Emergence of diversity in homogeneous coupled Boolean networks

Emergent Criticality in Coupled Boolean Networks

Early embryonic development involves forming all specialized cells from a fluid-like mass of identical stem cells. The differentiation process consists of a series of symmetry-breaking events, starting from a high-symmetry state (stem cells) to a low-symmetry state (specialized cells). This scenario closely resembles phase transitions in statistical mechanics. To theoretically study this hypothesis, we model embryonic stem cell (ESC) populations through a coupled Boolean network (BN) model. The interaction is applied using a multilayer Ising model that considers paracrine and autocrine signaling, along with external interventions. It is demonstrated that cell-to-cell variability can be interpreted as a mixture of steady-state probability distributions. Simulations have revealed that such models can undergo a series of first- and second-order phase transitions as a function of the system parameters that describe gene expression noise and interaction strengths. These phase transitions result in spontaneous symmetry-breaking events that generate new types of cells characterized by various steady-state distributions. Coupled BNs have also been shown to self-organize in states that allow spontaneous cell differentiation.

A generalizable data-driven multicellular model of pancreatic ductal adenocarcinoma

BACKGROUND

Mechanistic models, when combined with pertinent data, can improve our knowledge regarding important molecular and cellular mechanisms found in cancer. These models make the prediction of tissue-level response to drug treatment possible, which can lead to new therapies and improved patient outcomes. Here we present a data-driven multiscale modeling framework to study molecular interactions between cancer, stromal, and immune cells found in the tumor microenvironment. We also develop methods to use molecular data available in The Cancer Genome Atlas to generate sample-specific models of cancer.

RESULTS

By combining published models of different cells relevant to pancreatic ductal adenocarcinoma (PDAC), we built an agent-based model of the multicellular pancreatic tumor microenvironment, formally describing cell type-specific molecular interactions and cytokine-mediated cell-cell communications. We used an ensemble-based modeling approach to systematically explore how variations in the tumor microenvironment affect the viability of cancer cells. The results suggest that the autocrine loop involving EGF signaling is a key interaction modulator between pancreatic cancer and stellate cells. EGF is also found to be associated with previously described subtypes of PDAC. Moreover, the model allows a systematic exploration of the effect of possible therapeutic perturbations; our simulations suggest that reducing bFGF secretion by stellate cells will have, on average, a positive impact on cancer apoptosis.

CONCLUSIONS

The developed framework allows model-driven hypotheses to be generated regarding therapeutically relevant PDAC states with potential molecular and cellular drivers indicating specific intervention strategies.

On the Lyapunov Exponent of Monotone Boolean Networks †

Boolean networks are discrete dynamical systems comprised of coupled Boolean functions. An important parameter that characterizes such systems is the Lyapunov exponent, which measures the state stability of the system to small perturbations. We consider networks comprised of monotone Boolean functions and derive asymptotic formulas for the Lyapunov exponent of almost all monotone Boolean networks. The formulas are different depending on whether the number of variables of the constituent Boolean functions, or equivalently, the connectivity of the Boolean network, is even or odd.