Discrete Logic Modelling Optimization to Contextualize Prior Knowledge Networks Using PRUNET

High-throughput technologies have led to the generation of an increasing amount of data in different areas of biology. Datasets capturing the cell’s response to its intra- and extra-cellular microenvironment allows such data to be incorporated as signed and directed graphs or influence networks. These prior knowledge networks (PKNs) represent our current knowledge of the causality of cellular signal transduction. New signalling data is often examined and interpreted in conjunction with PKNs. However, different biological contexts, such as cell type or disease states, may have distinct variants of signalling pathways, resulting in the misinterpretation of new data. The identification of inconsistencies between measured data and signalling topologies, as well as the training of PKNs using context specific datasets (PKN contextualization), are necessary conditions to construct reliable, predictive models, which are current challenges in the systems biology of cell signalling. Here we present PRUNET, a user-friendly software tool designed to address the contextualization of a PKNs to specific experimental conditions. As the input, the algorithm takes a PKN and the expression profile of two given stable steady states or cellular phenotypes. The PKN is iteratively pruned using an evolutionary algorithm to perform an optimization process. This optimization rests in a match between predicted attractors in a discrete logic model (Boolean) and a Booleanized representation of the phenotypes, within a population of alternative subnetworks that evolves iteratively. We validated the algorithm applying PRUNET to four biological examples and using the resulting contextualized networks to predict missing expression values and to simulate well-characterized perturbations. PRUNET constitutes a tool for the automatic curation of a PKN to make it suitable for describing biological processes under particular experimental conditions. The general applicability of the implemented algorithm makes PRUNET suitable for a variety of biological processes, for instance cellular reprogramming or transitions between healthy and disease states.     

Stemness in Hydra - a current perspective

Hydra is a classic and simple model for pattern formation and regeneration research. More recently, it has also been promoted as a model to study ancestral stem cell biology. Three independent cell lineages form the body of the polyp and exhibit characteristics of stem cell systems. In order to define differences in stemness between the ectodermal and endodermal epitheliomuscular cell lineages and the interstitial cell lineage, we compare cellular properties and decision making. We argue that these three lineages are expected to show substantial variation in their stemness-related gene regulatory networks. Finally, we discuss Wnt signalling pathways and Myc oncoproteins, which are beginning to offer a perspective on how proliferation and differentiation might be regulated.     

Deactivation of Src family kinases: hypothesis testing using a Monte Carlo sensitivity analysis of systems-level properties.

Src family tyrosine kinases play a key role in many cellular signalling networks, but due to the high complexity of these networks their precise function remains elusive. Many factors involved in Src regulation, such as specific kinases and phosphatases, are still unknown. Mathematical models have been constructed to improve the understanding of the system and its dynamic behavior. Using a computational random parameter search, we characterized and compared the dynamics of three alternative models in order to assess their likelihoods. For this, we investigated how systems-level properties such as bistability and excitable behavior relate to kinetic and physiological parameters and how robust these properties were. Our results suggest the existence of a putative negative feedback loop in the Src system. A previously suggested role for PTPalpha in the deactivation of Src was not supported by the model.     

Cellulat: an agent-based intracellular signalling model

The theory of behaviour-based systems (or autonomous agents) constitutes a useful approach for the modelling of intracellular signalling networks. In this sense, a cell can be seen as an adaptive autonomous agent or as a society of such agents, where each can exhibit a particular behaviour depending on its cognitive capabilities. We present an intracellular signalling model obtained by integrating several computational techniques into an agent-based paradigm. Cellulat, the model, takes into account two essential aspects of the intracellular signalling networks: (1) cognitive capacities, which are modelled as the agent abilities to interact with the surrounding medium and (2) a spatial organisation, this last obtained using a shared data structure through which the agents communicate between them. We propose a methodology for the modelling of intracellular signalling pathway using Cellulat and we discuss the goal of a virtual laboratory based on our model and presently under development.     

A structured approach for the engineering of biochemical network models, illustrated for signalling pathways

Quantitative models of biochemical networks (signal transduction cascades, metabolic pathways, gene regulatory circuits) are a central component of modern systems biology. Building and managing these complex models is a major challenge that can benefit from the application of formal methods adopted from theoretical computing science. Here we provide a general introduction to the field of formal modelling, which emphasizes the intuitive biochemical basis of the modelling process, but is also accessible for an audience with a background in computing science and/or model engineering. We show how signal transduction cascades can be modelled in a modular fashion, using both a qualitative approach--qualitative Petri nets, and quantitative approaches--continuous Petri nets and ordinary differential equations (ODEs). We review the major elementary building blocks of a cellular signalling model, discuss which critical design decisions have to be made during model building, and present a number of novel computational tools that can help to explore alternative modular models in an easy and intuitive manner. These tools, which are based on Petri net theory, offer convenient ways of composing hierarchical ODE models, and permit a qualitative analysis of their behaviour. We illustrate the central concepts using signal transduction as our main example. The ultimate aim is to introduce a general approach that provides the foundations for a structured formal engineering of large-scale models of biochemical networks.     

Early embryonic vascular patterning by matrix-mediated paracrine signalling: a mathematical model study

During embryonic vasculogenesis, endothelial precursor cells of mesodermal origin known as angioblasts assemble into a characteristic network pattern. Although a considerable amount of markers and signals involved in this process have been identified, the mechanisms underlying the coalescence of angioblasts into this reticular pattern remain unclear. Various recent studies hypothesize that autocrine regulation of the chemoattractant vascular endothelial growth factor (VEGF) is responsible for the formation of vascular networks in vitro. However, the autocrine regulation hypothesis does not fit well with reported data on in vivo early vascular development. In this study, we propose a mathematical model based on the alternative assumption that endodermal VEGF signalling activity, having a paracrine effect on adjacent angioblasts, is mediated by its binding to the extracellular matrix (ECM). Detailed morphometric analysis of simulated networks and images obtained from in vivo quail embryos reveals the model mimics the vascular patterns with high accuracy. These results show that paracrine signalling can result in the formation of fine-grained cellular networks when mediated by angioblast-produced ECM. This lends additional support to the theory that patterning during early vascular development in the vertebrate embryo is regulated by paracrine signalling.     

Integration of Boolean models exemplified on hepatocyte signal transduction

The number of mathematical models for biological pathways is rapidly growing. In particular, Boolean modelling proved to be suited to describe large cellular signalling networks. Systems biology is at the threshold to holistic understanding of comprehensive networks. In order to reach this goal, connection and integration of existing models of parts of cellular networks into more comprehensive network models is necessary. We discuss model combination approaches for Boolean models. Boolean modelling is qualitative rather than quantitative and does not require detailed kinetic information. We show that these models are useful precursors for large-scale quantitative models and that they are comparatively easy to combine. We propose modelling standards for Boolean models as a prerequisite for smooth model integration. Using these standards, we demonstrate the coupling of two logical models on two different examples concerning cellular interactions in the liver. In the first example, we show the integration of two Boolean models of two cell types in order to describe their interaction. In the second example, we demonstrate the combination of two models describing different parts of the network of a single cell type. Combination of partial models into comprehensive network models will take systems biology to the next level of understanding. The combination of logical models facilitated by modelling standards is a valuable example for the next step towards this goal.     

Inferring Cell-Scale Signalling Networks via Compressive Sensing

Signalling network inference is a central problem in system biology. Previous studies investigate this problem by independently inferring local signalling networks and then linking them together via crosstalk. Since a cellular signalling system is in fact indivisible, this reductionistic approach may have an impact on the accuracy of the inference results. Preferably, a cell-scale signalling network should be inferred as a whole. However, the holistic approach suffers from three practical issues: scalability, measurement and overfitting. Here we make this approach feasible based on two key observations: 1) variations of concentrations are sparse due to separations of timescales; 2) several species can be measured together using cross-reactivity. We propose a method, CCELL, for cell-scale signalling network inference from time series generated by immunoprecipitation using Bayesian compressive sensing. A set of benchmark networks with varying numbers of time-variant species is used to demonstrate the effectiveness of our method. Instead of exhaustively measuring all individual species, high accuracy is achieved from relatively few measurements.     

An investigation of spatial signal transduction in cellular networks

ABSTRACT: BACKGROUND: Spatial signal transduction plays a vital role in many intracellular processes such as eukaryotic chemotaxis, polarity generation, cell division. Furthermore it is being increasingly realized that the spatial dimension to signalling may play an important role in other apparently purely temporal signal transduction processes. It is being recognized that a conceptual basis for studying spatial signal transduction in signalling networks is necessary. RESULTS: In this work we examine spatial signal transduction in a series of standard motifs/networks. These networks include coherent and incoherent feedforward, positive and negative feedback, cyclic motifs, monostable switches, bistable switches and negative feedback oscillators. In all these cases, the driving signal has spatial variation. For each network we consider two cases, one where all elements are essentially non diffusible, and the other where one of the network elements may be highly diffusible. A careful analysis of steady state signal transduction provides many insights into the behaviour of all these modules. While in the non-diffusible case for the most part, spatial signalling reflects the temporal signalling behaviour, in the diffusible cases, we see significant differences between spatial and temporal signalling characteristics. Our results demonstrate that the presence of diffusible elements in the networks provides important constraints and capabilities for signalling. CONCLUSIONS: Our results provide a systematic basis for understanding spatial signalling in networks and the role of diffusible elements therein. This provides many insights into the signal transduction capabilities and constraints in such networks and suggests ways in which cellular signalling and information processing is organized to conform to or bypass those constraints. It also provides a framework for starting to understand the organization and regulation of spatial signal transduction in individual processes.     

Alternative complex formation of the Ca-regulated protein kinase CIPK1 controls abscisic acid-dependent and independent stress responses in Arabidopsis

Intracellular release of calcium ions belongs to the earliest events in cellular stress perception. The molecular mechanisms integrating signals from different environmental cues and translating them into an optimized response are largely unknown. We report here the functional characterization of CIPK1, a protein kinase interacting strongly with the calcium sensors CBL1 and CBL9. Comparison of the expression patterns indicates that the three proteins execute their functions in the same tissues. Physical interaction of CIPK1 with CBL1 and CBL9 targets the kinase to the plasma membrane. We show that, similarly to loss of CBL9 function, mutation of either CBL1 or CIPK1 renders plants hypersensitive to osmotic stress. Remarkably, in contrast to the cbl1 mutant and similarly to the cbl9 mutant, loss of CIPK1 function impairs abscisic acid (ABA) responsiveness. We therefore suggest that, by alternative complex formation with either CBL1 or CBL9, the kinase CIPK1 represents a convergence point for ABA-dependent and ABA-independent stress responses. Based on our genetic, physiological and protein-protein interaction data, we propose a general model for information processing in calcium-regulated signalling networks.     

Evolvability and robustness in a complex signalling circuit

Biological systems at various levels of organisation exhibit robustness, as well as phenotypic variability or evolvability, the ability to evolve novel phenotypes. We still know very little about the relationship between robustness and phenotypic variability at levels of organisation beyond individual macromolecules, and especially for signalling circuits. Here, we examine multiple alternate topologies of the Saccharomyces cerevisiae target-of-rapamycin (TOR) signalling circuit, in order to understand the circuit's robustness and phenotypic variability. We consider each of the topological variants a genotype, a set of alternative interactions between TOR circuit components. Two genotypes are neighbours in genotype space if they can be reached from each other by a single small genetic change. Each genotype (topology) has a signalling phenotype, which we define via the concentration trajectories of key signalling molecules. We find that the circuits we study can produce almost 300 different phenotypes. The number of genotypes with a given phenotype varies very widely among these phenotypes. Some phenotypes have few associated genotypes. Others have many genotypes that form genotype networks extending far through genotype space. A minority of phenotypes accounts for the vast majority of genotypes. Importantly, we find that these phenotypes tend to have large genotype networks, greater robustness and a greater ability to produce novel phenotypes. Thus, over a broad range of phenotypic robustness, robustness facilitates phenotypic variability in our study system. Our observations show parallels to studies on macromolecules, suggesting that similar principles might govern robustness and phenotypic variability in biological systems. Our approach points a way towards mapping genotype spaces in complex circuitry, and it exposes some challenges such mapping faces.     

Cross-talk between Rho and Rac GTPases drives deterministic exploration of cellular shape space and morphological heterogeneity

One goal of cell biology is to understand how cells adopt different shapes in response to varying environmental and cellular conditions. Achieving a comprehensive understanding of the relationship between cell shape and environment requires a systems-level understanding of the signalling networks that respond to external cues and regulate the cytoskeleton. Classical biochemical and genetic approaches have identified thousands of individual components that contribute to cell shape, but it remains difficult to predict how cell shape is generated by the activity of these components using bottom-up approaches because of the complex nature of their interactions in space and time. Here, we describe the regulation of cellular shape by signalling systems using a top-down approach. We first exploit the shape diversity generated by systematic RNAi screening and comprehensively define the shape space a migratory cell explores. We suggest a simple Boolean model involving the activation of Rac and Rho GTPases in two compartments to explain the basis for all cell shapes in the dataset. Critically, we also generate a probabilistic graphical model to show how cells explore this space in a deterministic, rather than a stochastic, fashion. We validate the predictions made by our model using live-cell imaging. Our work explains how cross-talk between Rho and Rac can generate different cell shapes, and thus morphological heterogeneity, in genetically identical populations.     

Towards mechanistic models of plant organ growth

Modelling and simulation are increasingly used as tools in the study of plant growth and developmental processes. By formulating experimentally obtained knowledge as a system of interacting mathematical equations, it becomes feasible for biologists to gain a mechanistic understanding of the complex behaviour of biological systems. In this review, the modelling tools that are currently available and the progress that has been made to model plant development, based on experimental knowledge, are described. In terms of implementation, it is argued that, for the modelling of plant organ growth, the cellular level should form the cornerstone. It integrates the output of molecular regulatory networks to two processes, cell division and cell expansion, that drive growth and development of the organ. In turn, these cellular processes are controlled at the molecular level by hormone signalling. Therefore, combining a cellular modelling framework with regulatory modules for the regulation of cell division, expansion, and hormone signalling could form the basis of a functional organ growth simulation model. The current state of progress towards this aim is that the regulation of the cell cycle and hormone transport have been modelled extensively and these modules could be integrated. However, much less progress has been made on the modelling of cell expansion, which urgently needs to be addressed. A limitation of the current generation models is that they are largely qualitative. The possibilities to characterize existing and future models more quantitatively will be discussed. Together with experimental methods to measure crucial model parameters, these modelling techniques provide a basis to develop a Systems Biology approach to gain a fundamental insight into the relationship between gene function and whole organ behaviour.     

Cell–cell interaction networks regulate blood stem and progenitor cell fate

Communication networks between cells and tissues are necessary for homeostasis in multicellular organisms. Intercellular (between cell) communication networks are particularly relevant in stem cell biology, as stem cell fate decisions (self‐renewal, proliferation, lineage specification) are tightly regulated based on physiological demand. We have developed a novel mathematical model of blood stem cell development incorporating cell‐level kinetic parameters as functions of secreted molecule‐mediated intercellular networks. By relation to quantitative cellular assays, our model is capable of predictively simulating many disparate features of both normal and malignant hematopoiesis, relating internal parameters and microenvironmental variables to measurable cell fate outcomes. Through integrated in silico and experimental analyses, we show that blood stem and progenitor cell fate is regulated by cell–cell feedback, and can be controlled non‐cell autonomously by dynamically perturbing intercellular signalling. We extend this concept by demonstrating that variability in the secretion rates of the intercellular regulators is sufficient to explain heterogeneity in culture outputs, and that loss of responsiveness to cell–cell feedback signalling is both necessary and sufficient to induce leukemic transformation in silico.