Computational multiscale modeling of embryo development

Recent advances in live imaging and genetics of mammalian development which integrate observations of biochemical activity, cell–cell signaling and mechanical interactions between cells pave the way for predictive mathematical multi-scale modeling. In early mammalian embryo development, two of the most critical events which lead to tissue patterning involve changes in gene expression as well as mechanical interactions between cells. We discuss the relevance of mathematical modeling of multi-cellular systems and in particular in simulating these patterns and describe some of the technical challenges one encounters. Many of these issues are not unique for the embryonic system but are shared by other multi-cellular modeling areas.

Introduction

The early mammalian embryo development is characterized by cell differentiation events leading to the formation of two extraembryonic lineages: trophectoderm (TE) and primitive endoderm (PE). Valuable insights into this process have been gained with single cell expression studies and live imaging techniques [1, 2, 3, 4, 5•, 6]. Most efforts have focused on determining the gene expression patterns that characterize the different lineages. Identified transcription factors for specific cell fates are, for example, Cdx2 and Gata6, accompanied by pluripotency genes: Nanog, Oct4 and Sox2 (Figure 1). The dynamics of the genetic network involving these genes has been explored in several deterministic [7, 8] as well as stochastic models [9, 10]. Single cell experiments [11] could provide the impetus to understand what drives cell commitment, that is, permissive versus instructive cell fate decision [12, 13]. While genetic network approaches offer invaluable insight into tissue differentiation at the genetic level, embryogenesis involves also co-ordination of cell division, movement and cell differentiation leading to tissue formation [14^••]. The high plasticity of single cell developmental fate and adaptivity to changing conditions within early embryo [6, 15•] suggests that robust formation of precisely localized specialized tissue precursors involves mechanisms going beyond single cells. Events like cell polarization during specification of the TE, directional cell migration and selective apoptosis during PE formation, require cell–cell signaling and interactions which convey relative positional information to cells [16^••]. Hence, a complete understanding of early embryogenesis regulation must consider different scales of multicellular interactions, including intracellular and intercellular biochemical signaling. In addition to these effects, the importance of mechanical properties of cells in the processes of morphogenesis has been recognized [17]. Therefore, successful models of embryogenetic events should integrate genetic, biochemical and mechanical interactions at the cellular level. Recent research in the plant sciences has shown the success of the tight integration of theory and experiment in understanding how bio-chemistry and mechanics leads to the development of organs such as the shoot, roots and leaves [18]. Here we discuss computational multicellular, multiscale modeling techniques [19, 20] and their implementations in early developmental events of mammalian embryogenesis. In addition to the current state-of-the-art in modeling, we describe future challenges that must be met to successfully integrate multicellular models of different scales. We also suggest how these models could be useful in other areas such as models of tumor evolution in cancer and stem cell regeneration.