Multi-scale Dynamical Modeling of T Cell Development from an Early Thymic Progenitor State to Lineage Commitment.

Intrathymic development of committed progenitor (pro)-T cells from multipotent hematopoietic precursors offers an opportunity to dissect the molecular circuitry establishing cell identity in response to environmental signals. This transition encompasses programmed shutoff of stem/progenitor genes, upregulation of T cell specification genes, proliferation, and ultimately commitment. To explain these features in light of reported cis-acting chromatin effects and experimental kinetic data, we develop a three-level dynamic model of commitment based upon regulation of the commitment-linked gene Bcl11b. The levels are (1) a core gene regulatory network (GRN) architecture from transcription factor (TF) perturbation data, (2) a stochastically controlled chromatin-state gate, and (3) a single-cell proliferation model validated by experimental clonal growth and commitment kinetic assays. Using RNA fluorescence in situ hybridization (FISH) measurements of genes encoding key TFs and measured bulk population dynamics, this single-cell model predicts state-switching kinetics validated by measured clonal proliferation and commitment times. The resulting multi-scale model provides a mechanistic framework for dissecting commitment dynamics.

The self-organization of plant microtubules inside the cell volume yields their cortical localization, stable alignment, and sensitivity to external cues.

Many cell functions rely on the ability of microtubules to self-organize as complex networks. In plants, cortical microtubules are essential to determine cell shape as they guide the deposition of cellulose microfibrils, and thus control mechanical anisotropy of the cell wall. Here we analyze how, in turn, cell shape may influence microtubule behavior. Building upon previous models that confined microtubules to the cell surface, we introduce an agent model of microtubules enclosed in a three-dimensional volume. We show that the microtubule network has spontaneous aligned configurations that could explain many experimental observations without resorting to specific regulation. In particular, we find that the preferred cortical localization of microtubules emerges from directional persistence of the microtubules, and their interactions with each other and with the stiff wall. We also identify microtubule parameters that seem relatively insensitive to cell shape, such as length or number. In contrast, microtubule array anisotropy depends on local curvature of the cell surface and global orientation follows robustly the longest axis of the cell. Lastly, we find that geometric cues may be overcome, as the network is capable of reorienting toward weak external directional cues. Altogether our simulations show that the microtubule network is a good transducer of weak external polarity, while at the same time, easily reaching stable global configurations.

Mechanochemical Polarization of Contiguous Cell Walls Shapes Plant Pavement Cells.

The epidermis of aerial plant organs is thought to be limiting for growth, because it acts as a continuous load-bearing layer, resisting tension. Leaf epidermis contains jigsaw puzzle piece-shaped pavement cells whose shape has been proposed to be a result of subcellular variations in expansion rate that induce local buckling events. Paradoxically, such local compressive buckling should not occur given the tensile stresses across the epidermis. Using computational modeling, we show that the simplest scenario to explain pavement cell shapes within an epidermis under tension must involve mechanical wall heterogeneities across and along the anticlinal pavement cell walls between adjacent cells. Combining genetics, atomic force microscopy, and immunolabeling, we demonstrate that contiguous cell walls indeed exhibit hybrid mechanochemical properties. Such biochemical wall heterogeneities precede wall bending. Altogether, this provides a possible mechanism for the generation of complex plant cell shapes.

A continuous growth model for plant tissue.

Morphogenesis in plants and animals involves large irreversible deformations. In plants, the response of the cell wall material to internal and external forces is determined by its mechanical properties. An appropriate model for plant tissue growth must include key features such as anisotropic and heterogeneous elasticity and cell dependent evaluation of mechanical variables such as turgor pressure, stress and strain. In addition, a growth model needs to cope with cell divisions as a necessary part of the growth process. Here we develop such a growth model, which is capable of employing not only mechanical signals but also morphogen signals for regulating growth. The model is based on a continuous equation for updating the resting configuration of the tissue. Simultaneously, material properties can be updated at a different time scale. We test the stability of our model by measuring convergence of growth results for a tissue under the same mechanical and material conditions but with different spatial discretization. The model is able to maintain a strain field in the tissue during re-meshing, which is of particular importance for modeling cell division. We confirm the accuracy of our estimations in two and three-dimensional simulations, and show that residual stresses are less prominent if strain or stress is included as input signal to growth. The approach results in a model implementation that can be used to compare different growth hypotheses, while keeping residual stresses and other mechanical variables updated and available for feeding back to the growth and material properties.

A Model Analysis of Mechanisms for Radial Microtubular Patterns at Root Hair Initiation Sites.

Plant cells have two main modes of growth generating anisotropic structures. Diffuse growth where whole cell walls extend in specific directions, guided by anisotropically positioned cellulose fibers, and tip growth, with inhomogeneous addition of new cell wall material at the tip of the structure. Cells are known to regulate these processes via molecular signals and the cytoskeleton. Mechanical stress has been proposed to provide an input to the positioning of the cellulose fibers via cortical microtubules in diffuse growth. In particular, a stress feedback model predicts a circumferential pattern of fibers surrounding apical tissues and growing primordia, guided by the anisotropic curvature in such tissues. In contrast, during the initiation of tip growing root hairs, a star-like radial pattern has recently been observed. Here, we use detailed finite element models to analyze how a change in mechanical properties at the root hair initiation site can lead to star-like stress patterns in order to understand whether a stress-based feedback model can also explain the microtubule patterns seen during root hair initiation. We show that two independent mechanisms, individually or combined, can be sufficient to generate radial patterns. In the first, new material is added locally at the position of the root hair. In the second, increased tension in the initiation area provides a mechanism. Finally, we describe how a molecular model of Rho-of-plant (ROP) GTPases activation driven by auxin can position a patch of activated ROP protein basally along a 2D root epidermal cell plasma membrane, paving the way for models where mechanical and molecular mechanisms cooperate in the initial placement and outgrowth of root hairs.

Physical forces regulate plant development and morphogenesis.

Plant cells in tissues experience mechanical stress not only as a result of high turgor, but also through interaction with their neighbors. Cells can expand at different rates and in different directions from neighbors with which they share a cell wall. This in connection with specific tissue shapes and properties of the cell wall material can lead to intricate stress patterns throughout the tissue. Two cellular responses to mechanical stress are a microtubule cytoskeletal response that directs new wall synthesis so as to resist stress, and a hormone transporter response that regulates transport of the hormone auxin, a regulator of cell expansion. Shape changes in plant tissues affect the pattern of stresses in the tissues, and at the same time, via the cellular stress responses, the pattern of stresses controls cell growth, which in turn changes tissue shape, and stress pattern. This feedback loop controls plant morphogenesis, and explains several previously mysterious aspects of plant growth.

Subcellular and supracellular mechanical stress prescribes cytoskeleton behavior in Arabidopsis cotyledon pavement cells.

Although it is a central question in biology, how cell shape controls intracellular dynamics largely remains an open question. Here, we show that the shape of Arabidopsis pavement cells creates a stress pattern that controls microtubule orientation, which then guides cell wall reinforcement. Live-imaging, combined with modeling of cell mechanics, shows that microtubules align along the maximal tensile stress direction within the cells, and atomic force microscopy demonstrates that this leads to reinforcement of the cell wall parallel to the microtubules. This feedback loop is regulated: cell-shape derived stresses could be overridden by imposed tissue level stresses, showing how competition between subcellular and supracellular cues control microtubule behavior. Furthermore, at the microtubule level, we identified an amplification mechanism in which mechanical stress promotes the microtubule response to stress by increasing severing activity. These multiscale feedbacks likely contribute to the robustness of microtubule behavior in plant epidermis. DOI: http://dx.doi.org/10.7554/eLife.01967.001.

Stress and strain provide positional and directional cues in development.

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.

Computational multiscale modeling of embryo development.

Recent advances in live imaging and genetics of mammalian development which integrate observations of biochemical activity, cell-cell signaling and mechanical interactions between cells pave the way for predictive mathematical multi-scale modeling. In early mammalian embryo development, two of the most critical events which lead to tissue patterning involve changes in gene expression as well as mechanical interactions between cells. We discuss the relevance of mathematical modeling of multi-cellular systems and in particular in simulating these patterns and describe some of the technical challenges one encounters. Many of these issues are not unique for the embryonic system but are shared by other multi-cellular modeling areas.

On evaluating models in Computational Morphodynamics.

Recent advances in experimental plant biology have led to an increased potential to investigate plant development at a systems level. The emerging research field of Computational Morphodynamics has the aim to lead this development by combining dynamic spatial experimental data with computational models of molecular networks, growth, and mechanics in a multicellular context. The increased number of published models may lead to a diversification of our understanding of the systems, and methods for evaluating, comparing, and sharing models are main challenges for the future. We will discuss this problem using ideas originating from physics and use recent computational models of plant development as examples.

Simulating the mammalian blastocyst--molecular and mechanical interactions pattern the embryo.

Mammalian embryogenesis is a dynamic process involving gene expression and mechanical forces between proliferating cells. The exact nature of these interactions, which determine the lineage patterning of the trophectoderm and endoderm tissues occurring in a highly regulated manner at precise periods during the embryonic development, is an area of debate. We have developed a computational modeling framework for studying this process, by which the combined effects of mechanical and genetic interactions are analyzed within the context of proliferating cells. At a purely mechanical level, we demonstrate that the perpendicular alignment of the animal-vegetal (a-v) and embryonic-abembryonic (eb-ab) axes is a result of minimizing the total elastic conformational energy of the entire collection of cells, which are constrained by the zona pellucida. The coupling of gene expression with the mechanics of cell movement is important for formation of both the trophectoderm and the endoderm. In studying the formation of the trophectoderm, we contrast and compare quantitatively two hypotheses: (1) The position determines gene expression, and (2) the gene expression determines the position. Our model, which couples gene expression with mechanics, suggests that differential adhesion between different cell types is a critical determinant in the robust endoderm formation. In addition to differential adhesion, two different testable hypotheses emerge when considering endoderm formation: (1) A directional force acts on certain cells and moves them into forming the endoderm layer, which separates the blastocoel and the cells of the inner cell mass (ICM). In this case the blastocoel simply acts as a static boundary. (2) The blastocoel dynamically applies pressure upon the cells in contact with it, such that cell segregation in the presence of differential adhesion leads to the endoderm formation. To our knowledge, this is the first attempt to combine cell-based spatial mechanical simulations with genetic networks to explain mammalian embryogenesis. Such a framework provides the means to test hypotheses in a controlled in silico environment.

Alignment between PIN1 polarity and microtubule orientation in the shoot apical meristem reveals a tight coupling between morphogenesis and auxin transport.

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.

Modeling auxin-regulated development.

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.

Modeling plant growth and pattern formation.

Plants continue to grow and generate new organs in symmetric patterns throughout their lives. This development requires an interconnected regulation of genes, hormones, and anisotropic growth, which in part is guided by environmental cues. Recently, several studies have used a combination of experiments and mathematical modeling to elucidate the mechanisms behind different growth and molecular patterns in plants. The computational models were used to investigate the often non-intuitive consequences of different hypotheses, and the in silico simulations of the models inspired further experimentation.

Developmental patterning by mechanical signals in Arabidopsis.

A central question in developmental biology is whether and how mechanical forces serve as cues for cellular behavior and thereby regulate morphogenesis. We found that morphogenesis at the Arabidopsis shoot apex depends on the microtubule cytoskeleton, which in turn is regulated by mechanical stress. A combination of experiments and modeling shows that a feedback loop encompassing tissue morphology, stress patterns, and microtubule-mediated cellular properties is sufficient to account for the coordinated patterns of microtubule arrays observed in epidermal cells, as well as for patterns of apical morphogenesis.