Are microtubules tension sensors?

Mechanical stimulation prevents impairment of axon growth and overcompensates microtubule destabilization in cellular models of Alzheimer's disease and related Tau pathologies

Alzheimer's disease (AD) and related tauopathies such as frontotemporal dementia (FTD) or traumatic brain injury (TBI) are neurodegenerative disorders characterized by progressive loss of memory and cognitive function. The main histopathological features of AD are amyloid-β plaques and Tau neurofibrillary tangles, suggested to interfere with neuronal function and to cause microtubule (MT) destabilization. We recently demonstrated that low mechanical forces promote MT stabilization, which in turn promotes axon growth and neuronal maturation. As neurites may become dystrophic due to MT destabilization in tauopathies, we hypothesized that force-induced MT stabilization is neuroprotective in cell models subjected to tauopathy-like stress. We set up two different pathological cellular models subjecting them to AD-related Tau pathology stressors. We found that exposure of mouse primary neurons to Tau oligomers and neurons derived from human induced pluripotent stem cell (hiPSC) to amyloid-β oligomers resulted in neurotoxic effects such as axonal shortening, reduction in dendrite number, and MT destabilization. Mechanical stimulation (i) prevented delays in axonal extensions and dendrite sprouting, restoring axon outgrowth to physiological levels, and (ii) compensated for axonal MT destabilization by increasing MT stability to levels higher than in control conditions. In summary, we here demonstrate that low mechanical force can be used as a neuroprotective extrinsic factor to prevent MT destabilization and axon degeneration caused by AD-like or tauopathy-like stressors.

The CIN-TCP transcription factors regulate endocycle progression and pavement cell size by promoting cell wall pectin degradation

In plants, endoreplication, the process where nuclear DNA replicates in the absence of mitosis, and remodeling of the primary cell walls are both coupled with cell expansion. However, the mechanisms by which these two processes coordinate to determine cell size remain largely elusive. Here, employing the tcpΔ7 septuple mutant disabling seven of the eight CIN-TCP transcription factors in Arabidopsis, we find that hindered endoreplication progression in tcpΔ7 whereby ploidy increases from 8 C to beyond is correlated with an increase in cell wall pectin. CIN-TCPs transcriptionally activate POLYGALACTURONASE LIKE 1 (PGL1), which encodes a polygalacturonase downregulating both abundance and molecular mass of pectin polymers. Genetic analysis of PGL1 in both the wild type and tcpΔ7 backgrounds confirm that pectin reduction promotes endocycle progression and cell enlargement. Collectively, these findings reveal a critical role of pectin in regulating endoreplication, providing insights in the understanding of cell growth and organ development in plants.

Between Host and Invaders: The Subcellular Cell Wall Dynamics at the Plant-Pathogen Interface

Plant-pathogen interactions have profound ecological implications and are crucial for food security. Usually studied at the two extreme scales of plant organ symptomatology and host-microbe molecules, they are a cell-cell event mainly occurring at the subcellular level of the plant apoplast. Here, the cell walls of both organisms suffer an intense alteration as a consequence of active degradation by the opponent and self-protection mechanisms to survive and continue growing. The plant cell wall modifications and their role in defense as danger signals and activators of signaling cascades have been studied for a few decades, mainly at the organ plane. Still, much remains unknown about this process, including cellular and subcellular minority decorations, proteins, and mechanical cues. Comparatively, the microbial cell wall changes in planta are virtually unexplored. By investigating the interface between plant and microbial cell walls biochemically, structurally, and mechanically, we aim to highlight the dynamic interplay in these subcellular areas and its significance for the host-invader interaction.

Modulation of morphogenesis and metabolism by plant cell biomechanics: from model plants to traditional herbs

The quality of traditional herbs depends on organ morphogenesis and the accumulation of active pharmaceutical ingredients. While recent research highlights the significance of cell mechanobiology in model plant morphogenesis, our understanding of mechanical signal initiation and transduction in traditional herbs remains incomplete. Recent studies reveal a close correlation between cell wall (CW) biosynthesis and active ingredient production, yet the role of cell mechanics in balancing morphogenesis and secondary metabolism is often overlooked. This review explores how the cell wall, plasma membrane, cytoskeleton, and vacuole collaborate to regulate cell mechanics and respond to mechanical changes. We propose CW biosynthesis as a hub in connecting cell mechanics with secondary metabolism and emphasize that understanding the relationship between mechanical remodeling and secondary metabolism could provide new insights into plant cell mechanobiology and the breeding of high-quality herbs.

Three levels of heterogeneity - growth of Arabidopsis leaf epidermis

BACKGROUND

Growth of leaf epidermis is symplastic, i.e. cell contacts are preserved, but strongly heterogeneous because of variation in cell identity and differentiation status. Heterogeneous growth requires coordination to allow a predictable leaf shape to be formed. Here we investigate growth heterogeneity and coordination using expanding leaf epidermis of Arabidopsis (Arabidopsis thaliana) as a model system. We first analyse relationships between heterogeneity of epidermis growth at different scales: from subcellular via cellular to tissue scale. Next, based on the heterogeneity analysis, we verify the hypothesis that growth heterogeneity and coordination are affected by microtubule defects in mor1-1 mutant treated with high temperature.

RESULTS

Using microbeads labelling and original protocols to compute growth we show high growth heterogeneity of epidermal pavement cells at cellular and subcellular scales, and influence of stomata lineage on pavement cells growth. However, despite this high growth variation between cells (cellular scale) and within cells (subcellular scale), growth coordination is revealed at the tissue (supracellular) scale by the pattern of streamlines that follow subcellular growth directions. In leaf epidermis of mor1-1 plants treated with high temperature we reveal local disturbances in growth coordination, which are related to contact changes between cells that are likely a consequence of aberrant cytokinesis and reduction of cell adhesion. Otherwise, the growth pattern in high-temperature treated mor1-1 is similar to the non-treated mor1-1 and wild type. The high temperature treatment results only in a tendency to increase growth heterogeneity in the mutant more than in wild type grown in the same conditions.

CONCLUSIONS

Overall, our study reveals high heterogeneity of growth within and between cells of leaf epidermis. Despite this heterogeneity, a defined supracellular growth pattern exists that changes in time. Our analysis shows only a weak and likely indirect influence of defective microtubules on leaf epidermis growth.

Microtubule Reorganization and Quiescence: an Intertwined Relationship

Quiescence is operationally defined as a reversible proliferation arrest. This cellular state is central to both organism development and homeostasis, and its dysregulation causes many pathologies. The quiescent state encompasses very diverse cellular situations depending on the cell type and its environment. Further, quiescent cell properties evolve with time, a process that is thought to be the origin of aging in multicellular organisms. Microtubules are found in all eukaryotes and are essential for cell proliferation as they support chromosome segregation and intracellular trafficking. Upon proliferation cessation and quiescence establishment, the microtubule cytoskeleton was shown to undergo significant remodeling. The purpose of this review is to examine the literature in search of evidence to determine whether the observed microtubule reorganizations are merely a consequence of quiescence establishment or if they somehow participate in this cell fate decision.

Visualization of Apical-Basal Stress Polarity Regulating Directed Cell Migration with a FRET-Based Biosensor

Intracellular morphological apical-basal polarity, regulated by conserved polarity proteins, plays a crucial role in cell migration and metastasis. In this study, using a genetically encoded Förster resonance energy transfer (FRET) biosensor to visually present the spatiotemporal stress state between the lipid rafts on the membrane and the linked actin, we first provide the evidence for the existence of intrinsic apical-basal stress polarity in tumor cells and demonstrate that this polarity is a prerequisite for the formation of flow-induced front-back stress polarity. Interestingly, our study revealed that the front-back stress polarity disappeared upon the disruption of intrinsic apical-basal stress discrepancy, resulting in a large attenuated cell migration activity reduced from 76.2 ± 3.5% to 10 ± 4.9%. This unexpected discovery not only highlights the significance of apical-basal stress polarity as another factor influencing cell migration but also indicates that the disruption of apical-basal polarity in stress might be a novel therapeutic approach for tumor metastasis.

Mechanical stimulation in plants: molecular insights, morphological adaptations, and agricultural applications in monocots

Mechanical stimulation, including wind exposure, is a common environmental factor for plants and can significantly impact plant phenotype, development, and growth. Most responses to external mechanical stimulation are defined by the term thigmomorphogenesis. While these morphogenetic changes in growth and development may not be immediately apparent, their end-results can be substantial. Although mostly studied in dicotyledonous plants, recently monocot grasses, particularly cereal crops, have received more attention. This review summarizes current knowledge on mechanical stimulation in plants, particularly focusing on the molecular, physiological, and phenological responses in cereals, and explores practical applications to sustainably improve the resilience of agricultural crops.

Longitudinal growth of the Saccharina kelp embryo depends on actin filaments that control the formation of a corset-like structure composed of alginate

The initiation of embryogenesis in the kelp Saccharina latissima is accompanied by significant anisotropy in cell shape. Using monoclonal antibodies, we show that this anisotropy coincides with a spatio-temporal pattern of accumulation of alginates in the cell wall of the zygote and embryo. Alginates rich in guluronates as well as sulphated fucans show a homogeneous distribution in the embryo throughout Phase I of embryogenesis, but mannuronate alginates accumulate mainly on the sides of the zygote and embryo, disappearing as the embryo enlarges at the start of Phase II. This pattern depends on the presence of cortical actin filaments. In contrast, within the embryo lamina, the alginate composition of the walls newly formed by cytokinesis is not affected by the depolymerisation of actin filaments. Thus, in addition to revealing the existence of a mannuronate-rich alginate corset-like structure that may restrict the enlargement of the zygote and the embryo, thereby promoting the formation of the apico-basal growth axis, we demonstrate stage- and cytoskeleton-dependent differences in cell wall deposition in Saccharina embryos.

Tubulin Acetylation Enhances Microtubule Stability in Trabecular Meshwork Cells Under Mechanical Stress

Purpose

To study the roles of tubulin acetylation and cyclic mechanical stretch (CMS) in trabecular meshwork (TM) cells and their impact on outflow pathway physiology and pathology.

Methods

Primary TM cell cultures were subjected to CMS (8% elongation, 24 hours), and acetylated α-tubulin at lysine 40 (Ac-TUBA4) was assessed by western blotting and immunofluorescence. Enzymes regulating tubulin acetylation were identified via siRNA-mediated knockdowns of ATAT1, HDAC6, and SIRT2. Ac-TUBA4 levels were compared between glaucomatous (GTM) and non-glaucomatous (NTM) TM cells and in frozen sections of human cadaver eyes. The effect of tubulin acetylation on substrate stiffness and cell contractility was evaluated by culturing cells on substrates with varying stiffness and by collagen gel contraction assays, respectively. Microtubule stability was examined by monitoring resistance to nocodazole-induced depolymerization. The in vivo effect on intraocular pressure (IOP) was evaluated following intracameral injections of tubacin in mice.

Results

CMS induced tubulin acetylation in human TM cells by downregulating the deacetylase HDAC6. Elevated Ac-TUBA4 levels were observed in GTM compared NTM cells and tissues. Tubulin acetylation was not affected by substrate stiffness and did not show a direct effect on TM cell contractility. Tubulin acetylation was found to provide protection against microtubule destabilization induced by nocodazole. Importantly, intracameral injection of tubacin, an HDAC6 inhibitor, significantly lowered IOP in mice.

Conclusions

Our study highlights a critical role of tubulin acetylation in TM cell response to mechanical stress and its potential impact on IOP regulation. Tubulin acetylation could represent a therapeutic target for glaucoma.

Interplay of force and local mechanisms in axonal plasticity and beyond

The interactions between mechanical forces and neuronal dynamics have long intrigued researchers. Several studies revealed that force plays a pivotal role in shaping axonal outgrowth. However, the molecular mechanisms underpinning force-driven axonal plasticity remain not completely elucidated. This review explores the relationship between force and axonal plasticity, with a focus on local mechanisms, including local translation and axonal transport, and the emerging concept of force-driven cross-talk, a dialogue in which local dynamics are tightly regulated. Recent experimental evidence suggests that microtubules may serve as key mediators of this cross-talk, orchestrating the coordination between local mechanisms and facilitating mass addition.

The mutual influence of microtubules and the cortical ER on their coordinated organisation

The endoplasmic reticulum (ER) is the largest organelle in terms of membrane content, occupying the entire cytoplasmic volume. It is tethered to the cell cortex through ER-plasma membrane contact sites (EPCS). Previous studies have shown that EPCSs labelled by VAP27 align with cortical microtubules, and that ER tubules elongate along microtubules. Here, we addressed the question whether this relationship is bidirectional, with EPCSs influencing microtubule organisation. Using TIRF microscopy to track EPCSs and microtubule dynamics simultaneously, we demonstrate that while EPCSs remain stable, microtubules are highly dynamic and can adjust their positioning based on nearby EPCS in Arabidopsis cotyledon epidermis. In lobes of epidermal cells enclosed by two indentations, where microtubules bundle together, EPCSs flank the bundles and exhibit a distinctive arrangement, forming symmetric arcs in relation to the lobe axis. In guard cells, transversely oriented ER tubules co-align with microtubules. Disrupting microtubules with the drug oryzalin leads to transient guard cells-ER remodelling, followed by its reorganisation into transverse tubules before microtubule recovery. Taken together our observations suggest, that the positioning of EPCSs and cortical microtubules, can affect each other and the organisation of cortical ER.

Heterogeneity in Mechanical Properties of Plant Cell Walls

The acquisition and utilization of cell walls have fundamentally shaped the plant lifestyle. While the walls provide mechanical strength and enable plants to grow and occupy a three-dimensional space, successful sessile life also requires the walls to undergo dynamic modifications to accommodate size and shape changes accurately. Plant cell walls exhibit substantial mechanical heterogeneity due to the diverse polysaccharide composition and different development stages. Here, we review recent research advances, both methodological and experimental, that shed new light on the architecture of cell walls, with a focus on the mechanical heterogeneity of plant cell walls. Facilitated by advanced techniques and tools, especially atomic force microscopy (AFM), research efforts over the last decade have contributed to impressive progress in our understanding of how mechanical properties are associated with cell growth. In particular, the pivotal importance of pectin, the most complex wall polysaccharide, in wall mechanics is rapidly emerging. Pectin is regarded as an important determinant for establishing anisotropic growth patterns of elongating cells. Altogether, the diversity of plant cell walls can lead to heterogeneity in the mechanical properties, which will help to reveal how mechanical factors regulate plant cell growth and organ morphogenesis.

Mechanical forces instruct division plane orientation of cambium stem cells during radial growth in Arabidopsis thaliana

Robust regulation of cell division is central to the formation of complex multi-cellular organisms and is a hallmark of stem cell activity. In plants, due to the absence of cell migration, the correct placement of newly produced cell walls during cell division is of eminent importance for generating functional tissues and organs. In particular, during the radial growth of plant shoots and roots, precise regulation and organization of cell divisions in the cambium are essential to produce adjacent xylem and phloem tissues in a strictly bidirectional manner. Although several intercellular signaling cascades have been identified to instruct tissue organization during radial growth, the role of mechanical forces in guiding cambium stem cell activity has been frequently proposed but, so far, not been functionally investigated on the cellular level. Here, we coupled anatomical analyses with a cell-based vertex model to analyze the role of mechanical stress in radial plant growth at the cell and tissue scale. Simulations based on segmented cellular outlines of radially growing Arabidopsis hypocotyls revealed a distinct stress pattern with circumferential stresses in cambium stem cells, which coincided with the orientation of cortical microtubules. Integrating stress patterns as a cue instructing cell division orientation was sufficient for the emergence of typical cambium-derived cell files and agreed with experimental results for stress-related tissue organization in confining mechanical environments. Our work thus underlines the significance of mechanical forces in tissue organization through self-emerging stress patterns during the growth of plant organs.

Regulation of cytoskeleton dynamics and its interplay with force in plant cells

The plant cytoskeleton is an intricate network composed of actin filaments and microtubules. The cytoskeleton undergoes continuous dynamic changes that provide the basis for rapidly responding to intrinsic and extrinsic stimuli, including mechanical stress. Microtubules can respond to alterations of mechanical stress and reorient along the direction of maximal tensile stress in plant cells. The cytoskeleton can also generate driving force for cytoplasmic streaming, organelle movement, and vesicle transportation. In this review, we discuss the progress of how the plant cytoskeleton responds to mechanical stress. We also summarize the roles of the cytoskeleton in generating force that drive organelles and nuclear transportation in plant cells. Finally, some hypotheses concerning the link between the roles of the cytoskeleton in force response and organelle movement, as well as several key questions that remain to be addressed in the field, are highlighted.

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 cellulose synthesis inhibitor affects cellulose synthase complex secretion and cortical microtubule dynamics

P4B (2-phenyl-1-[4-(6-(piperidin-1-yl) pyridazin-3-yl) piperazin-1-yl] butan-1-one) is a novel cellulose biosynthesis inhibitor (CBI) discovered in a screen for molecules to identify inhibitors of Arabidopsis (Arabidopsis thaliana) seedling growth. Growth and cellulose synthesis inhibition by P4B were greatly reduced in a novel mutant for the cellulose synthase catalytic subunit gene CESA3 (cesa3pbr1). Cross-tolerance to P4B was also observed for isoxaben-resistant (ixr) cesa3 mutants ixr1-1 and ixr1-2. P4B has an original mode of action as compared with most other CBIs. Indeed, short-term treatments with P4B did not affect the velocity of cellulose synthase complexes (CSCs) but led to a decrease in CSC density in the plasma membrane without affecting their accumulation in microtubule-associated compartments. This was observed in the wild type but not in a cesa3pbr1 background. This reduced density correlated with a reduced delivery rate of CSCs to the plasma membrane but also with changes in cortical microtubule dynamics and orientation. At longer timescales, however, the responses to P4B treatments resembled those to other CBIs, including the inhibition of CSC motility, reduced growth anisotropy, interference with the assembly of an extensible wall, pectin demethylesterification, and ectopic lignin and callose accumulation. Together, the data suggest that P4B either directly targets CESA3 or affects another cellular function related to CSC plasma membrane delivery and/or microtubule dynamics that is bypassed specifically by mutations in CESA3.

Sphingolipid inhibitor response gene GhMYB86 controls fiber elongation by regulating microtubule arrangement

Although the cell membrane and cytoskeleton play essential roles in cellular morphogenesis, the interaction between the membrane and cytoskeleton is poorly understood. Cotton fibers are extremely elongated single cells, which makes them an ideal model for studying cell development. Here, we used the sphingolipid biosynthesis inhibitor, fumonisin B1 (FB1), and found that it effectively suppressed the myeloblastosis (MYB) transcription factor GhMYB86, thereby negatively affecting fiber elongation. A direct target of GhMYB86 is GhTUB7, which encodes the tubulin protein, the major component of the microtubule cytoskeleton. Interestingly, both the overexpression of GhMYB86 and GhTUB7 caused an ectopic microtubule arrangement at the fiber tips, and then leading to shortened fibers. Moreover, we found that GhMBE2 interacted with GhMYB86 and that FB1 and reactive oxygen species induced its transport into the nucleus, thereby enhancing the promotion of GhTUB7 by GhMYB86. Overall, we established a GhMBE2-GhMYB86-GhTUB7 regulation module for fiber elongation and revealed that membrane sphingolipids affect fiber elongation by altering microtubule arrangement.

A transient radial cortical microtubule array primes cell division in Arabidopsis

Although the formation of new walls during plant cell division tends to follow maximal tensile stress direction, analyses of individual cells over time reveal a much more variable behavior. The origin of such variability as well as the exact role of interphasic microtubule behavior before cell division have remained mysterious so far. To approach this question, we took advantage of the Arabidopsis stem, where the tensile stress pattern is both highly anisotropic and stable. Although cortical microtubules (CMTs) generally align with maximal tensile stress, we detected a specific time window, ca. 3 h before cell division, where cells form a radial pattern of CMTs. This microtubule array organization preceded preprophase band (PPB) formation, a transient CMT array predicting the position of the future division plane. It was observed under different growth conditions and was not related to cell geometry or polar auxin transport. Interestingly, this cortical radial pattern correlated with the well-documented increase of cytoplasmic microtubule accumulation before cell division. This radial organization was prolonged in cells of the trm678 mutant, where CMTs are unable to form a PPB. Whereas division plane orientation in trm678 is noisier, we found that cell division symmetry was in contrast less variable between daughter cells. We propose that this "radial step" reflects a trade-off in robustness for two essential cell division attributes: symmetry and orientation. This involves a "reset" stage in G2, where an increased cytoplasmic microtubule accumulation transiently disrupts CMT alignment with tissue stress.

Spatiotemporally distinct responses to mechanical forces shape the developing seed of Arabidopsis

Organ morphogenesis depends on mechanical interactions between cells and tissues. These interactions generate forces that can be sensed by cells and affect key cellular processes. However, how mechanical forces, together with biochemical signals, contribute to the shaping of complex organs is still largely unclear. We address this question using the seed of Arabidopsis as a model system. We show that seeds first experience a phase of rapid anisotropic growth that is dependent on the response of cortical microtubule (CMT) to forces, which guide cellulose deposition according to shape-driven stresses in the outermost layer of the seed coat. However, at later stages of development, we show that seed growth is isotropic and depends on the properties of an inner layer of the seed coat that stiffens its walls in response to tension but has isotropic material properties. Finally, we show that the transition from anisotropic to isotropic growth is due to the dampening of cortical microtubule responses to shape-driven stresses. Altogether, our work supports a model in which spatiotemporally distinct mechanical responses control the shape of developing seeds in Arabidopsis.

Tensile Stress on Microtubules Facilitates Dynein-Driven Cargo Transport

Mechanical stress significantly affects the physiological functions of cells, including tissue homeostasis, cytoskeletal alterations, and intracellular transport. As a major cytoskeletal component, microtubules respond to mechanical stimulation by altering their alignment and polymerization dynamics. Previously, we reported that microtubules may modulate cargo transport by one of the microtubule-associated motor proteins, dynein, under compressive mechanical stress. Despite the critical role of tensile stress in many biological functions, how tensile stress on microtubules regulates cargo transport is yet to be unveiled. The present study demonstrates that the low-level tensile stress-induced microtubule deformation facilitates dynein-driven transport. We validate our experimental findings using all-atom molecular dynamics simulation. Our study may provide important implications for developing new therapies for diseases that involve impaired intracellular transport.

Can repetitive mechanical motion cause structural damage to axons?

Biological structures have evolved to very efficiently generate, transmit, and withstand mechanical forces. These biological examples have inspired mechanical engineers for centuries and led to the development of critical insights and concepts. However, progress in mechanical engineering also raises new questions about biological structures. The past decades have seen the increasing study of failure of engineered structures due to repetitive loading, and its origin in processes such as materials fatigue. Repetitive loading is also experienced by some neurons, for example in the peripheral nervous system. This perspective, after briefly introducing the engineering concept of mechanical fatigue, aims to discuss the potential effects based on our knowledge of cellular responses to mechanical stresses. A particular focus of our discussion are the effects of mechanical stress on axons and their cytoskeletal structures. Furthermore, we highlight the difficulty of imaging these structures and the promise of new microscopy techniques. The identification of repair mechanisms and paradigms underlying long-term stability is an exciting and emerging topic in biology as well as a potential source of inspiration for engineers.

Top five unanswered questions in plant cell surface research

Plant cell wall researchers were asked their view on what the major unanswered questions are in their field. This article summarises the feedback that was received from them in five questions. In this issue you can find equivalent syntheses for researchers working on bacterial, unicellular parasite and fungal systems.

Mechanical forces in plant tissue matrix orient cell divisions via microtubule stabilization

Plant morphogenesis relies exclusively on oriented cell expansion and division. Nonetheless, the mechanism(s) determining division plane orientation remain elusive. Here, we studied tissue healing after laser-assisted wounding in roots of Arabidopsis thaliana and uncovered how mechanical forces stabilize and reorient the microtubule cytoskeleton for the orientation of cell division. We identified that root tissue functions as an interconnected cell matrix, with a radial gradient of tissue extendibility causing predictable tissue deformation after wounding. This deformation causes instant redirection of expansion in the surrounding cells and reorientation of microtubule arrays, ultimately predicting cell division orientation. Microtubules are destabilized under low tension, whereas stretching of cells, either through wounding or external aspiration, immediately induces their polymerization. The higher microtubule abundance in the stretched cell parts leads to the reorientation of microtubule arrays and, ultimately, informs cell division planes. This provides a long-sought mechanism for flexible re-arrangement of cell divisions by mechanical forces for tissue reconstruction and plant architecture.

The plant cell wall-dynamic, strong, and adaptable-is a natural shapeshifter

Mythology is replete with good and evil shapeshifters, who, by definition, display great adaptability and assume many different forms-with several even turning themselves into trees. Cell walls certainly fit this definition as they can undergo subtle or dramatic changes in structure, assume many shapes, and perform many functions. In this review, we cover the evolution of knowledge of the structures, biosynthesis, and functions of the 5 major cell wall polymer types that range from deceptively simple to fiendishly complex. Along the way, we recognize some of the colorful historical figures who shaped cell wall research over the past 100 years. The shapeshifter analogy emerges more clearly as we examine the evolving proposals for how cell walls are constructed to allow growth while remaining strong, the complex signaling involved in maintaining cell wall integrity and defense against disease, and the ways cell walls adapt as they progress from birth, through growth to maturation, and in the end, often function long after cell death. We predict the next century of progress will include deciphering cell type-specific wall polymers; regulation at all levels of polymer production, crosslinks, and architecture; and how walls respond to developmental and environmental signals to drive plant success in diverse environments.

Structure and growth of plant cell walls

Plant cells build nanofibrillar walls that are central to plant growth, morphogenesis and mechanics. Starting from simple sugars, three groups of polysaccharides, namely, cellulose, hemicelluloses and pectins, with very different physical properties are assembled by the cell to make a strong yet extensible wall. This Review describes the physics of wall growth and its regulation by cellular processes such as cellulose production by cellulose synthase, modulation of wall pH by plasma membrane H+-ATPase, wall loosening by expansin and signalling by plant hormones such as auxin and brassinosteroid. In addition, this Review discusses the nuanced roles, properties and interactions of cellulose, matrix polysaccharides and cell wall proteins and describes how wall stress and wall loosening cooperatively result in cell wall growth.

Transcriptome and functional analyses of phenotypic plasticity in sea grape Caulerpa okamurae

Caulerpa is a marine green macroalga distinguished by a large single cell with multiple nuclei. It also exhibits remarkable morphological intraspecies variations, in response to diverse environmental types. However, the molecular mechanisms underlying this phenotypic plasticity remain poorly understood. In this work, we compare the transcriptomes of Caulerpa okamurae Weber Bosse, 1897 displaying altered phenotypes of cultivation and natural phenotypes and investigate significantly regulated genes and their biological functions using differential expression analyses. We observe light-harvesting complex upregulation and cellular framework stability downregulation in altered phenotypes compared to the natural phenotypes. Intertidal macrophytes reduce light capture to avoid photodamage and regulate their morphology to protect against wave damage. In contrast, the lower light conditions and the cultivation environment augment light capture and increase a morphology prioritizing light trapping. Moreover, the addition of simulated wave-sweeping stimuli induces a return to the natural morphology under high-light conditions, showing how mechanical stress affects morphological organization in C. okamurae. We provide detailed gene expression patterns in C. okamurae under varying light intensities and water conditions, suggesting a distinct influence on its morphological traits.

Nuclear envelope dynamics in connection to chromatin remodeling

The nucleus is a central organelle of eukaryotic cells undergoing dynamic structural changes during cellular fundamental processes such as proliferation and differentiation. These changes rely on the integration of developmental and stress signals at the nuclear envelope (NE), orchestrating responses at the nucleo-cytoplasmic interface for efficient genomic functions such as DNA transcription, replication and repair. While in animals, correlation has already been established between NE dynamics and chromatin remodeling using last-generation tools and cutting-edge technologies, this topic is just emerging in plants, especially in response to mechanical cues. This review summarizes recent data obtained in this field with more emphasis on the mechanical stress response. It also highlights similarities/differences between animal and plant cells at multiples scales, from the structural organization of the nucleo-cytoplasmic continuum to the functional impacts of NE dynamics.

Role of tubulin C-terminal tail on mechanical properties of microtubule

Tubulin C-terminal tail (CTT) is a disordered segment extended from each tubulin monomer of αβ tubulin heterodimers, the building blocks of microtubules. The tubulin CTT contributes to the cellular function of microtubules such as intracellular transportation by regulating their interaction with other proteins and cell shape regulation by controlling microtubule polymerization dynamics. Although the mechanical integrity of microtubules is crucial for their functions, the role of tubulin CTT on microtubule mechanical properties has remained elusive. In this work, we investigate the role of tubulin CTTs in regulating the mechanical properties of microtubules by estimating the persistence lengths and investigating the buckling behavior of microtubules with and without CTT. We find that microtubules with intact CTTs exhibit twice the rigidity of microtubules lacking tubulin CTTs. Our study will widen the scope of altering microtubule mechanical properties for its application in nano bio-devices and lead to novel therapeutic approaches for neurodegenerative diseases with altered microtubule properties.

Cooperation of Various Cytoskeletal Components Orchestrates Intercellular Spread of Mitochondria between B-Lymphoma Cells through Tunnelling Nanotubes

Membrane nanotubes (NTs) are dynamic communication channels connecting spatially separated cells even over long distances and promoting the transport of different cellular cargos. NTs are also involved in the intercellular spread of different pathogens and the deterioration of some neurological disorders. Transport processes via NTs may be controlled by cytoskeletal elements. NTs are frequently observed membrane projections in numerous mammalian cell lines, including various immune cells, but their functional significance in the 'antibody factory' B cells is poorly elucidated. Here, we report that as active channels, NTs of B-lymphoma cells can mediate bidirectional mitochondrial transport, promoted by the cooperation of two different cytoskeletal motor proteins, kinesin along microtubules and myosin VI along actin, and bidirectional transport processes are also supported by the heterogeneous arrangement of the main cytoskeletal filament systems of the NTs. We revealed that despite NTs and axons being different cell extensions, the mitochondrial transport they mediate may exhibit significant similarities. Furthermore, we found that microtubules may improve the stability and lifespan of B-lymphoma-cell NTs, while F-actin strengthens NTs by providing a structural framework for them. Our results may contribute to a better understanding of the regulation of the major cells of humoral immune response to infections.

Growth and tension in explosive fruit

Exploding seed pods of the common weed Cardamine hirsuta have the remarkable ability to launch seeds far from the plant. The energy for this explosion comes from tension that builds up in the fruit valves. Above a critical threshold, the fruit fractures along its dehiscence zone and the two valves coil explosively, ejecting the seeds. A common mechanism to generate tension is drying, causing tissues to shrink. However, this does not happen in C. hirsuta fruit. Instead, tension is produced by active contraction of growing exocarp cells in the outer layer of the fruit valves. Exactly how growth causes the exocarp tissue to contract and generate pulling force is unknown. Here we show that the reorientation of microtubules in the exocarp cell cortex changes the orientation of cellulose microfibrils in the cell wall and the consequent cellular growth pattern. We used mechanical modeling to show how tension emerges through growth due to the highly anisotropic orientation of load-bearing cellulose microfibrils and their effect on cell shape. By explicitly defining the cell wall as multi-layered in our model, we discovered that a cross-lamellate pattern of cellulose microfibrils further enhances the developing tension in growing cells. Therefore, the interplay of cell wall properties with turgor-driven growth enables the fruit exocarp to generate sufficient tension to power explosive seed dispersal.

Life under tension: the relevance of force on biological polymers

Optical tweezers have elucidated numerous biological processes, particularly by enabling the precise manipulation and measurement of tension. One question concerns the biological relevance of these experiments and the generalizability of these experiments to wider biological systems. Here, we categorize the applicability of the information garnered from optical tweezers in two distinct categories: the direct relevance of tension in biological systems, and what experiments under tension can tell us about biological systems, while these systems do not reach the same tension as the experiment, still, these artificial experimental systems reveal insights into the operations of biological machines and life processes.

Microtubules as a signal hub for axon growth in response to mechanical force

Microtubules are highly polar structures and are characterized by high anisotropy and stiffness. In neurons, they play a key role in the directional transport of vesicles and organelles. In the neuronal projections called axons, they form parallel bundles, mostly oriented with the plus-end towards the axonal termination. Their physico-chemical properties have recently attracted attention as a potential candidate in sensing, processing and transducing physical signals generated by mechanical forces. Here, we discuss the main evidence supporting the role of microtubules as a signal hub for axon growth in response to a traction force. Applying a tension to the axon appears to stabilize the microtubules, which, in turn, coordinate a modulation of axonal transport, local translation and their cross-talk. We speculate on the possible mechanisms modulating microtubule dynamics under tension, based on evidence collected in neuronal and non-neuronal cell types. However, the fundamental question of the causal relationship between these mechanisms is still elusive because the mechano-sensitive element in this chain has not yet been identified.

Building on-chip cytoskeletal circuits via branched microtubule networks

Controllable platforms to engineer robust cytoskeletal scaffolds have the potential to create novel on-chip nanotechnologies. Inspired by axons, we combined the branching microtubule (MT) nucleation pathway with microfabrication to develop "cytoskeletal circuits." This active matter platform allows control over the adaptive self-organization of uniformly polarized MT arrays via geometric features of microstructures designed within a microfluidic confinement. We build and characterize basic elements, including turns and divisions, as well as complex regulatory elements, such as biased division and MT diodes, to construct various MT architectures on a chip. Our platform could be used in diverse applications, ranging from efficient on-chip molecular transport to mechanical nano-actuators. Further, cytoskeletal circuits can serve as a tool to study how the physical environment contributes to MT architecture in living cells.

Sema3A secreted by sensory nerve induces bone formation under mechanical loads

Bone formation and deposition are initiated by sensory nerve infiltration in adaptive bone remodeling. Here, we focused on the role of Semaphorin 3A (Sema3A), expressed by sensory nerves, in mechanical loads-induced bone formation and nerve withdrawal using orthodontic tooth movement (OTM) model. Firstly, bone formation was activated after the 3rd day of OTM, coinciding with a decrease in sensory nerves and an increase in pain threshold. Sema3A, rather than nerve growth factor (NGF), highly expressed in both trigeminal ganglion and the axons of periodontal ligament following the 3rd day of OTM. Moreover, in vitro mechanical loads upregulated Sema3A in neurons instead of in human periodontal ligament cells (hPDLCs) within 24 hours. Furthermore, exogenous Sema3A restored the suppressed alveolar bone formation and the osteogenic differentiation of hPDLCs induced by mechanical overload. Mechanistically, Sema3A prevented overstretching of F-actin induced by mechanical overload through ROCK2 pathway, maintaining mitochondrial dynamics as mitochondrial fusion. Therefore, Sema3A exhibits dual therapeutic effects in mechanical loads-induced bone formation, both as a pain-sensitive analgesic and a positive regulator for bone formation.

The plasma membrane - cell wall nexus in plant cells: focus on the Hechtian structure

Across all kingdoms of life, cells secrete an extracellular polymer mesh that in turn feeds back onto them. This entails physical connections between the plasma membrane and the polymer mesh. In plant cells, one connection stands out: the Hechtian strand which, during plasmolysis, reflects the existence of a physical link between the plasma membrane of the retracting protoplast and the cell wall. The Hechtian strand is part of a larger structure, which we call the Hechtian structure, that comprises the Hechtian strand, the Hechtian reticulum and the Hechtian attachment sites. Although it has been observed for more than 100 years, its molecular composition and biological functions remain ill-described. A comprehensive characterization of the Hechtian structure is a critical step towards understanding this plasma membrane-cell wall connection and its relevance in cell signaling. This short review intends to highlight the main features of the Hechtian structure, in order to provide a clear framework for future research in this under-explored and promising field.

Straining the root on and off triggers local calcium signalling

A fundamental function of an organ is the ability to perceive mechanical cues. Yet, how this is accomplished is not fully understood, particularly in plant roots. In plants, the majority of studies dealing with the effects of mechanical stress have investigated the aerial parts. However, in natural conditions roots are also subjected to mechanical cues, for example when the root encounters a hard obstacle during its growth or when the soil settles. To investigate root cellular responses to root compression, we developed a microfluidic system associated with a microvalve allowing the delivery of controlled and reproducible mechanical stimulations to the root. In this study, examining plants expressing the R-GECO1-mTurquoise calcium reporter, we addressed the root cell deformation and calcium increase induced by the mechanical stimulation. Lateral pressure applied on the root induced a moderate elastic deformation of root cortical cells and elicited a multicomponent calcium signal at the onset of the pressure pulse, followed by a second one at the release of the pressure. This indicates that straining rather than stressing of tissues is relevant to trigger the calcium signal. Although the intensity of the calcium response increases with the pressure applied, successive pressure stimuli led to a remarkable attenuation of the calcium signal. The calcium elevation was restricted to the tissue under pressure and did not propagate. Strain sensing, spatial restriction and habituation to repetitive stimulation represent the fundamental properties of root signalling in response to local mechanical stimulation. These data linking mechanical properties of root cells to calcium elevation contribute to elucidating the pathway allowing the root to adapt to the mechanical cues generated by the soil.

Pick a side: Integrating gene expression and mechanical forces to polarize aerial organs

How organs acquire their shapes is a central question in developmental biology. In plants, aerial lateral organs such as leaves initiate at the flanks of the growing meristem as dome-shaped primordia. These simple structures then grow out along multiple polarity axes to achieve a dizzying array of final shapes. Many of the hormone signaling pathways and genetic interactions that influence growth along these axes have been identified in the past few decades. Open questions include how and when initial gene expression patterns are set in organ primordia, and how these patterns are translated into the physical outcomes observed at the cellular and tissue levels. In this review, we highlight recent studies into the auxin signaling and gene expression dynamics that govern adaxial-abaxial patterning, and the contributions of mechanical forces to the development of flattened structures.

Macromolecular crowding: Sensing without a sensor

All living cells are crowded with macromolecules. Crowding can directly modulate biochemical reactions to various degrees depending on the sizes, shapes, and binding affinities of the reactants. Here, we explore the possibility that cells can sense and adapt to changes in crowding through the widespread modulation of biochemical reactions without the need for a dedicated sensor. Additionally, we explore phase separation as a general physicochemical response to changes in crowding, and a mechanism to both transduce information and physically restore crowding homeostasis.

Regiospecific Cellulose Orientation and Anisotropic Mechanical Property in Plant Cell Walls

Cellulose microfibrils (CMFs) are a major load-bearing component in plant cell walls. Thus, their structures have been studied extensively with spectroscopic and microscopic characterization methods, but the findings from these two approaches were inconsistent, which hampers the mechanistic understanding of cell wall mechanics. Here, we report the regiospecific assembly of CMFs in the periclinal wall of plant epidermal cells. Using sum frequency generation spectroscopic imaging, we found that CMFs are highly aligned in the cell edge region where two cells form a junction, whereas they are mostly isotropic on average throughout the wall thickness in the flat face region of the epidermal cell. This subcellular-level heterogeneity in the CMF alignment provided a new perspective on tissue-level anisotropy in the tensile modulus of cell wall materials. This finding also has resolved a previous contradiction between the spectroscopic and microscopic imaging studies, which paves a foundation for better understanding of the cell wall architecture, especially structure-geometry relationships.

Multiple light signaling pathways control solar tracking in sunflowers

Sunflowers are famous for their ability to track the sun throughout the day and then reorient at night to face east the following morning. This occurs by differential growth patterns, with the east sides of stems growing more during the day and the west sides of stems growing more at night. This process, termed heliotropism, is generally believed to be a specialized form of phototropism; however, the underlying mechanism is unknown. To better understand heliotropism, we compared gene expression patterns in plants undergoing phototropism in a controlled environment and in plants initiating and maintaining heliotropic growth in the field. We found the expected transcriptome signatures of phototropin-mediated phototropism in sunflower stems bending towards monochromatic blue light. Surprisingly, the expression patterns of these phototropism-regulated genes are quite different in heliotropic plants. Most genes rapidly induced during phototropism display only minor differences in expression across solar tracking stems. However, some genes that are both rapidly induced during phototropism and are implicated in growth responses to foliar shade are rapidly induced on the west sides of stems at the onset of heliotropism, suggesting a possible role for red light photoreceptors in solar tracking. To test the involvement of different photoreceptor signaling pathways in heliotropism, we modulated the light environment of plants initiating solar tracking. We found that depletion of either red and far-red light or blue light did not hinder the initiation or maintenance of heliotropism in the field. Together, our results suggest that the transcriptional regulation of heliotropism is distinct from phototropin-mediated phototropism and likely involves inputs from multiple light signaling pathways.

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.

How to Grow a Flat Leaf

Growing a flat lamina such as a leaf is almost impossible without some feedback to stabilize long wavelength modes that are easy to trigger since they are energetically cheap. Here we combine the physics of thin elastic plates with feedback control theory to explore how a leaf can remain flat while growing. We investigate both in-plane (metric) and out-of-plane (curvature) growth variation and account for both local and nonlocal feedback laws. We show that a linearized feedback theory that accounts for both spatially nonlocal and temporally delayed effects suffices to suppress long wavelength fluctuations effectively and explains recently observed statistical features of growth in tobacco leaves. Our work provides a framework for understanding the regulation of the shape of leaves and other leaflike laminar objects.

Update: on selected ROP cell polarity mechanisms in plant cell morphogenesis

The unequal (asymmetric) distribution of cell structures and proteins within a cell is designated as cell polarity. Cell polarity is a crucial prerequisite for morphogenetic processes such as oriented cell division and directed cell expansion. Rho-related GTPase from plants (ROPs) are required for cellular morphogenesis through the reorganization of the cytoskeleton and vesicle transport in various tissues. Here, I review recent advances in ROP-dependent tip growth, vesicle transport, and tip architecture. I report on the regulatory mechanisms of ROP upstream regulators found in different cell types. It appears that these regulators assemble in nanodomains with specific lipid compositions and recruit ROPs for activation in a stimulus-dependent manner. Current models link mechanosensing/mechanotransduction to ROP polarity signaling involved in feedback mechanisms via the cytoskeleton. Finally, I discuss ROP signaling components that are upregulated by tissue-specific transcription factors and exhibit specific localization patterns during cell division, clearly suggesting ROP signaling in division plane alignment.

Computer models of cell polarity establishment in plants

Plant development is a complex task, and many processes involve changes in the asymmetric subcellular distribution of cell components that strongly depend on cell polarity. Cell polarity regulates anisotropic growth and polar localization of membrane proteins and helps to identify the cell's position relative to its neighbors within an organ. Cell polarity is critical in a variety of plant developmental processes, including embryogenesis, cell division, and response to external stimuli. The most conspicuous downstream effect of cell polarity is the polar transport of the phytohormone auxin, which is the only known hormone transported in a polar fashion in and out of cells by specialized exporters and importers. The biological processes behind the establishment of cell polarity are still unknown, and researchers have proposed several models that have been tested using computer simulations. The evolution of computer models has progressed in tandem with scientific discoveries, which have highlighted the importance of genetic, chemical, and mechanical input in determining cell polarity and regulating polarity-dependent processes such as anisotropic growth, protein subcellular localization, and the development of organ shapes. The purpose of this review is to provide a comprehensive overview of the current understanding of computer models of cell polarity establishment in plants, focusing on the molecular and cellular mechanisms, the proteins involved, and the current state of the field.

Divided by fate: The interplay between division orientation and cell shape underlying lateral root initiation in Arabidopsis

The development of lateral roots starts with a round of anticlinal, asymmetric cell divisions in lateral root founder cells in the pericycle, deep within the root. The reorientation of the cell division plane occurs in parallel with changes in cell shape and needs to be coordinated with its direct neighbor, the endodermis. This accommodation response requires the integration of biochemical and mechanical signals in both cell types. Recently, it was reported that dynamic changes in the cytoskeleton and possibly the cell wall are part of the molecular mechanism required to correctly orient and position the cell division plane. Here we discuss the latest progress made towards our understanding of the regulation of cell shape and division plane orientation underlying lateral root initiation in Arabidopsis.

Cellular mechanotransduction in health and diseases: from molecular mechanism to therapeutic targets

Cellular mechanotransduction, a critical regulator of numerous biological processes, is the conversion from mechanical signals to biochemical signals regarding cell activities and metabolism. Typical mechanical cues in organisms include hydrostatic pressure, fluid shear stress, tensile force, extracellular matrix stiffness or tissue elasticity, and extracellular fluid viscosity. Mechanotransduction has been expected to trigger multiple biological processes, such as embryonic development, tissue repair and regeneration. However, prolonged excessive mechanical stimulation can result in pathological processes, such as multi-organ fibrosis, tumorigenesis, and cancer immunotherapy resistance. Although the associations between mechanical cues and normal tissue homeostasis or diseases have been identified, the regulatory mechanisms among different mechanical cues are not yet comprehensively illustrated, and no effective therapies are currently available targeting mechanical cue-related signaling. This review systematically summarizes the characteristics and regulatory mechanisms of typical mechanical cues in normal conditions and diseases with the updated evidence. The key effectors responding to mechanical stimulations are listed, such as Piezo channels, integrins, Yes-associated protein (YAP) /transcriptional coactivator with PDZ-binding motif (TAZ), and transient receptor potential vanilloid 4 (TRPV4). We also reviewed the key signaling pathways, therapeutic targets and cutting-edge clinical applications of diseases related to mechanical cues.

High-throughput characterization of cortical microtubule arrays response to anisotropic tensile stress

BACKGROUND

Plants can perceive and respond to mechanical signals. For instance, cortical microtubule (CMT) arrays usually reorganize following the predicted maximal tensile stress orientation at the cell and tissue level. While research in the last few years has started to uncover some of the mechanisms mediating these responses, much remains to be discovered, including in most cases the actual nature of the mechanosensors. Such discovery is hampered by the absence of adequate quantification tools that allow the accurate and sensitive detection of phenotypes, along with high throughput and automated handling of large datasets that can be generated with recent imaging devices.

RESULTS

Here we describe an image processing workflow specifically designed to quantify CMT arrays response to tensile stress in time-lapse datasets following an ablation in the epidermis - a simple and robust method to change mechanical stress pattern. Our Fiji-based workflow puts together several plugins and algorithms under the form of user-friendly macros that automate the analysis process and remove user bias in the quantification. One of the key aspects is also the implementation of a simple geometry-based proxy to estimate stress patterns around the ablation site and compare it with the actual CMT arrays orientation. Testing our workflow on well-established reporter lines and mutants revealed subtle differences in the response over time, as well as the possibility to uncouple the anisotropic and orientational response.

CONCLUSION

This new workflow opens the way to dissect with unprecedented detail the mechanisms controlling microtubule arrays re-organization, and potentially uncover the still largely elusive plant mechanosensors.

Maintaining asymmetry in cell division

Promoting asymmetric division through microtubule dynamics establishes cell fate.

Approximate simulation of cortical microtubule models using dynamical graph grammars

Dynamical graph grammars (DGGs) are capable of modeling and simulating the dynamics of the cortical microtubule array (CMA) in plant cells by using an exact simulation algorithm derived from a master equation; however, the exact method is slow for large systems. We present preliminary work on an approximate simulation algorithm that is compatible with the DGG formalism. The approximate simulation algorithm uses a spatial decomposition of the domain at the level of the system's time-evolution operator, to gain efficiency at the cost of some reactions firing out of order, which may introduce errors. The decomposition is more coarsely partitioned by effective dimension (d= 0 to 2 or 0 to 3), to promote exact parallelism between different subdomains within a dimension, where most computing will happen, and to confine errors to the interactions between adjacent subdomains of different effective dimensions. To demonstrate these principles we implement a prototype simulator, and run three simple experiments using a DGG for testing the viability of simulating the CMA. We find evidence indicating the initial formulation of the approximate algorithm is substantially faster than the exact algorithm, and one experiment leads to network formation in the long-time behavior, whereas another leads to a long-time behavior of local alignment.