Henrik Jönsson

The morphogenesis of organs necessarily involves mechanical interactions and changes in mechanical properties of a tissue. A long standing question is how such changes are directed on a cellular scale while being coordinated at a tissular scale. Growing evidence suggests that mechanical cues are participating in the control of growth and morphogenesis during development. We introduce a mechanical model that represents the deposition of cellulose fibers in primary plant walls. In the model both the degree of material anisotropy and the anisotropy direction are regulated by stress anisotropy. We show that the finite element shell model and the simpler triangular biquadratic springs approach provide equally adequate descriptions of cell mechanics in tissue pressure simulations of the epidermis. In a growing organ, where circumferentially organized fibers act as a main controller of longitudinal growth, we show that the fiber direction can be correlated with both the maximal stress direction and the direction orthogonal to the maximal strain direction. However, when dynamic updates of the fiber direction are introduced, the mechanical stress provides a robust directional cue for the circumferential organization of the fibers, whereas the orthogonal to maximal strain model leads to an unstable situation where the fibers reorient longitudinally. Our investigation of the more complex shape and growth patterns in the shoot apical meristem where new organs are initiated shows that a stress based feedback on fiber directions is capable of reproducing the main features of in vivo cellulose fiber directions, deformations and material properties in different regions of the shoot. In particular, we show that this purely mechanical model can create radially distinct regions such that cells expand slowly and isotropically in the central zone while cells at the periphery expand more quickly and in the radial direction, which is a well established growth pattern in the meristem. Development and morphogenesis of tissues are dependent on a coordination between cell differentiation, proliferation and growth. Plants, which lack cell migration, control directional growth of tissues by adjusting cellulose fiber directions so forming the organ shapes. It has recently been shown that mechanical cues can guide these fibers. We developed detailed mechanical models to investigate how fiber directions may be responding to mechanical cues and what consequences this may have for positional and directional growth patterns. We show that a model in which fibers align to maximal stress directions spontaneously generates a radial zonation in the shoot, recapitulating the slowly growing center and more rapidly growing peripheral region previously observed in the meristem. These radial patterns emerging from mechanics are in striking correspondence to the expression patterns of the genes important for stem cell maintenance, which attain similar radial domains. We also show that the stress model can robustly define anisotropically growing organs, which emphasizes the potential importance of stress in generating correct organ shapes in plants.

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Background: 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. Results: 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. Conclusions: 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.

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.

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.