Model simplification procedure for signal transduction pathway models: An application to IL-6 signaling

Building predictive signaling models by perturbing yeast cells with time-varying stimulations resulting in distinct signaling responses

This protocol provides a step-by-step approach to perturb single cells with time-varying stimulation profiles, collect distinct signaling responses, and use these to infer a system of ordinary differential equations to capture and predict dynamics of protein-protein regulation in signal transduction pathways. The models are validated by predicting the signaling activation upon new cell stimulation conditions. In comparison to using standard step-like stimulations, application of diverse time-varying cell stimulations results in better inference of model parameters and substantially improves model predictions.

For complete details on the use and results of this protocol, please refer to Jashnsaz et al. (2020).

•

Diverse time-varying cell stimulations result in distinct signaling activation dynamics

•

Signaling models fit step stimuli responses well but result in poor predictions

•

Distinct responses upon diverse time-varying stimulations improve model predictions

•

Temporal stimulation of pathways result in novel signaling dynamics and mechanisms

MODELING INTER-KINGDOM REGULATION OF INFLAMMATORY SIGNALING IN HUMAN INTESTINAL EPITHELIAL CELLS

The human gastrointestinal (GI) tract is colonized by a highly diverse and complex microbial community (i.e., microbiota). The microbiota plays an important role in the development of the immune system, specifically mediating inflammatory responses, however the exact mechanisms are poorly understood. We have developed a mathematical model describing the effect of indole on host inflammatory signaling in HCT-8 human intestinal epithelial cells. In this model, indole modulates transcription factor nuclear factor κ B (NF-κB) and produces the chemokine interleukin-8 (IL-8) through the activation of the aryl hydrocarbon receptor (AhR). Phosphorylated NF-κB exhibits dose and time-dependent responses to indole concentrations and IL-8 production shows a significant down-regulation for 0.1 ng/mL TNF-α stimulation. The model shows agreeable simulation results with the experimental data for IL-8 secretion and normalized NF-κB values. Our results suggest that microbial metabolites such as indole can modulate inflammatory signaling in HTC-8 cells through receptor-mediated processes.

Novel Influences of IL-10 on CNS Inflammation Revealed by Integrated Analyses of Cytokine Networks and Microglial Morphology

Coordinated interactions between cytokine signaling and morphological dynamics of microglial cells regulate neuroinflammation in CNS injury and disease. We found that pro-inflammatory cytokine gene expression in vivo showed a pronounced recovery following systemic LPS. We performed a novel multivariate analysis of microglial morphology and identified changes in specific morphological properties of microglia that matched the expression dynamics of pro-inflammatory cytokine TNFα. The adaptive recovery kinetics of TNFα expression and microglial soma size showed comparable profiles and dependence on anti-inflammatory cytokine IL-10 expression. The recovery of cytokine variations and microglial morphology responses to inflammation were negatively regulated by IL-10. Our novel morphological analysis of microglia is able to detect subtle changes and can be used widely. We implemented in silico simulations of cytokine network dynamics which showed—counter-intuitively, but in line with our experimental observations—that negative feedback from IL-10 was sufficient to impede the adaptive recovery of TNFα-mediated inflammation. Our integrative approach is a powerful tool to study changes in specific components of microglial morphology for insights into their functional states, in relation to cytokine network dynamics, during CNS injury and disease.

TGF-β and IL-6 family signalling crosstalk: an integrated model

Mathematical models for TGF-β and IL-6 signalling have been linked, providing a platform for analyzing the crosstalk between the systems. An integrated IL-6:TGF-β model was developed via a reduced set of reaction equations which incorporate both feedback loops and appropriate time-delays for transcription and translation processes. The model simulates stable, robust and realistic responses to both ligands. Pulsatile (multiple pulses) inputs for both TGF-β and IL-6 have been simulated to investigate the effects of each ligand on the sensitivity, equilibrium and dynamic responses of the integrated signalling system. In our simulations the crosstalk between constant IL-6 and TGF-β signalling via SMAD7 does not appear to be sufficient to render the cells resistant to TGF-β inhibition. However, the simulations predict that pulsatile IL-6 stimulation would increase SMAD7 levels substantially and consequentially, lead to resistance to TGF-β. The model also allows the prediction of the integrated signalling pathway responses to the mutation of key components, e.g. Gp130 ^F/F.

Clustering reveals limits of parameter identifiability in multi-parameter models of biochemical dynamics

Background

Compared to engineering or physics problems, dynamical models in quantitative biology typically depend on a relatively large number of parameters. Progress in developing mathematics to manipulate such multi-parameter models and so enable their efficient interplay with experiments has been slow. Existing solutions are significantly limited by model size.

Results

In order to simplify analysis of multi-parameter models a method for clustering of model parameters is proposed. It is based on a derived statistically meaningful measure of similarity between groups of parameters. The measure quantifies to what extend changes in values of some parameters can be compensated by changes in values of other parameters. The proposed methodology provides a natural mathematical language to precisely communicate and visualise effects resulting from compensatory changes in values of parameters. As a results, a relevant insight into identifiability analysis and experimental planning can be obtained. Analysis of NF- κB and MAPK pathway models shows that highly compensative parameters constitute clusters consistent with the network topology. The method applied to examine an exceptionally rich set of published experiments on the NF- κB dynamics reveals that the experiments jointly ensure identifiability of only 60 % of model parameters. The method indicates which further experiments should be performed in order to increase the number of identifiable parameters.

Conclusions

We currently lack methods that simplify broadly understood analysis of multi-parameter models. The introduced tools depict mutually compensative effects between parameters to provide insight regarding role of individual parameters, identifiability and experimental design. The method can also find applications in related methodological areas of model simplification and parameters estimation.

Electronic supplementary material

The online version of this article (doi:10.1186/s12918-015-0205-8) contains supplementary material, which is available to authorized users.

Mathematical model of dynamic behavior of microbial desalination cells for simultaneous wastewater treatment and water desalination

Microbial desalination cells (MDCs) are an emerging concept for simultaneous wastewater treatment and water desalination. This work presents a mathematical model to simulate dynamic behavior of MDCs for the first time through evaluating multiple factors such as organic supply, salt loading, and current generation. Ordinary differential equations were applied to describe the substrate as well as bacterial concentrations in the anode compartment. Local sensitivity analysis was employed to select model parameters that needed to be re-estimated from the previous studies. This model was validated by experimental data from both a bench- and a large-scale MDC system. It could fit current generation fairly well and simulate the change of salt concentration. It was able to predict the response of the MDC with time under various conditions, and also provide information for analyzing the effects of different operating conditions. Furthermore, optimal operating conditions for the MDC used in this study were estimated to have an acetate flow rate of 0.8 mL·min(-1), influent salt concentration of 15 g·L(-1) and salt solution flow rate of 0.04 mL·min(-1), and to be operated with an external resistor less than 30 Ω. The MDC model will be helpful with determining operational parameters to achieve optimal desalination in MDCs.

Memory effects in biochemical networks as the natural counterpart of extrinsic noise

We show that in the generic situation where a biological network, e.g. a protein interaction network, is in fact a subnetwork embedded in a larger "bulk" network, the presence of the bulk causes not just extrinsic noise but also memory effects. This means that the dynamics of the subnetwork will depend not only on its present state, but also its past. We use projection techniques to get explicit expressions for the memory functions that encode such memory effects, for generic protein interaction networks involving binary and unary reactions such as complex formation and phosphorylation. Remarkably, in the limit of low intrinsic copy-number noise such expressions can be obtained even for nonlinear dependences on the past. We illustrate the method with examples from a protein interaction network around epidermal growth factor receptor (EGFR), which is relevant to cancer signalling. These examples demonstrate that inclusion of memory terms is not only important conceptually but also leads to substantially higher quantitative accuracy in the predicted subnetwork dynamics.

A simple work flow for biologically inspired model reduction--application to early JAK-STAT signaling

BACKGROUND

Modeling of biological pathways is a key issue in systems biology. When constructing a model, it is tempting to incorporate all known interactions of pathway species, which results in models with a large number of unknown parameters. Fortunately, unknown parameters need not necessarily be measured directly, but some parameter values can be estimated indirectly by fitting the model to experimental data. However, parameter fitting, or, more precisely, maximum likelihood parameter estimation, only provides valid results, if the complexity of the model is in balance with the amount and quality of the experimental data. If this is the case the model is said to be identifiable for the given data. If a model turns out to be unidentifiable, two steps can be taken. Either additional experiments need to be conducted, or the model has to be simplified.

RESULTS

We propose a systematic procedure for model simplification, which consists of the following steps: estimate the parameters of the model, create an identifiability ranking for the estimated parameters, and simplify the model based on the identifiability analysis results. These steps need to be applied iteratively until the resulting model is identifiable, or equivalently, until parameter variances are small. We choose parameter variances as stopping criterion, since they are concise and easy to interpret. For both, the parameter estimation and the calculation of parameter variances, multi-start parameter estimations are run on a parallel cluster. In contrast to related work in systems biology, we do not suggest simplifying a model by fixing some of its parameters, but change the structure of the model.

CONCLUSIONS

We apply the proposed approach to a model of early signaling events in the JAK-STAT pathway. The resulting model is not only identifiable with small parameter variances, but also shows the best trade-off between goodness of fit and model complexity.