Lamberton Timothy O, Lefevre James, Short Kieran M, Smyth Ian M, Hamilton Nicholas A
Division of Genomics of Development and Disease, Institute for Molecular Biosciences, The University of Queensland, Brisbane QLD 4072, Australia.
Department of Biochemistry and Molecular Biology, Monash University, Clayton, Melbourne, Victoria, Australia.
J Theor Biol. 2015 Jan 21;365:226-37. doi: 10.1016/j.jtbi.2014.10.001. Epub 2014 Oct 13.
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.
分叉式发育分支形态发生产生了诸如肺和肾输尿管树等复杂器官。然而，在结构层面上，用于比较和区分这些重要生物系统关键特征的定量方法或工具却很少。在此，我们开发了新颖的图对齐技术来量化有根分叉树的结构差异，并展示其在正常和突变小鼠发育肾脏分析中的应用。我们开发了两种基于图的度量：图不一致性，用于衡量表示不同树状图分支结构的图能够对齐或叠加的程度；以及图包含度，用于衡量一个树状图在另一个树状图中的包含程度。为了证明这些方法的应用，我们首先在包含32个正常和28个Tgfβ(+/-)突变小鼠输尿管树的数据集上对不一致性度量进行基准测试。我们发现，与基于图大小和指纹（末梢深度分布）的替代度量相比，不一致性度量能更好地区分对照和突变小鼠的肾脏。使用该度量，我们接着表明突变树的结构与正常肾脏遵循相同模式，但在后期阶段的细化过程中出现了重大延迟。使用包含度度量对对照和突变体进行分析，有力地支持了输尿管树生长是定型的这一假设。此外，我们提出了一种新的广义多树对齐算法，该算法可使成对图不一致性的总和最小化，并且可用于生成代表固定发育阶段原型的最大共识树。这些工具代表了分支模式分析和量化方面的进展，对于深入理解驱动发育的机制将具有重要价值。所有代码将随本出版物提供文档和示例数据。
