Effects of community structure on the dynamics of random threshold networks

Landscape of epithelial-mesenchymal plasticity as an emergent property of coordinated teams in regulatory networks

Elucidating the design principles of regulatory networks driving cellular decision-making has fundamental implications in mapping and eventually controlling cell-fate decisions. Despite being complex, these regulatory networks often only give rise to a few phenotypes. Previously, we identified two 'teams' of nodes in a small cell lung cancer regulatory network that constrained the phenotypic repertoire and aligned strongly with the dominant phenotypes obtained from network simulations (Chauhan et al., 2021). However, it remained elusive whether these 'teams' exist in other networks, and how do they shape the phenotypic landscape. Here, we demonstrate that five different networks of varying sizes governing epithelial-mesenchymal plasticity comprised of two 'teams' of players - one comprised of canonical drivers of epithelial phenotype and the other containing the mesenchymal inducers. These 'teams' are specific to the topology of these regulatory networks and orchestrate a bimodal phenotypic landscape with the epithelial and mesenchymal phenotypes being more frequent and dynamically robust to perturbations, relative to the intermediary/hybrid epithelial/mesenchymal ones. Our analysis reveals that network topology alone can contain information about corresponding phenotypic distributions, thus obviating the need to simulate them. We propose 'teams' of nodes as a network design principle that can drive cell-fate canalization in diverse decision-making processes.

General method to find the attractors of discrete dynamic models of biological systems

Analyzing the long-term behaviors (attractors) of dynamic models of biological networks can provide valuable insight. We propose a general method that can find the attractors of multilevel discrete dynamical systems by extending a method that finds the attractors of a Boolean network model. The previous method is based on finding stable motifs, subgraphs whose nodes' states can stabilize on their own. We extend the framework from binary states to any finite discrete levels by creating a virtual node for each level of a multilevel node, and describing each virtual node with a quasi-Boolean function. We then create an expanded representation of the multilevel network, find multilevel stable motifs and oscillating motifs, and identify attractors by successive network reduction. In this way, we find both fixed point attractors and complex attractors. We implemented an algorithm, which we test and validate on representative synthetic networks and on published multilevel models of biological networks. Despite its primary motivation to analyze biological networks, our motif-based method is general and can be applied to any finite discrete dynamical system.

Unification of theoretical approaches for epidemic spreading on complex networks

Models of epidemic spreading on complex networks have attracted great attention among researchers in physics, mathematics, and epidemiology due to their success in predicting and controlling scenarios of epidemic spreading in real-world scenarios. To understand the interplay between epidemic spreading and the topology of a contact network, several outstanding theoretical approaches have been developed. An accurate theoretical approach describing the spreading dynamics must take both the network topology and dynamical correlations into consideration at the expense of increasing the complexity of the equations. In this short survey we unify the most widely used theoretical approaches for epidemic spreading on complex networks in terms of increasing complexity, including the mean-field, the heterogeneous mean-field, the quench mean-field, dynamical message-passing, link percolation, and pairwise approximation. We build connections among these approaches to provide new insights into developing an accurate theoretical approach to spreading dynamics on complex networks.

Structural determinants of criticality in biological networks

Many adaptive evolutionary systems display spatial and temporal features, such as long-range correlations, typically associated with the critical point of a phase transition in statistical physics. Empirical and theoretical studies suggest that operating near criticality enhances the functionality of biological networks, such as brain and gene networks, in terms for instance of information processing, robustness, and evolvability. While previous studies have explained criticality with specific system features, we still lack a general theory of critical behavior in biological systems. Here we look at this problem from the complex systems perspective, since in principle all critical biological circuits have in common the fact that their internal organization can be described as a complex network. An important question is how self-similar structure influences self-similar dynamics. Modularity and heterogeneity, for instance, affect the location of critical points and can be used to tune the system toward criticality. We review and discuss recent studies on the criticality of neuronal and genetic networks, and discuss the implications of network theory when assessing the evolutionary features of criticality.

Clustering dynamics of complex discrete-time networks and its application in community detection

The clustering phenomenon is common in real world networks. A discrete-time network model is proposed firstly in this paper, and then the phase clustering dynamics of the networks are studied carefully. The proposed model acts as a bridge between the dynamic phenomenon and the topology of a modular network. On one hand, phase clustering phenomenon will occur for a modular network by the proposed model; on the other hand, the communities can be identified from the clustering phenomenon. Beyond the phases' information, it is found that the frequencies of phases can be applied to community detection also with the proposed model. In specific, communities are identified from the information of phases and their frequencies of the nodes. Detailed algorithm for community detection is provided. Experiments show that the performance and efficiency of the dynamics based algorithm are competitive with recent modularity based algorithms in large scale networks.

Stability of Boolean networks: the joint effects of topology and update rules

We study the stability of orbits in large Boolean networks. We treat the case in which the network has a given complex topology, and we do not assume a specific form for the update rules, which may be correlated with local topological properties of the network. While recent past work has addressed the separate effects of complex network topology and certain classes of update rules on stability, only crude results exist about how these effects interact. We present a widely applicable solution to this problem. Numerical simulations confirm our theory and show that local correlations between topology and update rules can have profound effects on the qualitative behavior of these systems.

An effective network reduction approach to find the dynamical repertoire of discrete dynamic networks

Discrete dynamic models are a powerful tool for the understanding and modeling of large biological networks. Although a lot of progress has been made in developing analysis tools for these models, there is still a need to find approaches that can directly relate the network structure to its dynamics. Of special interest is identifying the stable patterns of activity, i.e., the attractors of the system. This is a problem for large networks, because the state space of the system increases exponentially with network size. In this work, we present a novel network reduction approach that is based on finding network motifs that stabilize in a fixed state. Notably, we use a topological criterion to identify these motifs. Specifically, we find certain types of strongly connected components in a suitably expanded representation of the network. To test our method, we apply it to a dynamic network model for a type of cytotoxic T cell cancer and to an ensemble of random Boolean networks of size up to 200. Our results show that our method goes beyond reducing the network and in most cases can actually predict the dynamical repertoire of the nodes (fixed states or oscillations) in the attractors of the system.