Robust Generation and Decoding of Morphogen Gradients

Morphogen gradients play a key role in multiple differentiation processes. Both the formation of the gradient and its interpretation by the receiving cells need to occur at high precision to ensure reproducible patterning. This need for quantitative precision is challenged by fluctuations in the environmental conditions and by variations in the genetic makeup of the developing embryos. We discuss mechanisms that buffer morphogen profiles against variations in gene dosage. Self-enhanced morphogen degradation and pre-steady-state decoding provide general means for buffering the morphogen profile against fluctuations in morphogen production rate. A more specific “shuttling” mechanism, which establishes a sharp and robust activation profile of a widely expressed morphogen, and enables the adjustment of morphogen profile with embryo size, is also described. Finally, we consider the transformation of the smooth gradient profile into sharp borders of gene expression in the signal-receiving cells. The integration theory and experiments are increasingly used, providing key insights into the system-level functioning of the developmental system.In order for a uniform field of cells to differentiate into a reproducible pattern of organs and tissues, cells need to receive information about their position within the field. During development, positional information is often conveyed by spatial gradients of morphogens (Wolpert 1989). In the presence of such gradients, cells are subject to different levels of morphogen, depending on their positions within the field, and activate, accordingly, one of several gene expression cassettes. The quantitative shape of the morphogen gradient is critical for patterning, with cell-fate boundaries established at specific concentration thresholds. Although these general features of morphogen-based patterning are universal, the range and form of the morphogen profile, and the pattern of induced target genes, vary significantly depending on the tissue setting and the signaling pathways used.The formation of a morphogen gradient is a dynamic process, influenced by the kinetics of morphogen production, diffusion, and degradation. These processes are tightly controlled through intricate networks of positive and negative feedback loops, which shape the gradient and enhance its reproducibility between individual embryos and developmental contexts. In the past three decades, many of the components comprising the morphogen signaling cascades have been identified and sorted into pathways, enabling one to start addressing seminal questions regarding their functionality: How is it that morphogen signaling is reproducible from one embryo to the next, despite fluctuations in the levels of signaling components, temperature differences, variations in size, or unequal distribution of components between daughter cells? Are there underlying mechanisms that assure a reproducible response? Are these mechanisms conserved across species, similar to the signaling pathways they control?In this review, we outline insights we gained by quantitatively analyzing the process of morphogen gradient formation. We focus on mechanisms that buffer morphogen profiles against fluctuations in gene dosage, and describe general means by which such buffering is enhanced. These mechanisms include self-enhanced morphogen degradation and pre-steady-state decoding. In addition, we describe a more specific “shuttling” mechanism that is used to generate a sharp and robust profile of a morphogen activity from a source that is broadly produced. We discuss the implication of the shuttling mechanism for the ability of embryos to adjust their pattern with size. Finally, we consider the transformation of the smooth gradient profile into sharp borders of gene expression in the signal-receiving cells.     

胚乳性状的遗传模型和世代平均数

谷类作物的胚乳是三倍体组织,胚乳性状受3N遗传控制。本文分析了胚乳性状的遗传特征,建立了相应的遗传模型,推导了世代群体的平均数分量,并提出了研究胚乳性状基因效应的一些简单的交配设计。     

Models of Plant Disease Epidemics. II: Gradients of Bean Rust

The spread of bean rust from three types of inoculum sources (area, line, and point) was studied under field conditions in two seasons. Disease intensity (y) over time was quantified as incidence of diseased plants, incidence of diseased leaves, and disease severity at distances (d) of 0.3, 0.7, 1.5, 2.7, 4.3, 6.5, and 8.7 m from the inoculum sources. Seven curvilinear models were compared and the models that best explained the gradients of bean rust were y = ad^?b exp(cd), y = a exp(–bd^c) and y = a exp(–bd); where a was proportion of disease near the source, d was distance in metres, b was the slope, and c was a shape parameter. For general analysis to compare the slopes of the gradients, the gradient curves were linearized by ln(y) versus d and the parameters ln(a) (intercept) and b (slope) were estimated. The three measures of disease intensity and the three types of inoculum sources had estimated gradient parameters that were statistically different. The incidence of diseased plants rapidly approached y = 1.0 and the gradient slopes were near zero. Also with the ln(y) linearization, the gradients of the incidence of diseased leaves had slopes flatter than the gradients of disease severity. The gradient slopes from area sources of inoculum were flatter than from line sources, which in turn were flatter than from point sources. Late in the epidemics, the b-values became similar for all combinations of inoculum sources × assessment types. The interpretation of flattening of the gradients was confounded because aberrations in transformations occurred with most models. That is, when the intensity of disease (incidence or severity) approached the maximum, the increases in the intercepts were restricted and this restriction was responsible for most of the flattening. No flattening of gradients occurred over time when the gompit gradient model [–ln(–ln(y/y_max)) = –ln(–ln(a))?b ln(d)] was used for these same disease values. The fitting of models to the gradients served little purpose except to classify the curves in a general way. A new statistic, the area under the disease gradient curve (AUDGC), is proposed to compare epidemics.     

Proton Pump Activity of Mitochondria-rich Cells : The Interpretation of External Proton-concentration Gradients

We have hypothesized that a major role of the apical H⁺-pump in mitochondria-rich (MR) cells of amphibian skin is to energize active uptake of Cl⁻ via an apical Cl⁻/HCO₃⁻-exchanger. The activity of the H⁺ pump was studied by monitoring mucosal [H⁺]-profiles with a pH-sensitive microelectrode. With gluconate as mucosal anion, pH adjacent to the cornified cell layer was 0.98 ± 0.07 (mean ± SEM) pH-units below that of the lightly buffered bulk solution (pH = 7.40). The average distance at which the pH-gradient is dissipated was 382 ± 18 μm, corresponding to an estimated “unstirred layer” thickness of 329 ± 29 μm. Mucosal acidification was dependent on serosal pCO₂, and abolished after depression of cellular energy metabolism, confirming that mucosal acidification results from active transport of H⁺. The [H⁺] was practically similar adjacent to all cells and independent of whether the microelectrode tip was positioned near an MR-cell or a principal cell. To evaluate [H⁺]-profiles created by a multitude of MR-cells, a mathematical model is proposed which assumes that the H⁺ distribution is governed by steady diffusion from a number of point sources defining a set of particular solutions to Laplace''s equation. Model calculations predicted that with a physiological density of MR cells, the [H⁺] profile would be governed by so many sources that their individual contributions could not be experimentally resolved. The flux equation was integrated to provide a general mathematical expression for an external standing [H⁺]–gradient in the unstirred layer. This case was treated as free diffusion of protons and proton-loaded buffer molecules carrying away the protons extruded by the pump into the unstirred layer; the expression derived was used for estimating stationary proton-fluxes. The external [H⁺]-gradient depended on the mucosal anion such as to indicate that base (HCO₃⁻) is excreted in exchange not only for Cl ⁻, but also for Br⁻ and I⁻, indicating that the active fluxes of these anions can be attributed to mitochondria-rich cells.     

Spore Dispersal and Plant Disease Gradients; a Comparison between two Empirical Models

Power law and exponential models were fitted to 325 sets of observations which described decreases with distance in deposition of air-borne or splash-borne spores, or pollen, or in amounts of plant disease caused by fungi, bacteria or viruses. There, was generally little difference between the models in the goodness of fit to these data, although deposition gradients for spores borne in splash droplets were fitted better by exponential models and gradients for fungi with air-borne spores less than 10 μm in diameter were fitted better by power law models. The exponential model has the property that the observed variable decreases by half as the distance from the source increases by a constant increment (the half-distance); this provides a measureof the gradient that is more easy to visualize than the exponent in power law model. The half-distances of gradients for air-borne pathogens were greater than those for splash-borne or soil-borne pathogens. The exponential model is easier to incorporate into models of disease development than the power law model because the boundary condition at the source (the estimated number of spores or amount of disease at the source) is finite rather than infinite. However, both these empirical models have limitations and should not be extrapolated to distances outside the observed range.     

Gradients for the evolution of bimatrix games

The evolutionary dynamics of bimatrix games is studied for rescaled partnership games and zero sum games. The former case leads to gradient systems. The selection equations for sexual and asexual reproduction of genotypes corresponding to mixed strategies are analysed. As examples, the origin of anisogamy and cyclic chases for predator-prey coevolution are studied.     

利用“复杂性”解说经济生态发展模式

前言在研究生态经济问题时,常常感到理论上的虚弱,不能从理论上解说生态经济这一庞大、复杂的综合体是如何由生态、经济的相互作用衍变而成的。在生态和经济的复杂性的尺度上我们能把握多少?我们对于生态、经济关系能否及时调控和调控到什么程度?等等,如能从理论上给这些问题作出说明,相信会对生态经济理论及实践都有裨益。为此,我们对生态经济系统作了简化,只讨论了工业增长、农业增长和环境质量三者间的相互作用并用微分方程组表述,试定量说明生态系统、经济系统的复合系统的复杂性和发展。生态系统的复杂性自牛顿建立牛顿力学以来,尽管经典物理     

Determination of Selection Gradients Using Multiple Regression versus Structural Equation Models (SEM)

Selection studies involving multiple intercorrelated independent variables have employed multiple regression analysis as a means to estimate and partition natural and sexual selection's direct and indirect effects. These statistical models assume that independent variables are measured without error. Most would conclude that such is not the case in the field studies for which these methods are employed. We demonstrate that the distortion of estimates resulting from error variance is not trivial. When independent variables are intercorrelated, extreme distortions may occur. We propose to use Structural Equation Models (SEM), to estimate error variance and produce highly accurate coefficients for formulation of selection gradients. This method is particularly appropriate when the selection is viewed as happening at the level of the latent variables.     

Generation of Gradients on a Microfluidic Device: Toward a High-Throughput Investigation of Spermatozoa Chemotaxis

Various research tools have been used for in vitro detection of sperm chemotaxis. However, they are typically poor in maintenance of gradient stability, not to mention their low efficiency. Microfluidic device offers a new experimental platform for better control over chemical concentration gradient than traditional ones. In the present study, an easy-handle diffusion-based microfluidic chip was established. This device allowed for conduction of three parallel experiments on the same chip, and improved the performance of sperm chemotaxis research. In such a chip, there were six channels surrounding a hexagonal pool. The channels are connected to the hexagon by microchannels. Firstly, the fluid flow in the system was characterized; secondly, fluorescein solution was used to calibrate gradient profiles formed in the central hexagon; thirdly, sperm behavior was observed under two concentration gradients of progesterone (100 pM and 1 mM, respectively) as a validation of the device. Significant differences in chemotactic parameters were recognized between experimental and control groups (p < 0.05). Compared with control group, sperm motility was greatly enhanced in 1 mM group (p < 0.05), but no significant difference was found in 100 pM group. In conclusion, we proposed a microfluidic device for the study of sperm chemotaxis that was capable of generating multi-channel gradients on a chip and would help reduce experimental errors and save time in experiment.     

The Physical Interpretation of Mathematical Models for Sodium Permeability Changes in Excitable Membranes

This paper deals with the physical interpretation of existing mathematical models which describe the transient sodium conductance changes in excitable membranes. It is shown that there are clear limitations to the specificity of inferences which may be drawn about physical mechanism from the behavior of abstract models. Within these limitations, it is shown that a pronounced inactivation shift is not necessarily evidence for coupling between the events responsible for the rise and inactivation of the sodium conductance, but that the inactivation shift may be associated with an event whose rate explicitly depends on the rate of continuous voltage change or magnitude of instantaneous voltage change.     

Explanatory Models of Female Pubertal Timing: Discordances Between Cultural Models of Maturation and the Recollection and Interpretation of Personal Developmental Experiences

Given the ambiguity surrounding the source of the continuing trend toward earlier menarche observed in Westernized nations, several competing explanatory models have emerged regarding variation in pubertal timing. While a biomedical model proposes that predominantly constitutional characteristics shape the maturation timetable, an alternative framework derived from Life History Theory (LHT) evolutionary principles emphasizes the influence of psychosocial factors on development. Working with a sample of women 19?C25?years of age (N?=?103) drawn from two Southeastern U.S. colleges, we combined cultural consensus analysis with retrospective self-report regarding childhood stress and menarcheal timing to investigate whether reported developmental experiences align with cultural models regarding factors that should drive pubertal timing. Results suggest a robust cultural model consistent with a biomedical framework concentrating principally on constitutional characteristics. However, participants?? personal developmental recollections support an association between higher childhood stress and earlier menarche. These findings support LHT predictions that early reproductive maturation is an evolutionary adaptive response to chronic childhood stress as well as clarify the extent to which cultural models of factors contributing to puberty concord with developmental experiences.     

Explicit Kinetic Heterogeneity: Mathematical Models for Interpretation of Deuterium Labeling of Heterogeneous Cell Populations

Estimation of division and death rates of lymphocytes in different conditions is vital for quantitative understanding of the immune system. Deuterium, in the form of deuterated glucose or heavy water, can be used to measure rates of proliferation and death of lymphocytes in vivo. Inferring these rates from labeling and delabeling curves has been subject to considerable debate with different groups suggesting different mathematical models for that purpose. We show that the three most common models, which are based on quite different biological assumptions, actually predict mathematically identical labeling curves with one parameter for the exponential up and down slope, and one parameter defining the maximum labeling level. By extending these previous models, we here propose a novel approach for the analysis of data from deuterium labeling experiments. We construct a model of “kinetic heterogeneity” in which the total cell population consists of many sub-populations with different rates of cell turnover. In this model, for a given distribution of the rates of turnover, the predicted fraction of labeled DNA accumulated and lost can be calculated. Our model reproduces several previously made experimental observations, such as a negative correlation between the length of the labeling period and the rate at which labeled DNA is lost after label cessation. We demonstrate the reliability of the new explicit kinetic heterogeneity model by applying it to artificially generated datasets, and illustrate its usefulness by fitting experimental data. In contrast to previous models, the explicit kinetic heterogeneity model 1) provides a novel way of interpreting labeling data; 2) allows for a non-exponential loss of labeled cells during delabeling, and 3) can be used to describe data with variable labeling length.     

生态模型中混沌与分形结构的屏幕造形

一、引言差分模型在理论生态研究中有重要意义。对于这种具有离散时间的半动态系统的传统研究,例如周期解,稳定性等(Lasalle,1976)有较为全面的系统研究。他发现Liapunov函数     

Gradients of seed photosynthesis and its role for oxygen balancing

Seeds are generally viewed in the context of plant reproduction and the supply of food and feed, but only seldom as a site of photosynthesis. However, the seeds of many plant species are green, at least during their early development, which raises the issue of the significance of this greening for seed development. Here we describe the two contrasting modes of photosynthesis in the developing seed. The dicotyledonous pea seed has a green embryo, while the monocotyledonous barley caryopsis has a chlorenchymatic layer surrounding its non-green endosperm (storage organ). We have employed pulse-amplitude-modulated fluorescence and oxygen-sensitive microsensors to localize and describe gradient distributions of photosynthetic activity across the seed/caryopsis, and have discussed its role in maintaining the endogenous O₂ balance. We also report the lack of photosynthetic activity in the stay-green embryo axis of the sacred lotus (Nelumbo nucifera) seed following imbibition. The observations are discussed with respect to in vivo light supply and contrasted with the characteristics of leaf photosynthesis.     

Adaptive-Control Model for Neutrophil Orientation in the Direction of Chemical Gradients

Neutrophils have a remarkable ability to detect the direction of chemoattractant gradients and move directionally in response to bacterial infections and tissue injuries. For their role in health and disease, neutrophils have been extensively studied, and many of the molecules involved in the signaling mechanisms of gradient detection and chemotaxis have been identified. However, the cellular-scale mechanisms of gradient sensing and directional neutrophil migration have been more elusive, and existent models provide only limited insight into these processes. Here, we propose a what we believe is a novel adaptive-control model for the initiation of cell polarization in response to gradients. In this model, the neutrophils first sample the environment by extending protrusions in random directions and subsequently adapt their sensitivity depending on localized, temporal changes in stimulation levels. Our results suggest that microtubules may play a critical role in integrating all the sensing events from the cellular periphery through their redistribution inside the neutrophils, and may also be involved in modulating local signaling. An unexpected finding was that model neutrophils exhibit significant randomness in timing and directionality of activation, comparable to our experimental observations in microfluidic devices. Moreover, their responses are robust against alterations of the rate and amplitude of the signaling reactions, and for a broad range in chemoattractant concentrations and spatial gradients.     

Membrane-Associated Non-Receptors and Morphogen Gradients

A previously investigated basic model (System B) for the study of signaling morphogen gradient formation that allows for reversible binding of morphogens (aka ligands) with signaling receptors, degradation of bound morphogens and diffusion of unbound morphogens is extended to include the effects of membrane-bound non-signaling molecules (or non-receptors for short) such as proteoglycans that bind reversibly with the same morphogens and degrade them. Our main goal is to delineate the effects of the presence of non-receptors on the existence and properties of the steady-state concentration gradient of signaling ligand–receptor complexes. Stability of the steady-state morphogen gradients is established and the time to reach steady-state behavior after the onset of morphogen production will be analyzed. The theoretical findings offer explanations for observations reported in several previous experiments on Drosophila wing imaginal discs.     

Gradients in the distribution of riverine benthos

SUMMARY. 1. Numerous hypotheses regarding the controls on species distributions in streams depend on longitudinal analyses of collections of stream organisms. Techniques for the detection of trends and for the detection of station groupings among biological collections have been widely reported, but rarely compared with each other. We have conducted an analysis of ten or eleven samples from each of thirteen stations along a stream abiotic gradient, and have compared several techniques.
2. An analysis of longitudinal distribution must first assess the existence of a gradient in biotic composition. Random skewers on species proportions were the most sensitive in demonstrating such a gradient. Q and M statistics were most useful in further describing the trend due to their additive properties; i.e. the importance of one or more stations in dictating the trend may be determined. Cluster analysis, as well as percent faunal similarity, was most efficient at isolating station groupings. Techniques such as faunal replacement and species loss calculations are generally more useful in testing hypotheses about controls on species distributions, and should be employed where potential causal factors may be isolated.     

Generation and Characterisation of Novel Pancreatic Adenocarcinoma Xenograft Models and Corresponding Primary Cell Lines

Pancreatic adenocarcinoma is one of the most lethal cancer types, currently lacking efficient treatment. The heterogeneous nature of these tumours are poorly represented by the classical pancreatic cell lines, which have been through strong clonal selection in vitro, and are often derived from metastases. Here, we describe the establishment of novel pancreatic adenocarcinoma models, xenografts and corresponding in vitro cell lines, from primary pancreatic tumours. The morphology, differentiation grade and gene expression pattern of the xenografts resemble the original tumours well. The cell lines were analysed for colony forming capacity, tumourigenicity and expression of known cancer cell surface markers and cancer stem-like characteristics. These primary cell models will be valuable tools for biological and preclinical studies for this devastating disease.     

Generation of Very Slow Neuronal Rhythms and Chaos Near the Hopf Bifurcation in Single Neuron Models

We have presented a new generation mechanism of slow spiking or repetitive discharges with extraordinarily long inter-spike intervals using the modified Hodgkin-Huxley equations (Doi and Kumagai, 2001). This generation process of slow firing is completely different from that of the well-known potassium A-current in that the steady-state current-voltage relation of the neuronal model is monotonic rather than the N-shaped one of the A-current. In this paper, we extend the previous results and show that the very slow spiking generically appears in both the three-dimensional Hodgkin-Huxley equations and the three dimensional Bonhoeffer-van der Pol (or FitzHugh-Nagumo) equations. The generation of repetitive discharges or the destabilization of the unique equilibrium point (resting potential) is a simple Hopf bifurcation. We also show that the generation of slow spiking does not depend on the stability of the Hopf bifurcation: supercritical or subcritical. The dynamics of slow spiking is investigated in detail and we demonstrate that the phenomenology of slow spiking can be categorized into two types according to the type of the corresponding bifurcation of a fast subsystem: Hopf or saddle-node bifurcation.