Towards an exact reconstruction of a time-invariant model from time series data

Dynamic processes in biological systems may be profiled by measuring system properties over time. One way of representing such time series data is through weighted interaction networks, where the nodes in the network represent the measurables and the weighted edges represent interactions between any pair of nodes. Construction of these network models from time series data may involve seeking a robust data-consistent and time-invariant model to approximate and describe system dynamics. Many problems in mathematics, systems biology and physics can be recast into this form and may require finding the most consistent solution to a set of first order differential equations. This is especially challenging in cases where the number of data points is less than or equal to the number of measurables. We present a novel computational method for network reconstruction with limited time series data. To test our method, we use artificial time series data generated from known network models. We then attempt to reconstruct the original network from the time series data alone. We find good agreement between the original and predicted networks

A new paradigm for SpeckNets:inspiration from fungal colonies

In this position paper, we propose the development of a new biologically inspired paradigm based on fungal colonies, for the application to pervasive adaptive systems. Fungal colonies have a number of properties that make them an excellent candidate for inspiration for engineered systems. Here we propose the application of such inspiration to a speckled computing platform. We argue that properties from fungal colonies map well to properties and requirements for controlling SpeckNets and suggest that an existing mathematical model of a fungal colony can developed into a new computational paradigm

Changing the view:towards the theory of visualisation comprehension

The core problem of the evaluation of information visualisation is that the end product of visualisation - the comprehension of the information from the data - is difficult to measure objectively. This paper outlines a description of visualisation comprehension based on two existing theories of perception: principles of perceptual organisation and the reverse hierarchy theory. The resulting account of the processes involved in visualisation comprehension enables evaluation that is not only objective, but also non-comparative, providing an absolute efficiency classification. Finally, as a sample application of this approach, an experiment studying the benefits of interactivity in 3D scatterplots is presented

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

Customizing the therapeutic response of signaling networks to promote antitumor responses by drug combinations

Drug resistance, de novo and acquired, pervades cellular signaling networks (SNs) from one signaling motif to another as a result of cancer progression and/or drug intervention. This resistance is one of the key determinants of efficacy in targeted anti-cancer drug therapy. Although poorly understood, drug resistance is already being addressed in combination therapy by selecting drug targets where SN sensitivity increases due to combination components or as a result of de novo or acquired mutations. Additionally, successive drug combinations have shown low resistance potential. To promote a rational, systematic development of combination therapies, it is necessary to establish the underlying mechanisms that drive the advantages of combination therapies, and design methods to determine drug targets for combination regimens. Based on a joint systems analysis of cellular SN response and its sensitivity to drug action and oncogenic mutations, we describe an in silico method to analyze the targets of drug combinations. Our method explores mechanisms of sensitizing the SN through a combination of two drugs targeting vertical signaling pathways. We propose a paradigm of SN response customization by one drug to both maximize the effect of another drug in combination and promote a robust therapeutic response against oncogenic mutations. The method was applied to customize the response of the ErbB/PI3K/PTEN/AKT pathway by combination of drugs targeting HER2 receptors and proteins in the down-stream pathway. The results of a computational experiment showed that the modification of the SN response from hyperbolic to smooth sigmoid response by manipulation of two drugs in combination leads to greater robustness in therapeutic response against oncogenic mutations determining cancer heterogeneity. The application of this method in drug combination co-development suggests a combined evaluation of inhibition effects together with the capability of drug combinations to suppress resistance mechanisms before they become clinically manifest

Kinetic modelling of in vitro data of PI3K, mTOR1, PTEN enzymes and on-target inhibitors Rapamycin, BEZ235, and LY294002

The phosphatidylinositide 3-kinases (PI3K) and mammalian target of rapamycin-1 (mTOR1) are two key targets for anti-cancer therapy. Predicting the response of the PI3K/AKT/mTOR1 signalling pathway to targeted therapy is made difficult because of network complexities. Systems biology models can help explore those complexities but the value of such models is dependent on accurate parameterisation. Motivated by a need to increase accuracy in kinetic parameter estimation, and therefore the predictive power of the model, we present a framework to integrate kinetic data from enzyme assays into a unified enzyme kinetic model. We present exemplar kinetic models of PI3K and mTOR1, calibrated on in vitro enzyme data and founded on Michaelis-Menten (MM) approximation. We describe the effects of an allosteric mTOR1 inhibitor (Rapamycin) and ATP-competitive inhibitors (BEZ2235 and LY294002) that show dual inhibition of mTOR1 and PI3K. We also model the kinetics of phosphatase and tensin homolog (PTEN), which modulates sensitivity of the PI3K/AKT/mTOR1 pathway to these drugs. Model validation with independent data sets allows investigation of enzyme function and drug dose dependencies in a wide range of experimental conditions. Modelling of the mTOR1 kinetics showed that Rapamycin has an IC50 independent of ATP concentration and that it is a selective inhibitor of mTOR1 substrates S6K1 and 4EBP1: it retains 40% of mTOR1 activity relative to 4EBP1 phosphorylation and inhibits completely S6K1 activity. For the dual ATP-competitive inhibitors of mTOR1 and PI3K, LY294002 and BEZ235, we derived the dependence of the IC50 on ATP concentration that allows prediction of the IC50 at different ATP concentrations in enzyme and cellular assays. Comparison of the drug effectiveness in enzyme and cellular assays showed that some features of these drugs arise from signalling modulation beyond the on-target action and MM approximation and require a systems-level consideration of the whole PI3K/PTEN/AKT/mTOR1 network in order to understand mechanisms of drug sensitivity and resistance in different cancer cell lines. We suggest that using these models in systems biology investigation of the PI3K/AKT/mTOR1 signalling in cancer cells can bridge the gap between direct drug target action and the therapeutic response to these drugs and their combinations

Matrix operations for the simulation and immediate reverse-engineering of time series data

We present a new method for constructing and decomposing square matrices. This method, based on the computed parameterisation of their implied determinants and minors, operates on the product of factors of a new form of matrix decomposition. This method may be employed to build new matrices with fixed determinant(s). We demonstrate that this new approach is fundamentally well-connected to the Cholesky decomposition if applied on symmetric matrices. We also demonstrate that it is related to the LU decomposition method via a diagonal matrix multiplier. Also through this new method a direct relation between Cholesky decomposition and LU factorisation is shown. This method, presented for the first time, is useful for (re)constructing matrices with a predefined determinant and simulating inverse problems. The inference method introduced here also is based on new matrix manipulation techniques that we have developed for the identification of systems from reproducible time series data

Understanding tissue morphology: model repurposing using the CoSMoS process

We present CoSMoS as a way of structuring thinking on how to reuse parts of an existing model and simulation in a new model and its implementation. CoSMoS provides a lens through which to consider, post-implementation, the assumptions made during the design and implementation of a software simulation of physical interactions in the formation of vascular structures from endothelial cells. We show how the abstract physical model and its software implementation can be adapted for a different problem: the growth of cancer cells under varying environmental perturbations. We identify the changes that must be made to adapt the model to its new context, along with the gaps in our knowledge of the domain that must be filled by wet-lab experimentation when recalibrating the model. Through parameter exploration, we identify the parameters that are critical to the dynamic physical structure of the modelled tissue, and we calibrate these parameters using a series of in vitro experiments. Drawing inspiration from the CoSMoS project structure, we maintain confidence in the repurposed model, and achieve a satisfactory degree of model reuse within our in silico experimental system

Quantitative analysis of NRF2 pathway reveals key elements of the regulatory circuits underlying antioxidant response and proliferation of ovarian cancer cells

Cells are constantly exposed to Reactive Oxygen Species (ROS) produced both endogenously to meet physiological requirements and from exogenous sources. While endogenous ROS are considered as important signalling molecules, high uncontrollable ROS are detrimental. It is unclear how cells can achieve a balance between maintaining physiological redox homeostasis and robustly activate the antioxidant system to remove exogenous ROS. We have utilised a Systems Biology approach to understand how this robust adaptive system fulfils homeostatic requirements of maintaining steady-state ROS and growth rate, while undergoing rapid readjustment under challenged conditions. Using a panel of human ovarian and normal cell lines, we experimentally quantified and established interrelationships between key elements of ROS homeostasis. The basal levels of NRF2 and KEAP1 were cell line specific and maintained in tight correlation with their growth rates and ROS. Furthermore, perturbation of this balance triggered cell specific kinetics of NRF2 nuclear–cytoplasmic relocalisation and sequestration of exogenous ROS. Our experimental data were employed to parameterise a mathematical model of the NRF2 pathway that elucidated key response mechanisms of redox regulation and showed that the dynamics of NRF2-H2O2 regulation defines a relationship between half-life, total and nuclear NRF2 level and endogenous H2O2 that is cell line specific

A signaling visualization toolkit to support rational design of combination therapies and biomarker discovery: SiViT

Targeted cancer therapy aims to disrupt aberrant cellular signalling pathways. Biomarkers are surrogates of pathway state, but there is limited success in translating candidate biomarkers to clinical practice due to the intrinsic complexity of pathway networks. Systems biology approaches afford better understanding of complex, dynamical interactions in signalling pathways targeted by anticancer drugs. However, adoption of dynamical modelling by clinicians and biologists is impeded by model inaccessibility. Drawing on computer games technology, we present a novel visualisation toolkit, SiViT, that converts systems biology models of cancer cell signalling into interactive simulations that can be used without specialist computational expertise. SiViT allows clinicians and biologists to directly introduce for example loss of function mutations and specific inhibitors. SiViT animates the effects of these introductions on pathway dynamics, suggesting further experiments and assessing candidate biomarker effectiveness. In a systems biology model of Her2 signalling we experimentally validated predictions using SiViT, revealing the dynamics of biomarkers of drug resistance and highlighting the role of pathway crosstalk. No model is ever complete: the iteration of real data and simulation facilitates continued evolution of more accurate, useful models. SiViT will make accessible libraries of models to support preclinical research, combinatorial strategy design and biomarker discovery