The plant stem cell regulator WUSCHEL is shown to repress differentiation-promoting transcription factors. This regulatory network is analyzed with a computational model of the three-dimensional shoot stem cell niche and a combination of genetic perturbation and live imaging.
We find that the transcription factor (TF) WUSCHEL (WUS) directly binds to the promoters and represses a group of genes including key TFs involved in differentiation thus keeping them repressed in the stem cells of the plant shoot, a mechanistic logic that is similar to animal stem cell regulation.We use a three-dimensional computational model of the plant shoot stem cell niche to show that the WUS-mediated repression of the differentiation program along with the previously reported activation of its own negative regulator leads to a robust stem cell homeostasis in a dynamic growth environment.Live imaging of target genes upon transient manipulation of WUS levels is combined with model perturbations to validate the proposed network and to connect it with a large body of previous experimental work.
In animal systems, master regulatory transcription factors (TFs) mediate stem cell maintenance through a direct transcriptional repression of differentiation promoting TFs. Whether similar mechanisms operate in plants is not known. In plants, shoot apical meristems serve as reservoirs of stem cells that provide cells for all above ground organs. WUSCHEL, a homeodomain TF produced in cells of the niche, migrates into adjacent cells where it specifies stem cells. Through high-resolution genomic analysis, we show that WUSCHEL represses a large number of genes that are expressed in differentiating cells including a group of differentiation promoting TFs involved in leaf development. We show that WUS directly binds to the regulatory regions of differentiation promoting TFs; KANADI1, KANADI2, ASYMMETRICLEAVES2 and YABBY3 to repress their expression. Predictions from a computational model, supported by live imaging, reveal that WUS-mediated repression prevents premature differentiation of stem cell progenitors, being part of a minimal regulatory network for meristem maintenance. Our work shows that direct transcriptional repression of differentiation promoting TFs is an evolutionarily conserved logic for stem cell regulation.
central zone; CLAVATA3; shoot apical meristem; stem cell niche; WUSCHEL
In many developing tissues, neighboring cells enter different developmental pathways, resulting in a fine-grained pattern of different cell states. The most common mechanism that generates such patterns is lateral inhibition, for example through Delta-Notch coupling. In this work, we simulate growth of tissues consisting of a hexagonal arrangement of cells laterally inhibiting their neighbors. We find that tissue growth by cell division and cell migration tends to produce ordered patterns, whereas lateral growth leads to disordered, patchy patterns. Ordered patterns are very robust to mutations (gene silencing or activation) in single cells. In contrast, mutation in a cell of a disordered tissue can produce a larger and more widespread perturbation of the pattern. In tissues where ordered and disordered patches coexist, the perturbations spread mostly at boundaries between patches. If cell division occurs on time scales faster than the degradation time, disordered patches will appear. Our work suggests that careful experimental characterization of the disorder in tissues could pinpoint where and how the tissue is susceptible to large-scale damage even from single cell mutations.
An intriguing phenomenon in plant development is the timing and positioning of lateral organ initiation, which is a fundamental aspect of plant architecture. Although important progress has been made in elucidating the role of auxin transport in the vegetative shoot to explain the phyllotaxis of leaf formation in a spiral fashion, a model study of the role of auxin transport in whorled organ patterning in the expanding floral meristem is not available yet. We present an initial simulation approach to study the mechanisms that are expected to play an important role. Starting point is a confocal imaging study of Arabidopsis floral meristems at consecutive time points during flower development. These images reveal auxin accumulation patterns at the positions of the organs, which strongly suggests that the role of auxin in the floral meristem is similar to the role it plays in the shoot apical meristem. This is the basis for a simulation study of auxin transport through a growing floral meristem, which may answer the question whether auxin transport can in itself be responsible for the typical whorled floral pattern. We combined a cellular growth model for the meristem with a polar auxin transport model. The model predicts that sepals are initiated by auxin maxima arising early during meristem outgrowth. These form a pre-pattern relative to which a series of smaller auxin maxima are positioned, which partially overlap with the anlagen of petals, stamens, and carpels. We adjusted the model parameters corresponding to properties of floral mutants and found that the model predictions agree with the observed mutant patterns. The predicted timing of the primordia outgrowth and the timing and positioning of the sepal primordia show remarkable similarities with a developing flower in nature.
A fundamental question in developmental biology is how spatial patterns are
self-organized from homogeneous structures. In 1952, Turing proposed the
reaction-diffusion model in order to explain this issue. Experimental evidence
of reaction-diffusion patterns in living organisms was first provided by the
pigmentation pattern on the skin of fishes in 1995. However, whether or not this
mechanism plays an essential role in developmental events of living organisms
remains elusive. Here we show that a reaction-diffusion model can successfully
explain the shoot apical meristem (SAM) development of plants. SAM of plants
resides in the top of each shoot and consists of a central zone (CZ) and a
surrounding peripheral zone (PZ). SAM contains stem cells and continuously
produces new organs throughout the lifespan. Molecular genetic studies using
Arabidopsis thaliana revealed that the formation and
maintenance of the SAM are essentially regulated by the feedback interaction
between WUSHCEL (WUS) and CLAVATA (CLV). We developed a mathematical model of
the SAM based on a reaction-diffusion dynamics of the WUS-CLV interaction,
incorporating cell division and the spatial restriction of the dynamics. Our
model explains the various SAM patterns observed in plants, for example,
homeostatic control of SAM size in the wild type, enlarged or fasciated SAM in
clv mutants, and initiation of ectopic secondary meristems
from an initial flattened SAM in wus mutant. In addition, the
model is supported by comparing its prediction with the expression pattern of
WUS in the wus mutant. Furthermore, the
model can account for many experimental results including reorganization
processes caused by the CZ ablation and by incision through the meristem center.
We thus conclude that the reaction-diffusion dynamics is probably indispensable
for the SAM development of plants.
Biomass yield of agronomic crops is influenced by a number of factors, including crop species, soil type, applied nutrients, water availability, and plant population. This article is focused on dependence of biomass yield (Mg ha−1 and g plant−1) on plant population (plants m−2). Analysis includes data from the literature for three independent studies with the warm-season annual corn (Zea mays L.) grown in the United States. Data are analyzed with a simple exponential mathematical model which contains two parameters, viz. Ym (Mg ha−1) for maximum yield at high plant population and c (m2 plant−1) for the population response coefficient. This analysis leads to a new parameter called characteristic plant population, xc = 1/c (plants m−2). The model is shown to describe the data rather well for the three field studies. In one study measurements were made of solar radiation at different positions in the plant canopy. The coefficient of absorption of solar energy was assumed to be the same as c and provided a physical basis for the exponential model. The three studies showed no definitive peak in yield with plant population, but generally exhibited asymptotic approach to maximum yield with increased plant population. Values of xc were very similar for the three field studies with the same crop species.
Stem cells reside in a plant's shoot meristem throughout its life and are main regulators of above-ground plant development. The stem cell maintenance depends on a feedback network between the CLAVATA and WUSCHEL genes. The CLAVATA3 peptide binds to the CLAVATA1 receptor leading to WUSCHEL inhibition. WUSCHEL, on the other hand, activates CLAVATA3 expression. Recent experiments suggest a second pathway where CLAVATA3 inhibits WUSCHEL via the CORYNE receptor pathway. An interesting question, central for understanding the receptor signaling, is why the clavata1-11 null mutant has a weaker phenotype compared with the clavata1-1 non-null mutant. It has been suggested that this relies on interference from the mutated CLAVATA1 acting on the CORYNE pathway.
We present two models for the CLAVATA-WUSCHEL feedback network including two receptor pathways for WUSCHEL repression and differing only by the hypothesized mechanisms for the clavata1-1 non-null mutant. The first model is an implementation of the previously suggested interference mechanism. The other model assumes an unaltered binding between CLAVATA3 and the mutated CLAVATA1 but with a loss of propagated signal into the cell. We optimize the models using data from wild type and four single receptor mutant experiments and use data from two receptor double mutant experiments in a validation step. Both models are able to explain all seven phenotypes and in addition qualitatively predict CLAVATA3 perturbations. The two models for the clavata1-1 mutant differ in the direct mechanism of the mutant, but they also predict other differences in the dynamics of the stem cell regulating network. We show that the interference hypothesis leads to an abundance of receptors, while the loss-of-signal hypothesis leads to sequestration of CLAVATA3 and relies on degradation or internalization of the bound CLAVATA1 receptor.
Using computational modeling, we show that an interference hypothesis and a more parsimonious loss-of-signal hypothesis for a clavata1 non-null mutant both lead to behaviors predicting wild type and six receptor mutant experiments. Although the two models have identical implementations of the unperturbed feedback network for stem cell regulation, we can point out model-predicted differences that may be resolved in future experiments.
The high rates of failure in oncology drug clinical trials highlight the problems of using pre-clinical data to predict the clinical effects of drugs. Patient population heterogeneity and unpredictable physiology complicate pre-clinical cancer modeling efforts. We hypothesize that gene networks associated with cancer outcome in heterogeneous patient populations could serve as a reference for identifying drug effects. Here we propose a novel in vivo genetic interaction which we call ‘synergistic outcome determination’ (SOD), a concept similar to ‘Synthetic Lethality’. SOD is defined as the synergy of a gene pair with respect to cancer patients' outcome, whose correlation with outcome is due to cooperative, rather than independent, contributions of genes. The method combines microarray gene expression data with cancer prognostic information to identify synergistic gene-gene interactions that are then used to construct interaction networks based on gene modules (a group of genes which share similar function). In this way, we identified a cluster of important epigenetically regulated gene modules. By projecting drug sensitivity-associated genes on to the cancer-specific inter-module network, we defined a perturbation index for each drug based upon its characteristic perturbation pattern on the inter-module network. Finally, by calculating this index for compounds in the NCI Standard Agent Database, we significantly discriminated successful drugs from a broad set of test compounds, and further revealed the mechanisms of drug combinations. Thus, prognosis-guided synergistic gene-gene interaction networks could serve as an efficient in silico tool for pre-clinical drug prioritization and rational design of combinatorial therapies.
Imaging and computational modeling of the Arabidopsis shoot meristem epidermis suggests that biomechanical signals coordinately regulate auxin efflux carrier distribution and microtubule patterning to orchestrate the extent and directionality of growth.
Morphogenesis during multicellular development is regulated by intercellular signaling molecules as well as by the mechanical properties of individual cells. In particular, normal patterns of organogenesis in plants require coordination between growth direction and growth magnitude. How this is achieved remains unclear. Here we show that in Arabidopsis thaliana, auxin patterning and cellular growth are linked through a correlated pattern of auxin efflux carrier localization and cortical microtubule orientation. Our experiments reveal that both PIN1 localization and microtubule array orientation are likely to respond to a shared upstream regulator that appears to be biomechanical in nature. Lastly, through mathematical modeling we show that such a biophysical coupling could mediate the feedback loop between auxin and its transport that underlies plant phyllotaxis.
The proper development of plant organs such as leaves or flowers depends both on localized growth, which can be controlled by the plant hormone auxin, and directional growth, which is dependent on each cell's microtubule cytoskeleton. In this paper we show that at the shoot apex where organs initiate the orientation of the microtubule cytoskeleton is correlated with the orientation of the auxin transporter PIN1, suggesting coordination between growth patterning at the tissue level and directional growth at the cellular level. Recent work has indicated that mechanical signals play a role in orienting the plant microtubule network, and here we show that such signals can also orient PIN1. In addition, we demonstrate through mathematical modeling that an auxin transport system that is coordinated by mechanical signals akin to those we observed in vivo is sufficient to give rise to the patterns of organ outgrowth found in the plant Arabidopsis thaliana.
Cell proliferation affects both cellular geometry and topology in a growing tissue, and hence rules for cell division are key to understanding multicellular development. Epithelial cell layers have for long times been used to investigate how cell proliferation leads to tissue-scale properties, including organism-independent distributions of cell areas and number of neighbors. We use a cell-based two-dimensional tissue growth model including mechanics to investigate how different cell division rules result in different statistical properties of the cells at the tissue level. We focus on isotropic growth and division rules suggested for plant cells, and compare the models with data from the Arabidopsis shoot. We find that several division rules can lead to the correct distribution of number of neighbors, as seen in recent studies. In addition we find that when also geometrical properties are taken into account other constraints on the cell division rules result. We find that division rules acting in favor of equally sized and symmetrically shaped daughter cells can best describe the statistical tissue properties.
Although bacteria are unicellular organisms, they have the ability to act in concert by synthesizing and detecting small diffusing autoinducer molecules. The phenomenon, known as quorum sensing, has mainly been proposed to serve as a means for cell-density measurement. Here, we use a cell-based model of growing bacterial microcolonies to investigate a quorum-sensing mechanism at a single cell level. We show that the model indeed predicts a density-dependent behavior, highly dependent on local cell-clustering and the geometry of the space where the colony is evolving. We analyze the molecular network with two positive feedback loops to find the multistability regions and show how the quorum-sensing mechanism depends on different model parameters. Specifically, we show that the switching capability of the network leads to more constraints on parameters in a natural environment where the bacteria themselves produce autoinducer than compared to situations where autoinducer is introduced externally. The cell-based model also allows us to investigate mixed populations, where non-producing cheater cells are shown to have a fitness advantage, but still cannot completely outcompete producer cells. Simulations, therefore, are able to predict the relative fitness of cheater cells from experiments and can also display and account for the paradoxical phenomenon seen in experiments; even though the cheater cells have a fitness advantage in each of the investigated groups, the overall effect is an increase in the fraction of producer cells. The cell-based type of model presented here together with high-resolution experiments will play an integral role in a more explicit and precise comparison of models and experiments, addressing quorum sensing at a cellular resolution.
Unicellular organisms have the ability to communicate with each other via signaling molecules, leading to correlated behaviors resembling that of higher organisms. This process, called quorum sensing, allows the cells to monitor the population size or density in a decentralized fashion and perform a common task when these parameters exceed predefined threshold values. The quorum sensing mechanism has been implicated in diverse functions such as producing bioluminescence, virulence factors, and initiating biofilm formation. Complex emergent behaviors, such as quorum sensing, can be hard to analyze and understand without the assistance of mathematical and computational models. Here, we present a cell-based model of proliferating bacterial microcolonies and investigate how population-level responses can emerge from the signaling and mechanical properties of individual cells. We study both signaling variations within homogeneous (homotypic) bacterial populations as well as signaling and competition in mixed heterotypic populations. We investigate in particular how population size, local cell density, and spatial confinement affect colony growth and predict strategies for facilitating quorum sensing. We also show that the interplay between “honest” quorum sensing signal producing bacteria and non-producing “cheaters” can lead to emergent feedback regulation via differentiated growth that provides only a transient benefit for cheating cells.
Plants maintain stem cells in their meristems as a source for new undifferentiated cells throughout their life. Meristems are small groups of cells that provide the microenvironment that allows stem cells to prosper. Homeostasis of a stem cell domain within a growing meristem is achieved by signalling between stem cells and surrounding cells. We have here simulated the origin and maintenance of a defined stem cell domain at the tip of Arabidopsis shoot meristems, based on the assumption that meristems are self-organizing systems. The model comprises two coupled feedback regulated genetic systems that control stem cell behaviour. Using a minimal set of spatial parameters, the mathematical model allows to predict the generation, shape and size of the stem cell domain, and the underlying organizing centre. We use the model to explore the parameter space that allows stem cell maintenance, and to simulate the consequences of mutations, gene misexpression and cell ablations.
The phytohormone auxin plays an essential role in many aspects of plant growth and development. Its patterning, intercellular transport, and means of signaling have been extensively studied both in experiments and computational models. Here, we present a review of models of auxin-regulated development in different plant tissues. This includes models of organ initiation in the shoot apical meristem, development of vascular strands in leafs and stems, and auxin-related functioning in roots. The examples show how mathematical modeling can help to examine expected and unexpected behavior of the system, challenge our knowledge and hypotheses, obtain quantitative results, or suggest new experiments and ways to approach a problem.
Computer simulations of plant responses to auxin explain previously perplexing aspects of the transport, regulation, and metabolism of this phytohormone.
Local activation of Rho GTPases is important for many functions including cell polarity, morphology, movement, and growth. Although a number of molecules affecting Rho-of-Plants small GTPase (ROP) signalling are known, it remains unclear how ROP activity becomes spatially organised. Arabidopsis root hair cells produce patches of ROP at consistent and predictable subcellular locations, where root hair growth subsequently occurs.
We present a mathematical model to show how interaction of the plant hormone auxin with ROPs could spontaneously lead to localised patches of active ROP via a Turing or Turing-like mechanism. Our results suggest that correct positioning of the ROP patch depends on the cell length, low diffusion of active ROP, a gradient in auxin concentration, and ROP levels. Our theory provides a unique explanation linking the molecular biology to the root hair phenotypes of multiple mutants and transgenic lines, including OX-ROP, CA-rop, aux1, axr3, tip1, eto1, etr1, and the triple mutant aux1 ein2 gnomeb.
We show how interactions between Rho GTPases (in this case ROPs) and regulatory molecules (in this case auxin) could produce characteristic subcellular patterning that subsequently affects cell shape. This has important implications for research on the morphogenesis of plants and other eukaryotes. Our results also illustrate how gradient-regulated Turing systems provide a particularly robust and flexible mechanism for pattern formation.
The ErbB family of receptors activates intracellular signaling pathways that control cellular proliferation, growth, differentiation and apoptosis. Given these central roles, it is not surprising that overexpression of the ErbB receptors is often associated with carcinogenesis. Therefore, extensive laboratory studies have been devoted to understanding the signaling events associated with ErbB activation.
Systems biology has contributed significantly to our current understanding of ErbB signaling networks. However, although computational models have grown in complexity over the years, little work has been done to consider the spatial-temporal dynamics of receptor interactions and to evaluate how spatial organization of membrane receptors influences signaling transduction. Herein, we explore the impact of spatial organization of the epidermal growth factor receptor (ErbB1/EGFR) on the initiation of downstream signaling. We describe the development of an algorithm that couples a spatial stochastic model of membrane receptors with a nonspatial stochastic model of the reactions and interactions in the cytosol. This novel algorithm provides a computationally efficient method to evaluate the effects of spatial heterogeneity on the coupling of receptors to cytosolic signaling partners.
Mathematical models of signal transduction rarely consider the contributions of spatial organization due to high computational costs. A hybrid stochastic approach simplifies analyses of the spatio-temporal aspects of cell signaling and, as an example, demonstrates that receptor clustering contributes significantly to the efficiency of signal propagation from ligand-engaged growth factor receptors.
Colonies of bacterial cells can display complex collective dynamics, frequently culminating in the formation of biofilms and other ordered super-structures. Recent studies suggest that to cope with local environmental challenges, bacterial cells can actively seek out small chambers or cavities and assemble there, engaging in quorum sensing behavior. By using a novel microfluidic device, we showed that within chambers of distinct shapes and sizes allowing continuous cell escape, bacterial colonies can gradually self-organize. The directions of orientation of cells, their growth, and collective motion are mutually correlated and dictated by the chamber walls and locations of chamber exits. The ultimate highly organized steady state is conducive to a more-organized escape of cells from the chambers and increased access of nutrients into and evacuation of waste out of the colonies. Using a computational model, we suggest that the lengths of the cells might be optimized to maximize self-organization while minimizing the potential for stampede-like exit blockage. The self-organization described here may be crucial for the early stage of the organization of high-density bacterial colonies populating small, physically confined growth niches. It suggests that this phenomenon can play a critical role in bacterial biofilm initiation and development of other complex multicellular bacterial super-structures, including those implicated in infectious diseases.
Bacterial cells form colonies with complex organization (aka biofilms), particularly in response to hostile environmental conditions. Recent studies have shown that biofilm development occurs when bacterial cells seek out small cavities and populate them at high densities. However, bacteria in cavities may suffer from poor nutrient supply or waste removal, or disorganized expansion leading to blockage of cell escape. In this study, we observed Escherichia coli in a microfluidic device that allows direct observation of the growth and development of cell colonies in microchambers of different shapes and sizes through multiple generations. Combining this experimentation with computational analysis of colony growth and expansion, we characterize a process of colony self-organization that results in a high degree of correlation between the directions of cell orientation and growth of collective cell movement. We also find that this self-organization can significantly facilitate efficient escape of cells from the confines of cavities where they reside, while improving the access of nutrients into the colony interior. Finally, we suggest that the aspect ratio of the shape of E. coli and other similar bacteria might be generally subject to a constraint related to colony self-organization.
In nature, bacteria often found themselves in high-density colonies. The combination of a novel microfluidic device and computational analysis reveals an unexpected self-organization behavior of tightly packed bacterial cells.
The brain-derived protein S100B has been shown to be a useful marker of brain injury of different etiologies. Cognitive dysfunction after cardiac surgery using cardiopulmonary bypass has been reported to occur in up to 70% of patients. In this study we tried to evaluate S100B as a marker for cognitive dysfunction after coronary bypass surgery with cardiopulmonary bypass in a model where the inflow of S100B from shed mediastinal blood was corrected for.
56 patients scheduled for coronary artery bypass grafting underwent prospective neuropsychological testing. The test scores were standardized and an impairment index was constructed. S100B was sampled at the end of surgery, hourly for the first 6 hours, and then 8, 10, 15, 24 and 48 hours after surgery. None of the patients received autotransfusion.
In simple linear analysis, no significant relation was found between S100B levels and neuropsychological outcome. In a backwards stepwise regression analysis the three variables, S100B levels at the end of cardiopulmonary bypass, S100B levels 1 hour later and the age of the patients were found to explain part of the neuropsychological deterioration (r = 0.49, p < 0.005).
In this study we found that S100B levels 1 hour after surgery seem to be the most informative. Our attempt to control the increased levels of S100B caused by contamination from the surgical field did not yield different results. We conclude that the clinical value of S100B as a predictive measurement of postoperative cognitive dysfunction after cardiac surgery is limited.