title: Relative stability of network states in Boolean network models of gene regulation in development.
abstract: Progress in cell type reprogramming has revived the interest in Waddington's concept of the epigenetic landscape. Recently researchers developed the quasi-potential theory to represent the Waddington's landscape. The Quasi-potential U(x), derived from interactions in the gene regulatory network (GRN) of a cell, quantifies the relative stability of network states, which determine the effort required for state transitions in a multi-stable dynamical system. However, quasi-potential landscapes, originally developed for continuous systems, are not suitable for discrete-valued networks which are important tools to study complex systems. In this paper, we provide a framework to quantify the landscape for discrete Boolean networks (BNs). We apply our framework to study pancreas cell differentiation where an ensemble of BN models is considered based on the structure of a minimal GRN for pancreas development. We impose biologically motivated structural constraints (corresponding to specific type of Boolean functions) and dynamical constraints (corresponding to stable attractor states) to limit the space of BN models for pancreas development. In addition, we enforce a novel functional constraint corresponding to the relative ordering of attractor states in BN models to restrict the space of BN models to the biological relevant class. We find that BNs with canalyzing/sign-compatible Boolean functions best capture the dynamics of pancreas cell differentiation. This framework can also determine the genes' influence on cell state transitions, and thus can facilitate the rational design of cell reprogramming protocols.
authors.affiliation: Institute for Systems Biology, Seattle, WA, USA; Kavli Institute for Theoretical Physics, UC Santa Barbara, CA, USA.
authors.forename: Joseph Xu
authors.initials: JX
authors.lastname: Zhou
authors.affiliation: Institute for Systems Biology, Seattle, WA, USA; The Institute of Mathematical Sciences, Chennai, India; The Abdus Salam International Centre for Theoretical Physics, Trieste, Italy.
authors.forename: Areejit
authors.initials: A
authors.lastname: Samal
authors.affiliation: Institute for Systems Biology, Seattle, WA, USA; Luxembourg Centre for Systems Biomedicine, Esch-sur-Alzette, Luxembourg.
authors.forename: Aymeric Fouquier
authors.initials: AF
authors.lastname: d'Hérouël
authors.affiliation: Institute for Systems Biology, Seattle, WA, USA.
authors.forename: Nathan D
authors.initials: ND
authors.lastname: Price
authors.affiliation: Institute for Systems Biology, Seattle, WA, USA. Electronic address: shuang@systemsbiology.org.
authors.forename: Sui
authors.initials: S
authors.lastname: Huang
mesh_terms: D000465:Algorithms; D002454:Cell Differentiation / Q000235:genetics; D003198:Computer Simulation; D005786:Gene Expression Regulation / Q000235:genetics*; D053263:Gene Regulatory Networks / Q000235:genetics*; D006801:Humans; D008957:Models, Genetic; D010179:Pancreas / Q000166:cytology / Q000378:metabolism; D015398:Signal Transduction / Q000235:genetics
keywords: Attractor states; Boolean network (BN); Cell differentiation; Epigenetic landscape; Gene regulatory network (GRN); Multistable dynamical system