Theoretical considerations for reprogramming multicellular systems

Engineering complex biological systems is fundamentally different from engineering nonliving systems. Multicellular living systems exhibit multistability, the coexistence of multiple stable attractors which arise from gene regulatory networks, encode the discrete cell types and collectively establish a 'rugged' potential-like landscape. While robustness of one attractor is the chief concern in engineering, the relevant dynamics in multicellular systems operates in the regime of frequent transitions among the attractors, corresponding to cell-type switching in development and in artificial cell reprogramming. This entails a more general formalism. Here we present a mathematical framework for constructing the quasi-potential landscape which relates the attractor to each other, derived from the decomposition of the vector field given by the ODEs which describe the dynamics of the gene networks. The rate for a transition between attractors and its 'least action path' are computed based on the Freidlin-Wentzell large deviation theory. These theoretical concepts provide the tools for rational design of gene network manipulations to steer cell fates for regenerative medicine instead of using trial-and-errors approaches.