Comparing and distinguishing the structure of biological branching

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.

A topological data analysis based classification method for multiple measurements

Background

Machine learning models for repeated measurements are limited. Using topological data analysis (TDA), we present a classifier for repeated measurements which samples from the data space and builds a network graph based on the data topology. A machine learning model with cross-validation is then applied for classification. When test this on three case studies, accuracy exceeds an alternative support vector machine (SVM) voting model in most situations tested, with additional benefits such as reporting data subsets with high purity along with feature values.

Results

For 100 examples of 3 different tree species, the model reached 80% classification accuracy after 30 datapoints, which was improved to 90% after increased sampling to 400 datapoints. The alternative SVM classifier achieved a maximum accuracy of 68.7%. Using data from 100 examples from each class of 6 different random point processes, the classifier achieved 96.8% accuracy, vastly outperforming the SVM. Using two outcomes in neuron spiking data, the TDA classifier was similarly accurate to the SVM in one case (both converged to 97.8% accuracy), but was outperformed in the other (relative accuracies 79.8% and 92.2%, respectively).

Conclusions

This algorithm and software can be beneficial for repeated measurement data common in biological sciences, as both an accurate classifier and a feature selection tool.

Branching morphogenesis in the developing kidney is governed by rules that pattern the ureteric tree

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. These findings demonstrate that kidney development occurs by way of a highly conserved reiterative pattern of asymmetric bifurcation that is governed by intrinsic and locally operative mechanisms.

Imaging, Analysing and Interpreting Branching Morphogenesis in the Developing Kidney

The kidney develops as an outgrowth of the epithelial nephric duct known as the ureteric bud, in a position specified by a range of rostral and caudal factors which serve to ensure two kidneys form in the appropriate positions in the body. At its simplest level, kidney development can be viewed as the process by which this single bud then undergoes a process of arborisation to form a complex connected network of ducts which will serve to drain urine from the nephrons in the adult organ. The process of bud elaboration is dictated by factors expressed by both the bud itself and by surrounding cells of the metanephric mesenchyme which control cell division and bifurcation. These cells play two critical roles. Firstly, they potentiate the ongoing elaboration of the ureteric tree: remove them and branching ceases. Secondly, they harbour progenitor cells which are fated to undergo their own process of tubulogenesis to form the nephrons of the adult organ. In this chapter, we will discuss how the ureteric bud arises in the developing embryo, how it undergoes branching, how we can measure and study this process and finally the likely relevance that this process has for our understanding of congenital and acquired kidney disease.

Looking Beyond the Genes: The Interplay Between Signaling Pathways and Mechanics in the Shaping and Diversification of Epithelial Tissues

The core of Evo-Devo lies in the intuition that the way tissues grow during embryonic development, the way they sustain their structure and function throughout lifetime, and the way they evolve are closely linked. Epithelial tissues are ubiquitous in metazoans, covering the gut and internal branched organs, as well as the skin and its derivatives (ie, teeth). Here, we discuss in vitro, in vivo, and in silico studies on epithelial tissues to illustrate the conserved, dynamical, and complex aspects of their development. We then explore the implications of the dynamical and nonlinear nature of development on the evolution of their size and shape at the phenotypic and genetic levels. In rare cases, when the interplay between signaling and mechanics is well understood at the cell level, it is becoming clear that the structure of development leads to covariation of characters, an integration which in turn provides some predictable structure to evolutionary changes. We suggest that such nonlinear systems are prone to genetic drift, cryptic genetic variation, and context-dependent mutational effects. We argue that experimental and theoretical studies at the cell level are critical to our understanding of the phenotypic and genetic evolution of epithelial tissues, including carcinomas.

Cell-cell interactions driving kidney morphogenesis

The mammalian kidney forms via cell-cell interactions between an epithelial outgrowth of the nephric duct and the surrounding nephrogenic mesenchyme. Initial morphogenetic events include ureteric bud branching to form the collecting duct (CD) tree and mesenchymal-to-epithelial transitions to form the nephrons, requiring reciprocal induction between adjacent mesenchyme and epithelial cells. Within the tips of the branching ureteric epithelium, cells respond to mesenchyme-derived trophic factors by proliferation, migration, and mitosis-associated cell dispersal. Self-inhibition signals from one tip to another play a role in branch patterning. The position, survival, and fate of the nephrogenic mesenchyme are regulated by ECM and secreted signals from adjacent tip and stroma. Signals from the ureteric tip promote mesenchyme self-renewal and trigger nephron formation. Subsequent fusion to the CDs, nephron segmentation and maturation, and formation of a patent glomerular basement membrane also require specialized cell-cell interactions. Differential cadherin, laminin, nectin, and integrin expression, as well as intracellular kinesin and actin-mediated regulation of cell shape and adhesion, underlies these cell-cell interactions. Indeed, the capacity for the kidney to form via self-organization has now been established both via the recapitulation of expected morphogenetic interactions after complete dissociation and reassociation of cellular components during development as well as the in vitro formation of 3D kidney organoids from human pluripotent stem cells. As we understand more about how the many cell-cell interactions required for kidney formation operate, this enables the prospect of bioengineering replacement structures based on these self-organizing properties.