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In the past 20-30 years, developmental biologists have made tremendous progress in identifying genes required for the specification of individual cell types of an organ and in describing how they interact in genetic networks. In comparison, very little is known about the mechanisms that regulate tissue polarity and overall organ patterning. Gynoecia and fruits from members of the Brassicaceae family of flowering plants provide excellent model systems to study organ patterning and tissue specification because they become partitioned into distinct domains whose formation is determined by polarity establishment both at a cellular and whole tissue level. Interactions among key regulators of Arabidopsis gynoecium and fruit development have revealed a network of upstream transcription factor activities required for such tissue differentiation. Regulation of the plant hormone auxin is emerging as both an immediate downstream output and input of these activities, and here we aim to provide an overview of the current knowledge regarding the link between auxin and female reproductive development in plants. In this review, we will also demonstrate how available data can be exploited in a mathematical modeling approach to reveal and understand the feedback regulatory circuits that underpin the polarity establishment, necessary to guide auxin flows. [ABSTRACT FROM AUTHOR]

Cdc42, Rac, and Rho are small GTPases known to play a central role in signal transduction to the actin cytoskeleton. These proteins regulate cell motility, by affecting nucleation, uncapping, and depolymerization of actin filaments, and acto-myosin contractility. Studies of crosstalk and mutual feedbacks in these three proteins have led to a number of proposals for their interaction. At the same time, observations of the spatiotemporal dynamics of Rho-family proteins give evidence of spatial polarization and mutual exclusion between Cdc42/Rac and Rho. In this paper, we formulate a mathematical model to account for such observations, based on the known underlying biology of these proteins. We first investigate which of the crosstalk schemes proposed in the literature is consistent with observed dynamics, and then derive a simple model that can correctly describe these dynamics (assuming crosstalk is mediated via Rho GEFs). We show that cooperativity is an essential ingredient in the interactions of the proteins. The co-occurrence of a stable rest state with the possibility of fast spatial segregation can be related to bistability in a set of underlying ODEs in which the inactive forms of these proteins are fixed at a constant level. We show that the fast diffusion of the inactive forms is essential for stabilizing the transition fronts in the PDE formulation of the model, leading to robust spatial polarization, rather than traveling waves. [ABSTRACT FROM AUTHOR]

Abstract: Macrophages from animals prone to autoimmune (type 1) diabetes differ from those of diabetes-resistant animals in processing and clearing apoptotic cells. Using in vitro time-course assays of the number of engulfed apoptotic cells observed within macrophages, we quantified these differences in non-obese diabetic (NOD) versus Balb/c mice. Simple models lead to several elementary parameter estimation techniques. We used these to compute approximate rates of macrophage engulfment and digestion of apoptotic cells from basic features of the data (such as initial rise-times, phagocytic index and percent phagocytosis). Combining these estimates with full fitting of a sequence of model variants to the data, we find that macrophages from normal (Balb/c) mice engulf apoptotic cells up to four times faster than macrophages from the diabetes-prone (NOD) mice. Further, Balb/c macrophages appear to undergo an activation step before achieving their high engulfment rate. In NOD macrophages, we did not see evidence for this activation step. Rates of digestion of engulfed apoptotic cells by macrophages are similar in both types. Since macrophage clearance is an important mechanism of disposal of self-antigen, these macrophage defects could potentially be a factor in predisposition to type 1 diabetes. [Copyright &y& Elsevier]

The phytohormone auxin is implied in steering various developmental decisions during plant morphogenesis in a concentration-dependent manner. Auxin maxima have been shown to maintain meristematic activity, for example, of the root apical meristem, and position new sites of outgrowth, such as during lateral root initiation and phyllotaxis. More recently, it has been demonstrated that sites of auxin minima also provide positional information. In the developing Arabidopsis fruit, auxin minima are required for correct differentiation of the valve margin. It remains unclear, however, how this auxin minimum is generated and maintained. Here, we employ a systems biology approach to model auxin transport based on experimental observations. This allows us to determine the minimal requirements for its establishment. Our simulations reveal that two alternative processes—which we coin "flux-barrier" and "flux-passage"—are both able to generate an auxin minimum, but under different parameter settings. Both models are in principle able to yield similar auxin profiles but present qualitatively distinct patterns of auxin flux. The models were tested by tissue-specific inducible ablation, revealing that the auxin minimum in the fruit is most likely generated by a flux-passage process. Model predictions were further supported through 3D PIN localization imaging and implementing experimentally observed transporter localization. Through such an experimental–modeling cycle, we predict how the auxin minimum gradually matures during fruit development to ensure timely fruit opening and seed dispersal. We investigate the mechanism leading to a spatially confined auxin minimum required for Arabidopsis fruit opening and seed dispersal. Our experiment–modeling cycle reveals a counterintuitive mechanism of its formation: efflux activity creates an auxin minimum strip that is accompanied by high auxin fluxes crossing it perpendicularly. This dynamical process can be associated with the maturation of the fruit. [ABSTRACT FROM AUTHOR]

Summary: In plants, where cells cannot migrate, asymmetric cell divisions (ACDs) must be confined to the appropriate spatial context. We investigate tissue-generating asymmetric divisions in a stem cell daughter within the Arabidopsis root. Spatial restriction of these divisions requires physical binding of the stem cell regulator SCARECROW (SCR) by the RETINOBLASTOMA-RELATED (RBR) protein. In the stem cell niche, SCR activity is counteracted by phosphorylation of RBR through a cyclinD6;1-CDK complex. This cyclin is itself under transcriptional control of SCR and its partner SHORT ROOT (SHR), creating a robust bistable circuit with either high or low SHR-SCR complex activity. Auxin biases this circuit by promoting CYCD6;1 transcription. Mathematical modeling shows that ACDs are only switched on after integration of radial and longitudinal information, determined by SHR and auxin distribution, respectively. Coupling of cell-cycle progression to protein degradation resets the circuit, resulting in a “flip flop” that constrains asymmetric cell division to the stem cell region. [Copyright &y& Elsevier]

Abstract: To initiate an adaptive immune response, T cells need to interact with dendritic cells (DCs), and the duration of these interactions plays an important role. In vitro and in vivo experiments have generally tried to estimate the required period of opportunity for T cell stimulation rather than the duration of individual T cell–DC interactions. Since the application of multi-photon microscopy (MPM) to living lymphoid tissues, the interactions between immune cells, as well as the duration thereof, can directly be observed in vivo. Indeed, long-lasting interactions between T cells and DCs were shown to be important for the onset of immune responses. However, because MPM imaging is typically restricted to experiments lasting 1 h, and because T cell–DC conjugates frequently move into and out of the imaged volume, it is difficult to estimate the true duration of interactions from MPM contact data. Here, we present a method to properly make such an estimate of (the average of) the distribution of contact durations. We validate the method by applying it to spatially explicit computer simulations where the true distribution of contact duration is known. Finally, we apply our analysis to a large experimental data set of T–DC contacts, and predict an average contact time of about three hours. However, we identify a mismatch between the experimental data and the model predictions, and investigate possible causes of the mismatch, including minor tissue drift during imaging experiments. We discuss in detail how future experiments can be optimized such that MPM contact data will be minimally affected by these factors. [Copyright &y& Elsevier]

A synthesis is presented of recent work by the authors and others on the formation of localised patterns, isolated spots, or sharp fronts in models of natural processes governed by reaction–diffusion equations. Contrasting with the well-known Turing mechanism of periodic pattern formation, a general picture is presented in one spatial dimension for models on long domains that exhibit sub-critical Turing instabilities. Localised patterns naturally emerge in generalised Schnakenberg models within the pinning region formed by bistability between the patterned state and the background. A further long-wavelength transition creates parameter regimes of isolated spots which can be described by semi-strong asymptotic analysis. In the species-conservation limit, another form of wave pinning leads to sharp fronts. Such fronts can also arise given only one active species and a weak spatial parameter gradient. Several important applications of this theory within natural systems are presented, at different lengthscales: cellular polarity formation in developmental biology, including root-hair formation, leaf pavement cells, keratocyte locomotion; and the transitions between vegetation states on continental scales. Philosophical remarks are offered on the connections between different pattern formation mechanisms and on the benefit of subcritical instabilities in the natural world. • Localised patterns, isolated spots and sharp fronts emerge in biological models. • These naturally occurring patterns can be linked to subcritical Turing instabilities. • Combining theoretical approaches helps elucidating the different mechanisms involved. • It sheds light on disjointed developmental and ecological phenomena in nature. • Biology favours multistability and hysteresis above supercritical instability. [ABSTRACT FROM AUTHOR]