Andrea Degasperi

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.

Bistability in the Rac1, PAK, and RhoA signaling network drives actin cytoskeleton dynamics and cell motility switches

Summary 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.

Mitochondrial reactive oxygen species enhance AMP-activated protein kinase activation in the endothelium of patients with coronary artery disease and diabetes

The aim of the present study was to determine whether the endothelial dysfunction associated with CAD (coronary artery disease) and T2D (Type 2 diabetes mellitus) is concomitant with elevated mtROS (mitochondrial reactive oxygen species) production in the endothelium and establish if this, in turn, regulates the activity of endothelial AMPK (AMP-activated protein kinase). We investigated endothelial function, mtROS production and AMPK activation in saphenous veins from patients with advanced CAD. Endothelium-dependent vasodilation was impaired in patients with CAD and T2D relative to those with CAD alone. Levels of mitochondrial H2O2 and activity of AMPK were significantly elevated in primary HSVECs (human saphenous vein endothelial cells) from patients with CAD and T2D compared with those from patients with CAD alone. Incubation with the mitochondria-targeted antioxidant, MitoQ10 significantly reduced AMPK activity in HSVECs from patients with CAD and T2D but not in cells from patients with CAD alone. Elevated mtROS production in the endothelium of patients with CAD and T2D increases AMPK activation, supporting a role for the kinase in defence against oxidative stress. Further investigation is required to determine whether pharmacological activators of AMPK will prove beneficial in the attenuation of endothelial dysfunction in patients with CAD and T2D.

Some Investigations Concerning the CTMC and the ODE Model Derived From Bio-PEPA

Bio-PEPA is a recently defined language for the modelling and analysis of biochemical networks. It supports an abstract style of modelling, in which discrete levels of concentration within a species are considered instead of individual molecules. A finer granularity for the system corresponds to a smaller concentration step size and therefore to a greater number of concentration levels. This style of model is amenable to a variety of different analysis techniques, including numerical analysis based on a CMTC with states reflecting the levels of concentration. In this paper we present a formal definition of the CTMC with levels derived from a Bio-PEPA system. Furthermore we investigate the relationship between this CTMC and the system of ordinary differential equations (ODEs) derived from the same model. Using Kurtzs theorem, we show that the set of ODEs derived from the Bio-PEPA model is able to capture the limiting behaviour of the CTMC obtained from the same system. Finally, we define an empirical methodology to find the granularity of the Bio-PEPA system for which the ODE and the CTMC with levels are in a good agreement. The proposed definition is based on a notion of distance between the two models. We demonstrate our approach on a model of the Repressilator, a simple biochemical network with oscillating behaviour.

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 Gillespies Stochastic Simulation Algorithm (SSA). We present an example of stochastic sensitivity analysis of a real pathway, the MAPK signalling pathway.

Modelling Biological Clocks with Bio-PEPA: Stochasticity and Robustness for the Neurospora crassa Circadian Network

Circadian clocks are biochemical networks, present in nearly all living organisms, whose function is to regulate the expression of specific mRNAs and proteins to synchronise rhythms of metabolism, physiology and behaviour to the 24 hour day/night cycle. Because of their experimental tractability and biological significance, circadian clocks have been the subject of a number of computational modelling studies. In this study we focus on the simple circadian clock of the fungus Neurospora crassa . We use the Bio-PEPA process algebra to develop both a stochastic and a deterministic model of the system. The light on/off mechanism responsible for entrainment to the day/night cycle is expressed using discrete time-dependent events in Bio-PEPA. In order to validate our model, we compare it against the results of previous work which demonstrated that the deterministic model is in agreement with experimental data. Here we investigate the effect of stochasticity on the robustness of the clocks function in biological timing. In particular, we focus on the variations in the phase and amplitude of oscillations in circadian proteins with respect to different factors such as the presence/absence of a positive feedback loop, and the presence/absence of light. The time-dependent sensitivity of the model with respect to some key kinetic parameters is also investigated.

Modelling and analysis of the NF-κB pathway in bio-PEPA

In this work we present a Bio-PEPA model describing the Nuclear Factor

DYVIPAC: an integrated analysis and visualisation framework to probe multi-dimensional biological networks.

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Multi-scale modelling of biological systems in process algebra with multi-way synchronisation

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Process Algebra with Hooks for Models of Pattern Formation

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