Application of Modular Response Analysis to Medium- to Large-Size Biological Systems

The development of high-throughput genomic technologies associated with recent genetic perturbation techniques such as short hairpin RNA (shRNA), gene trapping, or gene editing (CRISPR/Cas9) has made it possible to obtain large perturbation data sets. These data sets are invaluable sources of information regarding the function of genes, and they offer unique opportunities to reverse engineer gene regulatory networks in specific cell types. Modular response analysis (MRA) is a well-accepted mathematical modeling method that is precisely aimed at such network inference tasks, but its use has been limited to rather small biological systems so far. In this study, we show that MRA can be employed on large systems with almost 1,000 network components. In particular, we show that MRA performance surpasses general-purpose mutual information-based algorithms. Part of these competitive results was obtained by the application of a novel heuristic that pruned MRA-inferred interactions a posteriori. We also exploited a block structure in MRA linear algebra to parallelize large system resolutions.

An R package for generic modular response analysis and its application to estrogen and retinoic acid receptor crosstalk

Modular response analysis (MRA) is a widely used inference technique developed to uncover directions and strengths of connections in molecular networks under a steady-state condition by means of perturbation experiments. We devised several extensions of this methodology to search genomic data for new associations with a biological network inferred by MRA, to improve the predictive accuracy of MRA-inferred networks, and to estimate confidence intervals of MRA parameters from datasets with low numbers of replicates. The classical MRA computations and their extensions were implemented in a freely available R package called aiMeRA (https://github.com/bioinfo-ircm/aiMeRA/). We illustrated the application of our package by assessing the crosstalk between estrogen and retinoic acid receptors, two nuclear receptors implicated in several hormone-driven cancers, such as breast cancer. Based on new data generated for this study, our analysis revealed potential cross-inhibition mediated by the shared corepressors NRIP1 and LCoR. We designed aiMeRA for non-specialists and to allow biologists to perform their own analyses.

Model-based identification of the crosstalks and feedbacks that determine the doxorubicin response dynamics of the JNK-p38-p53 network

Cellular responses to perturbations and drugs are determined by interconnected networks, rather than linear pathways. Individually, the JNK, p38 and p53 stress and DNA-damage response networks are well understood and regulate critical cell-fate decisions, such as apoptosis, in response to many chemotherapeutical agents, such as doxorubicin. To better understand how interactions between these pathways determine the dynamic behaviour of the entire network, we constructed a data-driven mathematical model. This model contains mechanistic details about the kinase cascades that activate JNK, p38, AKT and p53, and free parameters that describe possible interactions between these pathways. Fitting this model to experimental time-course perturbation data (five time-courses with six time-points under five different conditions), identified specific network interactions that can explain the observed network responses. JNK emerged as an important control node. JNK exhibited a positive feedback loop, was tightly controlled by negative feedback and crosstalk from p38 and AKT, respectively, and was the strongest activator of p53. Compared to static network reconstruction methods, such as modular response analysis, the model-based approach identifies biochemical mechanisms and explains the dynamic control of cell signalling.

aiMeRA: A generic modular response analysis R package and its application to estrogen and retinoic acid receptors crosstalk

Modular response analysis (MRA) is a widely used modeling technique to uncover coupling strengths in molecular networks under a steady-state condition by means of perturbation experiments. We propose an extension of this methodology to search genomic data for new associations with a network modeled by MRA and to improve the predictive accuracy of MRA models. These extensions are illustrated by exploring the cross talk between estrogen and retinoic acid receptors, two nuclear receptors implicated in several hormone-driven cancers such as breast. We also present a novel, rigorous and elegant mathematical derivation of MRA equations, which is the foundation of this work and of an R package that is freely available at https://github.com/bioinfo-ircm/aiMeRA/. This mathematical analysis should facilitate MRA understanding by newcomers.Author summaryEstrogen and retinoic acid receptors play an important role in several hormone-driven cancers and share co-regulators and co-repressors that modulate their transcription factor activity. The literature shows evidence for crosstalk between these two receptors and suggests that spatial competition on the promoters could be a mechanism. We used MRA to explore the possibility that key co-repressors, i.e., NRIP1 (RIP140) and LCoR could also mediate crosstalk by exploiting new quantitative (qPCR) and RNA sequencing data. The transcription factor role of the receptors and the availability of genome-wide data enabled us to explore extensions of the MRA methodology to explore genome-wide data sets a posteriori, searching for genes associated with a molecular network that was sampled by perturbation experiments. Despite nearly two decades of use, we felt that MRA lacked a systematic mathematical derivation. We present here an elegant and rather simple analysis that should greatly facilitate newcomers’ understanding of MRA details. Moreover, an easy-to-use R package is released that should make MRA accessible to biology labs without mathematical expertise. Quantitative data are embedded in the R package and RNA sequencing data are available from GEO.

Reverse engineering gene regulatory networks by modular response analysis – a benchmark

Gene regulatory networks control the cellular phenotype by changing the RNA and protein composition. Despite its importance, the gene regulatory network in higher organisms is only partly mapped out. Here, we investigate the potential of reverse engineering methods to unravel the structure of these networks. Particularly, we focus on modular response analysis (MRA), a method that can disentangle networks from perturbation data. We benchmark a version of MRA that was previously successfully applied to reconstruct a signalling-driven genetic network, termed MLMSMRA, to test cases mimicking various aspects of gene regulatory networks. We then investigate the performance in comparison with other MRA realisations and related methods. The benchmark shows that MRA has the potential to predict functional interactions, but also shows that successful application of MRA is restricted to small sparse networks and to data with a low signal-to-noise ratio.

Modelling Signalling Networks from Perturbation Data

MotivationIntracellular signalling is realized by complex signalling networks which are almost impossible to understand without network models, especially if feedbacks are involved. Modular Response Analysis (MRA) is a convenient modelling method to study signalling networks in various contexts.ResultsWe developed a derivative of MRA that is suited to model signalling networks from incomplete perturbation schemes and multi-perturbation data. We applied the method to study the effect of SHP2, a protein that has been implicated in resistance to targeted therapy in colon cancer, using data from a knock out and parental colon cancer cell line. We find that SHP2 is required for MAPK signalling, whereas AKT signalling only partially depends on SHP2.AvailabilityAn R-package is available at https://github.com/MathurinD/[email protected]

Fitting mathematical models of biochemical pathways to steady state perturbation response data without simulating perturbation experiments

A common experimental approach for studying signal transduction networks (STNs) is to measure the steady state concentrations of their components following perturbations to individual components. Such data is frequently used to reconstruct topological models of STNs, but, are rarely used for calibrating kinetic models of these networks. This is because, existing calibration algorithms operate by assigning different sets of values to the parameters of the kinetic models, and for each set of values simulating all perturbations performed in the biochemical experiments. This process is highly computation intensive and may be infeasible when molecular level information of the perturbation experiments is unavailable. Here, I propose an algorithm which can calibrate ordinary differential equation (ODE) based kinetic models of STNs using steady-state perturbation responses (SSPRs) without simulating perturbation experiments. The proposed algorithm uses modular response analysis (MRA) to calculate the scaled Jacobian matrix of the ODE model of an STN using SSPR data. The model parameters are then calibrated to fit the scaled Jacobian matrix calculated in the above step. This procedure does not require simulating the perturbation experiments. Therefore, it is significantly less computation intensive than existing algorithms and can be implemented without molecular level knowledge of the mechanism of perturbations. It is also parallelizable, i.e. can explore multiple sets of parameter values simultaneously, and therefore is scalable. The capabilities and shortcomings of the proposed algorithm are demonstrated using both simulated and real perturbation responses of Mitogen Activated Protein Kinase (MAPK) STN.AvailabilityAll source codes and data needed to replicate the results in this manuscript are available from https://github.com/SBIUCD/MRA_SMC_ABC1

Discriminating direct and indirect connectivities in biological networks

Reverse engineering of biological pathways involves an iterative process between experiments, data processing, and theoretical analysis. Despite concurrent advances in quality and quantity of data as well as computing resources and algorithms, difficulties in deciphering direct and indirect network connections are prevalent. Here, we adopt the notions of abstraction, emulation, benchmarking, and validation in the context of discovering features specific to this family of connectivities. After subjecting benchmark synthetic circuits to perturbations, we inferred the network connections using a combination of nonparametric single-cell data resampling and modular response analysis. Intriguingly, we discovered that recovered weights of specific network edges undergo divergent shifts under differential perturbations, and that the particular behavior is markedly different between topologies. Our results point to a conceptual advance for reverse engineering beyond weight inference. Investigating topological changes under differential perturbations may address the longstanding problem of discriminating direct and indirect connectivities in biological networks.