Inferring genetic networks and identifying compound mode of action via expression profiling

Identifying a stochastic clock network with light entrainment for single cells of Neurospora crassa

Stochastic networks for the clock were identified by ensemble methods using genetic algorithms that captured the amplitude and period variation in single cell oscillators of Neurospora crassa. The genetic algorithms were at least an order of magnitude faster than ensemble methods using parallel tempering and appeared to provide a globally optimum solution from a random start in the initial guess of model parameters (i.e., rate constants and initial counts of molecules in a cell). The resulting goodness of fit [Formula: see text] was roughly halved versus solutions produced by ensemble methods using parallel tempering, and the resulting [Formula: see text] per data point was only [Formula: see text] = 2,708.05/953 = 2.84. The fitted model ensemble was robust to variation in proxies for "cell size". The fitted neutral models without cellular communication between single cells isolated by microfluidics provided evidence for only one Stochastic Resonance at one common level of stochastic intracellular noise across days from 6 to 36 h of light/dark (L/D) or in a D/D experiment. When the light-driven phase synchronization was strong as measured by the Kuramoto (K), there was degradation in the single cell oscillations away from the stochastic resonance. The rate constants for the stochastic clock network are consistent with those determined on a macroscopic scale of 10⁷ cells.

Perturbation-based gene regulatory network inference to unravel oncogenic mechanisms

The gene regulatory network (GRN) of human cells encodes mechanisms to ensure proper functioning. However, if this GRN is dysregulated, the cell may enter into a disease state such as cancer. Understanding the GRN as a system can therefore help identify novel mechanisms underlying disease, which can lead to new therapies. To deduce regulatory interactions relevant to cancer, we applied a recent computational inference framework to data from perturbation experiments in squamous carcinoma cell line A431. GRNs were inferred using several methods, and the false discovery rate was controlled by the NestBoot framework. We developed a novel approach to assess the predictiveness of inferred GRNs against validation data, despite the lack of a gold standard. The best GRN was significantly more predictive than the null model, both in cross-validated benchmarks and for an independent dataset of the same genes under a different perturbation design. The inferred GRN captures many known regulatory interactions central to cancer-relevant processes in addition to predicting many novel interactions, some of which were experimentally validated, thus providing mechanistic insights that are useful for future cancer research.

Identifiability and experimental design in perturbation studies

MOTIVATION

A common strategy to infer and quantify interactions between components of a biological system is to deduce them from the network's response to targeted perturbations. Such perturbation experiments are often challenging and costly. Therefore, optimizing the experimental design is essential to achieve a meaningful characterization of biological networks. However, it remains difficult to predict which combination of perturbations allows to infer specific interaction strengths in a given network topology. Yet, such a description of identifiability is necessary to select perturbations that maximize the number of inferable parameters.

RESULTS

We show analytically that the identifiability of network parameters can be determined by an intuitive maximum-flow problem. Furthermore, we used the theory of matroids to describe identifiability relationships between sets of parameters in order to build identifiable effective network models. Collectively, these results allowed to device strategies for an optimal design of the perturbation experiments. We benchmarked these strategies on a database of human pathways. Remarkably, full network identifiability was achieved, on average, with less than a third of the perturbations that are needed in a random experimental design. Moreover, we determined perturbation combinations that additionally decreased experimental effort compared to single-target perturbations. In summary, we provide a framework that allows to infer a maximal number of interaction strengths with a minimal number of perturbation experiments.

AVAILABILITY AND IMPLEMENTATION

IdentiFlow is available at github.com/GrossTor/IdentiFlow.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

GREMA: modelling of emulated gene regulatory networks with confidence levels based on evolutionary intelligence to cope with the underdetermined problem

Motivation

Non-linear ordinary differential equation (ODE) models that contain numerous parameters are suitable for inferring an emulated gene regulatory network (eGRN). However, the number of experimental measurements is usually far smaller than the number of parameters of the eGRN model that leads to an underdetermined problem. There is no unique solution to the inference problem for an eGRN using insufficient measurements.

Results

This work proposes an evolutionary modelling algorithm (EMA) that is based on evolutionary intelligence to cope with the underdetermined problem. EMA uses an intelligent genetic algorithm to solve the large-scale parameter optimization problem. An EMA-based method, GREMA, infers a novel type of gene regulatory network with confidence levels for every inferred regulation. The higher the confidence level is, the more accurate the inferred regulation is. GREMA gradually determines the regulations of an eGRN with confidence levels in descending order using either an S-system or a Hill function-based ODE model. The experimental results showed that the regulations with high-confidence levels are more accurate and robust than regulations with low-confidence levels. Evolutionary intelligence enhanced the mean accuracy of GREMA by 19.2% when using the S-system model with benchmark datasets. An increase in the number of experimental measurements may increase the mean confidence level of the inferred regulations. GREMA performed well compared with existing methods that have been previously applied to the same S-system, DREAM4 challenge and SOS DNA repair benchmark datasets.

Availability and implementation

All of the datasets that were used and the GREMA-based tool are freely available at https://nctuiclab.github.io/GREMA.

Supplementary information

Supplementary data are available at Bioinformatics online.

Single-cell transcriptional networks in differentiating preadipocytes suggest drivers associated with tissue heterogeneity

White adipose tissue plays an important role in physiological homeostasis and metabolic disease. Different fat depots have distinct metabolic and inflammatory profiles and are differentially associated with disease risk. It is unclear whether these differences are intrinsic to the pre-differentiated stage. Using single-cell RNA sequencing, a unique network methodology and a data integration technique, we predict metabolic phenotypes in differentiating cells. Single-cell RNA-seq profiles of human preadipocytes during adipogenesis in vitro identifies at least two distinct classes of subcutaneous white adipocytes. These differences in gene expression are separate from the process of browning and beiging. Using a systems biology approach, we identify a new network of zinc-finger proteins that are expressed in one class of preadipocytes and is potentially involved in regulating adipogenesis. Our findings gain a deeper understanding of both the heterogeneity of white adipocytes and their link to normal metabolism and disease.

The origin of the heterogeneity of metabolic and inflammatory profiles exhibited by white adipocytes is little understood. Here, using scRNA-seq and computational methods, the authors show that differentiating preadipocytes exhibit gene expression differences and suggest underlying regulators.

Molecular ecological network analysis of the response of soil microbial communities to depth gradients in farmland soils

Soil microorganisms are considered to be important indicators of soil fertility and soil quality. Most previous studies have focused solely on surface soil, but there were numerous active cells in deeper soil layers. However, studies regarding microbial communities in deeper soil layers were not comprehensive and sufficient. In this study, phylogenetic molecular ecological networks (pMENs) based on the 16S rRNA Miseq sequencing technique were applied to study the response of soil microbial communities to depth gradients and the changes of key genera along 3 meter depth gradients (0-0.2 m, 0.2-0.4 m 0.4-0.6 m, 0.6-0.8 m, 0.8-1.0 m, 1.0-1.3 m, 1.3-1.6 m, 1.6-2.0 m, 2.0-2.5 m, and 2.5-3.0 m). The results showed that the modularity of microbial communities was consistently high in all soil layers and each layer was similar, which indicated that microbial communities were more resistant to depth changes. The pMENs further demonstrated that microbial community interactions were stable as the depth increased and they cooperated well to adapt to changes in different soil gradients. This was evidenced by similar positive links, average degree, and average clustering coefficient. In addition, key genera were obtained by analyzing module hubs in the pMENs. There may be at least one dominant genus in each layer that adapted to and resisted changes in the soil environment. It seems microbial communities demonstrate a stable and strong adaptability to depth gradients in farmland soils.

Bayesian Data Fusion of Gene Expression and Histone Modification Profiles for Inference of Gene Regulatory Network

Accurately reconstructing gene regulatory networks (GRNs) from high-throughput gene expression data has been a major challenge in systems biology for decades. Many approaches have been proposed to solve this problem. However, there is still much room for the improvement of GRN inference. Integrating data from different sources is a promising strategy. Epigenetic modifications have a close relationship with gene regulation. Hence, epigenetic data such as histone modification profiles can provide useful information for uncovering regulatory interactions between genes. In this paper, we propose a method to integrate epigenetic data into the inference of GRNs. In particular, a dynamic Bayesian network (DBN) is employed to infer gene regulations from time-series gene expression data. Epigenetic data (histone modification profiles here) are integrated into the prior probability distribution of the Bayesian model. Our method has been validated on both synthetic and real datasets. Experimental results show that the integration of epigenetic data can significantly improve the performance of GRN inference. As more epigenetic datasets become available, our method would be useful for elucidating the gene regulatory mechanisms driving various cellular activities. The source code and testing datasets are available at https://github.com/Zheng-Lab/MetaGRN/tree/master/histonePrior.

Bayesian differential analysis of gene regulatory networks exploiting genetic perturbations

BACKGROUND

Gene regulatory networks (GRNs) can be inferred from both gene expression data and genetic perturbations. Under different conditions, the gene data of the same gene set may be different from each other, which results in different GRNs. Detecting structural difference between GRNs under different conditions is of great significance for understanding gene functions and biological mechanisms.

RESULTS

In this paper, we propose a Bayesian Fused algorithm to jointly infer differential structures of GRNs under two different conditions. The algorithm is developed for GRNs modeled with structural equation models (SEMs), which makes it possible to incorporate genetic perturbations into models to improve the inference accuracy, so we name it BFDSEM. Different from the naive approaches that separately infer pair-wise GRNs and identify the difference from the inferred GRNs, we first re-parameterize the two SEMs to form an integrated model that takes full advantage of the two groups of gene data, and then solve the re-parameterized model by developing a novel Bayesian fused prior following the criterion that separate GRNs and differential GRN are both sparse.

CONCLUSIONS

Computer simulations are run on synthetic data to compare BFDSEM to two state-of-the-art joint inference algorithms: FSSEM and ReDNet. The results demonstrate that the performance of BFDSEM is comparable to FSSEM, and is generally better than ReDNet. The BFDSEM algorithm is also applied to a real data set of lung cancer and adjacent normal tissues, the yielded normal GRN and differential GRN are consistent with the reported results in previous literatures. An open-source program implementing BFDSEM is freely available in Additional file 1.

Gene Regulatory Relationship Mining Using Improved Three-Phase Dependency Analysis Approach

How to mine the gene regulatory relationship and construct gene regulatory network (GRN) is of utmost interest within the whole biological community, however, which has been consistently a challenging problem since the tremendous complexity in cellular systems. In present work, we construct gene regulatory network using an improved three-phase dependency analysis algorithm (TPDA) Bayesian network learning method, which includes the steps of Drafting, Thickening, and Thinning. In order to solve the problem of learning result is not reliable due to the high order conditional independence test, we use the entropy estimation approach of Gaussian kernel probability density estimator to calculate the (conditional) mutual information between genes. The experiment on the public benchmark data sets show the improved method outperforms the other nine kinds of Bayesian network learning methods when to process the data with large sample size, with small number of discrete values, and the frequency of different discrete values is about same. In addition, the improved TPDA method was further applied on a real large gene expression data set on RNA-seq from a global collection with 368 elite maize inbred lines. Experiment results show it performs better than the original TPDA method and the other nine kinds of Bayesian network learning algorithms significantly.

Inference of differential gene regulatory networks based on gene expression and genetic perturbation data

MOTIVATION

Gene regulatory networks (GRNs) of the same organism can be different under different conditions, although the overall network structure may be similar. Understanding the difference in GRNs under different conditions is important to understand condition-specific gene regulation. When gene expression and other relevant data under two different conditions are available, they can be used by an existing network inference algorithm to estimate two GRNs separately, and then to identify the difference between the two GRNs. However, such an approach does not exploit the similarity in two GRNs, and may sacrifice inference accuracy.

RESULTS

In this paper, we model GRNs with the structural equation model (SEM) that can integrate gene expression and genetic perturbation data, and develop an algorithm named fused sparse SEM (FSSEM), to jointly infer GRNs under two conditions, and then to identify difference of the two GRNs. Computer simulations demonstrate that the FSSEM algorithm outperforms the approaches that estimate two GRNs separately. Analysis of a dataset of lung cancer and another dataset of gastric cancer with FSSEM inferred differential GRNs in cancer versus normal tissues, whose genes with largest network degrees have been reported to be implicated in tumorigenesis. The FSSEM algorithm provides a valuable tool for joint inference of two GRNs and identification of the differential GRN under two conditions.

AVAILABILITY AND IMPLEMENTATION

The R package fssemR implementing the FSSEM algorithm is available at https://github.com/Ivis4ml/fssemR.git. It is also available on CRAN.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Reverse engineering gene networks using global-local shrinkage rules

Inferring gene regulatory networks from high-throughput 'omics' data has proven to be a computationally demanding task of critical importance. Frequently, the classical methods break down owing to the curse of dimensionality, and popular strategies to overcome this are typically based on regularized versions of the classical methods. However, these approaches rely on loss functions that may not be robust and usually do not allow for the incorporation of prior information in a straightforward way. Fully Bayesian methods are equipped to handle both of these shortcomings quite naturally, and they offer the potential for improvements in network structure learning. We propose a Bayesian hierarchical model to reconstruct gene regulatory networks from time-series gene expression data, such as those common in perturbation experiments of biological systems. The proposed methodology uses global-local shrinkage priors for posterior selection of regulatory edges and relaxes the common normal likelihood assumption in order to allow for heavy-tailed data, which were shown in several of the cited references to severely impact network inference. We provide a sufficient condition for posterior propriety and derive an efficient Markov chain Monte Carlo via Gibbs sampling in the electronic supplementary material. We describe a novel way to detect multiple scales based on the corresponding posterior quantities. Finally, we demonstrate the performance of our approach in a simulation study and compare it with existing methods on real data from a T-cell activation study.

A Partial Correlation Screening Approach for Controlling the False Positive Rate in Sparse Gaussian Graphical Models

Gaussian Graphical Models (GGMs) are extensively used in many research areas, such as genomics, proteomics, neuroimaging, and psychology, to study the partial correlation structure of a set of variables. This structure is visualized by drawing an undirected network, in which the variables constitute the nodes and the partial correlations the edges. In many applications, it makes sense to impose sparsity (i.e., some of the partial correlations are forced to zero) as sparsity is theoretically meaningful and/or because it improves the predictive accuracy of the fitted model. However, as we will show by means of extensive simulations, state-of-the-art estimation approaches for imposing sparsity on GGMs, such as the Graphical lasso, ℓ1 regularized nodewise regression, and joint sparse regression, fall short because they often yield too many false positives (i.e., partial correlations that are not properly set to zero). In this paper we present a new estimation approach that allows to control the false positive rate better. Our approach consists of two steps: First, we estimate an undirected network using one of the three state-of-the-art estimation approaches. Second, we try to detect the false positives, by flagging the partial correlations that are smaller in absolute value than a given threshold, which is determined through cross-validation; the flagged correlations are set to zero. Applying this new approach to the same simulated data, shows that it indeed performs better. We also illustrate our approach by using it to estimate (1) a gene regulatory network for breast cancer data, (2) a symptom network of patients with a diagnosis within the nonaffective psychotic spectrum and (3) a symptom network of patients with PTSD.

A Multi-Laplacian Prior and Augmented Lagrangian Approach to the Exploratory Analysis of Time-Varying Gene and Transcriptional Regulatory Networks for Gene Microarray Data

This paper proposes a novel multi-Laplacian prior (MLP) and augmented Lagrangian method (ALM) approach for gene interactions and putative transcription factors (TFs) identification from time-course gene microarray data. It employs a non-linear time-varying auto-regressive (N-TVAR) model and the Maximum-A-Posteriori-Probability method for incorporating the multi-Laplacian prior and the continuity constraint. The MLP allows connections to/from a gene to be better preserved for putative TF identification in non-stationarity gene regulatory network as compared with conventional L₁-based penalties. Moreover, the ALM allows the resultant non-smooth L₁-based penalties to be decoupled from the remaining smooth terms, so that the former and latter can be efficiently solved using a low-complexity proximity operator and smooth optimization technique, respectively. Synthetic and real time-course gene microarray datasets are tested to evaluate the performance of the proposed method. Experimental results show that the proposed method gives better accuracy and higher computational speed than our previous work using smoothed approximation. Moreover, its performance, without the use of ChIP-chip data, is found to be highly comparable with other state-of-the-art methods integrating both ChIP-chip and gene microarray data. It suggests that the proposed method may serve as a useful exploratory tool for putative TF identification with reduced experimental cost.

An omnidirectional visualization model of personalized gene regulatory networks

Gene regulatory networks (GRNs) have been widely used as a fundamental tool to reveal the genomic mechanisms that underlie the individual's response to environmental and developmental cues. Standard approaches infer GRNs as holistic graphs of gene co-expression, but such graphs cannot quantify how gene-gene interactions vary among individuals and how they alter structurally across spatiotemporal gradients. Here, we develop a general framework for inferring informative, dynamic, omnidirectional, and personalized networks (idopNetworks) from routine transcriptional experiments. This framework is constructed by a system of quasi-dynamic ordinary differential equations (qdODEs) derived from the combination of ecological and evolutionary theories. We reconstruct idopNetworks using genomic data from a surgical experiment and illustrate how network structure is associated with surgical response to infrainguinal vein bypass grafting and the outcome of grafting. idopNetworks may shed light on genotype-phenotype relationships and provide valuable information for personalized medicine.

Comparative Network Reconstruction using mixed integer programming

Motivation

Signal-transduction networks are often aberrated in cancer cells, and new anti-cancer drugs that specifically target oncogenes involved in signaling show great clinical promise. However, the effectiveness of such targeted treatments is often hampered by innate or acquired resistance due to feedbacks, crosstalks or network adaptations in response to drug treatment. A quantitative understanding of these signaling networks and how they differ between cells with different oncogenic mutations or between sensitive and resistant cells can help in addressing this problem.

Results

Here, we present Comparative Network Reconstruction (CNR), a computational method to reconstruct signaling networks based on possibly incomplete perturbation data, and to identify which edges differ quantitatively between two or more signaling networks. Prior knowledge about network topology is not required but can straightforwardly be incorporated. We extensively tested our approach using simulated data and applied it to perturbation data from a BRAF mutant, PTPN11 KO cell line that developed resistance to BRAF inhibition. Comparing the reconstructed networks of sensitive and resistant cells suggests that the resistance mechanism involves re-establishing wild-type MAPK signaling, possibly through an alternative RAF-isoform.

Availability and implementation

CNR is available as a python module at https://github.com/NKI-CCB/cnr. Additionally, code to reproduce all figures is available at https://github.com/NKI-CCB/CNR-analyses.

Supplementary information

Supplementary data are available at Bioinformatics online.

Integration of Multiple Data Sources for Gene Network Inference Using Genetic Perturbation Data

The inference of gene networks from large-scale human genomic data is challenging due to the difficulty in identifying correct regulators for each gene in a high-dimensional search space. We present a Bayesian approach integrating external data sources with knockdown data from human cell lines to infer gene regulatory networks. In particular, we assemble multiple data sources, including gene expression data, genome-wide binding data, gene ontology, and known pathways, and use a supervised learning framework to compute prior probabilities of regulatory relationships. We show that our integrated method improves the accuracy of inferred gene networks as well as extends some previous Bayesian frameworks both in theory and applications. We apply our method to two different human cell lines, namely skin melanoma cell line A375 and lung cancer cell line A549, to illustrate the capabilities of our method. Our results show that the improvement in performance could vary from cell line to cell line and that we might need to choose different external data sources serving as prior knowledge if we hope to obtain better accuracy for different cell lines.

Network inference performance complexity: a consequence of topological, experimental and algorithmic determinants

MOTIVATION

Network inference algorithms aim to uncover key regulatory interactions governing cellular decision-making, disease progression and therapeutic interventions. Having an accurate blueprint of this regulation is essential for understanding and controlling cell behavior. However, the utility and impact of these approaches are limited because the ways in which various factors shape inference outcomes remain largely unknown.

RESULTS

We identify and systematically evaluate determinants of performance-including network properties, experimental design choices and data processing-by developing new metrics that quantify confidence across algorithms in comparable terms. We conducted a multifactorial analysis that demonstrates how stimulus target, regulatory kinetics, induction and resolution dynamics, and noise differentially impact widely used algorithms in significant and previously unrecognized ways. The results show how even if high-quality data are paired with high-performing algorithms, inferred models are sometimes susceptible to giving misleading conclusions. Lastly, we validate these findings and the utility of the confidence metrics using realistic in silico gene regulatory networks. This new characterization approach provides a way to more rigorously interpret how algorithms infer regulation from biological datasets.

AVAILABILITY AND IMPLEMENTATION

Code is available at http://github.com/bagherilab/networkinference/.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Differential network enrichment analysis reveals novel lipid pathways in chronic kidney disease

MOTIVATION

Functional enrichment testing methods can reduce data comprising hundreds of altered biomolecules to smaller sets of altered biological 'concepts' that help generate testable hypotheses. This study leveraged differential network enrichment analysis methodology to identify and validate lipid subnetworks that potentially differentiate chronic kidney disease (CKD) by severity or progression.

RESULTS

We built a partial correlation interaction network, identified highly connected network components, applied network-based gene-set analysis to identify differentially enriched subnetworks, and compared the subnetworks in patients with early-stage versus late-stage CKD. We identified two subnetworks 'triacylglycerols' and 'cardiolipins-phosphatidylethanolamines (CL-PE)' characterized by lower connectivity, and a higher abundance of longer polyunsaturated triacylglycerols in patients with severe CKD (stage ≥4) from the Clinical Phenotyping Resource and Biobank Core. These finding were replicated in an independent cohort, the Chronic Renal Insufficiency Cohort. Using an innovative method for elucidating biological alterations in lipid networks, we demonstrated alterations in triacylglycerols and cardiolipins-phosphatidylethanolamines that precede the clinical outcome of end-stage kidney disease by several years.

AVAILABILITY AND IMPLEMENTATION

A complete list of NetGSA results in HTML format can be found at http://metscape.ncibi.org/netgsa/12345-022118/cric_cprobe/022118/results_cric_cprobe/main.html. The DNEA is freely available at https://github.com/wiggie/DNEA. Java wrapper leveraging the cytoscape.js framework is available at http://js.cytoscape.org.

SUPPLEMENTARY INFORMATION

Supplementary data are available at Bioinformatics online.

Discovering the topology of complex networks via adaptive estimators

Behind any complex system in nature or engineering, there is an intricate network of interconnections that is often unknown. Using a control-theoretical approach, we study the problem of network reconstruction (NR): inferring both the network structure and the coupling weights based on measurements of each node's activity. We derive two new methods for NR, a low-complexity reduced-order estimator (which projects each node's dynamics to a one-dimensional space) and a full-order estimator for cases where a reduced-order estimator is not applicable. We prove their convergence to the correct network structure using Lyapunov-like theorems and persistency of excitation. Importantly, these estimators apply to systems with partial state measurements, a broad class of node dynamics and internode coupling functions, and in the case of the reduced-order estimator, node dynamics and internode coupling functions that are not fully known. The effectiveness of the estimators is illustrated using both numerical and experimental results on networks of chaotic oscillators.

Network perturbation analysis of gene transcriptional profiles reveals protein targets and mechanism of action of drugs and influenza A viral infection

Genome-wide transcriptional profiling provides a global view of cellular state and how this state changes under different treatments (e.g. drugs) or conditions (e.g. healthy and diseased). Here, we present ProTINA (Protein Target Inference by Network Analysis), a network perturbation analysis method for inferring protein targets of compounds from gene transcriptional profiles. ProTINA uses a dynamic model of the cell-type specific protein-gene transcriptional regulation to infer network perturbations from steady state and time-series differential gene expression profiles. A candidate protein target is scored based on the gene network's dysregulation, including enhancement and attenuation of transcriptional regulatory activity of the protein on its downstream genes, caused by drug treatments. For benchmark datasets from three drug treatment studies, ProTINA was able to provide highly accurate protein target predictions and to reveal the mechanism of action of compounds with high sensitivity and specificity. Further, an application of ProTINA to gene expression profiles of influenza A viral infection led to new insights of the early events in the infection.

Efficient proximal gradient algorithm for inference of differential gene networks

Background

Gene networks in living cells can change depending on various conditions such as caused by different environments, tissue types, disease states, and development stages. Identifying the differential changes in gene networks is very important to understand molecular basis of various biological process. While existing algorithms can be used to infer two gene networks separately from gene expression data under two different conditions, and then to identify network changes, such an approach does not exploit the similarity between two gene networks, and it is thus suboptimal. A desirable approach would be clearly to infer two gene networks jointly, which can yield improved estimates of network changes.

Results

In this paper, we developed a proximal gradient algorithm for differential network (ProGAdNet) inference, that jointly infers two gene networks under different conditions and then identifies changes in the network structure. Computer simulations demonstrated that our ProGAdNet outperformed existing algorithms in terms of inference accuracy, and was much faster than a similar approach for joint inference of gene networks. Gene expression data of breast tumors and normal tissues in the TCGA database were analyzed with our ProGAdNet, and revealed that 268 genes were involved in the changed network edges. Gene set enrichment analysis identified a significant number of gene sets related to breast cancer or other types of cancer that are enriched in this set of 268 genes. Network analysis of the kidney cancer data in the TCGA database with ProGAdNet also identified a set of genes involved in network changes, and the majority of the top genes identified have been reported in the literature to be implicated in kidney cancer. These results corroborated that the gene sets identified by ProGAdNet were very informative about the cancer disease status. A software package implementing the ProGAdNet, computer simulations, and real data analysis is available as Additional file 1.

Conclusion

With its superior performance over existing algorithms, ProGAdNet provides a valuable tool for finding changes in gene networks, which may aid the discovery of gene-gene interactions changed under different conditions.

Electronic supplementary material

The online version of this article (10.1186/s12859-019-2749-x) contains supplementary material, which is available to authorized users.

Detecting Hidden Units and Network Size from Perceptible Dynamics

The number of units of a network dynamical system, its size, arguably constitutes its most fundamental property. Many units of a network, however, are typically experimentally inaccessible such that the network size is often unknown. Here we introduce a detection matrix that suitably arranges multiple transient time series from the subset of accessible units to detect network size via matching rank constraints. The proposed method is model-free, applicable across system types and interaction topologies, and applies to nonstationary dynamics near fixed points, as well as periodic and chaotic collective motion. Even if only a small minority of units is perceptible and for systems simultaneously exhibiting nonlinearities, heterogeneities, and noise, exact size detection is feasible. We illustrate applicability for a paradigmatic class of biochemical reaction networks.

Modelling and Control of Gene Regulatory Networks for Perturbation Mitigation

Synthetic Biologists are increasingly interested in the idea of using synthetic feedback control circuits for the mitigation of perturbations to gene regulatory networks that may arise due to disease and/or environmental disturbances. Models employing Michaelis-Menten kinetics with Hill-type nonlinearities are typically used to represent the dynamics of gene regulatory networks. Here, we identify some fundamental problems with such models from the point of view of control system design, and argue that an alternative formalism, based on so-called S-System models, is more suitable. Using tools from system identification, we show how to build S-System models that capture the key dynamics of an example gene regulatory network, and design a genetic feedback controller with the objective of rejecting an external perturbation. Using a sine sweeping method, we show how the S-System model can be approximated by a linear transfer function and, based on this transfer function, we design our controller. Simulation results using the full nonlinear S-System model of the network show that the synthetic control circuit is able to mitigate the effect of external perturbations. Our study is the first to highlight the usefulness of the S-System modelling formalism for the design of synthetic control circuits for gene regulatory networks.

Restricted-derestricted dynamic Bayesian Network inference of transcriptional regulatory relationships among genes in cancer

Understanding transcriptional regulatory relationships among genes is important for gaining etiological insights into diseases such as cancer. To this end, high-throughput biological data have been generated through advancements in a variety of technologies. These rely on computational approaches to discover underlying structures in such data. Among these computational approaches, Bayesian networks (BNs) stand out because their probabilistic nature enables them to manage randomness in the dynamics of gene regulation and experimental data. Feedback loops inherent in networks of regulatory relationships are more tractable when enhancements to BNs are applied to them. Here, we propose Restricted-Derestricted dynamic BNs with a novel search technique, Restricted-Derestricted Greedy Method, for such tasks. This approach relies on the Restricted-Derestricted Greedy search technique to infer transcriptional regulatory networks in two phases: restricted inference and derestricted inference. An application of this approach to real data sets reveals it performs favourably well compared to other existing well performing dynamic BN approaches in terms of recovering true relationships among genes. In addition, it provides a balance between searching for optimal networks and keeping biologically relevant regulatory interactions among variables.

Exploring candidate biomarkers for lung and prostate cancers using gene expression and flux variability analysis

Genome-scale metabolic models have provided valuable resources for exploring changes in metabolism under normal and cancer conditions. However, metabolism itself is strongly linked to gene expression, so integration of gene expression data into metabolic models might improve the detection of genes involved in the control of tumor progression. Herein, we considered gene expression data as extra constraints to enhance the predictive powers of metabolic models. We reconstructed genome-scale metabolic models for lung and prostate, under normal and cancer conditions to detect the major genes associated with critical subsystems during tumor development. Furthermore, we utilized gene expression data in combination with an information theory-based approach to reconstruct co-expression networks of the human lung and prostate in both cohorts. Our results revealed 19 genes as candidate biomarkers for lung and prostate cancer cells. This study also revealed that the development of a complementary approach (integration of gene expression and metabolic profiles) could lead to proposing novel biomarkers and suggesting renovated cancer treatment strategies which have not been possible to detect using either of the methods alone.

Genome-wide dynamic network analysis reveals a critical transition state of flower development in Arabidopsis

BACKGROUND

The flowering transition which is controlled by a complex and intricate gene regulatory network plays an important role in the reproduction for offspring of plants. It is a challenge to identify the critical transition state as well as the genes that control the transition of flower development. With the emergence of massively parallel sequencing, a great number of time-course transcriptome data greatly facilitate the exploration of the developmental phase transition in plants. Although some network-based bioinformatics analyses attempted to identify the genes that control the phase transition, they generally overlooked the dynamics of regulation and resulted in unreliable results. In addition, the results of these methods cannot be self-explained.

RESULTS

In this work, to reveal a critical transition state and identify the transition-specific genes of flower development, we implemented a genome-wide dynamic network analysis on temporal gene expression data in Arabidopsis by dynamic network biomarker (DNB) method. In the analysis, DNB model which can exploit collective fluctuations and correlations of different metabolites at a network level was used to detect the imminent critical transition state or the tipping point. The genes that control the phase transition can be identified by the difference of weighted correlations between the genes interested and the other genes in the global network. To construct the gene regulatory network controlling the flowering transition, we applied NARROMI algorithm which can reduce the noisy, redundant and indirect regulations on the expression data of the transition-specific genes. In the results, the critical transition state detected during the formation of flowers corresponded to the development of flowering on the 7th to 9th day in Arabidopsis. Among of 233 genes identified to be highly fluctuated at the transition state, a high percentage of genes with maximum expression in pollen was detected, and 24 genes were validated to participate in stress reaction process, as well as other floral-related pathways. Composed of three major subnetworks, a gene regulatory network with 150 nodes and 225 edges was found to be highly correlated with flowering transition. The gene ontology (GO) annotation of pathway enrichment analysis revealed that the identified genes are enriched in the catalytic activity, metabolic process and cellular process.

CONCLUSIONS

This study provides a novel insight to identify the real causality of the phase transition with genome-wide dynamic network analysis.

Programming Bacteria With Light-Sensors and Applications in Synthetic Biology

Photo-receptors are widely present in both prokaryotic and eukaryotic cells, which serves as the foundation of tuning cell behaviors with light. While practices in eukaryotic cells have been relatively established, trials in bacterial cells have only been emerging in the past few years. A number of light sensors have been engineered in bacteria cells and most of them fall into the categories of two-component and one-component systems. Such a sensor toolbox has enabled practices in controlling synthetic circuits at the level of transcription and protein activity which is a major topic in synthetic biology, according to the central dogma. Additionally, engineered light sensors and practices of tuning synthetic circuits have served as a foundation for achieving light based real-time feedback control. Here, we review programming bacteria cells with light, introducing engineered light sensors in bacteria and their applications, including tuning synthetic circuits and achieving feedback controls over microbial cell culture.

Parallel Algorithms for Inferring Gene Regulatory Networks: A Review

System biology problems such as whole-genome network construction from large-scale gene expression data are sophisticated and time-consuming. Therefore, using sequential algorithms are not feasible to obtain a solution in an acceptable amount of time. Today, by using massively parallel computing, it is possible to infer large-scale gene regulatory networks. Recently, establishing gene regulatory networks from large-scale datasets have drawn the noticeable attention of researchers in the field of parallel computing and system biology. In this paper, we attempt to provide a more detailed overview of the recent parallel algorithms for constructing gene regulatory networks. Firstly, fundamentals of gene regulatory networks inference and large-scale datasets challenges are given. Secondly, a detailed description of the four parallel frameworks and libraries including CUDA, OpenMP, MPI, and Hadoop is discussed. Thirdly, parallel algorithms are reviewed. Finally, some conclusions and guidelines for parallel reverse engineering are described.

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.

Inferring power-grid topology in the face of uncertainties

We develop methods to efficiently reconstruct the topology and line parameters of a power grid from the measurement of nodal variables. We propose two compressed sensing algorithms that minimize the amount of necessary measurement resources by exploiting network sparsity, symmetry of connections, and potential prior knowledge about the connectivity. The algorithms are reciprocal to established state estimation methods, where nodal variables are estimated from few measurements given the network structure. Hence, they enable an advanced grid monitoring where both state and structure of a grid are subject to uncertainties or missing information.

Inferring Network Connectivity from Event Timing Patterns

Reconstructing network connectivity from the collective dynamics of a system typically requires access to its complete continuous-time evolution, although these are often experimentally inaccessible. Here we propose a theory for revealing physical connectivity of networked systems only from the event time series their intrinsic collective dynamics generate. Representing the patterns of event timings in an event space spanned by interevent and cross-event intervals, we reveal which other units directly influence the interevent times of any given unit. For illustration, we linearize an event-space mapping constructed from the spiking patterns in model neural circuits to reveal the presence or absence of synapses between any pair of neurons, as well as whether the coupling acts in an inhibiting or activating (excitatory) manner. The proposed model-independent reconstruction theory is scalable to larger networks and may thus play an important role in the reconstruction of networks from biology to social science and engineering.

Statistical inference approach to structural reconstruction of complex networks from binary time series

Complex networks hosting binary-state dynamics arise in a variety of contexts. In spite of previous works, to fully reconstruct the network structure from observed binary data remains challenging. We articulate a statistical inference based approach to this problem. In particular, exploiting the expectation-maximization (EM) algorithm, we develop a method to ascertain the neighbors of any node in the network based solely on binary data, thereby recovering the full topology of the network. A key ingredient of our method is the maximum-likelihood estimation of the probabilities associated with actual or nonexistent links, and we show that the EM algorithm can distinguish the two kinds of probability values without any ambiguity, insofar as the length of the available binary time series is reasonably long. Our method does not require any a priori knowledge of the detailed dynamical processes, is parameter-free, and is capable of accurate reconstruction even in the presence of noise. We demonstrate the method using combinations of distinct types of binary dynamical processes and network topologies, and provide a physical understanding of the underlying reconstruction mechanism. Our statistical inference based reconstruction method contributes an additional piece to the rapidly expanding "toolbox" of data based reverse engineering of complex networked systems.

Gene Regulatory Networks Reconstruction Using the Flooding-Pruning Hill-Climbing Algorithm

The explosion of genomic data provides new opportunities to improve the task of gene regulatory network reconstruction. Because of its inherent probability character, the Bayesian network is one of the most promising methods. However, excessive computation time and the requirements of a large number of biological samples reduce its effectiveness and application to gene regulatory network reconstruction. In this paper, Flooding-Pruning Hill-Climbing algorithm (FPHC) is proposed as a novel hybrid method based on Bayesian networks for gene regulatory networks reconstruction. On the basis of our previous work, we propose the concept of DPI Level based on data processing inequality (DPI) to better identify neighbors of each gene on the lack of enough biological samples. Then, we use the search-and-score approach to learn the final network structure in the restricted search space. We first analyze and validate the effectiveness of FPHC in theory. Then, extensive comparison experiments are carried out on known Bayesian networks and biological networks from the DREAM (Dialogue on Reverse Engineering Assessment and Methods) challenge. The results show that the FPHC algorithm, under recommended parameters, outperforms, on average, the original hill climbing and Max-Min Hill-Climbing (MMHC) methods with respect to the network structure and running time. In addition, our results show that FPHC is more suitable for gene regulatory network reconstruction with limited data.

Gene Regulatory Network Inference from Perturbed Time-Series Expression Data via Ordered Dynamical Expansion of Non-Steady State Actors

The reconstruction of gene regulatory networks from gene expression data has been the subject of intense research activity. A variety of models and methods have been developed to address different aspects of this important problem. However, these techniques are narrowly focused on particular biological and experimental platforms, and require experimental data that are typically unavailable and difficult to ascertain. The more recent availability of higher-throughput sequencing platforms, combined with more precise modes of genetic perturbation, presents an opportunity to formulate more robust and comprehensive approaches to gene network inference. Here, we propose a step-wise framework for identifying gene-gene regulatory interactions that expand from a known point of genetic or chemical perturbation using time series gene expression data. This novel approach sequentially identifies non-steady state genes post-perturbation and incorporates them into a growing series of low-complexity optimization problems. The governing ordinary differential equations of this model are rooted in the biophysics of stochastic molecular events that underlie gene regulation, delineating roles for both protein and RNA-mediated gene regulation. We show the successful application of our core algorithms for network inference using simulated and real datasets.

A Framework for Engineering Stress Resilient Plants Using Genetic Feedback Control and Regulatory Network Rewiring

Crop disease leads to significant waste worldwide, both pre- and postharvest, with subsequent economic and sustainability consequences. Disease outcome is determined both by the plants' response to the pathogen and by the ability of the pathogen to suppress defense responses and manipulate the plant to enhance colonization. The defense response of a plant is characterized by significant transcriptional reprogramming mediated by underlying gene regulatory networks, and components of these networks are often targeted by attacking pathogens. Here, using gene expression data from Botrytis cinerea-infected Arabidopsis plants, we develop a systematic approach for mitigating the effects of pathogen-induced network perturbations, using the tools of synthetic biology. We employ network inference and system identification techniques to build an accurate model of an Arabidopsis defense subnetwork that contains key genes determining susceptibility of the plant to the pathogen attack. Once validated against time-series data, we use this model to design and test perturbation mitigation strategies based on the use of genetic feedback control. We show how a synthetic feedback controller can be designed to attenuate the effect of external perturbations on the transcription factor CHE in our subnetwork. We investigate and compare two approaches for implementing such a controller biologically-direct implementation of the genetic feedback controller, and rewiring the regulatory regions of multiple genes-to achieve the network motif required to implement the controller. Our results highlight the potential of combining feedback control theory with synthetic biology for engineering plants with enhanced resilience to environmental stress.

Automated transition analysis of activated gene regulation during diauxic nutrient shift in Escherichia coli and adipocyte differentiation in mouse cells

Background

Comprehensively understanding the dynamics of biological systems is among the biggest current challenges in biology and medicine. To acquire this understanding, researchers have measured the time-series expression profiles of cell lines of various organisms. Biological technologies have also drastically improved, providing a huge amount of information with support from bioinformatics and systems biology. However, the transitions between the activation and inactivation of gene regulations, at the temporal resolution of single time points, are difficult to extract from time-course gene expression profiles.

Results

Our proposed method reports the activation period of each gene regulation from gene expression profiles and a gene regulatory network. The correctness and effectiveness of the method were validated by analyzing the diauxic shift from glucose to lactose in Escherichia coli. The method completely detected the three periods of the shift; 1) consumption of glucose as nutrient source, 2) the period of seeking another nutrient source and 3) consumption of lactose as nutrient source. We then applied the method to mouse adipocyte differentiation data. Cell differentiation into adipocytes is known to involve two waves of the gene regulation cascade, and sub-waves are predicted. From the gene expression profiles of the cell differentiation process from ES to adipose cells (62 time points), our method acquired four periods; three periods covering the two known waves of the cascade, and a final period of gene regulations when the differentiation to adipocytes was completed.

Conclusions

Our proposed method identifies the transitions of gene regulations from time-series gene expression profiles. Dynamic analyses are essential for deep understanding of biological systems and for identifying the causes of the onset of diseases such as diabetes and osteoporosis. The proposed method can greatly contribute to the progress of biology and medicine.

A Microfluidic Platform for Longitudinal Imaging in Caenorhabditis elegans

In the last decade, microfluidic techniques have been applied to study small animals, including the nematode Caenorhabditis elegans, and have proved useful as a convenient live imaging platform providing capabilities for precise control of experimental conditions in real time. In this article, we demonstrate live imaging of individual worms employing WormSpa, a previously-published custom microfluidic device. In the device, multiple worms are individually confined to separate chambers, allowing multiplexed longitudinal surveillance of various biological processes. To illustrate the capability, we performed proof-of-principle experiments in which worms were infected in the device with pathogenic bacteria, and the dynamics of expression of immune response genes and egg laying were monitored continuously in individual animals. The simple design and operation of this device make it suitable for users with no previous experience with microfluidic-based experiments. We propose that this approach will be useful for many researchers interested in longitudinal observations of biological processes under well-defined conditions.

Dynamics in Epistasis Analysis

Finding regulatory relationships between genes, including the direction and nature of influence between them, is a fundamental challenge in the field of molecular genetics. One classical approach to this problem is epistasis analysis. Broadly speaking, epistasis analysis infers the regulatory relationships between a pair of genes in a genetic pathway by considering the patterns of change in an observable trait resulting from single and double deletion of genes. While classical epistasis analysis has yielded deep insights on numerous genetic pathways, it is not without limitations. Here, we explore the possibility of dynamic epistasis analysis, in which, in addition to performing genetic perturbations of a pathway, we drive the pathway by a time-varying upstream signal. We explore the theoretical power of dynamical epistasis analysis by conducting an identifiability analysis of Boolean models of genetic pathways, comparing static and dynamic approaches. We find that even relatively simple input dynamics greatly increases the power of epistasis analysis to discriminate alternative network structures. Further, we explore the question of experiment design, and show that a subset of short time-varying signals, which we call dynamic primitives, allow maximum discriminative power with a reduced number of experiments.

Semi-supervised network inference using simulated gene expression dynamics

Motivation

Inferring the structure of gene regulatory networks from high-throughput datasets remains an important and unsolved problem. Current methods are hampered by problems such as noise, low sample size, and incomplete characterizations of regulatory dynamics, leading to networks with missing and anomalous links. Integration of prior network information (e.g. from pathway databases) has the potential to improve reconstructions.

Results

We developed a semi-supervised network reconstruction algorithm that enables the synthesis of information from partially known networks with time course gene expression data. We adapted partial least square-variable importance in projection (VIP) for time course data and used reference networks to simulate expression data from which null distributions of VIP scores are generated and used to estimate edge probabilities for input expression data. By using simulated dynamics to generate reference distributions, this approach incorporates previously known regulatory relationships and links the network to the dynamics to form a semi-supervised approach that discovers novel and anomalous connections. We applied this approach to data from a sleep deprivation study with KEGG pathways treated as prior networks, as well as to synthetic data from several DREAM challenges, and find that it is able to recover many of the true edges and identify errors in these networks, suggesting its ability to derive posterior networks that accurately reflect gene expression dynamics.

Availability and implementation

R code is available at https://github.com/pn51/postPLSR.

Contact

rbraun@northwestern.edu.

Supplementary information

Supplementary data are available at Bioinformatics online.

SCODE: an efficient regulatory network inference algorithm from single-cell RNA-Seq during differentiation

Motivation

The analysis of RNA-Seq data from individual differentiating cells enables us to reconstruct the differentiation process and the degree of differentiation (in pseudo-time) of each cell. Such analyses can reveal detailed expression dynamics and functional relationships for differentiation. To further elucidate differentiation processes, more insight into gene regulatory networks is required. The pseudo-time can be regarded as time information and, therefore, single-cell RNA-Seq data are time-course data with high time resolution. Although time-course data are useful for inferring networks, conventional inference algorithms for such data suffer from high time complexity when the number of samples and genes is large. Therefore, a novel algorithm is necessary to infer networks from single-cell RNA-Seq during differentiation.

Results

In this study, we developed the novel and efficient algorithm SCODE to infer regulatory networks, based on ordinary differential equations. We applied SCODE to three single-cell RNA-Seq datasets and confirmed that SCODE can reconstruct observed expression dynamics. We evaluated SCODE by comparing its inferred networks with use of a DNaseI-footprint based network. The performance of SCODE was best for two of the datasets and nearly best for the remaining dataset. We also compared the runtimes and showed that the runtimes for SCODE are significantly shorter than for alternatives. Thus, our algorithm provides a promising approach for further single-cell differentiation analyses.

Availability and Implementation

The R source code of SCODE is available at https://github.com/hmatsu1226/SCODE

Supplementary information

Supplementary data are available at Bioinformatics online.

Integrated network analysis reveals the importance of microbial interactions for maize growth

Microbes play a critical role in soil global biogeochemical circulation and microbe-microbe interactions have also evoked enormous interests in recent years. Utilization of green manures can stimulate microbial activity and affect microbial composition and diversity. However, few studies focus on the microbial interactions or detect the key functional members in communities. With the advances of metagenomic technologies, network analysis has been used as a powerful tool to detect robust interactions between microbial members. Here, random matrix theory-based network analysis was used to investigate the microbial networks in response to four different green manure fertilization regimes (Vicia villosa, common vetch, milk vetch, and radish) over two growth cycles from October 2012 to September 2014. The results showed that the topological properties of microbial networks were dramatically altered by green manure fertilization. Microbial network under milk vetch amendment showed substantially more intense complexity and interactions than other fertilization systems, indicating that milk vetch provided a favorable condition for microbial interactions and niche sharing. The shift of microbial interactions could be attributed to the changes in some major soil traits and the interactions might be correlated to plant growth and production. With the stimuli of green manures, positive interactions predominated the network eventually and the network complexity was in consistency with maize productivity, which suggested that the complex soil microbial networks might benefit to plants rather than simple ones, because complex networks would hold strong the ability to cope with environment changes or suppress soil-borne pathogen infection on plants. In addition, network analyses discerned some putative keystone taxa and seven of them had directly positive interactions with maize yield, which suggested their important roles in maintaining environmental functions and in improving plant growth.

Cell signaling heterogeneity is modulated by both cell-intrinsic and -extrinsic mechanisms: An integrated approach to understanding targeted therapy

During the last decade, our understanding of cancer cell signaling networks has significantly improved, leading to the development of various targeted therapies that have elicited profound but, unfortunately, short-lived responses. This is, in part, due to the fact that these targeted therapies ignore context and average out heterogeneity. Here, we present a mathematical framework that addresses the impact of signaling heterogeneity on targeted therapy outcomes. We employ a simplified oncogenic rat sarcoma (RAS)-driven mitogen-activated protein kinase (MAPK) and phosphoinositide 3-kinase-protein kinase B (PI3K-AKT) signaling pathway in lung cancer as an experimental model system and develop a network model of the pathway. We measure how inhibition of the pathway modulates protein phosphorylation as well as cell viability under different microenvironmental conditions. Training the model on this data using Monte Carlo simulation results in a suite of in silico cells whose relative protein activities and cell viability match experimental observation. The calibrated model predicts distributional responses to kinase inhibitors and suggests drug resistance mechanisms that can be exploited in drug combination strategies. The suggested combination strategies are validated using in vitro experimental data. The validated in silico cells are further interrogated through an unsupervised clustering analysis and then integrated into a mathematical model of tumor growth in a homogeneous and resource-limited microenvironment. We assess posttreatment heterogeneity and predict vast differences across treatments with similar efficacy, further emphasizing that heterogeneity should modulate treatment strategies. The signaling model is also integrated into a hybrid cellular automata (HCA) model of tumor growth in a spatially heterogeneous microenvironment. As a proof of concept, we simulate tumor responses to targeted therapies in a spatially segregated tissue structure containing tumor and stroma (derived from patient tissue) and predict complex cell signaling responses that suggest a novel combination treatment strategy.

A signaling pathway is a network of molecules in a cell that is typically initiated by stimuli (e.g., microenvironmental cues) acting on receptors and internal signaling molecules to determine cell fate. Signaling pathways in cancer cells are different from those in normal cells, and this difference helps cancer cells to grow and thrive indefinitely. Drugs that target the aberrant signaling pathways in cancer cells (often referred to as targeted therapy) are promising for improving treatment outcomes of many different cancers in patients. However, most patients eventually develop resistance to these drugs. Resistance may already be present in the tumor or may emerge via mutation or via microenvironmental mediation. Tumor heterogeneity, which is characterized by subtle or dramatic differences among tumor cells, plays a key role in the development of drug resistance. Some tumor cells respond well to therapy, while others may adapt to the stress induced by the drug within the microenvironment. Moreover, removal of drug-sensitive cells may result in the competitive release of drug-resistant cells. Here, we present mathematical models to assess the impact of heterogeneity in signaling pathways within tumor cells on the outcomes of targeted therapy. We consider a simplified version of two well-known signaling pathways that modulate the growth of lung cancer cells. By using different targeted therapies, we quantify the effect of pathway inhibition on protein activity and cell viability and developed a mathematical model of the network, which is trained to reproduce these data and to develop a panel of heterogeneous in silico cells. The model predicts potential mechanisms of drug resistance and proposes combination therapies that are effective across the panel. We validate these combination therapies experimentally using the lung cancer cells and integrated the in silico cells into a computational lung tissue model that explicitly captures the microenvironment of lung cancer. Our results suggest that heterogeneity in both the tumor and microenvironment impacts treatment response in different ways and suggest a novel combination therapy for a better response.

Sparse dynamical Boltzmann machine for reconstructing complex networks with binary dynamics

Revealing the structure and dynamics of complex networked systems from observed data is a problem of current interest. Is it possible to develop a completely data-driven framework to decipher the network structure and different types of dynamical processes on complex networks? We develop a model named sparse dynamical Boltzmann machine (SDBM) as a structural estimator for complex networks that host binary dynamical processes. The SDBM attains its topology according to that of the original system and is capable of simulating the original binary dynamical process. We develop a fully automated method based on compressive sensing and a clustering algorithm to construct the SDBM. We demonstrate, for a variety of representative dynamical processes on model and real world complex networks, that the equivalent SDBM can recover the network structure of the original system and simulates its dynamical behavior with high precision.