Evolution and Controllability of Cancer Networks: A Boolean Perspective

The Impact of Self-Loops on Boolean Networks Attractor Landscape and Implications for Cell Differentiation Modelling

Boolean networks are a notable model of gene regulatory networks and, particularly, prominent theories discuss how they can capture cellular differentiation processes. One frequent motif in gene regulatory networks, especially in those circuits involved in cell differentiation, is autoregulation. In spite of this, the impact of autoregulation on Boolean network attractor landscape has not yet been extensively discussed in literature. In this paper we propose to model autoregulation as self-loops, and analyse how the number of attractors and their robustness may change once they are introduced in a well-known and widely used Boolean networks model, namely random Boolean networks. Results show that self-loops provide an evolutionary advantage in dynamic mechanisms of cells, by increasing both number and maximal robustness of attractors. These results provide evidence to the hypothesis that autoregulation is a straightforward functional component to consolidate cell dynamics, mainly in differentiation processes.

Network control principles for identifying personalized driver genes in cancer

To understand tumor heterogeneity in cancer, personalized driver genes (PDGs) need to be identified for unraveling the genotype-phenotype associations corresponding to particular patients. However, most of the existing driver-focus methods mainly pay attention on the cohort information rather than on individual information. Recent developing computational approaches based on network control principles are opening a new way to discover driver genes in cancer, particularly at an individual level. To provide comprehensive perspectives of network control methods on this timely topic, we first considered the cancer progression as a network control problem, in which the expected PDGs are altered genes by oncogene activation signals that can change the individual molecular network from one health state to the other disease state. Then, we reviewed the network reconstruction methods on single samples and introduced novel network control methods on single-sample networks to identify PDGs in cancer. Particularly, we gave a performance assessment of the network structure control-based PDGs identification methods on multiple cancer datasets from TCGA, for which the data and evaluation package also are publicly available. Finally, we discussed future directions for the application of network control methods to identify PDGs in cancer and diverse biological processes.

A Middle-Out Modeling Strategy to Extend a Colon Cancer Logical Model Improves Drug Synergy Predictions in Epithelial-Derived Cancer Cell Lines

Cancer is a heterogeneous and complex disease and one of the leading causes of death worldwide. The high tumor heterogeneity between individuals affected by the same cancer type is accompanied by distinct molecular and phenotypic tumor profiles and variation in drug treatment response. In silico modeling of cancer as an aberrantly regulated system of interacting signaling molecules provides a basis to enhance our biological understanding of disease progression, and it offers the means to use computer simulations to test and optimize drug therapy designs on particular cancer types and subtypes. This sets the stage for precision medicine: the design of treatments tailored to individuals or groups of patients based on their tumor-specific molecular cancer profiles. Here, we show how a relatively large manually curated logical model can be efficiently enhanced further by including components highlighted by a multi-omics data analysis of data from Consensus Molecular Subtypes covering colorectal cancer. The model expansion was performed in a pathway-centric manner, following a partitioning of the model into functional subsystems, named modules. The resulting approach constitutes a middle-out modeling strategy enabling a data-driven expansion of a model from a generic and intermediate level of molecular detail to a model better covering relevant processes that are affected in specific cancer subtypes, comprising 183 biological entities and 603 interactions between them, partitioned in 25 functional modules of varying size and structure. We tested this model for its ability to correctly predict drug combination synergies, against a dataset of experimentally determined cell growth responses with 18 drugs in all combinations, on eight cancer cell lines. The results indicate that the extended model had an improved accuracy for drug synergy prediction for the majority of the experimentally tested cancer cell lines, although significant improvements of the model's predictive performance are still needed. Our study demonstrates how a tumor-data driven middle-out approach toward refining a logical model of a biological system can further customize a computer model to represent specific cancer cell lines and provide a basis for identifying synergistic effects of drugs targeting specific regulatory proteins. This approach bridges between preclinical cancer model data and clinical patient data and may thereby ultimately be of help to develop patient-specific in silico models that can steer treatment decisions in the clinic.

Next Generation Networks: Featuring the Potential Role of Emerging Applications in Translational Oncology

Nowadays, networks are pervasively used as examples of models suitable to mathematically represent and visualize the complexity of systems associated with many diseases, including cancer. In the cancer context, the concept of network entropy has guided many studies focused on comparing equilibrium to disequilibrium (i.e., perturbed) conditions. Since these conditions reflect both structural and dynamic properties of network interaction maps, the derived topological characterizations offer precious support to conduct cancer inference. Recent innovative directions have emerged in network medicine addressing especially experimental omics approaches integrated with a variety of other data, from molecular to clinical and also electronic records, bioimaging etc. This work considers a few theoretically relevant concepts likely to impact the future of applications in personalized/precision/translational oncology. The focus goes to specific properties of networks that are still not commonly utilized or studied in the oncological domain, and they are: controllability, synchronization and symmetry. The examples here provided take inspiration from the consideration of metastatic processes, especially their progression through stages and their hallmark characteristics. Casting these processes into computational frameworks and identifying network states with specific modular configurations may be extremely useful to interpret or even understand dysregulation patterns underlying cancer, and associated events (onset, progression) and disease phenotypes.

On the number of driver nodes for controlling a Boolean network when the targets are restricted to attractors

It is known that many driver nodes are required to control complex biological networks. Previous studies imply that O(N) driver nodes are required in both linear complex network and Boolean network models with N nodes if an arbitrary state is specified as the target. In order to cope with this intrinsic difficulty, we consider a special case of the control problem in which the targets are restricted to attractors. For this special case, we mathematically prove under the uniform distribution of states in basins that the expected number of driver nodes is only O(log₂N+log₂M) for controlling Boolean networks, where M is the number of attractors. Since it is expected that M is not very large in many practical networks, the new model requires a much smaller number of driver nodes. This result is based on discovery of novel relationships between control problems on Boolean networks and the coupon collector's problem, a well-known concept in combinatorics. We also provide lower bounds of the number of driver nodes as well as simulation results using artificial and realistic network data, which support our theoretical findings.

State feedback control design for Boolean networks

Background

Driving Boolean networks to desired states is of paramount significance toward our ultimate goal of controlling the progression of biological pathways and regulatory networks. Despite recent computational development of controllability of general complex networks and structural controllability of Boolean networks, there is still a lack of bridging the mathematical condition on controllability to real boolean operations in a network. Further, no realtime control strategy has been proposed to drive a Boolean network.

Results

In this study, we applied semi-tensor product to represent boolean functions in a network and explored controllability of a boolean network based on the transition matrix and time transition diagram. We determined the necessary and sufficient condition for a controllable Boolean network and mapped this requirement in transition matrix to real boolean functions and structure property of a network. An efficient tool is offered to assess controllability of an arbitrary Boolean network and to determine all reachable and non-reachable states. We found six simplest forms of controllable 2-node Boolean networks and explored the consistency of transition matrices while extending these six forms to controllable networks with more nodes. Importantly, we proposed the first state feedback control strategy to drive the network based on the status of all nodes in the network. Finally, we applied our reachability condition to the major switch of P53 pathway to predict the progression of the pathway and validate the prediction with published experimental results.

Conclusions

This control strategy allowed us to apply realtime control to drive Boolean networks, which could not be achieved by the current control strategy for Boolean networks. Our results enabled a more comprehensive understanding of the evolution of Boolean networks and might be extended to output feedback control design.

Control of complex networks requires both structure and dynamics

The study of network structure has uncovered signatures of the organization of complex systems. However, there is also a need to understand how to control them; for example, identifying strategies to revert a diseased cell to a healthy state, or a mature cell to a pluripotent state. Two recent methodologies suggest that the controllability of complex systems can be predicted solely from the graph of interactions between variables, without considering their dynamics: structural controllability and minimum dominating sets. We demonstrate that such structure-only methods fail to characterize controllability when dynamics are introduced. We study Boolean network ensembles of network motifs as well as three models of biochemical regulation: the segment polarity network in Drosophila melanogaster, the cell cycle of budding yeast Saccharomyces cerevisiae, and the floral organ arrangement in Arabidopsis thaliana. We demonstrate that structure-only methods both undershoot and overshoot the number and which sets of critical variables best control the dynamics of these models, highlighting the importance of the actual system dynamics in determining control. Our analysis further shows that the logic of automata transition functions, namely how canalizing they are, plays an important role in the extent to which structure predicts dynamics.

Not just a colourful metaphor: modelling the landscape of cellular development using Hopfield networks

The epigenetic landscape was introduced by Conrad Waddington as a metaphor of cellular development. Like a ball rolling down a hillside is channelled through a succession of valleys until it reaches the bottom, cells follow specific trajectories from a pluripotent state to a committed state. Transcription factors (TFs) interacting as a network (the gene regulatory network (GRN)) orchestrate this developmental process within each cell. Here, we quantitatively model the epigenetic landscape using a kind of artificial neural network called the Hopfield network (HN). An HN is composed of nodes (genes/TFs) and weighted undirected edges, resulting in a weight matrix (W) that stores interactions among the nodes over the entire network. We used gene co-expression to compute the edge weights. Through W, we then associate an energy score (E) to each input pattern (pattern of co-expression for a specific developmental stage) such that each pattern has a specific E. We propose that, based on the co-expression values stored in W, HN associates lower E values to stable phenotypic states and higher E to transient states. We validate our model using time course gene-expression data sets representing stages of development across 12 biological processes including differentiation of human embryonic stem cells into specialized cells, differentiation of THP1 monocytes to macrophages during immune response and trans-differentiation of epithelial to mesenchymal cells in cancer. We observe that transient states have higher energy than the stable phenotypic states, yielding an arc-shaped trajectory. This relationship was confirmed by perturbation analysis. HNs offer an attractive framework for quantitative modelling of cell differentiation (as a landscape) from empirical data. Using HNs, we identify genes and TFs that drive cell-fate transitions, and gain insight into the global dynamics of GRNs.

Modeling cancer metabolism on a genome scale

Cancer cells have fundamentally altered cellular metabolism that is associated with their tumorigenicity and malignancy. In addition to the widely studied Warburg effect, several new key metabolic alterations in cancer have been established over the last decade, leading to the recognition that altered tumor metabolism is one of the hallmarks of cancer. Deciphering the full scope and functional implications of the dysregulated metabolism in cancer requires both the advancement of a variety of omics measurements and the advancement of computational approaches for the analysis and contextualization of the accumulated data. Encouragingly, while the metabolic network is highly interconnected and complex, it is at the same time probably the best characterized cellular network. Following, this review discusses the challenges that genome-scale modeling of cancer metabolism has been facing. We survey several recent studies demonstrating the first strides that have been done, testifying to the value of this approach in portraying a network-level view of the cancer metabolism and in identifying novel drug targets and biomarkers. Finally, we outline a few new steps that may further advance this field.

Complex-based analysis of dysregulated cellular processes in cancer

Background

Differential expression analysis of (individual) genes is often used to study their roles in diseases. However, diseases such as cancer are a result of the combined effect of multiple genes. Gene products such as proteins seldom act in isolation, but instead constitute stable multi-protein complexes performing dedicated functions. Therefore, complexes aggregate the effect of individual genes (proteins) and can be used to gain a better understanding of cancer mechanisms. Here, we observe that complexes show considerable changes in their expression, in turn directed by the concerted action of transcription factors (TFs), across cancer conditions. We seek to gain novel insights into cancer mechanisms through a systematic analysis of complexes and their transcriptional regulation.

Results

We integrated large-scale protein-interaction (PPI) and gene-expression datasets to identify complexes that exhibit significant changes in their expression across different conditions in cancer. We devised a log-linear model to relate these changes to the differential regulation of complexes by TFs. The application of our model on two case studies involving pancreatic and familial breast tumour conditions revealed: (i) complexes in core cellular processes, especially those responsible for maintaining genome stability and cell proliferation (e.g. DNA damage repair and cell cycle) show considerable changes in expression; (ii) these changes include decrease and countering increase for different sets of complexes indicative of compensatory mechanisms coming into play in tumours; and (iii) TFs work in cooperative and counteractive ways to regulate these mechanisms. Such aberrant complexes and their regulating TFs play vital roles in the initiation and progression of cancer.

Conclusions

Complexes in core cellular processes display considerable decreases and countering increases in expression, strongly reflective of compensatory mechanisms in cancer. These changes are directed by the concerted action of cooperative and counteractive TFs. Our study highlights the roles of these complexes and TFs and presents several case studies of compensatory processes, thus providing novel insights into cancer mechanisms.