SPEDRE: a web server for estimating rate parameters for cell signaling dynamics in data-rich environments

Cell signaling pathways and metabolic networks are often modeled using ordinary differential equations (ODEs) to represent the production/consumption of molecular species over time. Regardless whether a model is built de novo or adapted from previous models, there is a need to estimate kinetic rate constants based on time-series experimental measurements of molecular abundance. For data-rich cases such as proteomic measurements of all species, spline-based parameter estimation algorithms have been developed to avoid solving all the ODEs explicitly. We report the development of a web server for a spline-based method. Systematic Parameter Estimation for Data-Rich Environments (SPEDRE) estimates reaction rates for biochemical networks. As input, it takes the connectivity of the network and the concentrations of the molecular species at discrete time points. SPEDRE is intended for large sparse networks, such as signaling cascades with many proteins but few reactions per protein. If data are available for all species in the network, it provides global coverage of the parameter space, at low resolution and with approximate accuracy. The output is an optimized value for each reaction rate parameter, accompanied by a range and bin plot. SPEDRE uses tools from COPASI for pre-processing and post-processing. SPEDRE is a free service at http://LTKLab.org/SPEDRE.Singapore-MIT Alliance (IUP R-154-001-348-646

Cardiac cell modelling: Observations from the heart of the cardiac physiome project

In this manuscript we review the state of cardiac cell modelling in the context of international initiatives such as the IUPS Physiome and Virtual Physiological Human Projects, which aim to integrate computational models across scales and physics. In particular we focus on the relationship between experimental data and model parameterisation across a range of model types and cellular physiological systems. Finally, in the context of parameter identification and model reuse within the Cardiac Physiome, we suggest some future priority areas for this field

Inferring diffusion in single live cells at the single molecule level

The movement of molecules inside living cells is a fundamental feature of biological processes. The ability to both observe and analyse the details of molecular diffusion in vivo at the single molecule and single cell level can add significant insight into understanding molecular architectures of diffusing molecules and the nanoscale environment in which the molecules diffuse. The tool of choice for monitoring dynamic molecular localization in live cells is fluorescence microscopy, especially so combining total internal reflection fluorescence (TIRF) with the use of fluorescent protein (FP) reporters in offering exceptional imaging contrast for dynamic processes in the cell membrane under relatively physiological conditions compared to competing single molecule techniques. There exist several different complex modes of diffusion, and discriminating these from each other is challenging at the molecular level due to underlying stochastic behaviour. Analysis is traditionally performed using mean square displacements of tracked particles, however, this generally requires more data points than is typical for single FP tracks due to photophysical instability. Presented here is a novel approach allowing robust Bayesian ranking of diffusion processes (BARD) to discriminate multiple complex modes probabilistically. It is a computational approach which biologists can use to understand single molecule features in live cells.Comment: combined ms (1-37 pages, 8 figures) and SI (38-55, 3 figures

The Role of Control and System Theory in Systems Biology

The use of new technology and mathematics to study the systems of nature is one of the most significant scientific trends of the century. Driven by the need for more precise scientific understand, advances in automated measurement are providing rich new sources of biological and physiological data. This data provides information with which to create mathematical models of increasing sophistication and realism - models that can emulate the performance of biological and physiological systems with sufficient accuracy to advance our understanding of living systems and disease mechanisms. New measurement and modelling methods set the stage for control and systems theory to play their role in seeking out the mechanisms and principles that regulate life. It is of inestimable importance for the future of control as a discipline that this role is performed in the correct manner. If we handle the area wisely then living systems will present a seemly boundless range of important new problems - just as physical and engineering systems have done in previous centuries. But there is a crucial difficulty. Faced with a bewildering array of choices in an unfamiliar area, how does a researcher select a worthwhile and fruitful problem? This lecture is an attempt to help by offering a control oriented guide to the labyrinthine world of biology/physiology and the control research opportunity that it holds

Evolutionary dynamics of glucose-deprived cancer cells: insights from experimentally-informed mathematical modelling

Glucose is a primary energy source for cancer cells. Several lines of evidence support the idea that monocarboxylate transporters, such as MCT1, elicit metabolic reprogramming of cancer cells in glucose-poor environments, allowing them to reuse lactate, a byproduct of glucose metabolism, as an alternative energy source with serious consequences for disease progression. We employ a synergistic experimental and mathematical modelling approach to explore the evolutionary processes at the root of cancer cell adaptation to glucose deprivation, with particular focus on the mechanisms underlying the increase in MCT1 expression observed in glucose-deprived aggressive cancer cells. Data from in vitro experiments on breast cancer cells are used to inform and calibrate a mathematical model that comprises a partial integro-differential equation for the dynamics of a population of cancer cells structured by the level of MCT1 expression. Analytical and numerical results of this model suggest that environment-induced changes in MCT1 expression mediated by lactate-associated signalling pathways enable a prompt adaptive response of glucose-deprived cancer cells, whilst fluctuations in MCT1 expression due to epigenetic changes create the substrate for environmental selection to act upon, speeding up the selective sweep underlying cancer cell adaptation to glucose deprivation, and may constitute a long-term bet-hedging mechanism.Comment: Main manuscript: 14 pages, 4 figures. Supplementary material: 29 pages, 11 figures, 2 table

Mathematical and Statistical Techniques for Systems Medicine: The Wnt Signaling Pathway as a Case Study

The last decade has seen an explosion in models that describe phenomena in systems medicine. Such models are especially useful for studying signaling pathways, such as the Wnt pathway. In this chapter we use the Wnt pathway to showcase current mathematical and statistical techniques that enable modelers to gain insight into (models of) gene regulation, and generate testable predictions. We introduce a range of modeling frameworks, but focus on ordinary differential equation (ODE) models since they remain the most widely used approach in systems biology and medicine and continue to offer great potential. We present methods for the analysis of a single model, comprising applications of standard dynamical systems approaches such as nondimensionalization, steady state, asymptotic and sensitivity analysis, and more recent statistical and algebraic approaches to compare models with data. We present parameter estimation and model comparison techniques, focusing on Bayesian analysis and coplanarity via algebraic geometry. Our intention is that this (non exhaustive) review may serve as a useful starting point for the analysis of models in systems medicine.Comment: Submitted to 'Systems Medicine' as a book chapte

Dynamical models of the mammalian target of rapamycin network in ageing

Phd ThesisThe mammalian Target of Rapamycin (mTOR)kinase is a central regulator of cellular growth and metabolism and plays an important role in ageing and age- related diseases. The increase of invitro data collected to extend our knowledge on its regulation, and consequently improve drug intervention,has highlighted the complexity of the mTOR network. This complexity is also aggravated by the intrinsic time-dependent nature of cellular regulatory network cross-talks and feedbacks. Systems biology constitutes a powerful tool for mathematically for- malising biological networks and investigating such dynamical properties. The present work discusses the development of three dynamical models of the mTOR network. The first aimed at the analysis of the current literature-based hypotheses of mTOR Complex2(mTORC2)regulation. For each hypothesis, the model predicted specific differential dynamics which were systematically tested by invitro experiments. Surprisingly, nocurrent hypothesis could explain the data and a new hypothesis of mTORC2 activation was proposed.The second model extended the previous one with an AMPK module. In this study AMPK was reported to be activated by insulin. Using a hypothesis ranking approach based on model goodness-of-fit, AMPK activity was insilico predicted and in vitro tested to be activated by the insulin receptor substrate(IRS).Finally,the last model linked mTOR with the oxidative stress response, mitochondrial reg- ulation, DNA damage and FoxO transcription factors. This work provided the characterisation of a dynamical mechanism to explain the state transition from normal to senescent cells and their reversibility of the senescentphenotype.European Council 6FP NoE LifeSpan, School of the Faculty of Medical Sciences, Newcastle Universit