Mathematical Modelling of Genetic Network for Regulating the Fate Determination of Hematopoietic Stem Cells

Inference of genetic network is an important task to explore and predict the regulatory mechanism inside the cell. Although a number of algorithms have been designed to reverse-engineer regulatory networks effective, it is still a challenge to introduce non-linearity into mathematical models effectively. To address this issue, this work proposes a novel framework to infer genetic networks with non-linearity. A new mathematical model using exponential ordinary differential equations is introduced to realize the non-linearity. Using the hematopoietic stem cell fate determination as the test problem, this work successfully reconstructs two networks for erythroid and granulocyte differentiation respectively, each of which includes 11 genes. Numerical results suggest that our new framework is able to provide accurate realizations of the system states. This work provide new ideas to infer regulatory networks effectively and explore novel regulatory mechanisms.

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