microtubule behaviors influenced by local mechanical stress in order to probe the mechanisms of stress-dependent patterning. Specifically, we varied the sensitivity of four types of dynamic behaviors observed on the plus end of microtubules - growth, shrinkage, catastrophe, and rescue - to local stress. Then, we evaluated the extent and rate of microtubule alignments in a two-dimensional computational domain that reflects the structural organization of the cortical array in plant cells.

CONCLUSION

Our modeling approaches reproduced microtubule patterns observed in simple cell types and demonstrated that a spatial variation in the magnitude and anisotropy of stress can mediate mechanical feedback between the wall and of the cortical microtubule array.

The mechanics of plant morphogenesis

Understanding the mechanism by which patterned gene activity leads to mechanical deformation of cells and tissues to create complex forms is a major challenge for developmental biology. Plants offer advantages for addressing this problem because their cells do not migrate or rearrange during morphogenesis, which simplifies analysis. We synthesize results from experimental analysis and computational modeling to show how mechanical interactions between cellulose fibers translate through wall, cell, and tissue levels to generate complex plant tissue shapes. Genes can modify mechanical properties and stresses at each level, though the values and pattern of stresses differ from one level to the next. The dynamic cellulose network provides elastic resistance to deformation while allowing growth through fiber sliding, which enables morphogenesis while maintaining mechanical strength.

The microtubule end-binding proteins EB1 and Patronin modulate the spatiotemporal dynamics of myosin and pattern pulsed apical constriction

Apical constriction powers amnioserosa contraction during Drosophila dorsal closure. The nucleation, movement and dispersal of apicomedial actomyosin complexes generates pulsed apical constrictions during early closure. Persistent apicomedial and circumapical actomyosin complexes drive unpulsed constrictions that follow. Here, we show that the microtubule end-binding proteins EB1 and Patronin pattern constriction dynamics and contraction kinetics by coordinating the balance of actomyosin forces in the apical plane. We find that microtubule growth from moving Patronin platforms governs the spatiotemporal dynamics of apicomedial myosin through the regulation of RhoGTPase signaling by transient EB1-RhoGEF2 interactions. We uncover the dynamic reorganization of a subset of short non-centrosomally nucleated apical microtubules that surround the coalescing apicomedial myosin complex, trail behind it as it moves and disperse as the complex dissolves. We demonstrate that apical microtubule reorganization is sensitive to Patronin levels. Microtubule depolymerization compromised apical myosin enrichment and altered constriction dynamics. Together, our findings uncover the importance of reorganization of an intact apical microtubule meshwork, by moving Patronin platforms and growing microtubule ends, in enabling the spatiotemporal modulation of actomyosin contractility and, through it, apical constriction.

Cycling in a crowd: Coordination of plant cell division, growth, and cell fate

The reiterative organogenesis that drives plant growth relies on the constant production of new cells, which remain encased by interconnected cell walls. For these reasons, plant morphogenesis strictly depends on the rate and orientation of both cell division and cell growth. Important progress has been made in recent years in understanding how cell cycle progression and the orientation of cell divisions are coordinated with cell and organ growth and with the acquisition of specialized cell fates. We review basic concepts and players in plant cell cycle and division, and then focus on their links to growth-related cues, such as metabolic state, cell size, cell geometry, and cell mechanics, and on how cell cycle progression and cell division are linked to specific cell fates. The retinoblastoma pathway has emerged as a major player in the coordination of the cell cycle with both growth and cell identity, while microtubule dynamics are central in the coordination of oriented cell divisions. Future challenges include clarifying feedbacks between growth and cell cycle progression, revealing the molecular basis of cell division orientation in response to mechanical and chemical signals, and probing the links between cell fate changes and chromatin dynamics during the cell cycle.

Cytoplasmic Linker Protein-Associating Protein at the Nexus of Hormone Signaling, Microtubule Organization, and the Transition From Division to Differentiation in Primary Roots

The transition from cell division to differentiation in primary roots is dependent on precise gradients of phytohormones, including auxin, cytokinins and brassinosteroids. The reorganization of microtubules also plays a key role in determining whether a cell will enter another round of mitosis or begin to rapidly elongate as the first step in terminal differentiation. In the last few years, progress has been made to establish connections between signaling pathways at distinct locations within the root. This review focuses on the different factors that influence whether a root cell remains in the division zone or transitions to elongation and differentiation using Arabidopsis thaliana as a model system. We highlight the role of the microtubule-associated protein CLASP as an intermediary between sustaining hormone signaling and controlling microtubule organization. We discuss new, innovative tools and methods, such as hormone sensors and computer modeling, that are allowing researchers to more accurately visualize the belowground growth dynamics of plants.

Shaping the Organ: A Biologist Guide to Quantitative Models of Plant Morphogenesis

Organ morphogenesis is the process of shape acquisition initiated with a small reservoir of undifferentiated cells. In plants, morphogenesis is a complex endeavor that comprises a large number of interacting elements, including mechanical stimuli, biochemical signaling, and genetic prerequisites. Because of the large body of data being produced by modern laboratories, solving this complexity requires the application of computational techniques and analyses. In the last two decades, computational models combined with wet-lab experiments have advanced our understanding of plant organ morphogenesis. Here, we provide a comprehensive review of the most important achievements in the field of computational plant morphodynamics. We present a brief history from the earliest attempts to describe plant forms using algorithmic pattern generation to the evolution of quantitative cell-based models fueled by increasing computational power. We then provide an overview of the most common types of "digital plant" paradigms, and demonstrate how models benefit from diverse techniques used to describe cell growth mechanics. Finally, we highlight the development of computational frameworks designed to resolve organ shape complexity through integration of mechanical, biochemical, and genetic cues into a quantitative standardized and user-friendly environment.

Solving the Puzzle of Shape Regulation in Plant Epidermal Pavement Cells

The plant epidermis serves many essential functions, including interactions with the environment, protection, mechanical strength, and regulation of tissue and organ growth. To achieve these functions, specialized epidermal cells develop into particular shapes. These include the intriguing interdigitated jigsaw puzzle shape of cotyledon and leaf pavement cells seen in many species, the precise functions of which remain rather obscure. Although pavement cell shape regulation is complex and still a long way from being fully understood, the roles of the cell wall, mechanical stresses, cytoskeleton, cytoskeletal regulatory proteins, and phytohormones are becoming clearer. Here, we provide a review of this current knowledge of pavement cell morphogenesis, generated from a wealth of experimental evidence and assisted by computational modeling approaches. We also discuss the evolution and potential functions of pavement cell interdigitation. Throughout the review, we highlight some of the thought-provoking controversies and creative theories surrounding the formation of the curious puzzle shape of these cells.

TANGLED1 mediates microtubule interactions that may promote division plane positioning in maize

The microtubule cytoskeleton serves as a dynamic structural framework for mitosis in eukaryotic cells. TANGLED1 (TAN1) is a microtubule-binding protein that localizes to the division site and mitotic microtubules and plays a critical role in division plane orientation in plants. Here, in vitro experiments demonstrate that TAN1 directly binds microtubules, mediating microtubule zippering or end-on microtubule interactions, depending on their contact angle. Maize tan1 mutant cells improperly position the preprophase band (PPB), which predicts the future division site. However, cell shape–based modeling indicates that PPB positioning defects are likely a consequence of abnormal cell shapes and not due to TAN1 absence. In telophase, colocalization of growing microtubules ends from the phragmoplast with TAN1 at the division site suggests that TAN1 interacts with microtubule tips end-on. Together, our results suggest that TAN1 contributes to microtubule organization to ensure proper division plane orientation.

Graph prolongation convolutional networks: explicitly multiscale machine learning on graphs with applications to modeling of cytoskeleton

We define a novel type of ensemble graph convolutional network (GCN) model. Using optimized linear projection operators to map between spatial scales of graph, this ensemble model learns to aggregate information from each scale for its final prediction. We calculate these linear projection operators as the infima of an objective function relating the structure matrices used for each GCN. Equipped with these projections, our model (a Graph Prolongation-Convolutional Network) outperforms other GCN ensemble models at predicting the potential energy of monomer subunits in a coarse-grained mechanochemical simulation of microtubule bending. We demonstrate these performance gains by measuring an estimate of the Floating Point OPerations spent to train each model, as well as wall-clock time. Because our model learns at multiple scales, it is possible to train at each scale according to a predetermined schedule of coarse vs. fine training. We examine several such schedules adapted from the algebraic multigrid literature, and quantify the computational benefit of each. We also compare this model to another model which features an optimized coarsening of the input graph. Finally, we derive backpropagation rules for the input of our network model with respect to its output, and discuss how our method may be extended to very large graphs.

A plausible mechanism for longitudinal lock-in of the plant cortical microtubule array after light-induced reorientation

The light-induced reorientation of the cortical microtubule array in dark-grown Arabidopsis thaliana hypocotyl cells is a striking example of the dynamical plasticity of the microtubule cytoskeleton. A consensus model, based on katanin-mediated severing at microtubule crossovers, has been developed that successfully describes the onset of the observed switch between a transverse and longitudinal array orientation. However, we currently lack an understanding of why the newly populated longitudinal array direction remains stable for longer times and re-equilibration effects would tend to drive the system back to a mixed orientation state. Using both simulations and analytical calculations, we show that the assumption of a small orientation-dependent shift in microtubule dynamics is sufficient to explain the long-term lock-in of the longitudinal array orientation. Furthermore, we show that the natural alternative hypothesis that there is a selective advantage in severing longitudinal microtubules, is neither necessary nor sufficient to achieve cortical array reorientation, but is able to accelerate this process significantly.

Unlocking the mechanisms behind the formation of interlocking pavement cells

The leaf epidermal pavement cells with the puzzle-piece shape offer an attractive system for studying the mechanisms underpinning cell morphogenesis in a plant tissue. The formation of the interdigitated lobes and indentations in these interlocking cells relies on the integration of chemical and mechanical signals and cell-to-cell signals to establish interdigitated polar sites defining lobes and indentations. Recent computational and experimental studies have suggested new roles of cell walls, their interplay with mechanical signals, cell polarity signaling regulated by auxin and brassinosteriods, and the cytoskeleton in the regulation of pavement cell morphogenesis. This review summarizes the current state of knowledge on these regulatory mechanisms behind pavement cell morphogenesis in plants and discusses how they could be integrated spatiotemporally to generate the interdigitated polarity patterns and the interlocking shape in pavement cells.

Cytoskeletal organization in isolated plant cells under geometry control

The cytoskeleton plays a key role in establishing robust cell shape. In animals, it is well established that cell shape can also influence cytoskeletal organization. Cytoskeletal proteins are well conserved between animal and plant kingdoms; nevertheless, because plant cells exhibit major structural differences to animal cells, the question arises whether the plant cytoskeleton also responds to geometrical cues. Recent numerical simulations predicted that a geometry-based rule is sufficient to explain the microtubule (MT) organization observed in cells. Due to their high flexural rigidity and persistence length of the order of a few millimeters, MTs are rigid over cellular dimensions and are thus expected to align along their long axis if constrained in specific geometries. This hypothesis remains to be tested in cellulo Here, we explore the relative contribution of geometry to the final organization of actin and MT cytoskeletons in single plant cells of Arabidopsis thaliana We show that the cytoskeleton aligns with the long axis of the cells. We find that actin organization relies on MTs but not the opposite. We develop a model of self-organizing MTs in three dimensions, which predicts the importance of MT severing, which we confirm experimentally. This work is a first step toward assessing quantitatively how cellular geometry contributes to the control of cytoskeletal organization in living plant cells.

The importance of being edgy: cell geometric edges as an emerging polar domain in plant cells

Polarity is an essential feature of multicellular organisms and underpins growth and development as well as physiological functions. In polyhedral plant cells, polar domains at different faces have been studied in detail. In recent years, cell edges (where two faces meet) have emerged as discrete spatial domains with distinct biochemical identities. Here, we review and discuss recent advances in our understanding of cell edges as functional polar domains in plant cells and other organisms, highlighting conceptual parallels and open questions regarding edge polarity.

The 2020 motile active matter roadmap

Activity and autonomous motion are fundamental in living and engineering systems. This has stimulated the new field of 'active matter' in recent years, which focuses on the physical aspects of propulsion mechanisms, and on motility-induced emergent collective behavior of a larger number of identical agents. The scale of agents ranges from nanomotors and microswimmers, to cells, fish, birds, and people. Inspired by biological microswimmers, various designs of autonomous synthetic nano- and micromachines have been proposed. Such machines provide the basis for multifunctional, highly responsive, intelligent (artificial) active materials, which exhibit emergent behavior and the ability to perform tasks in response to external stimuli. A major challenge for understanding and designing active matter is their inherent nonequilibrium nature due to persistent energy consumption, which invalidates equilibrium concepts such as free energy, detailed balance, and time-reversal symmetry. Unraveling, predicting, and controlling the behavior of active matter is a truly interdisciplinary endeavor at the interface of biology, chemistry, ecology, engineering, mathematics, and physics. The vast complexity of phenomena and mechanisms involved in the self-organization and dynamics of motile active matter comprises a major challenge. Hence, to advance, and eventually reach a comprehensive understanding, this important research area requires a concerted, synergetic approach of the various disciplines. The 2020 motile active matter roadmap of Journal of Physics: Condensed Matter addresses the current state of the art of the field and provides guidance for both students as well as established scientists in their efforts to advance this fascinating area.

The Winner Takes It All: Auxin-The Main Player during Plant Embryogenesis

In plants, the first asymmetrical division of a zygote leads to the formation of two cells with different developmental fates. The establishment of various patterns relies on spatial and temporal gene expression, however the precise mechanism responsible for embryonic patterning still needs elucidation. Auxin seems to be the main player which regulates embryo development and controls expression of various genes in a dose-dependent manner. Thus, local auxin maxima and minima which are provided by polar auxin transport underlie cell fate specification. Diverse auxin concentrations in various regions of an embryo would easily explain distinct cell identities, however the question about the mechanism of cellular patterning in cells exposed to similar auxin concentrations still remains open. Thus, specification of cell fate might result not only from the cell position within an embryo but also from events occurring before and during mitosis. This review presents the impact of auxin on the orientation of the cell division plane and discusses the mechanism of auxin-dependent cytoskeleton alignment. Furthermore, close attention is paid to auxin-induced calcium fluxes, which regulate the activity of MAPKs during postembryonic development and which possibly might also underlie cellular patterning during embryogenesis.

Formal description of plant morphogenesis

Plant morphogenesis may be characterized by complex feedback mechanisms between signals specifying growth and by the growth of the plant body itself. Comprehension of such feedback mechanisms is an ongoing research task and can be aided with formal descriptions of morphogenesis. In this review, we present a number of established mathematical paradigms that are useful to the formal representation of plant shape, and of biomechanical and biochemical signaling. Specifically, we discuss work from a range of research areas including plant biology, material sciences, fluid dynamics, and computer graphics. Treating plants as organized systems of information processing allows us to compare these different mathematical methods in terms of their expressive power of biological hypotheses. This is an attempt to bring together a large number of computational modeling concepts and make them accessible to the analytical as well as empirical student of plant morphogenesis.

Emergence of robust patterns from local rules during plant development

The formation of spatial and temporal patterns is an essential component of organismal development. Patterns can be observed on every level from subcellular to organismal and may emerge from local rules that correspond to the interactions between molecules, cells, or tissues. The emergence of robust patterns may seem in contradiction with the prominent heterogeneity at subcellular and cellular scales, however it has become increasingly clear that heterogeneity can be instrumental for pattern formation. Here we review recent examples in plant development, involving genetic regulation, cell arrangement, growth and signal gradient. We discuss how patterns emerge from local rules, whether heterogeneity is stochastic or can be patterned, and whether stochastic noise is amplified or requires filtering for robust patterns to be achieved. We also stress the importance of modelling in investigating such questions.

Cellular basis of growth in plants: geometry matters

The growth of individual cells underlies the development of biological forms. In plants, cells are interconnected by rigid walls, fixing their position with respect to one another and generating mechanical feedbacks between cells. Current research is shedding new light on how plant growth is controlled by physical inputs at the level of individual cells and growing tissues. In this review, we discuss recent progress in our understanding of the cellular basis of growth from a biomechanical perspective. We describe the role of the cell wall and turgor pressure in growth and highlight the often-overlooked role of cell geometry in this process. It is becoming apparent that a combination of experimental and theoretical approaches is required to answer new emerging questions in the biomechanics of plant morphogenesis. We summarise how this multidisciplinary approach brings us closer to a unified understanding of the generation of biological forms in plants.

Mechanics, geometry and genetics of epidermal cell shape regulation: different pieces of the same puzzle

Pavement cells in the leaf epidermis of many plant species have intricate shapes that fit together much like the pieces of a jigsaw puzzle. They provide an accessible system to understand the development of complex cell shape. Since a protrusion in one cell must fit into the indentation in its neighbor, puzzle cells are also a good system to study how cell shape is coordinated across a plant tissue. Although molecular mechanisms have been proposed for both the patterning and coordination of puzzle cells, evidence is accumulating that mechanical and/or geometric cues may play a more significant role than previously thought.

Quantitative and Comparative Analysis of Global Patterns of (Microtubule) Cytoskeleton Organization with CytoskeletonAnalyzer2D

The microtubule cytoskeleton plays important roles in cell morphogenesis. To investigate the mechanisms of cytoskeletal organization, for example, during growth or development, in genetic studies, or in response to environmental stimuli, image analysis tools for quantitative assessment are needed. Here, we present a method for texture measure-based quantification and comparative analysis of global microtubule cytoskeleton patterns and subsequent visualization of output data. In contrast to other approaches that focus on the extraction of individual cytoskeletal fibers and analysis of their orientation relative to the growth axis, CytoskeletonAnalyzer2D quantifies cytoskeletal organization based on the analysis of local binary patterns. CytoskeletonAnalyzer2D thus is particularly well suited to study cytoskeletal organization in cells where individual fibers are difficult to extract or which lack a clearly defined growth axis, such as leaf epidermal pavement cells. The tool is available as ImageJ plugin and can be combined with publicly available software and tools, such as R and Cytoscape, to visualize similarity networks of cytoskeletal patterns.

Organogenesis at the Shoot Apical Meristem

Lateral organ initiation at the shoot apical meristem involves complex changes in growth rates and directions, ultimately leading to the formation of leaves, stems and flowers. Extensive molecular analysis identifies auxin and downstream transcriptional regulation as major elements in this process. This molecular regulatory network must somehow interfere with the structural elements of the cell, in particular the cell wall, to induce specific morphogenetic events. The cell wall is composed of a network of rigid cellulose microfibrils embedded in a matrix composed of water, polysaccharides such as pectins and hemicelluloses, proteins, and ions. I will discuss here current views on how auxin dependent pathways modulate wall structure to set particular growth rates and growth directions. This involves complex feedbacks with both the cytoskeleton and the cell wall.

Multi-scale regulation of cell branching: Modeling morphogenesis

Plant growth and development are driven by extended phases of irreversible cell expansion generating cells that increase in volume from 10- to 100-fold. Some specialized cell types define cortical sites that reinitiate polarized growth and generate branched cell morphology. This structural specialization of individual cells has a major importance for plant adaptation to diverse environments and practical importance in agricultural contexts. The patterns of cell shape are defined by highly integrated cytoskeletal and cell wall systems. Microtubules and actin filaments locally define the material properties of a tough outer cell wall to generate complex shapes. Forward genetics, powerful live cell imaging experiments, and computational modeling have provided insights into understanding of mechanisms of cell shape control. In particular, finite element modeling of the cell wall provides a new way to discover which cell wall heterogeneities generate complex cell shapes, and how cell shape and cell wall stress can feedback on the cytoskeleton to maintain growth patterns. This review focuses on cytoskeleton-dependent cell wall patterning during cell branching, and how combinations of multi-scale imaging experiments and computational modeling are being used to unravel systems-level control of morphogenesis.

Microtubule nucleation and organization without centrosomes

Centrosomes play various critical roles in animal cells such as microtubule nucleation and stabilization, mitotic spindle morphogenesis, and spindle orientation. Land plants have lost centrosomes and yet must execute many of these functions. Recent studies have revealed the crucial roles played by morphologically distinct cytoplasmic microtubule-organizing centers (MTOCs) in initiating spindle bipolarity and maintaining spindle orientation robustness. These MTOCs resemble centrosomes in many aspects, implying an evolutionary divergence of MT-organizing structures in plants. However, their functions rely on conserved nucleation and amplification mechanisms, indicating a similarity in MT network establishment between animals and plants. Moreover, recent characterization of a plant-specific MT minus-end tracking protein suggests that plants have developed functionally equivalent modules to stabilize and organize MTs at minus ends. These findings support the theory that plants overcome centrosome loss by utilizing modified but substantially conserved mechanisms to organize MT networks.

Getting into shape: the mechanics behind plant morphogenesis

The process of shape change in cells and tissues inevitably involves the modification of structural elements, therefore it is necessary to integrate mechanics with biochemistry to develop a full understanding of morphogenesis. Here, we discuss recent findings on the role of biomechanics and biochemical processes in plant cell growth and development. In particular, we focus on how the plant cytoskeleton components, which are known to regulate morphogenesis, are influenced by biomechanical stress. We also discuss new insights into the role that pectin plays in biomechanics and morphogenesis. Using the jigsaw-shaped pavement cells of the leaf as a case study, we review new findings on the biomechanics behind the morphogenesis of these intricately-shaped cell types. Finally, we summarize important quantitative techniques that has allowed for the testing and the generation of hypotheses that link biomechanics to morphogenesis.

Predicting Division Planes of Three-Dimensional Cells by Soap-Film Minimization

One key aspect of cell division in multicellular organisms is the orientation of the division plane. Proper division plane establishment contributes to normal plant body organization. To determine the importance of cell geometry in division plane orientation, we designed a three-dimensional probabilistic mathematical model to directly test the century-old hypothesis that cell divisions mimic soap-film minima. According to this hypothesis, daughter cells have equal volume and the division plane occurs where the surface area is at a minimum. We compared predicted division planes to a plant microtubule array that marks the division site, the preprophase band (PPB). PPB location typically matched one of the predicted divisions. Predicted divisions offset from the PPB occurred when a neighboring cell wall or PPB was directly adjacent to the predicted division site to avoid creating a potentially structurally unfavorable four-way junction. By comparing divisions of differently shaped plant cells (maize [Zea mays] epidermal cells and developing ligule cells and Arabidopsis thaliana guard cells) and animal cells (Caenorhabditis elegans embryonic cells) to divisions simulated in silico, we demonstrate the generality of this model to accurately predict in vivo division. This powerful model can be used to separate the contribution of geometry from mechanical stresses or developmental regulation in predicting division plane orientation.

Predicting Division Planes of Three-Dimensional Cells by Soap-Film Minimization

One key aspect of cell division in multicellular organisms is the orientation of the division plane. Proper division plane establishment contributes to normal plant body organization. To determine the importance of cell geometry in division plane orientation, we designed a three-dimensional probabilistic mathematical model to directly test the century-old hypothesis that cell divisions mimic soap-film minima. According to this hypothesis, daughter cells have equal volume and the division plane occurs where the surface area is at a minimum. We compared predicted division planes to a plant microtubule array that marks the division site, the preprophase band (PPB). PPB location typically matched one of the predicted divisions. Predicted divisions offset from the PPB occurred when a neighboring cell wall or PPB was directly adjacent to the predicted division site to avoid creating a potentially structurally unfavorable four-way junction. By comparing divisions of differently shaped plant cells (maize [Zea mays] epidermal cells and developing ligule cells and Arabidopsis thaliana guard cells) and animal cells (Caenorhabditis elegans embryonic cells) to divisions simulated in silico, we demonstrate the generality of this model to accurately predict in vivo division. This powerful model can be used to separate the contribution of geometry from mechanical stresses or developmental regulation in predicting division plane orientation.

A Plausible Microtubule-Based Mechanism for Cell Division Orientation in Plant Embryogenesis

Oriented cell divisions are significant in plant morphogenesis because plant cells are embedded in cell walls and cannot relocate. Cell divisions follow various regular orientations, but the underlying mechanisms have not been clarified. We propose that cell-shape-dependent self-organization of cortical microtubule arrays is able to provide a mechanism for determining planes of early tissue-generating divisions and may form the basis for robust control of cell division orientation in the embryo. To show this, we simulate microtubules on actual cell surface shapes, from which we derive a minimal set of three rules for proper array orientation. The first rule captures the effects of cell shape alone on microtubule organization, the second rule describes the regulation of microtubule stability at cell edges, and the third rule includes the differential effect of auxin on local microtubule stability. These rules generate early embryonic division plane orientations and potentially offer a framework for understanding patterned cell divisions in plant morphogenesis.