Quasi-stable gradients of signaling protein molecules (known as morphogens or ligands) bound to cell receptors are known to be responsible for differential cell signaling and gene expressions. From these follow different stable cell fates and visually patterned tissues in biological development. Recent studies have shown that the relevant basic biological processes yield gradients that are sensitive to small changes in system characteristics (such as expression level of morphogens or receptors) or environmental conditions (such as temperature changes). Additional biological activities must play an important role in the high level of robustness observed in embryonic patterning for example. It is natural to attribute observed robustness to various type of feedback control mechanisms. However, our own simulation studies have shown that feedback control is neither necessary nor sufficient for robustness of the morphogen decapentaplegic (Dpp) gradient in wing imaginal disc of Drosophilas. Furthermore, robustness can be achieved by substantial binding of the signaling morphogen Dpp with nonsignaling cell surface bound molecules (such as heparan sulfate proteoglygans) and degrading the resulting complexes at a sufficiently rapid rate. The present work provides a theoretical basis for the results of our numerical simulation studies.
Morphogen gradient; nonlinear boundary value problem; robustness; mathematical modeling
How morphogen gradients form has long been a subject of controversy. The strongest support for the view that morphogens do not simply spread by free diffusion has come from a variety of studies of the Decapentaplegic (Dpp) gradient of the Drosophila larval wing disc.
In the present study, we initially show how the failure, in such studies, to consider the coupling of transport to receptor-mediated uptake and degradation has led to estimates of transport rates that are orders of magnitude too low, lending unwarranted support to a variety of hypothetical mechanisms, such as “planar transcytosis” and “restricted extracellular diffusion”. Using several independent dynamic methods, we obtain data that are inconsistent with such models, and that show directly that Dpp transport occurs by simple, rapid diffusion in the extracellular space. We discuss the implications of these findings for other morphogen systems in which complex transport mechanisms have been proposed.
We believe that these findings resolve a major, longstanding question about morphogen gradient formation, and provide a solid framework for interpreting experimental observations of morphogen gradient dynamics.
Cell surface heparan sulfate (HS) potentiates the activities of various growth factors. Here we show that HS stimulates bone morphogenetic protein (BMP) activity by enhancing recruitment of type II receptor subunits to BMP-type I receptor complexes, suggesting a view of HS as a catalyst of the formation of signaling complexes.
Cell surface heparan sulfate (HS) not only binds several major classes of growth factors but also sometimes potentiates their activities—an effect usually termed “coreception.” A view that coreception is due to the stabilization of growth factor–receptor interactions has emerged primarily from studies of the fibroblast growth factors (FGFs). Recent in vivo studies have strongly suggested that HS also plays an important role in regulating signaling by the bone morphogenetic proteins (BMPs). Here, we provide evidence that the mechanism of coreception for BMPs is markedly different from that established for FGFs. First, we demonstrate a direct, stimulatory role for cell surface HS in the immediate signaling activities of BMP2 and BMP4, and we provide evidence that HS–BMP interactions are required for this effect. Next, using several independent assays of ligand binding and receptor assembly, including coimmunoprecipitation, cross-linking, and fluorescence fluctuation microscopy, we show that HS does not affect BMP binding to type I receptor subunits but instead enhances the subsequent recruitment of type II receptor subunits to BMP-type I receptor complexes. This suggests a view of HS as a catalyst of the formation of signaling complexes, rather than as a stabilizer of growth factor binding.
Few mechanistic ideas from the pre-molecular era of biology have had as enduring an impact as the morphogen concept. In the classical view, cells in developing embryos obtain positional information by measuring morphogen concentrations and comparing them with fixed concentration thresholds; as a result, graded morphogen distributions map into discrete spatial arrangements of gene expression. Recent studies on Hedgehog and other morphogens suggest that establishing patterns of gene expression may be less a function of absolute morphogen concentrations, than of the dynamics of signal transduction, gene expression, and gradient formation. The data appoint away from any universal model of morphogen interpretation and suggest that organisms use multiple mechanisms for reading out developmental signals in order to accomplish specific patterning goals.
Colon crypts, a single sheet of epithelia cells, consist of a periodic pattern of stem cells, transit-amplifying cells, and terminally differentiated cells that constantly renew and turnover. Experimental evidence suggests that Wnt signaling promotes and regulates stem cell division, differentiation, and possible cell migrations while intestinal BMP signaling inhibits stem cell self-renewal and repression in crypt formation. As more molecular details on Wnt and BMP in crypts are being discovered, little is still known about how complex interactions among Wnt, BMP, and different types of cells, and surrounding environments may lead to de novo formation of multiple crypts or how such interactions affect regeneration and stability of crypts.
We present a mathematical model that contains Wnt and BMP, a cell lineage, and their feedback regulations to study formation, regeneration, and stability of multiple crypts. The computational explorations and linear stability analysis of the model suggest a reaction–diffusion mechanism, which exhibits a short-range activation of Wnt plus a long-range inhibition with modulation of BMP signals in a growing tissue of cell lineage, can account for spontaneous formation of multiple crypts with the spatial and temporal pattern observed in experiments. Through this mechanism, the model can recapitulate some distinctive and important experimental findings such as crypt regeneration and crypt multiplication. BMP is important in maintaining stability of crypts and loss of BMP usually leads to crypt multiplication with a fingering pattern.
The study provides a mechanism for de novo formation of multiple intestinal crypts and demonstrates a synergetic role of Wnt and BMP in regeneration and stability of intestinal crypts. The proposed model presents a robust framework for studying spatial and temporal dynamics of cell lineages in growing tissues driven by multiple signaling molecules.
The cell surface heparan sulfate proteoglycan (HSPG) glypican-1 is up-regulated by pancreatic and breast cancer cells, and its removal renders such cells insensitive to many growth factors. We sought to explain why the cell surface HSPG syndecan-1, which is also up-regulated by these cells and is a known growth factor coreceptor, does not compensate for glypican-1 loss. We show that the initial responses of these cells to the growth factor FGF2 are not glypican dependent, but they become so over time as FGF2 induces shedding of syndecan-1. Manipulations that retain syndecan-1 on the cell surface make long-term FGF2 responses glypican independent, whereas those that trigger syndecan-1 shedding make initial FGF2 responses glypican dependent. We further show that syndecan-1 shedding is mediated by matrix metalloproteinase-7 (MMP7), which, being anchored to cells by HSPGs, also causes its own release in a complex with syndecan-1 ectodomains. These results support a specific role for shed syndecan-1 or MMP7–syndecan-1 complexes in tumor progression and add to accumulating evidence that syndecans and glypicans have nonequivalent functions in vivo.
Network motifs provided a “conceptual tool” for understanding the functional principles of biological networks, but such motifs have primarily been used to consider static network structures. Static networks, however, cannot be used to reveal time- and region-specific traits of biological systems. To overcome this limitation, we proposed the concept of a “spatiotemporal network motif,” a spatiotemporal sequence of network motifs of sub-networks which are active only at specific time points and body parts.
On the basis of this concept, we analyzed the developmental gene regulatory network of the Drosophila melanogaster embryo. We identified spatiotemporal network motifs and investigated their distribution pattern in time and space. As a result, we found how key developmental processes are temporally and spatially regulated by the gene network. In particular, we found that nested feedback loops appeared frequently throughout the entire developmental process. From mathematical simulations, we found that mutual inhibition in the nested feedback loops contributes to the formation of spatial expression patterns.
Taken together, the proposed concept and the simulations can be used to unravel the design principle of developmental gene regulatory networks.
The view of biology as goal-directed engineering has deep historical roots in developmental biology, a field currently benefitting from an influx of ideas and methods from systems biology. Systems biology draws on non-biological paradigms to explain developmental mechanisms of control, the specific type of regulation that achieves or maintains a desired end. This review highlights some of the current efforts designed to elucidate basic design principles underlying the engineering objectives of robustness, precision, and scaling that are required during developmental control of growth and pattern formation. Examples from vertebrate and invertebrate development are used to illustrate general principles including the value of integral feedback in achieving set-point control; the usefulness of self-organizing behavior; the importance of recognizing and appropriately handling noise; and the No Free Lunch theory. Through the examination of such principles, systems biology offers a functional framework to make sense of the mechanistic complexity of organismal development.
Biological systems are so complex that we must ask: "What purpose does all this complexity serve?" Lander argues that computational biology may help provide answers
A culture's icons are a window onto its soul. Few would disagree that, in the culture of molecular biology that dominated much of the life sciences for the last third of the 20th century, the dominant icon was the double helix. In the present, post-modern, 'systems biology' era, however, it is, arguably, the hairball.
Developmental biology, regenerative medicine and cancer biology are increasingly occupied with the molecular characterization of stem cells. Yet recent work adds to a growing body of literature suggesting that 'stemness' cannot be reduced to the molecular features of cell types, and is instead an emergent property of cell lineages under feedback control.
Studies of developing and self-renewing tissues have shown that differentiated cell types are typically specified through the actions of multistage cell lineages. Such lineages commonly include a stem cell and multiple progenitor (transit amplifying; TA) cell stages, which ultimately give rise to terminally differentiated (TD) cells. In several cases, self-renewal and differentiation of stem and progenitor cells within such lineages have been shown to be under feedback regulation. Together, the existence of multiple cell stages within a lineage and complex feedback regulation are thought to confer upon a tissue the ability to autoregulate development and regeneration, in terms of both cell number (total tissue volume) and cell identity (the proportions of different cell types, especially TD cells, within the tissue). In this paper, we model neurogenesis in the olfactory epithelium (OE) of the mouse, a system in which the lineage stages and mediators of feedback regulation that govern the generation of terminally differentiated olfactory receptor neurons (ORNs) have been the subject of much experimental work. Here we report on the existence and uniqueness of steady states in this system, as well as local and global stability of these steady states. In particular, we identify parameter conditions for the stability of the system when negative feedback loops are represented either as Hill functions, or in more general terms. Our results suggest that two factors – autoregulation of the proliferation of transit amplifying (TA) progenitor cells, and a low death rate of TD cells – enhance the stability of this system.
cell lineage; olfactory epithelium; neurogenesis; feedback; stem cell; transit amplifying cell; terminally differentiated cell; neuronal progenitor; stability; modeling
Cell surface heparan sulfate proteoglycans (HSPGs) act as co-receptors for multiple families of growth factors that regulate animal cell proliferation, differentiation and patterning. Elimination of heparan sulfate during brain development is known to produce severe structural abnormalities. Here we investigate the developmental role played by one particular HSPG, glypican-1 (Gpc1), which is especially abundant on neuronal cell membranes, and is the major HSPG of the adult rodent brain.
Mice with a null mutation in Gpc1 were generated and found to be viable and fertile. The major phenotype associated with Gpc1 loss is a highly significant reduction in brain size, with only subtle effects on brain patterning (confined to the anterior cerebellum). The brain size difference emerges very early during neurogenesis (between embryonic days 8.5 and 9.5), and remains roughly constant throughout development and adulthood. By examining markers of different signaling pathways, and the differentiation behaviors of cells in the early embryonic brain, we infer that Gpc1-/- phenotypes most likely result from a transient reduction in fibroblast growth factor (FGF) signaling. Through the analysis of compound mutants, we provide strong evidence that Fgf17 is the FGF family member through which Gpc1 controls brain size.
These data add to a growing literature that implicates the glypican family of HSPGs in organ size control. They also argue that, among heparan sulfate-dependent signaling molecules, FGFs are disproportionately sensitive to loss of HSPGs. Finally, because heterozygous Gpc1 mutant mice were found to have brain sizes half-way between homozygous and wild type, the data imply that endogenous HSPG levels quantitatively control growth factor signaling, a finding that is both novel and relevant to the general question of how the activities of co-receptors are exploited during development.
We have identified a unique heparan sulfate (HeS) proteoglycan synthesized by the neuronal-like cell line PC12. The proteoglycan, purified with monoclonal antibodies from medium conditioned by PC12 cells, has an apparent molecular weight of 350,000, and it contains a Mr 80,000 core protein and HeS side chains of Mr 15,000 each. The purified molecule has the same apparent size and density as it has in conditioned medium.
HeS proteoglycans that are indistinguishable antigenically but very difficult to solubilize are found on the external surface and in the interior of PC12 cells and neurons. Mild proteolysis converts the surface proteoglycan into a molecule closely resembling that found in the medium. The same surface antigens are also present on a subpopulation of T-cells and on a non-neuronal accessory cell found in dorsal root ganglion cultures.
The PC12 cell line and the non-neuronal dorsal root ganglion cells secrete a factor into medium that, after adsorption to polylysine-coated surfaces, induces rapid neurite outgrowth by primary sympathetic neurons. The monoclonal antibodies used to purify the neuronal HeS proteoglycan from PC12 cells are capable of depleting this conditioned medium of its neurite-promoting activity. These studies suggest that a HeS proteoglycan synthesized and secreted by neurons and certain accessory cells plays a role in regulating neurite outgrowth.
A large, diverse, and growing number of strategies have been proposed to explain how morphogen gradients achieve robustness and precision. We argue that, to be useful, the evaluation of such strategies must take into account the constraints imposed by competing objectives and performance tradeoffs. This point is illustrated through a mathematical and computational analysis of the strategy of self-enhanced morphogen clearance. The results suggest that the usefulness of this strategy comes less from its ability to increase robustness to morphogen source fluctuations per se, than from its ability to overcome specific kinds of noise, and to increase the fraction of a morphogen gradient within which robust threshold positions may be established. This work also provides new insights into the longstanding question of why morphogen gradients show a maximum range in vivo.
Mathematical “cost-benefit” analyses provide insight into the prices developing organisms pay for strategies that increase robustness in morphogen-mediated patterning.
It is widely accepted that the growth and regeneration of tissues and organs is tightly controlled. Although experimental studies are beginning to reveal molecular mechanisms underlying such control, there is still very little known about the control strategies themselves. Here, we consider how secreted negative feedback factors (“chalones”) may be used to control the output of multistage cell lineages, as exemplified by the actions of GDF11 and activin in a self-renewing neural tissue, the mammalian olfactory epithelium (OE). We begin by specifying performance objectives—what, precisely, is being controlled, and to what degree—and go on to calculate how well different types of feedback configurations, feedback sensitivities, and tissue architectures achieve control. Ultimately, we show that many features of the OE—the number of feedback loops, the cellular processes targeted by feedback, even the location of progenitor cells within the tissue—fit with expectations for the best possible control. In so doing, we also show that certain distinctions that are commonly drawn among cells and molecules—such as whether a cell is a stem cell or transit-amplifying cell, or whether a molecule is a growth inhibitor or stimulator—may be the consequences of control, and not a reflection of intrinsic differences in cellular or molecular character.
Many tissues and organs grow to precise sizes and, when injured, regenerate accurately and rapidly. Here, we ask whether the organization of cells into lineages, and the feedback interactions that occur within lineages, are necessary elements of control strategies that make such behavior possible. Drawing on mathematical modeling and the results of experimental manipulation of the mouse olfactory epithelium, we show that performance objectives, such as robust size specification, fast regeneration from a variety of initial conditions, and maintenance of high ratios of differentiated to undifferentiated cells, can be simultaneously achieved through a combination of lineage structures, signaling mechanisms, and spatial distributions of cell types that correspond well with what is observed in many growing and regenerating tissues. Key to successful control is an integral-feedback mechanism that is implemented when terminally differentiated cells secrete molecules that lower the probability that progenitor cells replicate versus differentiate. Interestingly, this mechanism also explains how the distinctive proliferative behaviors of stem cell and “transit-amplifying” cell populations can emerge as a consequence of feedback effects, rather than intrinsic programming of cell types.
Are common, generic strategies used in the quantitative control of tissue growth and regeneration? An investigation of feedback effects in multistage lineages suggests they are.
Cells isolated from many types of human cancers express heparin-binding growth factors (HBGFs) that drive tumor growth, metastasis, and angiogenesis. The heparan sulfate proteoglycan glypican-1 (GPC1) is a coreceptor for HBGFs. Here we show that both cancer cell–derived and host-derived GPC1 are crucial for efficient growth, metastasis, and angiogenesis of human and mouse cancer cells. Thus downregulation of GPC1 in the human pancreatic cancer cell line PANC-1, using antisense approaches, resulted in prolonged doubling times and decreased anchorage-independent growth in vitro as well as attenuated tumor growth, angiogenesis, and metastasis when these cells were transplanted into athymic mice. Moreover, athymic mice that lacked GPC1 exhibited decreased tumor angiogenesis and metastasis following intrapancreatic implantation with either PANC-1 or T3M4 human pancreatic cancer cells and fewer pulmonary metastases following intravenous injection of murine B16-F10 melanoma cells. In addition, hepatic endothelial cells isolated from these mice exhibited an attenuated mitogenic response to VEGF-A. These data indicate that cancer cell– and host-derived GPC1 are crucial for full mitogenic, angiogenic, and metastatic potential of cancer cells. Thus targeting GPC1 might provide new avenues for cancer therapy and for the prevention of cancer metastasis.
Positional identities along the anterior–posterior axis of the vertebrate nervous system are assigned during gastrulation by multiple posteriorizing signals, including retinoic acid (RA), fibroblast growth factors (Fgfs), and Wnts. Experimental evidence has suggested that RA, which is produced in paraxial mesoderm posterior to the hindbrain by aldehyde dehydrogenase 1a2 (aldh1a2/raldh2), forms a posterior-to-anterior gradient across the hindbrain field, and provides the positional information that specifies the locations and fates of rhombomeres. Recently, alternative models have been proposed in which RA plays only a permissive role, signaling wherever it is not degraded. Here we use a combination of experimental and modeling tools to address the role of RA in providing long-range positional cues in the zebrafish hindbrain. Using cell transplantation and implantation of RA-coated beads into RA-deficient zebrafish embryos, we demonstrate that RA can directly convey graded positional information over long distances. We also show that expression of Cyp26a1, the major RA-degrading enzyme during gastrulation, is under complex feedback and feedforward control by RA and Fgf signaling. The predicted consequence of such control is that RA gradients will be both robust to fluctuations in RA synthesis and adaptive to changes in embryo length during gastrulation. Such control also provides an explanation for the fact that loss of an endogenous RA gradient can be compensated for by RA that is provided in a spatially uniform manner.
The formation of gradients of morphogens, signaling molecules that determine cell fates in a concentration-dependent manner, is a fundamental process in developmental biology. Several morphogens pattern the anterior–posterior (head to tail) axis of the vertebrate nervous system, including the vitamin A derivative, retinoic acid (RA) and fibroblast growth factors (Fgfs). However, it remains unclear how the activities of such morphogen gradients are coordinated. We have addressed this question by combining genetic experiments in zebrafish and computational analyses. We show that RA acts as a graded signal over long distances and that its gradient is shaped, to a large extent, by local control of RA degradation. In particular, RA promotes and Fgf suppresses RA degradation, thereby linking the shapes of RA and Fgf gradients. Computational models suggest that this linkage helps make RA-mediated patterning robust to changes in the rate at which RA is synthesized (which may vary with levels of dietary vitamin A) as well as in the size and shape of the embryo during development. Analogous regulatory loops may be used for similar purposes in other tissues in which RA and Fgfs interact, as well as in other morphogen systems.
Experimental and computational studies in zebrafish reveal a complex system regulating degradation of the vitamin A derivative retinoic acid along the anterior-posterior axis, which helps explain how morphogen gradients are established and maintained.
The dorsoventral axis of the Drosophila embryo is patterned by a gradient of bone morphogenetic protein (BMP) ligands. In a process requiring at least three additional extracellular proteins, a broad domain of weak signaling forms and then abruptly sharpens into a narrow dorsal midline peak. Using experimental and computational approaches, we investigate how the interactions of a multiprotein network create the unusual shape and dynamics of formation of this gradient. Starting from observations suggesting that receptor-mediated BMP degradation is an important driving force in gradient dynamics, we develop a general model that is capable of capturing both subtle aspects of gradient behavior and a level of robustness that agrees with in vivo results.
The transcription rate of a gene is often controlled by several regulators that bind specific sites in the gene's
cis-regulatory region. The combined effect of these regulators is described by a
cis-regulatory input function. What determines the form of an input function, and how variable is it with respect to mutations? To address this, we employ the well-characterized
lac operon of
Escherichia coli, which has an elaborate input function, intermediate between Boolean AND-gate and OR-gate logic. We mapped in detail the input function of 12 variants of the
lac promoter, each with different point mutations in the regulator binding sites, by means of accurate expression measurements from living cells. We find that even a few mutations can significantly change the input function, resulting in functions that resemble Pure AND gates, OR gates, or single-input switches. Other types of gates were not found. The variant input functions can be described in a unified manner by a mathematical model. The model also lets us predict which functions cannot be reached by point mutations. The input function that we studied thus appears to be plastic, in the sense that many of the mutations do not ruin the regulation completely but rather result in new ways to integrate the inputs.
A few point mutations in the
lac operon of
Escherichia coli are sufficient to change the nature of the transcriptional computation.
A single-molecule imaging study reveals that heparan sulfate chains in the pericellular matrix present a structured network of binding sites that controls FGF2 transport.
The heparan sulfate (HS) chains of proteoglycans are a key regulatory component of the extracellular matrices of animal cells, including the pericellular matrix around the plasma membrane. In these matrices they regulate transport, gradient formation, and effector functions of over 400 proteins central to cell communication. HS from different matrices differs in its selectivity for its protein partners. However, there has been no direct test of how HS in the matrix regulates the transport of its partner proteins. We address this issue by single molecule imaging and tracking in fibroblast pericellular matrix of fibroblast growth factor 2 (FGF2), stoichiometrically labelled with small gold nanoparticles. Transmission electron microscopy and photothermal heterodyne imaging (PHI) show that the spatial distribution of the HS-binding sites for FGF2 in the pericellular matrix is heterogeneous over length scales ranging from 22 nm to several µm. Tracking of individual FGF2 by PHI in the pericellular matrix of living cells demonstrates that they undergo five distinct types of motion. They spend much of their time in confined motion (∼110 nm diameter), but they are not trapped and can escape by simple diffusion, which may be slow, fast, or directed. These substantial translocations (µm) cover distances far greater than the length of a single HS chain. Similar molecular motion persists in fixed cells, where the movement of membrane PGs is impeded. We conclude that FGF2 moves within the pericellular matrix by translocating from one HS-binding site to another. The binding sites on HS chains form non-random, heterogeneous networks. These promote FGF2 confinement or substantial translocation depending on their spatial organisation. We propose that this spatial organisation, coupled to the relative selectivity and the availability of HS-binding sites, determines the transport of FGF2 in matrices. Similar mechanisms are likely to underpin the movement of many other HS-binding effectors.
The development, homeostasis, and repair of animal tissues requires communication between cells mediated by effector proteins, which are released from source cells and must move through the surrounding extracellular matrix to reach their receptors on target cells. A major component of the extracellular matrix is the polysaccharide heparan sulfate (HS); it binds the majority of these effectors and has the crucial function of regulating their transport. The mechanism underlying this function, however, is still unknown. To understand how HS regulates the transport of effectors, in this study we labelled molecules of the effector protein fibroblast growth factor 2 (FGF2) each with a gold nanoparticle, which we could visualise and quantify by electron microscopy and by a new approach called photothermal heterodyne imaging. By imaging the gold nanoparticles, we found that the binding sites for FGF2 on HS are distributed heterogeneously in the extracellular matrix that surrounds cells in culture. Single molecule tracking indicated that these binding sites are organised into local networks that confine the FGF2 and into paths that allow its translocation over long distances (up to several micrometers). Thus, the spatial distribution of the binding sites in HS and their physicochemical properties of binding are major factors controlling the transport of effectors in extracellular matrices.