Dynamical systems theory informed learning of cellular differentiation landscapes

Successful development from a single cell to a complex, multicellular organism requires that cells differentiate in a coordinated, organized manner, in response to a number of chemical morphogens. While the molecular underpinnings may be extremely complex, the resulting phenomenon, in which a cell decides between one fate or another, is relatively simple. A body of work, rooted in dynamical systems theory, has formalized this notion of cellular decision making as flow in a landscape, in which cells evolve according to gradient-like dynamics within a potential that changes shape in response to a number of signals. This mathematical realization of Waddington’s landscape suggests that certain quantifiable characteristics of cellular differentiation can be captured in relatively simple mathematical models, defined by an underlying potential function and a mapping of prescribed signals to their effect on the landscape. We provide a framework leveraging tools of machine learning to infer such a parameterized landscape model directly from gene expression data. The resulting model provides an intuitive, visualizable, and interpretable model of cellular differentiation dynamics. While previous approaches have successfully constructed models capturing cellular decision making, these typically model dynamics in an abstract space, rely on the identification of a discrete number of cell types, and significant prior knowledge of qualitative features of decision-making. In contrast, our data-driven approach infers a governing landscape atop a manifold within expression space, and thus describes the dynamics of interest within a space with direct, biological meaning.