A PLETHORA-auxin transcription module controls cell division plane rotation through MAP65 and CLASP.

Despite their pivotal role in plant development, control mechanisms for oriented cell divisions have remained elusive. Here, we describe how a precisely regulated cell division orientation switch in an Arabidopsis stem cell is controlled by upstream patterning factors. We show that the stem cell regulatory PLETHORA transcription factors induce division plane reorientation by local activation of auxin signaling, culminating in enhanced expression of the microtubule-associated MAP65 proteins. MAP65 upregulation is sufficient to reorient the cortical microtubular array through a CLASP microtubule-cell cortex interaction mediator-dependent mechanism. CLASP differentially localizes to cell faces in a microtubule- and MAP65-dependent manner. Computational simulations clarify how precise 90° switches in cell division planes can follow self-organizing properties of the microtubule array in combination with biases in CLASP localization. Our work demonstrates how transcription factor-mediated processes regulate the cellular machinery to control orientation of formative cell divisions in plants.

Microtubule nucleation complex behavior is critical for cortical array homogeneity and xylem wall patterning.

Plant cell walls are versatile materials that can adopt a wide range of mechanical properties through controlled deposition of cellulose fibrils. Wall integrity requires a sufficiently homogeneous fibril distribution to cope effectively with wall stresses. Additionally, specific conditions, such as the negative pressure in water transporting xylem vessels, may require more complex wall patterns, e.g., bands in protoxylem. The orientation and patterning of cellulose fibrils are guided by dynamic cortical microtubules. New microtubules are predominantly nucleated from parent microtubules causing positive feedback on local microtubule density with the potential to yield highly inhomogeneous patterns. Inhomogeneity indeed appears in all current cortical array simulations that include microtubule-based nucleation, suggesting that plant cells must possess an as-yet unknown balancing mechanism to prevent it. Here, in a combined simulation and experimental approach, we show that a limited local recruitment of nucleation complexes to microtubules can counter the positive feedback, whereas local tubulin depletion cannot. We observe that nucleation complexes preferentially appear at the plasma membrane near microtubules. By incorporating our experimental findings in stochastic simulations, we find that the spatial behavior of nucleation complexes delicately balances the positive feedback, such that differences in local microtubule dynamics-as in developing protoxylem-can quickly turn a homogeneous array into a banded one. Our results provide insight into how the plant cytoskeleton has evolved to meet diverse mechanical requirements and greatly increase the predictive power of computational cell biology studies.

Rho of Plants patterning: linking mathematical models and molecular diversity.

ROPs (Rho of Plants) are plant specific small GTPases involved in many membrane patterning processes and play important roles in the establishment and communication of cell polarity. These small GTPases can produce a wide variety of patterns, ranging from a single cluster in tip-growing root hairs and pollen tubes to an oriented stripe pattern controlling protoxylem cell wall deposition. For an understanding of what controls these various patterns, models are indispensable. Consequently, many modelling studies on small GTPase patterning exist, often focusing on yeast or animal cells. Multiple patterns occurring in plants, however, require the stable co-existence of multiple active ROP clusters, which does not occur with the most common yeast/animal models. The possibility of such patterns critically depends on the precise model formulation. Additionally, different small GTPases are usually treated interchangeably in models, even though plants possess two types of ROPs with distinct molecular properties, one of which is unique to plants. Furthermore, the shape and even the type of ROP patterns may be affected by the cortical cytoskeleton, and cortex composition and anisotropy differ dramatically between plants and animals. Here, we review insights into ROP patterning from modelling efforts across kingdoms, as well as some outstanding questions arising from these models and recent experimental findings.

Robust banded protoxylem pattern formation through microtubule-based directional ROP diffusion restriction.

In plant vascular tissue development, different cell wall patterns are formed, offering different mechanical properties optimised for different growth stages. Critical in these patterning processes are Rho of Plants (ROP) proteins, a class of evolutionarily conserved small GTPase proteins responsible for local membrane domain formation in many organisms. While te spotted metaxylem pattern can easily be understood as a result of a Turing-style reaction-diffusion mechanism, it remains an open question how the consistent orientation of evenly spaced bands and spirals as found in protoxylem is achieved. We hypothesise that this orientation results from an interaction between ROPs and an array of transversely oriented cortical microtubules that acts as a directional diffusion barrier. Here, we explore this hypothesis using partial differential equation models with anisotropic ROP diffusion and show that a horizontal microtubule array acting as a vertical diffusion barrier to active ROP can yield a horizontally banded ROP pattern. We then study the underlying mechanism in more detail, finding that it can only orient curved pattern features but not straight lines. This implies that, once formed, banded and spiral patterns cannot be reoriented by this mechanism. Finally, we observe that ROPs and microtubules together only form ultimately static patterns if the interaction is implemented with sufficient biological realism.

How selective severing by katanin promotes order in the plant cortical microtubule array.

Plant morphogenesis requires differential and often asymmetric growth. A key role in controlling anisotropic expansion of individual cells is played by the cortical microtubule array. Although highly organized, the array can nevertheless rapidly change in response to internal and external cues. Experiments have identified the microtubule-severing enzyme katanin as a central player in controlling the organizational state of the array. Katanin action is required both for normal alignment and the adaptation of array orientation to mechanical, environmental, and developmental stimuli. How katanin fulfills its controlling role, however, remains poorly understood. On the one hand, from a theoretical perspective, array ordering depends on the "weeding out" of discordant microtubules through frequent catastrophe-inducing collisions among microtubules. Severing would reduce average microtubule length and lifetime, and consequently weaken the driving force for alignment. On the other hand, it has been suggested that selective severing at microtubule crossovers could facilitate the removal of discordant microtubules. Here we show that this apparent conflict can be resolved by systematically dissecting the role of all of the relevant interactions in silico. This procedure allows the identification of the sufficient and necessary conditions for katanin to promote array alignment, stresses the critical importance of the experimentally observed selective severing of the "crossing" microtubule at crossovers, and reveals a hitherto not appreciated role for microtubule bundling. We show how understanding the underlying mechanism can aid with interpreting experimental results and designing future experiments.

Auxin transport, metabolism, and signalling during nodule initiation: indeterminate and determinate nodules.

Most legumes can form a unique type of lateral organ on their roots: root nodules. These structures host symbiotic nitrogen-fixing bacteria called rhizobia. Several different types of nodules can be found in nature, but the two best-studied types are called indeterminate and determinate nodules. These two types differ with respect to the presence or absence of a persistent nodule meristem, which consistently correlates with the cortical cell layers giving rise to the nodule primordia. Similar to other plant developmental processes, auxin signalling overlaps with the site of organ initiation and meristem activity. Here, we review how auxin contributes to early nodule development. We focus on changes in auxin transport, signalling, and metabolism during nodule initiation, describing both experimental evidence and computer modelling. We discuss how indeterminate and determinate nodules may differ in their mechanisms for generating localized auxin response maxima and highlight outstanding questions for future research.

Fate map of Medicago truncatula root nodules.

Legume root nodules are induced by N-fixing rhizobium bacteria that are hosted in an intracellular manner. These nodules are formed by reprogramming differentiated root cells. The model legume Medicago truncatula forms indeterminate nodules with a meristem at their apex. This organ grows by the activity of the meristem that adds cells to the different nodule tissues. In Medicago sativa it has been shown that the nodule meristem is derived from the root middle cortex. During nodule initiation, inner cortical cells and pericycle cells are also mitotically activated. However, whether and how these cells contribute to the mature nodule has not been studied. Here, we produce a nodule fate map that precisely describes the origin of the different nodule tissues based on sequential longitudinal sections and on the use of marker genes that allow the distinction of cells originating from different root tissues. We show that nodule meristem originates from the third cortical layer, while several cell layers of the base of the nodule are directly formed from cells of the inner cortical layers, root endodermis and pericycle. The latter two differentiate into the uninfected tissues that are located at the base of the mature nodule, whereas the cells derived from the inner cortical cell layers form about eight cell layers of infected cells. This nodule fate map has then been used to re-analyse several mutant nodule phenotypes. This showed, among other things, that intracellular release of rhizobia in primordium cells and meristem daughter cells are regulated in a different manner.

Recent Evolution in Rattus norvegicus Is Shaped by Declining Effective Population Size.

The brown rat, Rattus norvegicus, is both a notorious pest and a frequently used model in biomedical research. By analyzing genome sequences of 12 wild-caught brown rats from their presumed ancestral range in NE China, along with the sequence of a black rat, Rattus rattus, we investigate the selective and demographic forces shaping variation in the genome. We estimate that the recent effective population size (Ne) of this species = [Formula: see text], based on silent site diversity. We compare patterns of diversity in these genomes with patterns in multiple genome sequences of the house mouse (Mus musculus castaneus), which has a much larger Ne. This reveals an important role for variation in the strength of genetic drift in mammalian genome evolution. By a Pairwise Sequentially Markovian Coalescent analysis of demographic history, we infer that there has been a recent population size bottleneck in wild rats, which we date to approximately 20,000 years ago. Consistent with this, wild rat populations have experienced an increased flux of mildly deleterious mutations, which segregate at higher frequencies in protein-coding genes and conserved noncoding elements. This leads to negative estimates of the rate of adaptive evolution (α) in proteins and conserved noncoding elements, a result which we discuss in relation to the strongly positive estimates observed in wild house mice. As a consequence of the population bottleneck, wild rats also show a markedly slower decay of linkage disequilibrium with physical distance than wild house mice.

Quantitative modelling of legume root nodule primordium induction by a diffusive signal of epidermal origin that inhibits auxin efflux.

BACKGROUND: Rhizobium nitrogen fixation in legumes takes place in specialized organs called root nodules. The initiation of these symbiotic organs has two important components. First, symbiotic rhizobium bacteria are recognized at the epidermis through specific bacterially secreted lipo-chitooligosaccharides (LCOs). Second, signaling processes culminate in the formation of a local auxin maximum marking the site of cell divisions. Both processes are spatially separated. This separation is most pronounced in legumes forming indeterminate nodules, such as model organism Medicago truncatula, in which the nodule primordium is formed from pericycle to most inner cortical cell layers. RESULTS: We used computer simulations of a simplified root of a legume that can form indeterminate nodules. A diffusive signal that inhibits auxin transport is produced in the epidermis, the site of rhizobium contact. In our model, all cells have the same response characteristics to the diffusive signal. Nevertheless, we observed the fastest and strongest auxin accumulation in the pericycle and inner cortex. The location of these auxin maxima correlates with the first dividing cells of future nodule primordia in M. truncatula. The model also predicts a transient reduction of the vascular auxin concentration rootward of the induction site as is experimentally observed. We use our model to investigate how competition for the vascular auxin source could contribute to the regulation of nodule number and spacing. CONCLUSION: Our simulations show that the diffusive signal may invoke the strongest auxin accumulation response in the inner root layers, although the signal itself is strongest close to its production site.

Global population divergence and admixture of the brown rat (Rattus norvegicus).

Native to China and Mongolia, the brown rat (Rattus norvegicus) now enjoys a worldwide distribution. While black rats and the house mouse tracked the regional development of human agricultural settlements, brown rats did not appear in Europe until the 1500s, suggesting their range expansion was a response to relatively recent increases in global trade. We inferred the global phylogeography of brown rats using 32 k SNPs, and detected 13 evolutionary clusters within five expansion routes. One cluster arose following a southward expansion into Southeast Asia. Three additional clusters arose from two independent eastward expansions: one expansion from Russia to the Aleutian Archipelago, and a second to western North America. Westward expansion resulted in the colonization of Europe from which subsequent rapid colonization of Africa, the Americas and Australasia occurred, and multiple evolutionary clusters were detected. An astonishing degree of fine-grained clustering between and within sampling sites underscored the extent to which urban heterogeneity shaped genetic structure of commensal rodents. Surprisingly, few individuals were recent migrants, suggesting that recruitment into established populations is limited. Understanding the global population structure of R. norvegicus offers novel perspectives on the forces driving the spread of zoonotic disease, and aids in development of rat eradication programmes.

Cortical microtubule arrays are initiated from a nonrandom prepattern driven by atypical microtubule initiation.

The ordered arrangement of cortical microtubules in growing plant cells is essential for anisotropic cell expansion and, hence, for plant morphogenesis. These arrays are dismantled when the microtubule cytoskeleton is rearranged during mitosis and reassembled following completion of cytokinesis. The reassembly of the cortical array has often been considered as initiating from a state of randomness, from which order arises at least partly through self-organizing mechanisms. However, some studies have shown evidence for ordering at early stages of array assembly. To investigate how cortical arrays are initiated in higher plant cells, we performed live-cell imaging studies of cortical array assembly in tobacco (Nicotiana tabacum) Bright Yellow-2 cells after cytokinesis and drug-induced disassembly. We found that cortical arrays in both cases did not initiate randomly but with a significant overrepresentation of microtubules at diagonal angles with respect to the cell axis, which coincides with the predominant orientation of the microtubules before their disappearance from the cell cortex in preprophase. In Arabidopsis (Arabidopsis thaliana) root cells, recovery from drug-induced disassembly was also nonrandom and correlated with the organization of the previous array, although no diagonal bias was observed in these cells. Surprisingly, during initiation, only about one-half of the new microtubules were nucleated from locations marked by green fluorescent protein-γ-tubulin complex protein2-tagged γ-nucleation complexes (γ-tubulin ring complex), therefore indicating that a large proportion of early polymers was initiated by a noncanonical mechanism not involving γ-tubulin ring complex. Simulation studies indicate that the high rate of noncanonical initiation of new microtubules has the potential to accelerate the rate of array repopulation.

More Insights from Ultrastructural and Functional Plasmodesmata Data Using PDinsight.

PDinsight is a Python-based tool for computing effective wall permeability for symplasmic transport based on plasmodesma (PD) size and distribution data. PDinsight can be used for direct computation of such permeabilities if full data is available, as well as in an explorative way if some data is either not available or considered unreliable. In this chapter, we briefly describe the basic model underlying the PDinsight calculations and discuss how the different modes of PDinsight can be used in relation to typical research questions. We also offer advice on choosing appropriate values for diffusion coefficients and particle size based on the currently most used experimental probes.

Taking directions: the role of microtubule-bound nucleation in the self-organization of the plant cortical array.

The highly aligned cortical microtubule array of interphase plant cells is a key regulator of anisotropic cell expansion. Recent computational and analytical work has shown that the non-equilibrium self-organization of this structure can be understood on the basis of experimentally observed collisional interactions between dynamic microtubules attached to the plasma membrane. Most of these approaches assumed that new microtubules are homogeneously and isotropically nucleated on the cortical surface. Experimental evidence, however, shows that nucleation mostly occurs from other microtubules and under specific relative angles. Here, we investigate the impact of directed microtubule-bound nucleations on the alignment process using computer simulations. The results show that microtubule-bound nucleations can increase the degree of alignment achieved, decrease the timescale of the ordering process and widen the regime of dynamic parameters for which the system can self-organize. We establish that the major determinant of this effect is the degree of co-alignment of the nucleations with the parent microtubule. The specific role of sideways branching nucleations appears to allow stronger alignment while maintaining a measure of overall spatial homogeneity. Finally, we investigate the suggestion that observed persistent rotation of microtubule domains can be explained through a handedness bias in microtubule-bound nucleations, showing that this is possible only for an extreme bias and over a limited range of parameters.

Long-term single-cell imaging and simulations of microtubules reveal principles behind wall patterning during proto-xylem development.

Plants are the tallest organisms on Earth; a feature sustained by solute-transporting xylem vessels in the plant vasculature. The xylem vessels are supported by strong cell walls that are assembled in intricate patterns. Cortical microtubules direct wall deposition and need to rapidly re-organize during xylem cell development. Here, we establish long-term live-cell imaging of single Arabidopsis cells undergoing proto-xylem trans-differentiation, resulting in spiral wall patterns, to understand microtubule re-organization. We find that the re-organization requires local microtubule de-stabilization in band-interspersing gaps. Using microtubule simulations, we recapitulate the process in silico and predict that spatio-temporal control of microtubule nucleation is critical for pattern formation, which we confirm in vivo. By combining simulations and live-cell imaging we further explain how the xylem wall-deficient and microtubule-severing KATANIN contributes to microtubule and wall patterning. Hence, by combining quantitative microscopy and modelling we devise a framework to understand how microtubule re-organization supports wall patterning.

Small GTPase patterning: How to stabilise cluster coexistence.

Many biological processes have to occur at specific locations on the cell membrane. These locations are often specified by the localised activity of small GTPase proteins. Some processes require the formation of a single cluster of active GTPase, also called unipolar polarisation (here "polarisation"), whereas others need multiple coexisting clusters. Moreover, sometimes the pattern of GTPase clusters is dynamically regulated after its formation. This raises the question how the same interacting protein components can produce such a rich variety of naturally occurring patterns. Most currently used models for GTPase-based patterning inherently yield polarisation. Such models may at best yield transient coexistence of at most a few clusters, and hence fail to explain several important biological phenomena. These existing models are all based on mass conservation of total GTPase and some form of direct or indirect positive feedback. Here, we show that either of two biologically plausible modifications can yield stable coexistence: including explicit GTPase turnover, i.e., breaking mass conservation, or negative feedback by activation of an inhibitor like a GAP. Since we start from two different polarising models our findings seem independent of the precise self-activation mechanism. By studying the net GTPase flows among clusters, we provide insight into how these mechanisms operate. Our coexistence models also allow for dynamical regulation of the final pattern, which we illustrate with examples of pollen tube growth and the branching of fungal hyphae. Together, these results provide a better understanding of how cells can tune a single system to generate a wide variety of biologically relevant patterns.

From plasmodesma geometry to effective symplasmic permeability through biophysical modelling.

Regulation of molecular transport via intercellular channels called plasmodesmata (PDs) is important for both coordinating developmental and environmental responses among neighbouring cells, and isolating (groups of) cells to execute distinct programs. Cell-to-cell mobility of fluorescent molecules and PD dimensions (measured from electron micrographs) are both used as methods to predict PD transport capacity (i.e., effective symplasmic permeability), but often yield very different values. Here, we build a theoretical bridge between both experimental approaches by calculating the effective symplasmic permeability from a geometrical description of individual PDs and considering the flow towards them. We find that a dilated central region has the strongest impact in thick cell walls and that clustering of PDs into pit fields strongly reduces predicted permeabilities. Moreover, our open source multi-level model allows to predict PD dimensions matching measured permeabilities and add a functional interpretation to structural differences observed between PDs in different cell walls.

An active second dihydrofolate reductase enzyme is not a feature of rat and mouse, but they do have activity in their mitochondria.

The identification of a second functional dihydrofolate reductase enzyme in humans, DHFRL1, led us to consider whether this is also a feature of rodents. We demonstrate that dihydrofolate reductase activity is also a feature of the mitochondria in both rat and mouse but this is not due to a second enzyme. While our phylogenetic analysis revealed that RNA-mediated DHFR duplication events did occur across the mammal tree, the duplicates in brown rat and mouse are likely to be processed pseudogenes. Humans have evolved the need for two separate enzymes while laboratory rats and mice have just one.

Rhizobium Lipo-chitooligosaccharide Signaling Triggers Accumulation of Cytokinins in Medicago truncatula Roots.

Legume rhizobium symbiosis is initiated upon perception of bacterial secreted lipo-chitooligosaccharides (LCOs). Perception of these signals by the plant initiates a signaling cascade that leads to nodule formation. Several studies have implicated a function for cytokinin in this process. However, whether cytokinin accumulation and subsequent signaling are an integral part of rhizobium LCO signaling remains elusive. Here, we show that cytokinin signaling is required for the majority of transcriptional changes induced by rhizobium LCOs. In addition, we demonstrate that several cytokinins accumulate in the root susceptible zone 3 h after rhizobium LCO application, including the biologically most active cytokinins, trans-zeatin and isopentenyl adenine. These responses are dependent on calcium- and calmodulin-dependent protein kinase (CCaMK), a key protein in rhizobial LCO-induced signaling. Analysis of the ethylene-insensitive Mtein2/Mtsickle mutant showed that LCO-induced cytokinin accumulation is negatively regulated by ethylene. Together with transcriptional induction of ethylene biosynthesis genes, it suggests a feedback loop negatively regulating LCO signaling and subsequent cytokinin accumulation. We argue that cytokinin accumulation is a key step in the pathway leading to nodule organogenesis and that this is tightly controlled by feedback loops.

Modelling the role of microtubules in plant cell morphology.

Normal plant growth requires the anisotropic expansion of cells and the proper orientation of their divisions. Both are controlled by the architecture of the cortical microtubule array. Cortical microtubules interact through frequent collisions. Several modelling studies have shown that these interactions can be sufficient for spontaneous alignment. Further requirements to this self-organization are the homogeneous distribution of microtubule density and reliable control over the array orientation. We review the contribution of computer simulations and mathematical modelling on each of these challenges. These models now provide a good understanding of the basic alignment mechanism and will continue to be very useful tools for investigating more advanced questions, for example how microtubule severing contributes to alignment and array reorientation.