A spatially-averaged mathematical model of kidney branching morphogenesis (original) (raw)
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Dynamic modeling of branching morphogenesis of ureteric bud in early kidney development
Journal of Theoretical Biology, 2009
In the early kidney development, a simple epithelial tube called ureteric bud is derived from the intermediate mesoderm and undergoes a complex process of growth and terminal bifid branching. The branching of the ureteric bud is achieved by different cellular behaviors including cell proliferation and chemotaxis. In this paper, we examine how the branching morphology depends on different physical or chemical factors by constructing a cell-based model to describe the simple tube branching in the early kidney development. We conclude that a proper balance between growth speed of epithelial sheet due to cell proliferation and cell mobility due to chemotaxis is necessary to realize the development of normal Y-shaped pattern. When cell proliferation is fast compared to chemotaxis, kinked pattern is formed, and when cell proliferation is slow, bloated pattern is formed. These are consistent with experimental observations in different morphological anomalies of mutants. We show that the different branching patterns are accurately predicted by growth-chemotaxis ratio.
Branching morphogenesis in the developing kidney is governed by rules that pattern the ureteric tree
Development (Cambridge, England), 2017
Metanephric kidney development is orchestrated by the iterative branching morphogenesis of the ureteric bud. We describe an underlying patterning associated with the ramification of this structure and show that this pattern is conserved between developing kidneys, in different parts of the organ and across developmental time. This regularity is associated with a highly reproducible branching asymmetry that is consistent with locally operative growth mechanisms. We then develop a class of tip state models to represent elaboration of the ureteric tree and describe rules for 'half-delay' branching morphogenesis that describe almost perfectly the patterning of this structure. Spatial analysis suggests that the observed asymmetry may arise from mutual suppression of bifurcation, but not extension, between the growing ureteric tips, and demonstrates that disruption of patterning occurs in mouse mutants in which the distribution of tips on the surface of the kidney is altered. Thes...
Developmental Programming of Branching Morphogenesis in the Kidney
Journal of the American Society of Nephrology, 2015
The kidney developmental program encodes the intricate branching and organization of approximately 1 million functional units (nephrons). Branching regulation is poorly understood, as is the source of a 10-fold variation in nephron number. Notably, low nephron count increases the risk for developing hypertension and renal failure. To better understand the source of this variation, we analyzed the complete gestational trajectory of mouse kidney development. We constructed a computerized architectural map of the branching process throughout fetal life and found that organogenesis is composed of two distinct developmental phases, each with stage-specific rate and morphologic parameters. The early phase is characterized by a rapid acceleration in branching rate and by branching divisions that repeat with relatively reproducible morphology. The latter phase, however, is notable for a significantly decreased yet constant branching rate and the presence of nonstereotyped branching events that generate progressive variability in tree morphology until birth. Our map identifies and quantitates the contribution of four developmental mechanisms that guide organogenesis: growth, patterning, branching rate, and nephron induction. When applied to organs that developed under conditions of malnutrition or in the setting of growth factor mutation, our normative map provided an essential link between kidney architecture and the fundamental morphogenetic mechanisms that guide development. This morphogenetic map is expected to find widespread applications and help identify modifiable targets to prevent developmental programming of common diseases.
Architectural patterns in branching morphogenesis in the kidney
Kidney International, 1998
During kidney development, several discrete steps generate its three-dimensional pattern including specific branch types, regional differential growth of stems, the specific axes of growth and temporal progression of the pattern. The ureteric bud undergoes three different types of branching. In the first, terminal bifid type, a lateral branch arises and immediately bifurcates to form two terminal branches whose tips induce the formation of nephrons. After 15 such divisions (in humans) of this specifically renal type of branching, several nephrons are induced whose connecting tubules fuse and elongate to form the arcades. Finally, the last generations undergo strictly lateral branching to form the cortical system. The stems of these branches elongate in a highly regulated pattern. The molecular basis of these processes is unknown and we briefly review their potential mediators. Differential growth in three different axes of the kidney (cortico-medullary, dorsoventral and rostro-caudal) generate the characteristic shape of the kidney. Rapid advances in molecular genetics highlight the need for development of specific assays for each of these discrete steps, a prerequisite for identification of the involved pathways. The identification of molecules that control branching (the ultimate determinant of the number of nephrons) has acquired new urgency with the recent suggestion that a reduced nephron number predisposes humans to hypertension and to progression of renal failure.
Dynamic Image-Based Modelling of Kidney Branching Morphogenesis
Kidney branching morphogenesis has been studied extensively, but the mechanism that defines the branch points is still elusive. Here we obtained a 2D movie of kidney branching morphogenesis in culture to test different models of branching morphogenesis with physiological growth dynamics. We carried out image segmentation and calculated the displacement fields between the frames. The models were subsequently solved on the 2D domain, that was extracted from the movie. We find that Turing patterns are sensitive to the initial conditions when solved on the epithelial shapes. A previously proposed diffusion-dependent geometry effect allowed us to reproduce the growth fields reasonably well, both for an inhibitor of branching that was produced in the epithelium, and for an inducer of branching that was produced in the mesenchyme. The latter could be represented by Glial-derived neurotrophic factor (GDNF), which is expressed in the mesenchyme and induces outgrowth of ureteric branches. Considering that the Turing model represents the interaction between the GDNF and its receptor RET very well and that the model reproduces the relevant expression patterns in developing wildtype and mutant kidneys, it is well possible that a combination of the Turing mechanism and the geometry effect control branching morphogenesis.
2020
During early kidney organogenesis, nephron progenitor (NP) cells move from the tip to the corner region of the ureteric bud (UB) branches in order to form the pretubular aggregate, the early structure giving rise to nephron formation. Chemotaxis and cell-cell adhesion differences are believed to drive cell patterning during this critical period of organogenesis, but the spatiotemporal organization of this process is incompletely understood.We applied a Cellular Potts model to explore to how these processes contribute to directed cell movement and aggregation. Model parameters were estimated based on fitting to experimental data obtained inex vivokidney explant and dissociation-reaggregation organoid culture studies.Our simulations indicated that optimal enrichment and aggregation of NP cells in the UB corner niche requires chemoattractant secretion from both the UB epithelial cells and the NP cells themselves, as well as differences in cell-cell adhesion energies. Furthermore, NP ce...
Global Quantification of Tissue Dynamics in the Developing Mouse Kidney
Developmental Cell, 2014
Although kidneys of equal size can vary 10-fold in nephron number at birth, discovering what regulates such variation has been hampered by a lack of quantitative parameters defining kidney development. Here we report a comprehensive, quantitative, multiscale analysis of mammalian kidney development in which we measure changes in cell number, compartment volumes, and cellular dynamics across the entirety of organogenesis, focusing on two key nephrogenic progenitor populations: the ureteric epithelium and the cap mesenchyme. In doing so, we describe a discontinuous developmental program governed by dynamic changes in interactions between these key cellular populations occurring within a previously unappreciated structurally stereotypic organ architecture. We also illustrate the application of this approach to the detection of a subtle mutant phenotype. This baseline program of kidney morphogenesis provides a framework for assessing genetic and environmental developmental perturbation and will serve as a gold standard for the analysis of other organs.
The developmental nephrome: systems biology in the developing kidney
Current Opinion in Nephrology & Hypertension, 2007
Purpose of review A set of important genes and signaling pathways involved in kidney development is emerging from analyses of mutant mice, in-vitro models, and global gene expression patterns. Conversion of data into dynamic models or networks through the synthesis of information at multiple levels is crucial for a better understanding of kidney development. Recent findings Genetic and in-vitro evidence is beginning to provide a limited sense of the network topology in stages of kidney development. Intriguing data from other fields suggest how, with the aid of large-scale gene expression studies, these stages might be represented as dynamic attractor states. It is also suggested how branching morphogenesis of the epithelial ureteric bud may be sustained by an autocatalytic set of proteins whose interactions lead to repeated rounds of tip and stalk generation. Accumulating data in lower organisms suggest network topologies may be quite flexible, and the implications of these results for varieties of tubulogenesis and renal regeneration after acute injury are discussed. Summary Currently it may be feasible to build tentative dynamic multistage models of nephrogenesis that facilitate experimental thinking. As data accumulate, it may become possible to test their predictive value.
Quantitation of 3D ureteric branching morphogenesis in cultured embryonic mouse kidney
The International journal of developmental biology, 2002
The growth and branching of the epithelial ureteric tree is critical for development of the permanent kidney (metanephros). Current methods of analysis of ureteric branching are mostly qualitative. We have developed a method for measuring the length of individual branches, and thereby the total length of the ureteric tree in 3 dimensions (3D). The method involves confocal microscopy of whole-mount immunostained metanephroi and computer-based image segmentation, skeletonisation and measurement. The algorithm performs semi-automatic segmentation of a set of confocal images and skeletonisation of the resulting binary object. Length measurements and number of branch points are automatically obtained. The final representation can be reconstructed providing a fully rotating 3D perspective of the skeletonised tree. After 36 h culture of E12 mouse metanephroi, the total length of the ureteric tree was 6103 +/- 291 microm (mean +/- SD), a four-fold increase compared with metanephroi cultured...
EAI endorsed transactions on bioengineering and bioinformatics, 2021
INTRODUCTION: Modelling of kidney physiology can add to comprehension of its work by formalizing existing information into numerical conditions and computational methods. The study evaluates the mathematical models that have been created to comprehend kidney physiology and pathophysiology. OBJECTIVE: Kidneys play a critical role in maintaining the body's water balance, electrolyte equilibrium, and acidbase balance, Through current knowledge with numerical models and computational methods, kidney physiology modeling will improve understanding of kidney function. METHOD: A L-System fractal system is designed to develop symmetrical branching tree systems that can fuse the physiological concepts of arterial tree branching to find the efficiency of blood flow in the renal arterial tree. Hopf Bifurcation analysis is also performed on mathematical models of autoregulation mechanisms that evaluate kidney physiology and glomerular filtration. RESULT: Because of the fractal structure of arterial branching, the flow rate is reduced in line with Strahler's order, so that work required (energy loss) is minimized to the cube root of flow rate. According to bifurcation analysis, mean arterial pressures between 70 and 100 mmHg can cause glomerulosclerosis, and a high gain in TGF signal can cause Limit cycle oscillations. CONCLUSION: The study concludes that nature has developed an optimal way of transferring blood from the Aorta to the Capillary bed by an evolutionary process such that the energy loss along the pathway is progressively reduced. Bifurcation analysis concludes that long and sustained oscillations due to underlying conditions such as diabetes, hypertension can lead to kidney damage.