Mathematical Approaches of Branching Morphogenesis

A biomimetic branching signal-passing tile assembly model with dynamic growth and disassembly

Natural biological branching processes can form tree-like structures at all scales and, moreover, can perform various functions to achieve specific goals; these include receiving stimuli, performing two-way communication along their branches, and dynamically reforming (extending or retracting branches). They underlie many biological systems with considerable diversity, frequency, and geometric complexity; these include networks of neurons, organ tissue, mycorrhizal fungal networks, plant growth, foraging networks, etc. This paper presents a biomimetic DNA tile assembly model (Y-STAM) to implement dynamic branching processes. The Y-STAM is a relatively compact mathematical model providing a design space where complex, biomimetic branch-like growth and behaviour can emerge from the appropriate parametrization of the model. We also introduce a class of augmented models (Y-STAM+) that provide time- and space-dependent modulations of tile glue strengths, which enable further diverse behaviours that are not possible in the Y-STAM; these additional behaviours include refinement of network assemblies, obstacle avoidance, and programmable growth patterns. We perform and discuss extensive simulations of the Y-STAM and the Y-STAM+. We envision that these models could be applied at the mesoscale and the molecular scale to dynamically assemble branching DNA nanostructures and offer insights into complex biological self-assembly processes.

Mechanism of branching morphogenesis inspired by diatom silica formation

The silica-based cell walls of diatoms are prime examples of genetically controlled, species-specific mineral architectures. The physical principles underlying morphogenesis of their hierarchically structured silica patterns are not understood, yet such insight could indicate novel routes toward synthesizing functional inorganic materials. Recent advances in imaging nascent diatom silica allow rationalizing possible mechanisms of their pattern formation. Here, we combine theory and experiments on the model diatom Thalassiosira pseudonana to put forward a minimal model of branched rib patterns-a fundamental feature of the silica cell wall. We quantitatively recapitulate the time course of rib pattern morphogenesis by accounting for silica biochemistry with autocatalytic formation of diffusible silica precursors followed by conversion into solid silica. We propose that silica deposition releases an inhibitor that slows down up-stream precursor conversion, thereby implementing a self-replicating reaction-diffusion system different from a classical Turing mechanism. The proposed mechanism highlights the role of geometrical cues for guided self-organization, rationalizing the instructive role for the single initial pattern seed known as the primary silicification site. The mechanism of branching morphogenesis that we characterize here is possibly generic and may apply also in other biological systems.

Lung patterning: Is a distal-to-proximal gradient of cell allocation and fate decision a general paradigm?: A gradient of distal-to-proximal distribution and differentiation of tip progenitors produces distinct compartments in the lung

Recent studies support a model in which the progeny of SOX9+ epithelial progenitors at the distal tip of lung branches undergo cell allocation and differentiation sequentially along the distal-to-proximal axis. Concomitant with the elongation and ramification of lung branches, the descendants of the distal SOX9+ progenitors are distributed proximally, express SOX2, and differentiate into cell types in the conducting airways. Amid subsequent sacculation, the distal SOX9+ progenitors generate alveolar epithelial cells to form alveoli. Sequential cell allocation and differentiation are integrated with the branching process to generate a functional branching organ. This review focuses on the roles of SOX9+ cells as precursors for new branches, as the source of various cell types in the conducting airways, and as progenitors of the alveolar epithelium. All of these processes are controlled by multiple signaling pathways. Many mouse mutants with defective lung branching contain underlying defects in one or more steps of cell allocation and differentiation of SOX9+ progenitors. This model provides a framework to understand the molecular basis of lung phenotypes and to elucidate the molecular mechanisms of lung patterning. It builds a foundation on which comparing and contrasting the mechanisms employed by different branching organs in diverse species can be made.

Inflationary theory of branching morphogenesis in the mouse salivary gland

The mechanisms that regulate the patterning of branched epithelia remain a subject of long-standing debate. Recently, it has been proposed that the statistical organization of multiple ductal tissues can be explained through a local self-organizing principle based on the branching-annihilating random walk (BARW) in which proliferating tips drive a process of ductal elongation and stochastic bifurcation that terminates when tips encounter maturing ducts. Here, applied to mouse salivary gland, we show the BARW model struggles to explain the large-scale organization of tissue. Instead, we propose that the gland develops as a tip-driven branching-delayed random walk (BDRW). In this framework, a generalization of the BARW, tips inhibited through steric interaction with proximate ducts may continue their branching program as constraints become alleviated through the persistent expansion of the surrounding tissue. This inflationary BDRW model presents a general paradigm for branching morphogenesis when the ductal epithelium grows cooperatively with the domain into which it expands.

E26 transformation-specific transcription variant 5 in development and cancer: modification, regulation and function

E26 transformation-specific (ETS) transcription variant 5 (ETV5), also known as ETS-related molecule (ERM), exerts versatile functions in normal physiological processes, including branching morphogenesis, neural system development, fertility, embryonic development, immune regulation, and cell metabolism. In addition, ETV5 is repeatedly found to be overexpressed in multiple malignant tumors, where it is involved in cancer progression as an oncogenic transcription factor. Its roles in cancer metastasis, proliferation, oxidative stress response and drug resistance indicate that it is a potential prognostic biomarker, as well as a therapeutic target for cancer treatment. Post-translational modifications, gene fusion events, sophisticated cellular signaling crosstalk and non-coding RNAs contribute to the dysregulation and abnormal activities of ETV5. However, few studies to date systematically summarized the role and molecular mechanisms of ETV5 in benign diseases and in oncogenic progression. In this review, we specify the molecular structure and post-translational modifications of ETV5. In addition, its critical roles in benign and malignant diseases are summarized to draw a panorama for specialists and clinicians. The updated molecular mechanisms of ETV5 in cancer biology and tumor progression are delineated. Finally, we prospect the further direction of ETV5 research in oncology and its potential translational applications in the clinic.

Renal volume of five-year-old preterm children are not different than full-term controls

OBJECTIVE

In previous studies, smaller renal volumes were reported in prematurely born infants, however, these renal volumes were not corrected for body surface area, the main determinant of renal size. Given the rapid growth of the renal cortex after premature birth, the authors hypothesized that corrected volumes would not differ from healthy controls.

METHODS

Ambispective cohort study with prospective follow-up of prematurely born babies in a large specialized center and retrospectively recruited healthy control group. Children were assessed for renal length and renal volumes at age 5 by three independent ultrasonographers. Detailed anthropometry, blood pressure and renal function were also obtained. Age independent z-scores were calculated for all parameters and compared using descriptive statistics.

RESULTS

Eighty-nine premature study participants (median 32 weeks gestational age) and 33 healthy controls (median 38 weeks gestational age) were studied. Study participants did not differ in age, sex, Afro-Colombian descent, height, blood pressure, serum creatinine, or new Schwartz eGFR. Premature study participants had a significantly lower weight (17.65 ± 2.93 kg) than controls (19.05 ± 2.81 kg, p = 0.0072) and lower body surface area. The right renal volumes were significantly smaller (39.4 vs 43.4 mL), but after correction for body surface area, the renal volume and renal length z-scores were identical for both kidneys (mean right kidney -0.707 vs -0.507; mean left kidney -0.498 vs -0.524, respectively).

CONCLUSION

Renal volumes need to be corrected to body surface area. After correction for body surface area, 5-year-old healthy and prematurely born children have comparable renal volumes.

Organ-Specific Branching Morphogenesis

A common developmental process, called branching morphogenesis, generates the epithelial trees in a variety of organs, including the lungs, kidneys, and glands. How branching morphogenesis can create epithelial architectures of very different shapes and functions remains elusive. In this review, we compare branching morphogenesis and its regulation in lungs and kidneys and discuss the role of signaling pathways, the mesenchyme, the extracellular matrix, and the cytoskeleton as potential organ-specific determinants of branch position, orientation, and shape. Identifying the determinants of branch and organ shape and their adaptation in different organs may reveal how a highly conserved developmental process can be adapted to different structural and functional frameworks and should provide important insights into epithelial morphogenesis and developmental disorders.

Multi-scale simulation of early kidney branching morphogenesis

An important feature of the branch morphogenesis during kidney development is the termination of the tips on the outer surface of a kidney. This feature requires the avoidance of the intersection between the tips and existing ducts inside the kidney. Here, we started from a continuous model and implemented the coarse grained rules into a fast and discrete simulations. The ligand-receptor-based Turing mechanism suggests a repulsion that decreases exponentially with distance between interacting branches, preventing the intersection between neighboring branches. We considered this repulsive effect in numerical simulations and successfully reproduce the key features of the experimentally observed branch morphology for an E15.5 kidney. We examine the similarity of several geometrical parameters between the simulation results and experimental observations. The good agreement between the simulations and experiments suggests that the concentration decay caused by the absorption of glial cell line derived neurotrophic factor might be the key factor to affect the geometry in early kidney development.

Fgf10/Fgfr2b Signaling Orchestrates the Symphony of Molecular, Cellular, and Physical Processes Required for Harmonious Airway Branching Morphogenesis

Airway branching morphogenesis depends on the intricate orchestration of numerous biological and physical factors connected across different spatial scales. One of the key regulatory pathways controlling airway branching is fibroblast growth factor 10 (Fgf10) signaling via its epithelial fibroblast growth factor receptor 2b (Fgfr2b). Fine reviews have been published on the molecular mechanisms, in general, involved in branching morphogenesis, including those mechanisms, in particular, connected to Fgf10/Fgfr2b signaling. However, a comprehensive review looking at all the major biological and physical factors involved in branching, at the different scales at which branching operates, and the known role of Fgf10/Fgfr2b therein, is missing. In the current review, we attempt to summarize the existing literature on airway branching morphogenesis by taking a broad approach. We focus on the biophysical and mechanical forces directly shaping epithelial bud initiation, branch elongation, and branch tip bifurcation. We then shift focus to more passive means by which branching proceeds, via extracellular matrix remodeling and the influence of the other pulmonary arborized networks: the vasculature and nerves. We end the review by briefly discussing work in computational modeling of airway branching. Throughout, we emphasize the known or speculative effects of Fgfr2b signaling at each point of discussion. It is our aim to promote an understanding of branching morphogenesis that captures the multi-scalar biological and physical nature of the phenomenon, and the interdisciplinary approach to its study.

Simple Rules Determine Distinct Patterns of Branching Morphogenesis

Many metazoan organs are comprised of branching trees of epithelial tubes; how patterning occurs in these trees is a fundamental problem of development. Commonly, branch tips fill the volume of the organ approximately uniformly, e.g., in mammalian lung, airway branch tips are dispersed roughly uniformly throughout the volume of the lung. In contrast, in the developing metanephric kidney, the tips of the ureteric bud tree are located close to the outer surface of the kidney rather than filling the kidney. Here, we describe a simple alteration in the branching rules that accounts for the difference between the kidney pattern that leads to tips near the organ surface versus previously known patterns that lead to the branch tips being dispersed throughout the organ. We further use a simple toy model to deduce from first principles how this rule change accounts for the differences in the two types of trees.

Genetic manipulation of ureteric bud tip progenitors in the mammalian kidney through an Adamts18 enhancer driven tet-on inducible system

The ureteric epithelial progenitor (UEP) population within the embryonic kidney generates the arborized epithelial network of the kidney's collecting system and plays a critical role in the expansion and induction of the surrounding nephron progenitor pool. Adamts18 shows UEP- restricted expression in the kidney and progenitor tip-restricted expression in several other organs undergoing branching epithelial growth. Adamts18 is encoded by 23 exons. Genetic removal of genomic sequence spanning exons 1 to 3 led to a specific loss of Adamts18 expression in UEPs, suggesting this region may encode a UEP-specific enhancer. Intron 2 (3 ​kb) was shown to have enhancer activity driving expression of the doxycycline inducible tet-on transcriptional regulator (rtTA) in an Adamts18en-rtTA transgenic mouse strain. Crossing Adamts18en-rtTA mice to a doxycycline dependent GFP reporter mouse enabled the live imaging of embryonic kidney explants. This facilitated the analysis of ureteric epithelial branching events at the cellular level. Ablation of UEPs at the initiation of ureteric bud outgrowth through the doxycycline-mediated induction of Diphtheria Toxin A (DTA) generated a range of phenotypes from complete kidneys agenesis, to duplex kidneys with double ureters. The latter outcome points to the potential of regulative processes to restore UEPs. In contrast, overexpression of YAP prior to ureteric bud outgrowth led to a complete failure of kidney development. Elevating YAP levels at later stages retarded branching growth. A similar phenotype was observed with the overexpression of MYC within the branch-tip localized UEP population. These experiments showcase the utility of the Adamts18en-rtTA transgenic model to the investigation of cellular and molecular events specific to branch tip progenitors within the mammalian kidney complementing existing CRE-dependent genetic tools. Further, the illustrative examples point to areas where new insight may be gained into the regulation of UEP programs.

Current strategies and opportunities to manufacture cells for modeling human lungs

Chronic lung diseases remain major healthcare burdens, for which the only curative treatment is lung transplantation. In vitro human models are promising platforms for identifying and testing novel compounds to potentially decrease this burden. Directed differentiation of pluripotent stem cells is an important strategy to generate lung cells to create such models. Current lung directed differentiation protocols are limited as they do not 1) recapitulate the diversity of respiratory epithelium, 2) generate consistent or sufficient cell numbers for drug discovery platforms, and 3) establish the histologic tissue-level organization critical for modeling lung function. In this review, we describe how lung development has formed the basis for directed differentiation protocols, and discuss the utility of available protocols for lung epithelial cell generation and drug development. We further highlight tissue engineering strategies for manipulating biophysical signals during directed differentiation such that future protocols can recapitulate both chemical and physical cues present during lung development.

Design Principles of Branching Morphogenesis in Filamentous Organisms

The radiation of life on Earth was accompanied by the diversification of multicellular body plans in the eukaryotic kingdoms Animalia, Plantae, Fungi and Chromista. Branching forms are ubiquitous in nature and evolved repeatedly in the above lineages. The developmental and genetic basis of branch formation is well studied in the three-dimensional shoot and root systems of land plants, and in animal organs such as the lung, kidney, mammary gland, vasculature, etc. Notably, recent thought-provoking studies combining experimental analysis and computational modeling of branching patterns in whole animal organs have identified global patterning rules and proposed unifying principles of branching morphogenesis. Filamentous branching forms represent one of the simplest expressions of the multicellular body plan and constitute a key step in the evolution of morphological complexity. Similarities between simple and complex branching forms distantly related in evolution are compelling, raising the question whether shared mechanisms underlie their development. Here, we focus on filamentous branching organisms that represent major study models from three distinct eukaryotic kingdoms, including the moss Physcomitrella patens (Plantae), the brown alga Ectocarpus sp. (Chromista), and the ascomycetes Neurospora crassa and Aspergillus nidulans (Fungi), and bring to light developmental regulatory mechanisms and design principles common to these lineages. Throughout the review we explore how the regulatory mechanisms of branching morphogenesis identified in other models, and in particular animal organs, may inform our thinking on filamentous systems and thereby advance our understanding of the diverse strategies deployed across the eukaryotic tree of life to evolve similar forms.