Now showing 1 - 5 of 5
  • Publication
    A process algebra framework for multi-scale modelling of biological systems
    (Elsevier, 2013-06) ;
    We introduce a novel process algebra for modelling biological systems at multiple scales, called process algebra with hooks (PAH). Processes represent biological entities, such as molecules, cells and tissues, while two algebraic operators, both symmetric, define composition of processes within and between scales. Composed actions allow for biological events to interact within and between scales at the same time. The algebra has a stochastic semantics based on functional rates of reactions. Two bisimulations are defined on PAH processes. The first bisimulation is used to aid model development by checking that two biological scales can interact correctly. The second bisimulation is a congruence that relates models, or part of models, that can perform the same timed events at a specified scale. Finally, we provide a PAH model of pattern formation in a tissue and illustrate reasoning about its behaviour using the PAH framework.
      202Scopus© Citations 1
  • Publication
    Sensitivity Analysis of Stochastic Models of Bistable Biochemical Reactions
    Sensitivity Analysis (SA) provides techniques which can be used to identify the parameters which have the greatest influence on the results obtained from a model. Classical SA methods apply to deterministic simulations of ODE models. We extend these to stochastic simulations and consider the analysis of models with bifurcation points and bistable behaviour. We consider local, global and screening SA methods applied to multiple runs of Gillespie’s Stochastic Simulation Algorithm (SSA) . We present an example of stochastic sensitivity analysis of a real pathway, the MAPK signalling pathway.
      256Scopus© Citations 27
  • Publication
    Evaluating Strategies to Normalise Biological Replicates of Western Blot Data
    Western blot data are widely used in quantitative applications such as statistical testing and mathematical modelling. To ensure accurate quantitation and comparability between experiments, Western blot replicates must be normalised, but it is unclear how the available methods affect statistical properties of the data. Here we evaluate three commonly used normalisation strategies: (i) by fixed normalisation point or control; (ii) by sum of all data points in a replicate; and (iii) by optimal alignment of the replicates. We consider how these different strategies affect the coefficient of variation (CV) and the results of hypothesis testing with the normalised data. Normalisation by fixed point tends to increase the mean CV of normalised data in a manner that naturally depends on the choice of the normalisation point. Thus, in the context of hypothesis testing, normalisation by fixed point reduces false positives and increases false negatives. Analysis of published experimental data shows that choosing normalisation points with low quantified intensities results in a high normalised data CV and should thus be avoided. Normalisation by sum or by optimal alignment redistributes the raw data uncertainty in a mean-dependent manner, reducing the CV of high intensity points and increasing the CV of low intensity points. This causes the effect of normalisations by sum or optimal alignment on hypothesis testing to depend on the mean of the data tested; for high intensity points, false positives are increased and false negatives are decreased, while for low intensity points, false positives are decreased and false negatives are increased. These results will aid users of Western blotting to choose a suitable normalisation strategy and also understand the implications of this normalisation for subsequent hypothesis testing.
      303Scopus© Citations 134
  • Publication
    DYVIPAC: an integrated analysis and visualisation framework to probe multi-dimensional biological networks
    Biochemical networks are dynamic and multi-dimensional systems, consisting of tens or hundreds of molecular components. Diseases such as cancer commonly arise due to changes in the dynamics of signalling and gene regulatory networks caused by genetic alternations. Elucidating the network dynamics in health and disease is crucial to better understand the disease mechanisms and derive effective therapeutic strategies. However, current approaches to analyse and visualise systems dynamics can often provide only low-dimensional projections of the network dynamics, which often does not present the multi-dimensional picture of the system behaviour. More efficient and reliable methods for multi-dimensional systems analysis and visualisation are thus required. To address this issue, we here present an integrated analysis and visualisation framework for high-dimensional network behaviour which exploits the advantages provided by parallel coordinates graphs. We demonstrate the applicability of the framework, named “Dynamics Visualisation based on Parallel Coordinates” (DYVIPAC), to a variety of signalling networks ranging in topological wirings and dynamic properties. The framework was proved useful in acquiring an integrated understanding of systems behaviour.
      220Scopus© Citations 15
  • Publication
    Bistability in the Rac1, PAK, and RhoA Signaling Network Drives Actin Cytoskeleton Dynamics and Cell Motility Switches
    Dynamic interactions between RhoA and Rac1, members of the Rho small GTPase family, play a vital role in the control of cell migration. Using predictive mathematical modeling, mass spectrometry-based quantitation of network components, and experimental validation in MDA-MB-231 mesenchymal breast cancer cells, we show that a network containing Rac1, RhoA, and PAK family kinases can produce bistable, switch-like responses to a graded PAK inhibition. Using a small chemical inhibitor of PAK, we demonstrate that cellular RhoA and Rac1 activation levels respond in a history-dependent, bistable manner to PAK inhibition. Consequently, we show that downstream signaling, actin dynamics, and cell migration also behave in a bistable fashion, displaying switches and hysteresis in response to PAK inhibition. Our results demonstrate that PAK is a critical component in the Rac1-RhoA inhibitory crosstalk that governs bistable GTPase activity, cell morphology, and cell migration switches.
      314Scopus© Citations 108