No Arabic abstract
Cancer forms a robust system and progresses as stages over time typically with increasing aggressiveness and worsening prognosis. Characterizing these stages and identifying the genes driving transitions between them is critical to understand cancer progression and to develop effective anti-cancer therapies. Here, we propose a novel model of the cancer system as a Boolean state space in which a Boolean network, built from protein interaction and gene-expression data from different stages of cancer, transits between Boolean satisfiability states by editing interactions and flipping genes. The application of our model (called BoolSpace) on three case studies - pancreatic and breast tumours in human and post spinal-cord injury in rats - reveals valuable insights into the phenomenon of cancer progression. In particular, we notice that several of the genes flipped are serine/threonine kinases which act as natural cellular switches and that different sets of genes are flipped during the initial and final stages indicating a pattern to tumour progression. We hypothesize that robustness of cancer partly stems from passing of the baton between genes at different stages, and therefore an effective therapy should target a cover set of these genes. A C/C++ implementation of BoolSpace is freely available at: http://www.bioinformatics.org.au/tools-data
In spite of the recent interest and advances in linear controllability of complex networks, controlling nonlinear network dynamics remains to be an outstanding problem. We develop an experimentally feasible control framework for nonlinear dynamical networks that exhibit multistability (multiple coexisting final states or attractors), which are representative of, e.g., gene regulatory networks (GRNs). The control objective is to apply parameter perturbation to drive the system from one attractor to another, assuming that the former is undesired and the latter is desired. To make our framework practically useful, we consider RESTRICTED parameter perturbation by imposing the following two constraints: (a) it must be experimentally realizable and (b) it is applied only temporarily. We introduce the concept of ATTRACTOR NETWORK, in which the nodes are the distinct attractors of the system, and there is a directional link from one attractor to another if the system can be driven from the former to the latter using restricted control perturbation. Introduction of the attractor network allows us to formulate a controllability framework for nonlinear dynamical networks: a network is more controllable if the underlying attractor network is more strongly connected, which can be quantified. We demonstrate our control framework using examples from various models of experimental GRNs. A finding is that, due to nonlinearity, noise can counter-intuitively facilitate control of the network dynamics.
We study the stable attractors of a class of continuous dynamical systems that may be idealized as networks of Boolean elements, with the goal of determining which Boolean attractors, if any, are good approximations of the attractors of generic continuous systems. We investigate the dynamics in simple rings and rings with one additional self-input. An analysis of switching characteristics and pulse propagation explains the relation between attractors of the continuous systems and their Boolean approximations. For simple rings, reliable Boolean attractors correspond to stable continuous attractors. For networks with more complex logic, the qualitative features of continuous attractors are influenced by inherently non-Boolean characteristics of switching events.
Boolean networks are discrete dynamical systems for modeling regulation and signaling in living cells. We investigate a particular class of Boolean functions with inhibiting inputs exerting a veto (forced zero) on the output. We give analytical expressions for the sensitivity of these functions and provide evidence for their role in natural systems. In an intracellular signal transduction network [Helikar et al., PNAS (2008)], the functions with veto are over-represented by a factor exceeding the over-representation of threshold functions and canalyzing functions in the same system. In Boolean networks for control of the yeast cell cycle [Fangting Li et al., PNAS (2004), Davidich et al., PLoS One (2009)], none or minimal changes to the wiring diagrams are necessary to formulate their dynamics in terms of the veto functions introduced here.
Environmental and genetic mutations can transform the cells in a co-operating healthy tissue into an ecosystem of individualistic tumour cells that compete for space and resources. Various selection forces are responsible for driving the evolution of cells in a tumour towards more malignant and aggressive phenotypes that tend to have a fitness advantage over the older populations. Although the evolutionary nature of cancer has been recognised for more than three decades (ever since the seminal work of Nowell) it has been only recently that tools traditionally used by ecological and evolutionary researchers have been adopted to study the evolution of cancer phenotypes in populations of individuals capable of co-operation and competition. In this chapter we will describe game theory as an important tool to study the emergence of cell phenotypes in a tumour and will critically review some of its applications in cancer research. These applications demonstrate that game theory can be used to understand the dynamics of somatic cancer evolution and suggest new therapies in which this knowledge could be applied to gain some control over the evolution of the tumour.
One of the most challenging problems in biomedicine and genomics is the identification of disease biomarkers. In this study, proteomics data from seven major cancers were used to construct two weighted protein-protein interaction (PPI) networks i.e., one for the normal and another for the cancer conditions. We developed rigorous, yet mathematically simple, methodology based on the degeneracy at -1 eigenvalues to identify structural symmetry or motif structures in network. Utilising eigenvectors corresponding to degenerate eigenvalues in the weighted adjacency matrix, we identified structural symmetry in underlying weighted PPI networks constructed using seven cancer data. Functional assessment of proteins forming these structural symmetry exhibited the property of cancer hallmarks. Survival analysis refined further this protein list proposing BMI, MAPK11, DDIT4, CDKN2A, and FYN as putative multi-cancer biomarkers. The combined framework of networks and spectral graph theory developed here can be applied to identify symmetrical patterns in other disease networks to predict proteins as potential disease biomarkers.