How do digits emerge? – mathematical models of limb development

Abstract

(146)The mechanism that controls digit formation has long intrigued developmental and theoretical biologists, and many different models and mechanisms have been proposed. Here we review models of limb development with a specific focus on digit and long bone formation. Decades of experiments have revealed the basic signalling circuits that control limb development, and recent advances in imaging and molecular technologies provide us with unprecedented spatial detail and a broader view on the regulatory networks. Computational approaches are important to integrate the available information into a consistent framework that will allow us to achieve a deeper level of understanding and that will help with the future planning and interpretation of complex experiments, paving the way to in silico genetics. Previous models of development had to be focused on very few, simple regulatory interactions. Algorithmic developments and increasing computing power now enable the generation and validation of increasingly realistic models that can be used to test old theories and uncover new mechanisms.

Tracheal Ring Formation

“…Turing patterns can be obtained also with a single morphogen or growth factor if its binding to the cell-bound receptor upregulates the receptor concentration ( Figure 2A ), as is the case for SHH, FGF10, and BMP Menshykau et al (2012) ; Badugu et al (2012) ; Celliere et al (2012) ; Kurics et al (2014) ; Menshykau et al (2014) . Candidate networks for Turing models that yield periodic cartilage patterns have been studied extensively in limb development, where the cartilage condensations mark future digits and phalanges Iber and Germann (2014) . The patterns in wildtype and perturbed conditions could be explained with a variety of biological mechanisms, including a 3-node network composed of BMP, SOX9, and WNT Raspopovic et al (2014) , a negative feedback between TGF- β and either the extracellular matrix (ECM) or TGF- β antagonists Zhu et al (2010) , and the interaction between BMPs and its receptor Badugu et al (2012) .…”

Simulating Organogenesis

“…Recent advances in imaging technology, algorithms, and computer power now permit the development of such increasingly realistic simulations of biological processes. In particular, it is now possible to obtain 2D and 3D shapes of developing organs and to solve the models on those embryonic geometries [Gleghorn et al 2012;Clément et al 2012;Menshykau et al 2014;Iber et al 2015]. During embryonic development, growth and patterning are tightly linked [Iber et al 2015].…”

“…It is therefore insufficient to solve the reaction-diffusion equations on a static domain. When solving Equation (1) on a growing domain, we need to include advection and dilution terms [Iber et al 2015] and obtaiṅ…”

Image-based modelling of organogenesis

“…Imagebased modeling provides an opportunity to integrate the wide range of imagebased spatio-temporal data with other biological datasets, e.g. qPCR, RNASeq, and proteomic data, into a consistent framework to arrive at a mechanistic understanding of morphogenesis [12,14,[44][45][46][47]. Here, the gene expression domains indicate where the different model components are produced, while spatio-temporal information on protein distribution provide information regarding the spatio-temporal distribution of the model components.…”