James G. Lefevre

Global quantification of tissue dynamics in the developing mouse kidney.

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.

Independent Contrasts and PGLS Regression Estimators Are Equivalent

We prove that the slope parameter of the ordinary least squares regression of phylogenetically independent contrasts (PICs) conducted through the origin is identical to the slope parameter of the method of generalized least squares (GLSs) regression under a Brownian motion model of evolution. This equivalence has several implications: 1. Understanding the structure of the linear model for GLS regression provides insight into when and why phylogeny is important in comparative studies. 2. The limitations of the PIC regression analysis are the same as the limitations of the GLS model. In particular, phylogenetic covariance applies only to the response variable in the regression and the explanatory variable should be regarded as fixed. Calculation of PICs for explanatory variables should be treated as a mathematical idiosyncrasy of the PIC regression algorithm. 3. Since the GLS estimator is the best linear unbiased estimator (BLUE), the slope parameter estimated using PICs is also BLUE. 4. If the slope is estimated using different branch lengths for the explanatory and response variables in the PIC algorithm, the estimator is no longer the BLUE, so this is not recommended. Finally, we discuss whether or not and how to accommodate phylogenetic covariance in regression analyses, particularly in relation to the problem of phylogenetic uncertainty. This discussion is from both frequentist and Bayesian perspectives.

An integrated pipeline for the multidimensional analysis of branching morphogenesis

Developmental branching morphogenesis establishes organ architecture, and it is driven by iterative interactions between epithelial and mesenchymal progenitor cell populations. We describe an approach for analyzing this interaction and how it contributes to organ development. After initial in vivo cell labeling with the nucleoside analog 5-ethynyl-2′-deoxyuridine (EdU) and tissue-specific antibodies, optical projection tomography (OPT) and confocal microscopy are used to image the developing organ. These imaging data then inform a second analysis phase that quantifies (using Imaris and Tree Surveyor software), models and integrates these events at a cell and tissue level in 3D space and across developmental time. The protocol establishes a benchmark for assessing the impact of genetic change or fetal environment on organogenesis that does not rely on ex vivo organ culture or section-based reconstruction. By using this approach, examination of two developmental stages for an organ such as the kidney can be undertaken by a postdoctoral-level researcher in 6 weeks, with a full developmental analysis in mouse achievable in 5 months.

Cap mesenchyme cell swarming during kidney development is influenced by attraction, repulsion, and adhesion to the ureteric tip

Morphogenesis of the mammalian kidney requires reciprocal interactions between two cellular domains at the periphery of the developing organ: the tips of the epithelial ureteric tree and adjacent regions of cap mesenchyme. While the presence of the cap mesenchyme is essential for ureteric branching, how it is specifically maintained at the tips is unclear. Using ex vivo timelapse imaging we show that cells of the cap mesenchyme are highly motile. Individual cap mesenchyme cells move within and between cap domains. They also attach and detach from the ureteric tip across time. Timelapse tracks collected for >800 cells showed evidence that this movement was largely stochastic, with cell autonomous migration influenced by opposing attractive, repulsive and cell adhesion cues. The resulting swarming behaviour maintains a distinct cap mesenchyme domain while facilitating dynamic remodelling in response to underlying changes in the tip.

Comparing and distinguishing the structure of biological branching

Bifurcating developmental branching morphogenesis gives rise to complex organs such as the lung and the ureteric tree of the kidney. However, a few quantitative methods or tools exist to compare and distinguish, at a structural level, the critical features of these important biological systems. Here we develop novel graph alignment techniques to quantify the structural differences of rooted bifurcating trees and demonstrate their application in the analysis of developing kidneys from in normal and mutant mice. We have developed two graph based metrics: graph discordance, which measures how well the graphs representing the branching structures of distinct trees graphs can be aligned or overlayed; and graph inclusion, which measures the degree of containment of a tree graph within another. To demonstrate the application of these approaches we first benchmark the discordance metric on a data set of 32 normal and 28Tgfβ(+/-) mutant mouse ureteric trees. We find that the discordance metric better distinguishes control and mutant mouse kidneys than alternative metrics based on graph size and fingerprints - the distribution of tip depths. Using this metric we then show that the structure of the mutant trees follows the same pattern as the normal kidneys, but undergo a major delay in elaboration at later stages. Analysis of both controls and mutants using the inclusion metric gives strong support to the hypothesis that ureteric tree growth is stereotypic. Additionally, we present a new generalised multi-tree alignment algorithm that minimises the sum of pairwise graph discordance and which can be used to generate maximum consensus trees that represent the archetype for fixed developmental stages. These tools represent an advance in the analysis and quantification of branching patterns and will be invaluable in gaining a deeper understanding of the mechanisms that drive development. All code is being made available with documentation and example data with this publication.

Modelling cell turnover in a complex tissue during development.

The growth of organs results from proliferation within distinct cellular compartments. Organ development also involves transitions between cell types and variations in cell cycle duration as development progresses, and is regulated by a balance between entry into the compartment, proliferation of cells within the compartment, acquisition of quiescence and exit from that cell state via differentiation or death. While it is important to understand how environmental or genetic alterations can perturb such development, most approaches employed to date are descriptive rather than quantitative. This is because the identification and quantification of such parameters, while tractable in vitro, is challenging in the context of a complex tissue in vivo. Here we present a new framework for determining cell turnover in developing organs in vivo that combines cumulative cell-labelling and quantification of distinct cell-cycle phases without assuming homogeneity of behaviour within that compartment. A mathematical model is given that allows the calculation of cell cycle length in the context of a specific biological example and assesses the uncertainty of this calculation due to incomplete knowledge of cell cycle dynamics. This includes the development of a two population model to quantify possible heterogeneity of cell cycle length within a compartment and estimate the aggregate proliferation rate. These models are demonstrated on data collected from a progenitor cell compartment within the developing mouse kidney, the cap mesenchyme. This tissue was labelled by cumulative infusion, volumetrically quantified across time, and temporally analysed for the proportion of cells undergoing proliferation. By combining the cell cycle length predicted by the model with measurements of total cell population and mitotic rate, this approach facilitates the quantification of exit from this compartment without the need for a direct marker of that event. As a method specifically designed with assumptions appropriate to developing organs we believe this approach will be applicable to a range of developmental systems, facilitating estimations of cell cycle length and compartment behaviour that extend beyond simple comparisons of mitotic rates between normal and perturbed states.

A spatially-averaged mathematical model of kidney branching morphogenesis

Kidney development is initiated by the outgrowth of an epithelial ureteric bud into a population of mesenchymal cells. Reciprocal morphogenetic responses between these two populations generate a highly branched epithelial ureteric tree with the mesenchyme differentiating into nephrons, the functional units of the kidney. While we understand some of the mechanisms involved, current knowledge fails to explain the variability of organ sizes and nephron endowment in mice and humans. Here we present a spatially-averaged mathematical model of kidney morphogenesis in which the growth of the two key populations is described by a system of time-dependant ordinary differential equations. We assume that branching is symmetric and is invoked when the number of epithelial cells per tip reaches a threshold value. This process continues until the number of mesenchymal cells falls below a critical value that triggers cessation of branching. The mathematical model and its predictions are validated against experimentally quantified C57Bl6 mouse embryonic kidneys. Numerical simulations are performed to determine how the final number of branches changes as key system parameters are varied (such as the growth rate of tip cells, mesenchyme cells, or component cell population exit rate). Our results predict that the developing kidney responds differently to loss of cap and tip cells. They also indicate that the final number of kidney branches is less sensitive to changes in the growth rate of the ureteric tip cells than to changes in the growth rate of the mesenchymal cells. By inference, increasing the growth rate of mesenchymal cells should maximise branch number. Our model also provides a framework for predicting the branching outcome when ureteric tip or mesenchyme cells change behaviour in response to different genetic or environmental developmental stresses.

On Defining Sets of Full Designs with Block Size Three

A defining set of a t-(v, k, λ) design is a subcollection of its blocks which is contained in no other t-design with the given parameters, on the same point set. A minimal defining set is a defining set, none of whose proper subcollections is a defining set. The spectrum of minimal defining sets of a design D is the set {|M| | M is a minimal defining set of D}. We show that if a t-(v, k, λ) design D is contained in a design F, then for every minimal defining set dD of D there exists a minimal defining set dF of F such that

Quarter-regular biembeddings of Latin squares

{d_D = d_F\cap D}