Computational Modelling of Waddington’s Epigenetic Landscape
for Stem Cell Reprogramming
Jie Zheng
School of Computer Engineering, Nanyang Technological University, Singapore
Background: Induced pluripotent stem cells (iPSCs) represent a promising technology for
regenerative medicine. Numerous cocktails have been designed to generate iPSCs from
somatic cells to regain the pluripotent potential through reprogramming treatments, e.g. the
combinations of transcription factors, small chemical compounds, growth factors stimulus
and epigenetic modifiers. However, the underlying mechanisms for the generation of iPSCs
are still unclear, and some issues (e.g. cancer risk) still exist against the clinical usage.
Hence, computational modelling would be important for the science and engineering of
iPSCs.
Methods: In this work, we proposed a computational model to explore the dynamic
characteristics of the reprogramming process induced by lineage specifiers and pluripotency
factors. The computational model is developed based on a mouse stem cell developmental
network of 10 genes including two lineage specifiers, Gata6 and Sox1. The transcriptional
network was constructed manually according to literature and published databases. The
change rate of the concentration of each gene was encoded in the form of ordinary
differential equations (ODEs). The concept of Waddington’s epigenetic landscape is
employed to describe the kinetic potentials of the network. Following Langevin dynamics, we
constructed a probabilistic landscape as an implementation of the Waddington’s landscape.
The evolution of the probabilities of gene expression states is governed by Fokker-Planck
equation.
Results: The probabilistic landscape constructed based on the mathematical model is
composed of four stable steady states theoretically representing the stem cells,
mesendodermal cells, ectodermal cells and a complex attractor, respectively, according to
the gene expression levels of lineage marker genes. The simulated time series
concentrations of the 10 genes were generated to denote the trajectories to the four
attractors. We performed 10000 simulations with random initial ectoderm cells to calculate
the conversion rate under different reprogramming conditions of high expression of
pluripotency factors or lineage specifiers. The trajectory curves show bistability indicating the
unstable states during the reprogramming process.
Conclusions: The mathematical model has successfully simulated the reprogramming
process under various experimental conditions. It provides a quantitative method to study
the mechanisms of stem cell reprogramming. The quasi-potential landscape constructed can
be used for further studies of other cellular dynamics, e.g. ageing and cancer development.