Relative Stability of Network States in Boolean Network Models of Gene Regulation in Development

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.Comment: 24 pages, 6 figures, 1 tabl

Ensembles, Dynamics, and Cell Types: Revisiting the Statistical Mechanics Perspective on Cellular Regulation

Genetic regulatory networks control ontogeny. For fifty years Boolean networks have served as models of such systems, ranging from ensembles of random Boolean networks as models for generic properties of gene regulation to working dynamical models of a growing number of sub-networks of real cells. At the same time, their statistical mechanics has been thoroughly studied. Here we recapitulate their original motivation in the context of current theoretical and empirical research. We discuss ensembles of random Boolean networks whose dynamical attractors model cell types. A sub-ensemble is the critical ensemble. There is now strong evidence that genetic regulatory networks are dynamically critical, and that evolution is exploring the critical sub-ensemble. The generic properties of this sub-ensemble predict essential features of cell differentiation. In particular, the number of attractors in such networks scales as the DNA content raised to the 0.63 power. Data on the number of cell types as a function of the DNA content per cell shows a scaling relationship of 0.88. Thus, the theory correctly predicts a power law relationship between the number of cell types and the DNA contents per cell, and a comparable slope. We discuss these new scaling values and show prospects for new research lines for Boolean networks as a base model for systems biology.Comment: 22 pages, article will be included in a special issue of J. Theor. Biol. dedicated to the memory of Prof. Rene Thoma

Determining Relative Dynamic Stability of Cell States Using Boolean Network Model.

Cell state transition is at the core of biological processes in metazoan, which includes cell differentiation, epithelial-to-mesenchymal transition (EMT) and cell reprogramming. In these cases, it is important to understand the molecular mechanism of cellular stability and how the transitions happen between different cell states, which is controlled by a gene regulatory network (GRN) hard-wired in the genome. Here we use Boolean modeling of GRN to study the cell state transition of EMT and systematically compare four available methods to calculate the cellular stability of three cell states in EMT in both normal and genetically mutated cases. The results produced from four methods generally agree but do not totally agree with each other. We show that distribution of one-degree neighborhood of cell states, which are the nearest states by Hamming distance, causes the difference among the methods. From that, we propose a new method based on one-degree neighborhood, which is the simplest one and agrees with other methods to estimate the cellular stability in all scenarios of our EMT model. This new method will help the researchers in the field of cell differentiation and cell reprogramming to calculate cellular stability using Boolean model, and then rationally design their experimental protocols to manipulate the cell state transition

Science Forum: The Human Cell Atlas

The recent advent of methods for high-throughput single-cell molecular profiling has catalyzed a growing sense in the scientific community that the time is ripe to complete the 150-year-old effort to identify all cell types in the human body. The Human Cell Atlas Project is an international collaborative effort that aims to define all human cell types in terms of distinctive molecular profiles (such as gene expression profiles) and to connect this information with classical cellular descriptions (such as location and morphology). An open comprehensive reference map of the molecular state of cells in healthy human tissues would propel the systematic study of physiological states, developmental trajectories, regulatory circuitry and interactions of cells, and also provide a framework for understanding cellular dysregulation in human disease. Here we describe the idea, its potential utility, early proofs-of-concept, and some design considerations for the Human Cell Atlas, including a commitment to open data, code, and community

Decoding biological gene regulatory networks by quantitative modeling

Gene regulatory network is essential to regulate the biological functions of cells. With the rapid development of “omics” technologies, the network can be inferred for a certain biological function. However, it still remains a challenge to understand the complex network at a systematic level. In this thesis, we utilized quantitative modeling approaches to study the nonlinear dynamics and the design principles of these biological gene regulatory networks. We aim to explain the existing experimental observations with the model, and further propose reasonable hypothesis for future experimental designs. More importantly, the understanding of the circuit’s regulatory mechanism would benefit the design of a de novo gene circuit for a new biological function. We first studied the plasticity of cell migration phenotypes during cancer metastasis, which contains two key cellular plasticity mechanisms - epithelial-tomesenchymal transition (EMT) and mesenchymal-to-amoeboid transition (MAT). In this study, we quantitatively modeled the core Rac1/RhoA gene regulatory circuit for MAT and later connected it with the core regulatory circuit for EMT. We found four different stable states, consistent with the amoeboid (A), mesenchymal (M), the hybrid amoeboid/mesenchymal (A/M), and the hybrid epithelial/mesenchymal (E/M) phenotypes that are observed in the experiment. We also explored the effects of microRNAs and EMT-inducing signals like Hepatocyte Growth Factor (HGF), and provided a new insight for the transitions among these phenotypes. To improve the traditional modeling approaches, we developed a new computational modeling method called Random Circuit Perturbation (RACIPE) to explore the dynamic behavior of gene regulatory circuits without the requirement of detailed kinetic parameters. We applied RACIPE on several gene circuits, and found the existence of robust gene expression patterns even though the model parameters are wildly perturbed. We also showed the powerful aspect of RACIPE to decipher the operating principles of the circuits. This kind of quantitative models not only works for gene regulatory network, but also is capable to be extended to study the cell-cell interactions among cancer and immune cells. The results shown the co-occurrence of three cancer states: low risk cancer with intermediate immunity (L), intermediate risk cancer with high immunity (I) and high risk cancer with low immunity state (H). We further used the model to assess the different combinations of cancer therapies