Two-dimensional spatial patterning in developmental systems

A mathematical framework for understanding the spontaneous emergence of complexity applicable to growing multicellular systems

In embryonic development and organogenesis, cells sharing identical genetic codes acquire diverse gene expression states in a highly reproducible spatial distribution, crucial for multicellular formation and quantifiable through positional information. To understand the spontaneous growth of complexity, we constructed a one-dimensional division-decision model, simulating the growth of cells with identical genetic networks from a single cell. Our findings highlight the pivotal role of cell division in providing positional cues, escorting the system toward states rich in information. Moreover, we pinpointed lateral inhibition as a critical mechanism translating spatial contacts into gene expression. Our model demonstrates that the spatial arrangement resulting from cell division, combined with cell lineages, imparts positional information, specifying multiple cell states with increased complexity-illustrated through examples in C.elegans. This study constitutes a foundational step in comprehending developmental intricacies, paving the way for future quantitative formulations to construct synthetic multicellular patterns.

Recognition and reconstruction of cell differentiation patterns with deep learning

Cell lineage decisions occur in three-dimensional spatial patterns that are difficult to identify by eye. There is an ongoing effort to replicate such patterns using mathematical modeling. One approach uses long ranging cell-cell communication to replicate common spatial arrangements like checkerboard and engulfing patterns. In this model, the cell-cell communication has been implemented as a signal that disperses throughout the tissue. On the other hand, machine learning models have been developed for pattern recognition and pattern reconstruction tasks. We combined synthetic data generated by the mathematical model with spatial summary statistics and deep learning algorithms to recognize and reconstruct cell fate patterns in organoids of mouse embryonic stem cells. Application of Moran's index and pair correlation functions for in vitro and synthetic data from the model showed local clustering and radial segregation. To assess the patterns as a whole, a graph neural network was developed and trained on synthetic data from the model. Application to in vitro data predicted a low signal dispersion value. To test this result, we implemented a multilayer perceptron for the prediction of a given cell fate based on the fates of the neighboring cells. The results show a 70% accuracy of cell fate imputation based on the nine nearest neighbors of a cell. Overall, our approach combines deep learning with mathematical modeling to link cell fate patterns with potential underlying mechanisms.

Adjusting the range of cell-cell communication enables fine-tuning of cell fate patterns from checkerboard to engulfing

During development, spatio-temporal patterns ranging from checkerboard to engulfing occur with precise proportions of the respective cell fates. Key developmental regulators are intracellular transcriptional interactions and intercellular signaling. We present an analytically tractable mathematical model based on signaling that reliably generates different cell type patterns with specified proportions. Employing statistical mechanics, We derived a cell fate decision model for two cell types. A detailed steady state analysis on the resulting dynamical system yielded necessary conditions to generate spatially heterogeneous patterns. This allows the cell type proportions to be controlled by a single model parameter. Cell-cell communication is realized by local and global signaling mechanisms. These result in different cell type patterns. A nearest neighbor signal yields checkerboard patterns. Increasing the signal dispersion, cell fate clusters and an engulfing pattern can be generated. Altogether, the presented model allows us to reliably generate heterogeneous cell type patterns of different kinds as well as desired proportions.

Mutations in NAKED-ENDOSPERM IDD genes reveal functional interactions with SCARECROW during leaf patterning in C4 grasses

Leaves comprise a number of different cell-types that are patterned in the context of either the epidermal or inner cell layers. In grass leaves, two distinct anatomies develop in the inner leaf tissues depending on whether the leaf carries out C3 or C4 photosynthesis. In both cases a series of parallel veins develops that extends from the leaf base to the tip but in ancestral C3 species veins are separated by a greater number of intervening mesophyll cells than in derived C4 species. We have previously demonstrated that the GRAS transcription factor SCARECROW (SCR) regulates the number of photosynthetic mesophyll cells that form between veins in the leaves of the C4 species maize, whereas it regulates the formation of stomata in the epidermal leaf layer in the C3 species rice. Here we show that SCR is required for inner leaf patterning in the C4 species Setaria viridis but in this species the presumed ancestral stomatal patterning role is also retained. Through a comparative mutant analysis between maize, setaria and rice we further demonstrate that loss of NAKED-ENDOSPERM (NKD) INDETERMINATE DOMAIN (IDD) protein function exacerbates loss of function scr phenotypes in the inner leaf tissues of maize and setaria but not rice. Specifically, in both setaria and maize, scr;nkd mutants exhibit an increased proportion of fused veins with no intervening mesophyll cells. Thus, combined action of SCR and NKD may control how many mesophyll cells are specified between veins in the leaves of C4 but not C3 grasses. Together our results provide insight into the evolution of cell patterning in grass leaves and demonstrate a novel patterning role for IDD genes in C4 leaves.

microRNA-124 regulates Notch and NeuroD1 to mediate transition states of neuronal development

MicroRNAs regulate gene expression by destabilizing target mRNA and/or inhibiting translation in animal cells. The ability to mechanistically dissect miR-124's function during specification, differentiation, and maturation of neurons during development within a single system has not been accomplished. Using the sea urchin embryo, we take advantage of the manipulability of the embryo and its well-documented gene regulatory networks (GRNs). We incorporated NeuroD1 as part of the sea urchin neuronal GRN and determined that miR-124 inhibition resulted in aberrant gut contractions, swimming velocity, and neuronal development. Inhibition of miR-124 resulted in an increased number of cells expressing transcription factors (TFs) associated with progenitor neurons and a concurrent decrease of mature and functional neurons. Results revealed that in the early blastula/gastrula stages, miR-124 regulates undefined factors during neuronal specification and differentiation. In the late gastrula/larval stages, miR-124 regulates Notch and NeuroD1 during the transition between neuronal differentiation and maturation. Overall, we have improved the neuronal GRN and identified miR-124 to play a prolific role in regulating various transitions of neuronal development.

Cell biology of the leaf epidermis: Fate specification, morphogenesis, and coordination

As the outermost layer of plants, the epidermis serves as a critical interface between plants and the environment. During leaf development, the differentiation of specialized epidermal cell types, including stomatal guard cells, pavement cells, and trichomes, occurs simultaneously, each providing unique and pivotal functions for plant growth and survival. Decades of molecular-genetic and physiological studies have unraveled key players and hormone signaling specifying epidermal differentiation. However, most studies focus on only one cell type at a time, and how these distinct cell types coordinate as a unit is far from well-comprehended. Here we provide a review on the current knowledge of regulatory mechanisms underpinning the fate specification, differentiation, morphogenesis, and positioning of these specialized cell types. Emphasis is given to their shared developmental origins, fate flexibility, as well as cell cycle and hormonal controls. Furthermore, we discuss computational modeling approaches to integrate how mechanical properties of individual epidermal cell types and entire tissue/organ properties mutually influence each other. We hope to illuminate the underlying mechanisms coordinating the cell differentiation that ultimately generate a functional leaf epidermis.

Beyond Turing: far-from-equilibrium patterns and mechano-chemical feedback

Turing patterns are commonly understood as specific instabilities of a spatially homogeneous steady state, resulting from activator-inhibitor interaction destabilized by diffusion. We argue that this view is restrictive and its agreement with biological observations is problematic. We present two alternatives to the classical Turing analysis of patterns. First, we employ the abstract framework of evolution equations to enable the study of far-from-equilibrium patterns. Second, we introduce a mechano-chemical model, with the surface on which the pattern forms being dynamic and playing an active role in the pattern formation, effectively replacing the inhibitor. We highlight the advantages of these two alternatives vis-à-vis the classical Turing analysis, and give an overview of recent results and future challenges for both approaches. This article is part of the theme issue 'Recent progress and open frontiers in Turing's theory of morphogenesis'.

Discovery of spatial pattern of prickles on stem of Rosa hybrida 'Red Queen' and mathematical model of the pattern

The developmental patterns of many organisms are orchestrated by the diffusion of factors. Here, we report a novel pattern on plant stems that appears to be controlled by inhibitor diffusion. Prickles on rose stems appear to be randomly distributed, but we deciphered spatial patterns of prickles on Rosa hybrida cv. ‘Red Queen’ stem. The prickles primarily emerged at 90 to 135 degrees from the spiral phyllotaxis that connected leaf primordia. We proposed a simple mathematical model that explained the emergence of the spatial patterns and reproduced the prickle density distribution on rose stems. We confirmed the model can reproduce the observed prickle patterning on stems of other plant species using other model parameters. These results indicated that the spatial patterns of prickles on stems of different plant species are organized by similar systems. Rose cultivation by humans has a long history. However, prickle development is still unclear and this is the first report of prickle spatial pattern with a mathematical model. Comprehensive analysis of the spatial pattern, genome, and metabolomics of other plant species may lead to novel insights for prickle development.

Effective range of non-cell autonomous activator and inhibitor peptides specifying plant stomatal patterning

Stomata are epidermal valves that facilitate gas exchange between plants and their environment. Stomatal patterning is regulated by the EPIDERMAL PATTERING FACTOR (EPF) family of secreted peptides: EPF1 enforces stomatal spacing, whereas EPIDERMAL PATTERNING FACTOR-LIKE9 (EPFL9), also known as Stomagen, promotes stomatal development. It remains unknown, however, how far these signaling peptides act. Utilizing Cre-lox recombination-based mosaic sectors that overexpress either EPF1 or Stomagen in Arabidopsis cotyledons, we reveal a range within the epidermis and across the cell layers in which these peptides influence patterns. To determine their effective ranges quantitatively, we developed a computational pipeline, SPACE (stomata patterning autocorrelation on epidermis), that describes probabilistic two-dimensional stomatal distributions based upon spatial autocorrelation statistics used in astrophysics. The SPACE analysis shows that, whereas both peptides act locally, the inhibitor EPF1 exerts longer range effects than the activator Stomagen. Furthermore, local perturbation of stomatal development has little influence on global two-dimensional stomatal patterning. Our findings conclusively demonstrate the nature and extent of EPF peptides as non-cell autonomous local signals and provide a means for quantitative characterization of complex spatial patterns in development.This article has an associated 'The people behind the papers' interview.

Leaf Trichome Distribution Pattern in Arabidopsis Reveals Gene Expression Variation Associated with Environmental Adaptation

Gene expression varies stochastically even in both heterogenous and homogeneous cell populations. This variation is not simply useless noise; rather, it is important for many biological processes. Unicellular organisms or cultured cell lines are useful for analyzing the variation in gene expression between cells; however, owing to technical challenges, the biological relevance of this variation in multicellular organisms such as higher plants remain unclear. Here, we addressed the biological relevance of this variation between cells by examining the genetic basis of trichome distribution patterns in Arabidopsis thaliana. The distribution pattern of a trichome on a leaf is stochastic and can be mathematically represented using Turing’s reaction-diffusion (RD) model. We analyzed simulations based on the RD model and found that the variability in the trichome distribution pattern increased with the increase in stochastic variation in a particular gene expression. Moreover, differences in heat-dependent variability of the trichome distribution pattern between the accessions showed a strong correlation with environmental factors to which each accession was adapted. Taken together, we successfully visualized variations in gene expression by quantifying the variability in the Arabidopsis trichome distribution pattern. Thus, our data provide evidence for the biological importance of variations in gene expression for environmental adaptation.

GOLVEN peptide signalling through RGI receptors and MPK6 restricts asymmetric cell division during lateral root initiation

During lateral root initiation, lateral root founder cells undergo asymmetric cell divisions that generate daughter cells with different sizes and fates, a prerequisite for correct primordium organogenesis. An excess of the GLV6/RGF8 peptide disrupts these initial asymmetric cell divisions, resulting in more symmetric divisions and the failure to achieve lateral root organogenesis. Here, we show that loss-of-function GLV6 and its homologue GLV10 increase asymmetric cell divisions during lateral root initiation, and we identified three members of the RGF1 INSENSITIVE/RGF1 receptor subfamily as likely GLV receptors in this process. Through a suppressor screen, we found that MITOGEN-ACTIVATED PROTEIN KINASE6 is a downstream regulator of the GLV pathway. Our data indicate that GLV6 and GLV10 act as inhibitors of asymmetric cell divisions and signal through RGF1 INSENSITIVE receptors and MITOGEN-ACTIVATED PROTEIN KINASE6 to restrict the number of initial asymmetric cell divisions that take place during lateral root initiation.

A Genetic Dissection of Natural Variation for Stomatal Abundance Traits in Arabidopsis

Stomatal abundance varies widely across natural populations of Arabidopsis thaliana, and presumably affects plant performance because it influences water and CO2 exchange with the atmosphere and thence photosynthesis and transpiration. In order to determine the genetic basis of this natural variation, we have analyzed a recombinant inbred line (RIL) population derived from the wild accession Ll-0 and the reference strain Landsberg erecta (Ler), which show low and high stomatal abundance, respectively. Quantitative trait locus (QTL) analyses of stomatal index, stomatal density, and pavement cell density measured in the adaxial cotyledon epidermis, identified five loci. Three of the genomic regions affect all traits and were named MID (Modulator of Cell Index and Density) 1 to 3. MID2 is a large-effect QTL overlapping with ERECTA (ER), the er-1 allele from Ler increasing all trait values. Additional analyses of natural and induced loss-of-function er mutations in different genetic backgrounds revealed that ER dysfunctions have differential and opposite effects on the stomatal index in adaxial and abaxial cotyledon epidermis and confirmed that ER is the gene underlying MID2. Ll-0 alleles at MID1 and MID3 displayed moderate and positive effects on the various traits. Furthermore, detailed developmental studies tracking primary and satellite stomatal lineages show that MID3-Ll-0 allele promotes the spacing divisions that initiate satellite lineages, while the ER allele limits them. Finally, expression analyses suggest that ER and MID3 modulate satellization through partly different regulatory pathways. Our characterization of MID3 indicates that genetic modulation of satellization contributes to the variation for stomatal abundance in natural populations, and subsequently that this trait might be involved in plant adaptation.

Self-organization of Plk4 regulates symmetry breaking in centriole duplication

During centriole duplication, a single daughter centriole is formed next to the mother centriole. The molecular mechanism that determines a single duplication site remains a long-standing question. Here, we show that intrinsic self-organization of Plk4 is implicated in symmetry breaking in the process of centriole duplication. We demonstrate that Plk4 has an ability to phase-separate into condensates via an intrinsically disordered linker and that the condensation properties of Plk4 are regulated by autophosphorylation. Consistently, the dissociation dynamics of centriolar Plk4 are controlled by autophosphorylation. We further found that autophosphorylated Plk4 is already distributed as a single focus around the mother centriole before the initiation of procentriole formation, and is subsequently targeted for STIL-HsSAS6 loading. Perturbation of Plk4 self-organization affects the asymmetry of centriolar Plk4 distribution and proper centriole duplication. Overall, we propose that the spatial pattern formation of Plk4 is a determinant of a single duplication site per mother centriole.

Self-organization across scales: from molecules to organisms

Creating ordered structures from chaotic environments is at the core of biological processes at the subcellular, cellular and organismic level. In this perspective, we explore the physical as well as biological features of two prominent concepts driving self-organization, namely phase transition and reaction-diffusion, before closing with a discussion on open questions and future challenges associated with studying self-organizing systems.This article is part of the theme issue 'Self-organization in cell biology'.

Dynamical Patterning Modules, Biogeneric Materials, and the Evolution of Multicellular Plants

Comparative analyses of developmental processes across a broad spectrum of organisms are required to fully understand the mechanisms responsible for the major evolutionary transitions among eukaryotic photosynthetic lineages (defined here as the polyphyletic algae and the monophyletic land plants). The concepts of dynamical patterning modules (DPMs) and biogeneric materials provide a framework for studying developmental processes in the context of such comparative analyses. In the context of multicellularity, DPMs are defined as sets of conserved gene products and molecular networks, in conjunction with the physical morphogenetic and patterning processes they mobilize. A biogeneric material is defined as mesoscale matter with predictable morphogenetic capabilities that arise from complex cellular conglomerates. Using these concepts, we outline some of the main events and transitions in plant evolution, and describe the DPMs and biogeneric properties associated with and responsible for these transitions. We identify four primary DPMs that played critical roles in the evolution of multicellularity (i.e., the DPMs responsible for cell-to-cell adhesion, identifying the future cell wall, cell differentiation, and cell polarity). Three important conclusions emerge from a broad phyletic comparison: (1) DPMs have been achieved in different ways, even within the same clade (e.g., phycoplastic cell division in the Chlorophyta and phragmoplastic cell division in the Streptophyta), (2) DPMs had their origins in the co-option of molecular species present in the unicellular ancestors of multicellular plants, and (3) symplastic transport mediated by intercellular connections, particularly plasmodesmata, was critical for the evolution of complex multicellularity in plants.

Notch signaling patterns neurogenic ectoderm and regulates the asymmetric division of neural progenitors in sea urchin embryos

We have examined regulation of neurogenesis by Delta/Notch signaling in sea urchin embryos. At gastrulation, neural progenitors enter S phase coincident with expression of Sp-SoxC. We used a BAC containing GFP knocked into the Sp-SoxC locus to label neural progenitors. Live imaging and immunolocalizations indicate that Sp-SoxC-expressing cells divide to produce pairs of adjacent cells expressing GFP. Over an interval of about 6 h, one cell fragments, undergoes apoptosis and expresses high levels of activated Caspase3. A Notch reporter indicates that Notch signaling is activated in cells adjacent to cells expressing Sp-SoxC. Inhibition of γ-secretase, injection of Sp-Delta morpholinos or CRISPR/Cas9-induced mutation of Sp-Delta results in supernumerary neural progenitors and neurons. Interfering with Notch signaling increases neural progenitor recruitment and pairs of neural progenitors. Thus, Notch signaling restricts the number of neural progenitors recruited and regulates the fate of progeny of the asymmetric division. We propose a model in which localized signaling converts ectodermal and ciliary band cells to neural progenitors that divide asymmetrically to produce a neural precursor and an apoptotic cell.

Finite cell-size effects on protein variability in Turing patterned tissues

Herein we present a framework to characterize different sources of protein expression variability in Turing patterned tissues. In this context, we introduce the concept of granular noise to account for the unavoidable fluctuations due to finite cell-size effects and show that the nearest-neighbours autocorrelation function provides the means to measure it. To test our findings, we perform in silico experiments of growing tissues driven by a generic activator-inhibitor dynamics. Our results show that the relative importance of different sources of noise depends on the ratio between the characteristic size of cells and that of the pattern domains and on the ratio between the pattern amplitude and the effective intensity of the biochemical fluctuations. Importantly, our framework provides the tools to measure and distinguish different stochastic contributions during patterning: granularity versus biochemical noise. In addition, our analysis identifies the protein species that buffer the stochasticity the best and, consequently, it can help to determine key instructive signals in systems driven by a Turing instability. Altogether, we expect our study to be relevant in developmental processes leading to the formation of periodic patterns in tissues.

Chronic stress and intestinal barrier dysfunction: Glucocorticoid receptor and transcription repressor HES1 regulate tight junction protein Claudin-1 promoter

Chronic stress and elevated glucocorticoid hormone are associated with decreases in the intestinal epithelial tight junction protein claudin-1 (CLDN1). Human/rat CLDN1 promoters contain glucocorticoid response elements (GREs) and adjacent transcription repressor HES1 binding N-boxes. Notch signaling target HES1 expression was high and glucocorticoid receptor (NR3C1) low at the crypt base and the pattern reversed at the crypt apex. Chronic stress reduced overall rat colon HES1 and NR3C1 that was associated with CLDN1 downregulation. Chromatin-immunoprecipitation experiments showed that HES1 and NR3C1 bind to the CLDN1 promoter in rat colon crypts. The binding of NR3C1 but not HES1 to CLDN1 promoter significantly decreased in chronically stressed animals, which was prevented by the NR3C1 antagonist RU486. We employed the 21-day Caco-2/BBe cell model to replicate cell differentiation along the crypt axis. HES1 siRNA treatment early in differentiation increased CLDN1. In contrast, stress levels of cortisol decreased CLDN1 in late differentiation stage but not in the early stage. HES1 was high, whereas NR3C1 and CLDN1 were low in the early stage which reversed in the late stage, e.g. HES1/NR3C1 binding to CLDN1 promoter demonstrates a dynamic and reciprocal pattern. These results suggest that chronic stress impairs colon epithelium homeostasis and barrier function via different mechanisms along the crypt axis.

Live-cell imaging and optical manipulation of Arabidopsis early embryogenesis

Intercellular communications are essential for cell proliferation and differentiation during plant embryogenesis. However, analysis of intercellular communications in living material in real time is difficult owing to the restricted accessibility of the embryo within the flower. We established a live-embryo imaging system to visualize cell division and cell fate specification in Arabidopsis thaliana from zygote division in real time. We generated a cell-division lineage tree for early embryogenesis in Arabidopsis. Lineage analysis showed that both the direction and time course of cell division between sister cells differed along the apical-basal or radial axes. Using the Arabidopsis kpl mutant, in which single-fertilization events are frequent, we showed that endosperm development is not required for pattern formation during early embryogenesis. Optical manipulation demonstrated that damage to the embryo initial cell induces cell fate conversion of the suspensor cell to compensate for the disrupted embryo initial cell even after cell fate is specified.

Molecular Framework of a Regulatory Circuit Initiating Two-Dimensional Spatial Patterning of Stomatal Lineage

Stomata, valves on the plant epidermis, are critical for plant growth and survival, and the presence of stomata impacts the global water and carbon cycle. Although transcription factors and cell-cell signaling components regulating stomatal development have been identified, it remains unclear as to how their regulatory interactions are translated into two-dimensional patterns of stomatal initial cells. Using molecular genetics, imaging, and mathematical simulation, we report a regulatory circuit that initiates the stomatal cell-lineage. The circuit includes a positive feedback loop constituting self-activation of SCREAMs that requires SPEECHLESS. This transcription factor module directly binds to the promoters and activates a secreted signal, EPIDERMAL PATTERNING FACTOR2, and the receptor modifier TOO MANY MOUTHS, while the receptor ERECTA lies outside of this module. This in turn inhibits SPCH, and hence SCRMs, thus constituting a negative feedback loop. Our mathematical model accurately predicts all known stomatal phenotypes with the inclusion of two additional components to the circuit: an EPF2-independent negative-feedback loop and a signal that lies outside of the SPCH•SCRM module. Our work reveals the intricate molecular framework governing self-organizing two-dimensional patterning in the plant epidermis.

Tunable diffusive lateral inhibition in chemical cells

The Belousov-Zhabotinsky (BZ) reaction has become the prototype of nonlinear chemical dynamics. Microfluidic techniques provide a convenient method for emulsifying BZ solutions into monodispersed drops with diameters of tens to hundreds of microns, providing a unique system in which reaction-diffusion theory can be quantitatively tested. In this work, we investigate monolayers of microfluidically generated BZ drops confined in close-packed two-dimensional (2D) arrays through experiments and finite element simulations. We describe the transition from oscillatory to stationary chemical states with increasing coupling strength, controlled by independently varying the reaction chemistry within a drop and diffusive flux between drops. For stationary drops, we studied how the ratio of stationary oxidized to stationary reduced drops varies with coupling strength. In addition, using simulation, we quantified the chemical heterogeneity sufficient to induce mixed stationary and oscillatory patterns.

The green seaweed Ulva: a model system to study morphogenesis

Green macroalgae, mostly represented by the Ulvophyceae, the main multicellular branch of the Chlorophyceae, constitute important primary producers of marine and brackish coastal ecosystems. Ulva or sea lettuce species are some of the most abundant representatives, being ubiquitous in coastal benthic communities around the world. Nonetheless the genus also remains largely understudied. This review highlights Ulva as an exciting novel model organism for studies of algal growth, development and morphogenesis as well as mutualistic interactions. The key reasons that Ulva is potentially such a good model system are: (i) patterns of Ulva development can drive ecologically important events, such as the increasing number of green tides observed worldwide as a result of eutrophication of coastal waters, (ii) Ulva growth is symbiotic, with proper development requiring close association with bacterial epiphytes, (iii) Ulva is extremely developmentally plastic, which can shed light on the transition from simple to complex multicellularity and (iv) Ulva will provide additional information about the evolution of the green lineage.

Complex, non-monotonic dose-response curves with multiple maxima: Do we (ever) sample densely enough?

We usually expect the dose-response curves of biological responses to quantifiable stimuli to be simple, either monotonic or exhibiting a single maximum or minimum. Deviations are often viewed as experimental noise. However, detailed measurements in plant primary tissue cultures (stem pith explants of kale and tobacco) exposed to varying doses of sucrose, cytokinins (BA or kinetin) or auxins (IAA or NAA) revealed that growth and several biochemical parameters exhibit multiple reproducible, statistically significant maxima over a wide range of exogenous substance concentrations. This results in complex, non-monotonic dose-response curves, reminiscent of previous reports of analogous observations in both metazoan and plant systems responding to diverse pharmacological treatments. These findings suggest the existence of a hitherto neglected class of biological phenomena resulting in dose-response curves exhibiting periodic patterns of maxima and minima, whose causes remain so far uncharacterized, partly due to insufficient sampling frequency used in many studies.

Quantification of variability in trichome patterns

While pattern formation is studied in various areas of biology, little is known about the noise leading to variations between individual realizations of the pattern. One prominent example for de novo pattern formation in plants is the patterning of trichomes on Arabidopsis leaves, which involves genetic regulation and cell-to-cell communication. These processes are potentially variable due to, e.g., the abundance of cell components or environmental conditions. To elevate the understanding of regulatory processes underlying the pattern formation it is crucial to quantitatively analyze the variability in naturally occurring patterns. Here, we review recent approaches toward characterization of noise on trichome initiation. We present methods for the quantification of spatial patterns, which are the basis for data-driven mathematical modeling and enable the analysis of noise from different sources. Besides the insight gained on trichome formation, the examination of observed trichome patterns also shows that highly regulated biological processes can be substantially affected by variability.

Message in a bottle: small signalling peptide outputs during growth and development

Classical and recently found phytohormones play an important role in plant growth and development, but plants additionally control these processes through small signalling peptides. Over 1000 potential small signalling peptide sequences are present in the Arabidopsis genome. However, to date, a mere handful of small signalling peptides have been functionally characterized and few have been linked to a receptor. Here, we assess the potential small signalling peptide outputs, namely the molecular, biochemical, and morphological changes they trigger in Arabidopsis. However, we also include some notable studies in other plant species, in order to illustrate the varied effects that can be induced by small signalling peptides. In addition, we touch on some evolutionary aspects of small signalling peptides, as studying their signalling outputs in single-cell green algae and early land plants will assist in our understanding of more complex land plants. Our overview illustrates the growing interest in the small signalling peptide research area and its importance in deepening our understanding of plant growth and development.

Biophysical and size-dependent perspectives on plant evolution

Physical laws and processes have profoundly influenced plant evolution. Their effects are invariably size dependent and thus subject to scaling as well as biophysical analyses even though these effects differ depending upon the fluid (water or air) in which plants evolve. Although organisms cannot obviate the effects of physical laws and processes, the consequences of these effects can be altered by ontogenetic or phylogenetic alterations in geometry, shape, or orientation as well as in body size. These assertions are examined using theoretical insights and empirical data drawn from extant and fossil plants pertinent to four evolutionary transitions: (1) the evolution of multicellularity, (2) the transition from an aquatic to an aerial habitat, (3) the evolution of vascular tissues, and (4) the evolution of secondary growth by the independent acquisition of cambia. This examination shows how physical laws limit phenotypic expression, but how they also simultaneously provide alternative, potentially adaptive possibilities.

The origins of multicellular organisms

Multicellularity has evolved in several eukaryotic lineages leading to plants, fungi, and animals. Theoretically, in each case, this involved (1) cell-to-cell adhesion with an alignment-of-fitness among cells, (2) cell-to-cell communication, cooperation, and specialization with an export-of-fitness to a multicellular organism, and (3) in some cases, a transition from "simple" to "complex" multicellularity. When mapped onto a matrix of morphologies based on developmental and physical rules for plants, these three phases help to identify a "unicellular ⇒ colonial ⇒ filamentous (unbranched ⇒ branched) ⇒ pseudoparenchymatous ⇒ parenchymatous" morphological transformation series that is consistent with trends observed within each of the three major plant clades. In contrast, a more direct "unicellular ⇒ colonial or siphonous ⇒ parenchymatous" series is observed in fungal and animal lineages. In these contexts, we discuss the roles played by the cooptation, expansion, and subsequent diversification of ancestral genomic toolkits and patterning modules during the evolution of multicellularity. We conclude that the extent to which multicellularity is achieved using the same toolkits and modules (and thus the extent to which multicellularity is homologous among different organisms) differs among clades and even among some closely related lineages.