Modelling and analysis of structure in cellular signalling systems

Cellular signalling is an important area of study in biology. Signalling pathways are well-known abstractions that explain the mechanisms whereby cells respond to signals. Collections of pathways form signalling networks, and interactions between pathways in a network, known as cross-talk, enables further complex signalling behaviours. Increasingly, computational modelling and analysis is required to handle the complexity of such systems. While there are several computational modelling approaches for signalling pathways, none make cross-talk explicit. We present a modular modelling framework for pathways and their cross-talk. Networks are formed by composing pathways: different cross-talks result from different synchronisations of reactions between, and overlaps of, the pathways. We formalise five types of cross-talk and give approaches to reason about possible cross-talks in a network. The complementary problem is how to handle unstructured signalling networks, i.e. networks with no explicit notion of pathways or cross-talk. We present an approach to better understand unstructured signalling networks by modelling them as a set of signal flows through the network. We introduce the Reaction Minimal Paths (RMP) algorithm that computes the set of signal flows in a model. To the best of our knowledge, current algorithms cannot guarantee both correctness and completeness of the set of signal flows in a model. The RMP algorithm is the first. Finally, the RMP algorithm suffers from the well-known state space explosion problem. We use suitable partial order reduction algorithms to improve the efficiency of this algorithm

Engineering simulations for cancer systems biology

Computer simulation can be used to inform in vivo and in vitro experimentation, enabling rapid, low-cost hypothesis generation and directing experimental design in order to test those hypotheses. In this way, in silico models become a scientific instrument for investigation, and so should be developed to high standards, be carefully calibrated and their findings presented in such that they may be reproduced. Here, we outline a framework that supports developing simulations as scientific instruments, and we select cancer systems biology as an exemplar domain, with a particular focus on cellular signalling models. We consider the challenges of lack of data, incomplete knowledge and modelling in the context of a rapidly changing knowledge base. Our framework comprises a process to clearly separate scientific and engineering concerns in model and simulation development, and an argumentation approach to documenting models for rigorous way of recording assumptions and knowledge gaps. We propose interactive, dynamic visualisation tools to enable the biological community to interact with cellular signalling models directly for experimental design. There is a mismatch in scale between these cellular models and tissue structures that are affected by tumours, and bridging this gap requires substantial computational resource. We present concurrent programming as a technology to link scales without losing important details through model simplification. We discuss the value of combining this technology, interactive visualisation, argumentation and model separation to support development of multi-scale models that represent biologically plausible cells arranged in biologically plausible structures that model cell behaviour, interactions and response to therapeutic interventions

Partial differential equations for self-organization in cellular and developmental biology

Understanding the mechanisms governing and regulating the emergence of structure and heterogeneity within cellular systems, such as the developing embryo, represents a multiscale challenge typifying current integrative biology research, namely, explaining the macroscale behaviour of a system from microscale dynamics. This review will focus upon modelling how cell-based dynamics orchestrate the emergence of higher level structure. After surveying representative biological examples and the models used to describe them, we will assess how developments at the scale of molecular biology have impacted on current theoretical frameworks, and the new modelling opportunities that are emerging as a result. We shall restrict our survey of mathematical approaches to partial differential equations and the tools required for their analysis. We will discuss the gap between the modelling abstraction and biological reality, the challenges this presents and highlight some open problems in the field

Data-driven modelling of biological multi-scale processes

Biological processes involve a variety of spatial and temporal scales. A holistic understanding of many biological processes therefore requires multi-scale models which capture the relevant properties on all these scales. In this manuscript we review mathematical modelling approaches used to describe the individual spatial scales and how they are integrated into holistic models. We discuss the relation between spatial and temporal scales and the implication of that on multi-scale modelling. Based upon this overview over state-of-the-art modelling approaches, we formulate key challenges in mathematical and computational modelling of biological multi-scale and multi-physics processes. In particular, we considered the availability of analysis tools for multi-scale models and model-based multi-scale data integration. We provide a compact review of methods for model-based data integration and model-based hypothesis testing. Furthermore, novel approaches and recent trends are discussed, including computation time reduction using reduced order and surrogate models, which contribute to the solution of inference problems. We conclude the manuscript by providing a few ideas for the development of tailored multi-scale inference methods.Comment: This manuscript will appear in the Journal of Coupled Systems and Multiscale Dynamics (American Scientific Publishers

The impact of cellular characteristics on the evolution of shape homeostasis

The importance of individual cells in a developing multicellular organism is well known but precisely how the individual cellular characteristics of those cells collectively drive the emergence of robust, homeostatic structures is less well understood. For example cell communication via a diffusible factor allows for information to travel across large distances within the population, and cell polarisation makes it possible to form structures with a particular orientation, but how do these processes interact to produce a more robust and regulated structure? In this study we investigate the ability of cells with different cellular characteristics to grow and maintain homeostatic structures. We do this in the context of an individual-based model where cell behaviour is driven by an intra-cellular network that determines the cell phenotype. More precisely, we investigated evolution with 96 different permutations of our model, where cell motility, cell death, long-range growth factor (LGF), short-range growth factor (SGF) and cell polarisation were either present or absent. The results show that LGF has the largest positive impact on the fitness of the evolved solutions. SGF and polarisation also contribute, but all other capabilities essentially increase the search space, effectively making it more difficult to achieve a solution. By perturbing the evolved solutions, we found that they are highly robust to both mutations and wounding. In addition, we observed that by evolving solutions in more unstable environments they produce structures that were more robust and adaptive. In conclusion, our results suggest that robust collective behaviour is most likely to evolve when cells are endowed with long range communication, cell polarisation, and selection pressure from an unstable environment

Colorectal Cancer Through Simulation and Experiment

Colorectal cancer has continued to generate a huge amount of research interest over several decades, forming a canonical example of tumourigenesis since its use in Fearon and Vogelstein’s linear model of genetic mutation. Over time, the field has witnessed a transition from solely experimental work to the inclusion of mathematical biology and computer-based modelling. The fusion of these disciplines has the potential to provide valuable insights into oncologic processes, but also presents the challenge of uniting many diverse perspectives. Furthermore, the cancer cell phenotype defined by the ‘Hallmarks of Cancer’ has been extended in recent times and provides an excellent basis for future research. We present a timely summary of the literature relating to colorectal cancer, addressing the traditional experimental findings, summarising the key mathematical and computational approaches, and emphasising the role of the Hallmarks in current and future developments. We conclude with a discussion of interdisciplinary work, outlining areas of experimental interest which would benefit from the insight that mathematical and computational modelling can provide

Modelling and analysis of biochemical signalling pathway cross-talk

Signalling pathways are abstractions that help life scientists structure the coordination of cellular activity. Cross-talk between pathways accounts for many of the complex behaviours exhibited by signalling pathways and is often critical in producing the correct signal-response relationship. Formal models of signalling pathways and cross-talk in particular can aid understanding and drive experimentation. We define an approach to modelling based on the concept that a pathway is the (synchronising) parallel composition of instances of generic modules (with internal and external labels). Pathways are then composed by (synchronising) parallel composition and renaming; different types of cross-talk result from different combinations of synchronisation and renaming. We define a number of generic modules in PRISM and five types of cross-talk: signal flow, substrate availability, receptor function, gene expression and intracellular communication. We show that Continuous Stochastic Logic properties can both detect and distinguish the types of cross-talk. The approach is illustrated with small examples and an analysis of the cross-talk between the TGF-b/BMP, WNT and MAPK pathways

ATM in focus:a damage sensor and cancer target

The ability of a cell to conserve and maintain its native DNA sequence is fundamental for the survival and normal functioning of the whole organism and protection from cancer development. Here we review recently obtained results and current topics concerning the role of the ataxia-telangiectasia mutated (ATM) protein kinase as a damage sensor and its potential as therapeutic target for treating cancer. This monograph discusses DNA repair mechanisms activated after DNA double-strand breaks (DSBs), i.e. non-homologous end joining, homologous recombination and single strand annealing and the role of ATM in the above types of repair. In addition to DNA repair, ATM participates in a diverse set of physiological processes involving metabolic regulation, oxidative stress, transcriptional modulation, protein degradation and cell proliferation. Full understanding of the complexity of ATM functions and the design of therapeutics that modulate its activity to combat diseases such as cancer necessitates parallel theoretical and experimental efforts. This could be best addressed by employing a systems biology approach, involving mathematical modelling of cell signalling pathways

Reverse engineering of drug induced DNA damage response signalling pathway reveals dual outcomes of ATM kinase inhibition

The DNA Damage Response (DDR) pathway represents a signalling mechanism that is activated in eukaryotic cells following DNA damage and comprises of proteins involved in DNA damage detection, DNA repair, cell cycle arrest and apoptosis. This pathway consists of an intricate network of signalling interactions driving the cellular ability to recognise DNA damage and recruit specialised proteins to take decisions between DNA repair or apoptosis. ATM and ATR are central components of the DDR pathway. The activities of these kinases are vital in DNA damage induced phosphorylational induction of DDR substrates. Here, firstly we have experimentally determined DDR signalling network surrounding the ATM/ATR pathway induced following double stranded DNA damage by monitoring and quantifying time dependent inductions of their phosphorylated forms and their key substrates. We next involved an automated inference of unsupervised predictive models of time series data to generate in silico (molecular) interaction maps. We characterized the complex signalling network through system analysis and gradual utilisation of small time series measurements of key substrates through a novel network inference algorithm. Furthermore, we demonstrate an application of an assumption-free reverse engineering of the intricate signalling network of the activated ATM/ATR pathway. We next studied the consequences of such drug induced inductions as well as of time dependent ATM kinase inhibition on cell survival through further biological experiments. Intermediate and temporal modelling outcomes revealed the distinct signaling profile associated with ATM kinase activity and inhibition and explained the underlying signalling mechanism for dual ATM functionality in cytotoxic and cytoprotective pathways

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

http://dx.doi.org/10.1093/bib/bbn026Quantitative 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. 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 ..