One of the critical steps to characterize metabolic alterations in multifactorial diseases, as well as their heterogeneity across different patients, is the identification of reactions that exhibit significantly different usage (or flux) between cohorts. However, since metabolic fluxes cannot be determined directly, researchers typically use constraint-based metabolic network models, customized on post-genomics datasets. The use of random sampling within the feasible region of metabolic networks is becoming more prevalent for comparing these networks. While many algorithms have been proposed and compared for efficiently and uniformly sampling the feasible region of metabolic networks, their impact on the risk of making false discoveries when comparing different samples has not been investigated yet, and no sampling strategy has been so far specifically designed to mitigate the problem. To be able to precisely assess the False Discovery Rate (FDR), in this work we compared different samples obtained from the very same metabolic model. We compared the FDR obtained for different model scales, sample sizes, parameters of the sampling algorithm, and strategies to filter out non-significant variations. To be able to compare the largely used hit-and-run strategy with the much less investigated corner-based strategy, we first assessed the intrinsic capability of current corner-based algorithms and of a newly proposed one to visit all vertices of a constraint-based region. We show that false discoveries can occur at high rates even for large samples of small-scale networks. However, we demonstrate that a statistical test based on the empirical null distribution of Kullback-Leibler divergence can effectively correct for false discoveries. We also show that our proposed corner-based algorithm is more efficient than state-of-the-art alternatives and much less prone to false discoveries than hit-and-run strategies. We report that the differences in the marginal distributions obtained with the two strategies are related to but not fully explained by differences in sample standard deviation, as previously thought. Overall, our study provides insights into the impact of sampling strategies on FDR in metabolic network analysis and offers new guidelines for more robust and reproducible analyses.

Characterizing the heterogeneity of cancer metabolism requires the knowledge of metabolic fluxes in different tumor types. These fluxes cannot be directly determined, especially at a sub-cellular level. Still, they can be obtained numerically through constraint-based steady-state models after integrating other high-throughput -omics data, such as transcriptomics. In this work, we proposed to study cancer metabolism through data analysis and machine learning methodologies. To this aim, we considered transcriptomics profiles for a large set of cancer cells. Using a core metabolic network as a scaffold, we generated many feasible flux distributions for each cancer cell. Then, we used cluster analysis to analyze these data. This preliminary analysis revealed three well-separated clusters having different metabolic behaviors.

BACKGROUND: Longitudinal single-cell sequencing experiments of patient-derived models are increasingly employed to investigate cancer evolution. In this context, robust computational methods are needed to properly exploit the mutational profiles of single cells generated via variant calling, in order to reconstruct the evolutionary history of a tumor and characterize the impact of therapeutic strategies, such as the administration of drugs. To this end, we have recently developed the LACE framework for the Longitudinal Analysis of Cancer Evolution. RESULTS: The LACE 2.0 release aimed at inferring longitudinal clonal trees enhances the original framework with new key functionalities: an improved data management for preprocessing of standard variant calling data, a reworked inference engine, and direct connection to public databases. CONCLUSIONS: All of this is accessible through a new and interactive Shiny R graphical interface offering the possibility to apply filters helpful in discriminating relevant or potential driver mutations, set up inferential parameters, and visualize the results. The software is available at: github.com/BIMIB-DISCo/LACE.

A key challenge in computer vision and deep learning is the definition of robust strategies for the detection of adversarial examples. In this work, we propose the adoption of ensemble approaches to leverage the effectiveness of multiple detectors in exploiting distinct properties of the input data. To this end, the ENsemble Adversarial Detector (ENAD) framework integrates scoring functions from state-of-the-art detectors based on Mahalanobis distance, Local Intrinsic Dimensionality, and One-Class Support Vector Machines, which process the hidden features of deep neural networks. ENAD is designed to ensure high standardization and reproducibility to the computational workflow. Extensive tests on benchmark datasets, models and adversarial attacks show that ENAD outperforms all competing methods in the large majority of settings. The improvement over the state-of-the-art and the intrinsic generality of the framework, which allows one to easily extend ENAD to include any set of detectors and integration strategies, set the foundations for the new area of ensemble adversarial detection.

MOTIVATION: Driver (epi)genomic alterations underlie the positive selection of cancer subpopulations, which promotes drug resistance and relapse. Even though substantial heterogeneity is witnessed in most cancer types, mutation accumulation patterns can be regularly found and can be exploited to reconstruct predictive models of cancer evolution. Yet, available methods can not infer logical formulas connecting events to represent alternative evolutionary routes or convergent evolution. RESULTS: We introduce PMCE, an expressive framework that leverages mutational profiles from cross-sectional sequencing data to infer probabilistic graphical models of cancer evolution including arbitrary logical formulas, and which outperforms the state-of-the-art in terms of accuracy and robustness to noise, on simulations. The application of PMCE to 7866 samples from the TCGA database allows us to identify a highly significant correlation between the predicted evolutionary paths and the overall survival in 7 tumor types, proving that our approach can effectively stratify cancer patients in reliable risk groups. AVAILABILITY AND IMPLEMENTATION: PMCE is freely available at https://github.com/BIMIB-DISCo/PMCE, in addition to the code to replicate all the analyses presented in the manuscript. SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

BACKGROUND: Sophisticated methods to properly pre-process and analyze the increasing collection of single-cell RNA sequencing (scRNA-seq) data are increasingly being developed. On the contrary, the best practices to integrate these data into metabolic networks, aiming at describing metabolic phenotypes within a heterogeneous cell population, have been poorly investigated. In this regard, a critical factor is the presence of false zero values in reactions essential for a fundamental metabolic function, such as biomass or energy production. Here, we investigate the role of denoising strategies in mitigating this problem. METHODS: We applied state-of-the-art denoising strategies - namely MAGIC, ENHANCE, and SAVER - on three public scRNA-seq datasets. We then associated a metabolic flux distribution with every single cell by embedding its noise-free transcriptomics profile in the constraints of the optimization of a core metabolic model. Finally, we used the obtained single-cell optimal metabolic fluxes as features for cluster analysis. We compared the results obtained with different techniques, and with or without the use of denoising. We also investigated the possibility of applying denoising directly on the Reaction Activity Scores, which are metabolic features extracted from the read counts, rather than on the read counts. RESULTS: We show that denoising of transcriptomics data improves the clustering of single cells. We also illustrate that denoising restores important metabolic properties, such as the correlation between cell cycle phase and biomass accumulation, and between the RAS scores of reactions belonging to the same metabolic pathway. We show that MAGIC performs better than ENHANCE and SAVER, and that, denoising applied directly on the RAS matrix could be an effective alternative in removing false zero values from essential metabolic reactions. CONCLUSIONS: Our results indicate that including denoising as a pre-processing operation represents a milestone to integrate scRNA-seq data into Flux Balance Analysis simulations and to perform single-cell cluster analysis with a focus on metabolic phenotypes.

Metabolism is directly and indirectly fine-tuned by a complex web of interacting regulatory mechanisms that fall into two major classes. On the one hand, the expression level of the catalyzing enzyme sets the maximal theoretical flux level (i.e., the net rate of the reaction) for each enzyme-controlled reaction. On the other hand, metabolic regulation controls the metabolic flux through the interactions of metabolites (substrates, cofactors, allosteric modulators) with the responsible enzyme. High-throughput data, such as metabolomics and transcriptomics data, if analyzed separately, do not accurately characterize the hierarchical regulation of metabolism outlined above. They must be integrated to disassemble the interdependence between different regulatory layers controlling metabolism. To this aim, we propose INTEGRATE, a computational pipeline that integrates metabolomics and transcriptomics data, using constraint-based stoichiometric metabolic models as a scaffold. We compute differential reaction expression from transcriptomics data and use constraint-based modeling to predict if the differential expression of metabolic enzymes directly originates differences in metabolic fluxes. In parallel, we use metabolomics to predict how differences in substrate availability translate into differences in metabolic fluxes. We discriminate fluxes regulated at the metabolic and/or gene expression level by intersecting these two output datasets. We demonstrate the pipeline using a set of immortalized normal and cancer breast cell lines. In a clinical setting, knowing the regulatory level at which a given metabolic reaction is controlled will be valuable to inform targeted, truly personalized therapies in cancer patients.

BACKGROUND: Genome-wide reconstructions of metabolism opened the way to thorough investigations of cell metabolism for health care and industrial purposes. However, the predictions offered by Flux Balance Analysis (FBA) can be strongly affected by the choice of flux boundaries, with particular regard to the flux of reactions that sink nutrients into the system. To mitigate possible errors introduced by a poor selection of such boundaries, a rational approach suggests to focus the modeling efforts on the pivotal ones. METHODS: In this work, we present a methodology for the automatic identification of the key fluxes in genome-wide constraint-based models, by means of variance-based sensitivity analysis. The goal is to identify the parameters for which a small perturbation entails a large variation of the model outcomes, also referred to as sensitive parameters. Due to the high number of FBA simulations that are necessary to assess sensitivity coefficients on genome-wide models, our method exploits a master-slave methodology that distributes the computation on massively multi-core architectures. We performed the following steps: (1) we determined the putative parameterizations of the genome-wide metabolic constraint-based model, using Saltelli's method; (2) we applied FBA to each parameterized model, distributing the massive amount of calculations over multiple nodes by means of MPI; (3) we then recollected and exploited the results of all FBA runs to assess a global sensitivity analysis. RESULTS: We show a proof-of-concept of our approach on latest genome-wide reconstructions of human metabolism Recon2.2 and Recon3D. We report that most sensitive parameters are mainly associated with the intake of essential amino acids in Recon2.2, whereas in Recon 3D they are associated largely with phospholipids. We also illustrate that in most cases there is a significant contribution of higher order effects. CONCLUSION: Our results indicate that interaction effects between different model parameters exist, which should be taken into account especially at the stage of calibration of genome-wide models, supporting the importance of a global strategy of sensitivity analysis.

Metabolic network models are increasingly being used in health care and industry. As a consequence, many tools have been released to automate their reconstruction process de novo. In order to enable gene deletion simulations and integration of gene expression data, these networks must include gene-protein-reaction (GPR) rules, which describe with a Boolean logic relationships between the gene products (e.g., enzyme isoforms or subunits) associated with the catalysis of a given reaction. Nevertheless, the reconstruction of GPRs still remains a largely manual and time consuming process. Aiming at fully automating the reconstruction process of GPRs for any organism, we propose the open-source python-based framework GPRuler. By mining text and data from 9 different biological databases, GPRuler can reconstruct GPRs starting either from just the name of the target organism or from an existing metabolic model. The performance of the developed tool is evaluated at small-scale level for a manually curated metabolic model, and at genome-scale level for three metabolic models related to Homo sapiens and Saccharomyces cerevisiae organisms. By exploiting these models as benchmarks, the proposed tool shown its ability to reproduce the original GPR rules with a high level of accuracy. In all the tested scenarios, after a manual investigation of the mismatches between the rules proposed by GPRuler and the original ones, the proposed approach revealed to be in many cases more accurate than the original models. By complementing existing tools for metabolic network reconstruction with the possibility to reconstruct GPRs quickly and with a few resources, GPRuler paves the way to the study of context-specific metabolic networks, representing the active portion of the complete network in given conditions, for organisms of industrial or biomedical interest that have not been characterized metabolically yet.

The metabolic processes related to the synthesis of the molecules needed for a new round of cell division underlie the complex behaviour of cell populations in multi-cellular systems, such as tissues and organs, whereas their deregulation can lead to pathological states, such as cancer. Even within genetically homogeneous populations, complex dynamics, such as population oscillations or the emergence of specific metabolic and/or proliferative patterns, may arise, and this aspect is highly amplified in systems characterized by extreme heterogeneity. To investigate the conditions and mechanisms that link metabolic processes to cell population dynamics, we here employ a previously introduced multi-scale model of multi-cellular system, named FBCA (Flux Balance Analysis with Cellular Automata), which couples biomass accumulation, simulated via Flux Balance Analysis of a metabolic network, with the simulation of population and spatial dynamics via Cellular Potts Models. In this work, we investigate the influence that different modes of nutrients diffusion within the system may have on the emerging behaviour of cell populations. In our model, metabolic communication among cells is allowed by letting secreted metabolites to diffuse over the lattice, in addition to diffusion of nutrients from given sources. The inclusion of the diffusion processes in the model proved its effectiveness in characterizing plausible biological scenarios.

Metabolic reprogramming is a general feature of cancer cells.Regrettably, the comprehensive quantification of metabolites in biological specimens does not promptly translate into knowledge on the utilization of metabolic pathways.By estimating fluxes across metabolic pathways, computational models hold the promise to bridge this gap between data and biological functionality.These models currently portray the average behavior of cell populations however, masking the inherent heterogeneity that is part and parcel of tumorigenesis as much as drug resistance.To remove this limitation, we propose single-cell Flux Balance Analysis (scFBA) as a computational framework to translate single-cell transcriptomes into single-cell fluxomes.We show that the integration of single-cell RNA-seq profiles of cells derived from lung adenocarcinoma and breast cancer patients into a multi-scale stoichiometric model of a cancer cell population: significantly 1) reduces the space of feasible single-cell fluxomes; 2) allows to identify clusters of cells with different growth rates within the population; 3) points out the possible metabolic interactions among cells via exchange of metabolites.The scFBA suite of MATLAB functions is available at https://github.com/ BIMIB-DISCo/scFBA, as well as the case study datasets. Author summaryCytotoxicity of chemotherapeutic agents and resistance to targeted treatments are the main reasons why cancer is still one of the top causes of death.As tumor cells are intrinsically resistant to therapies that target signaling pathways, targeting the metabolic hallmarks of cancer holds promise for more incisive treatments.Regrettably, the

BACKGROUND: Determining the value of kinetic constants for a metabolic system in the exact physiological conditions is an extremely hard task. However, this kind of information is of pivotal relevance to effectively simulate a biological phenomenon as complex as metabolism. RESULTS: To overcome this issue, we propose to investigate emerging properties of ensembles of sets of kinetic constants leading to the biological readout observed in different experimental conditions. To this aim, we exploit information retrievable from constraint-based analyses (i.e. metabolic flux distributions at steady state) with the goal to generate feasible values for kinetic constants exploiting the mass action law. The sets retrieved from the previous step will be used to parametrize a mechanistic model whose simulation will be performed to reconstruct the dynamics of the system (until reaching the metabolic steady state) for each experimental condition. Every parametrization that is in accordance with the expected metabolic phenotype is collected in an ensemble whose features are analyzed to determine the emergence of properties of a phenotype. In this work we apply the proposed approach to identify ensembles of kinetic parameters for five metabolic phenotypes of E. Coli, by analyzing five different experimental conditions associated with the ECC2comp model recently published by Hädicke and collaborators. CONCLUSIONS: Our results suggest that the parameter values of just few reactions are responsible for the emergence of a metabolic phenotype. Notably, in contrast with constraint-based approaches such as Flux Balance Analysis, the methodology used in this paper does not require to assume that metabolism is optimizing towards a specific goal.

MOTIVATION: Intratumour heterogeneity poses many challenges to the treatment of cancer. Unfortunately, the transcriptional and metabolic information retrieved by currently available computational and experimental techniques portrays the average behaviour of intermixed and heterogeneous cell subpopulations within a given tumour. Emerging single-cell genomic analyses are nonetheless unable to characterize the interactions among cancer subpopulations. In this study, we propose popFBA , an extension to classic Flux Balance Analysis, to explore how metabolic heterogeneity and cooperation phenomena affect the overall growth of cancer cell populations. RESULTS: We show how clones of a metabolic network of human central carbon metabolism, sharing the same stoichiometry and capacity constraints, may follow several different metabolic paths and cooperate to maximize the growth of the total population. We also introduce a method to explore the space of possible interactions, given some constraints on plasma supply of nutrients. We illustrate how alternative nutrients in plasma supply and/or a dishomogeneous distribution of oxygen provision may affect the landscape of heterogeneous phenotypes. We finally provide a technique to identify the most proliferative cells within the heterogeneous population. AVAILABILITY AND IMPLEMENTATION: the popFBA MATLAB function and the SBML model are available at https://github.com/BIMIB-DISCo/popFBA . CONTACT: [email protected].

Cancer cells share several metabolic traits, including aerobic production of lactate from glucose (Warburg effect), extensive glutamine utilization and impaired mitochondrial electron flow. It is still unclear how these metabolic rearrangements, which may involve different molecular events in different cells, contribute to a selective advantage for cancer cell proliferation. To ascertain which metabolic pathways are used to convert glucose and glutamine to balanced energy and biomass production, we performed systematic constraint-based simulations of a model of human central metabolism. Sampling of the feasible flux space allowed us to obtain a large number of randomly mutated cells simulated at different glutamine and glucose uptake rates. We observed that, in the limited subset of proliferating cells, most displayed fermentation of glucose to lactate in the presence of oxygen. At high utilization rates of glutamine, oxidative utilization of glucose was decreased, while the production of lactate from glutamine was enhanced. This emergent phenotype was observed only when the available carbon exceeded the amount that could be fully oxidized by the available oxygen. Under the latter conditions, standard Flux Balance Analysis indicated that: this metabolic pattern is optimal to maximize biomass and ATP production; it requires the activity of a branched TCA cycle, in which glutamine-dependent reductive carboxylation cooperates to the production of lipids and proteins; it is sustained by a variety of redox-controlled metabolic reactions. In a K-ras transformed cell line we experimentally assessed glutamine-induced metabolic changes. We validated computational results through an extension of Flux Balance Analysis that allows prediction of metabolite variations. Taken together these findings offer new understanding of the logic of the metabolic reprogramming that underlies cancer cell growth.

BACKGROUND: Dynamical models of gene regulatory networks (GRNs) are highly effective in describing complex biological phenomena and processes, such as cell differentiation and cancer development. Yet, the topological and functional characterization of real GRNs is often still partial and an exhaustive picture of their functioning is missing. RESULTS: We here introduce CABERNET, a Cytoscape app for the generation, simulation and analysis of Boolean models of GRNs, specifically focused on their augmentation when a only partial topological and functional characterization of the network is available. By generating large ensembles of networks in which user-defined entities and relations are added to the original core, CABERNET allows to formulate hypotheses on the missing portions of real networks, as well to investigate their generic properties, in the spirit of complexity science. CONCLUSIONS: CABERNET offers a series of innovative simulation and modeling functions and tools, including (but not being limited to) the dynamical characterization of the gene activation patterns ruling cell types and differentiation fates, and sophisticated robustness assessments, as in the case of gene knockouts. The integration within the widely used Cytoscape framework for the visualization and analysis of biological networks, makes CABERNET a new essential instrument for both the bioinformatician and the computational biologist, as well as a computational support for the experimentalist. An example application concerning the analysis of an augmented T-helper cell GRN is provided.