Waddington’s epigenetic landscape provides a phenomenological understanding of the cell differentiation pathways from the pluripotent to mature lineage-committed cell lines. In light of recent successes in the reverse programming process there has been significant interest in quantifying the underlying landscape picture through the mathematics of gene regulatory networks. We investigate the role of time delays arising from multi-step chemical reactions and epigenetic rearrangement on the cell differentiation landscape for a realistic two-gene regulatory network, consisting of self-promoting and mutually inhibiting genes. Our work provides the first theoretical basis of the transdifferentiation process in the presence of delays, where one differentiated cell type can transition to another directly without passing through the undifferentiated state. Additionally, the interplay of time-delayed feedback and a time dependent chemical drive leads to long-lived oscillatory states in appropriate parameter regimes. This work emphasizes the important role played by time-delayed feedback loops in gene regulatory circuits and provides a framework for the characterization of epigenetic landscapes.

Drosophila embryogenesis begins with nuclear division in a common cytoplasm forming a syncytial cell. Morphogen gradient molecules spread across nucleo-cytoplasmic domains to pattern the body axis of the syncytial embryo. The diffusion of molecules across the syncytial nucleo-cytoplasmic domains is potentially constrained by association with the components of cellular architecture. However, the extent of restriction has not been examined. Here we use photoactivation (PA) to generate a source of cytoplasmic or cytoskeletal molecules in order to monitor the kinetics of their spread in the syncytial Drosophila embryo. Photoactivated PA-GFP and PA-GFP-Tubulin generated within a fixed anterior area diffused along the antero-posterior axis. These molecules were enriched in the cortical cytoplasm above the yolk-filled center, suggesting that the cortical cytoplasm is phase separated from the yolk-filled center. The length scales of diffusion were extracted using exponential fits under steady state assumptions. PA-GFP spread a greater distance as compared to PA-GFP-Tubulin. Both molecules were more restricted when generated in the center of the embryo. The length scale of spread for PA-GFP-Tubulin increased in mutant embryos containing short plasma membrane furrows and a disrupted tubulin cytoskeleton. PA-GFP spread was unaffected by cyto-architecture perturbation. Taken together, these data show that PA-GFP-Tubulin spread is restricted by its incorporation in the microtubule network and intact plasma membrane furrows. This photoactivation based analysis of protein spread allows for interpretation of the dependence of gradient formation on syncytial cyto-architecture.

No abstract

Waddington's epigenetic landscape provides a phenomenological understanding of the cell differentiation pathways from the pluripotent to mature lineage-committed cell lines. In light of recent successes in the reverse programming process there has been significant interest in quantifying the underlying landscape picture through the mathematics of gene regulatory networks. We investigate the role of time delays arising from multistep chemical reactions and epigenetic rearrangement on the cell differentiation landscape for a realistic two-gene regulatory network, consisting of selfpromoting and mutually inhibiting genes. Our work provides the first theoretical basis of the transdifferentiation process in the presence of delays, where one differentiated cell type can transition to another directly without passing through the undifferentiated state. Additionally, the interplay of time-delayed feedback and a time dependent chemical drive leads to long-lived oscillatory states in appropriate parameter regimes. This work emphasizes the important role played by time-delayed feedback loops in gene regulatory circuits and provides a framework for the characterization of epigenetic landscapes.

No abstract