Analysing the role of UVB-induced translational inhibition and PP2Ac deactivation in NF-κB signalling using a minimal mathematical model

BlotIt—Optimal alignment of Western blot and qPCR experiments

Biological systems are frequently analyzed by means of mechanistic mathematical models. In order to infer model parameters and provide a useful model that can be employed for systems understanding and hypothesis testing, the model is often calibrated on quantitative, time-resolved data. To do so, it is typically important to compare experimental measurements over broad time ranges and various experimental conditions, e.g. perturbations of the biological system. However, most of the established experimental techniques such as Western blot, or quantitative real-time polymerase chain reaction only provide measurements on a relative scale, since different sample volumes, experimental adjustments or varying development times of a gel lead to systematic shifts in the data. In turn, the number of measurements corresponding to the same scale enabling comparability is limited. Here, we present a new flexible method to align measurement data that obeys different scaling factors and compare it to existing normalization approaches. We propose an alignment model to estimate these scaling factors and provide the possibility to adapt this model depending on the measurement technique of interest. In addition, an error model can be specified to adequately weight the different data points and obtain scaling-model based confidence intervals of the finally scaled data points. Our approach is applicable to all sorts of relative measurements and does not need a particular experimental condition that has been measured over all available scales. An implementation of the method is provided with the R package blotIt including refined ways of visualization.

Identification of new IκBα complexes by an iterative experimental and mathematical modeling approach

The transcription factor nuclear factor kappa-B (NFκB) is a key regulator of pro-inflammatory and pro-proliferative processes. Accordingly, uncontrolled NFκB activity may contribute to the development of severe diseases when the regulatory system is impaired. Since NFκB can be triggered by a huge variety of inflammatory, pro-and anti-apoptotic stimuli, its activation underlies a complex and tightly regulated signaling network that also includes multi-layered negative feedback mechanisms. Detailed understanding of this complex signaling network is mandatory to identify sensitive parameters that may serve as targets for therapeutic interventions. While many details about canonical and non-canonical NFκB activation have been investigated, less is known about cellular IκBα pools that may tune the cellular NFκB levels. IκBα has so far exclusively been described to exist in two different forms within the cell: stably bound to NFκB or, very transiently, as unbound protein. We created a detailed mathematical model to quantitatively capture and analyze the time-resolved network behavior. By iterative refinement with numerous biological experiments, we yielded a highly identifiable model with superior predictive power which led to the hypothesis of an NFκB-lacking IκBα complex that contains stabilizing IKK subunits. We provide evidence that other but canonical pathways exist that may affect the cellular IκBα status. This additional IκBα:IKKγ complex revealed may serve as storage for the inhibitor to antagonize undesired NFκB activation under physiological and pathophysiological conditions.

In unstimulated cells, the transcription factor NFκB resides in the cytosol bound to its inhibitor IκBα. Canonical activation of NFκB by numerous stimuli leads to proteasomal depletion of IκBα, thereby liberating NFκB to translocate into the nucleus to induce transcription of genes leading to proliferation, angiogenesis, metastasis, or chronic inflammation. Consequently, only transient activity needs to be warranted by immediate NFκB-dependent induction of negative regulatory mechanisms, including up-regulation of its inhibitor IκBα. Resynthesized IκBα consequently terminates NFκB activity by binding to its nuclear localization sequence. However, under physiological or pathophysiological conditions, random NFκB activation may occur, which needs to be avoided in order to guarantee proper cellular function. Using detailed dynamical modeling, we have now identified an additional IκBα containing complex to exist in un-stimulated cells which lacks NFκB but includes IKKγ (IκBα:IKKγ complex). This additional IκBα is not depleted from cells in the canonical fashion and may therefore serve as a cellular backup to avoid random NFκB activation.

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.