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Network theory has led to the abstraction of many real-world systems and enabled their modelling as simple networks comprising nodes and edges. In particular, in the field of biological sciences, network theory provides a robust framework to capture the complexity inherent to biological systems. Networks in biology have been modelled at different scales, starting from cells to population levels. These models have provided crucial insights into the evolution, mechanism, and functions of several biological systems. However, most natural and engineered systems are composed of multiple subsystems and layers of connectivity. A multilayer network paradigm has proven useful in understanding such systems. Here, we have briefly introduced the network formalism of modelling biological systems at various levels. This is followed by an introduction to multilayer networks. Multilayer networks have been utilized to model biological systems at multiple scales ranging from protein–protein interactions, transcription and metabolic networks, to ecological networks involving interactions between species. Recent advances in studying the structure and dynamics of such multilayer networks have enabled a better understanding of the complexity in these biological systems. Finally, we discuss the recent advances in studying the structure and dynamics of such multilayered networks followed by the challenges and future prospects.

Computational modeling and simulation of biological systems have become valuable tools for understanding and predicting cellular performance and phenotype generation. This work aimed to construct, model, and dynamically simulate the virulence factor pyoverdine (PVD) biosynthesis in Pseudomonas aeruginosa through a systemic approach, considering that the metabolic pathway of PVD synthesis is regulated by the quorum-sensing (QS) phenomenon. The methodology comprised three main stages: (i) Construction, modeling, and validation of the QS gene regulatory network that controls PVD synthesis in P. aeruginosa strain PAO1; (ii) construction, curating, and modeling of the metabolic network of P. aeruginosa using the flux balance analysis (FBA) approach; (iii) integration and modeling of these two networks into an integrative model using the dynamic flux balance analysis (DFBA) approximation, followed, finally, by an in vitro validation of the integrated model for PVD synthesis in P. aeruginosa as a function of QS signaling. The QS gene network, constructed using the standard System Biology Markup Language, comprised 114 chemical species and 103 reactions and was modeled as a deterministic system following the kinetic based on mass action law. This model showed that the higher the bacterial growth, the higher the extracellular concentration of QS signal molecules, thus emulating the natural behavior of P. aeruginosa PAO1. The P. aeruginosa metabolic network model was constructed based on the iMO1056 model, the P. aeruginosa PAO1 strain genomic annotation, and the metabolic pathway of PVD synthesis. The metabolic network model included the PVD synthesis, transport, exchange reactions, and the QS signal molecules. This metabolic network model was curated and then modeled under the FBA approximation, using biomass maximization as the objective function (optimization problem, a term borrowed from the engineering field). Next, chemical reactions shared by both network models were chosen to combine them into an integrative model. To this end, the fluxes of these reactions, obtained from the QS network model, were fixed in the metabolic network model as constraints of the optimization problem using the DFBA approximation. Finally, simulations of the integrative model (CCBM1146, comprising 1123 reactions and 880 metabolites) were run using the DFBA approximation to get (i) the flux profile for each reaction, (ii) the bacterial growth profile, (iii) the biomass profile, and (iv) the concentration profiles of metabolites of interest such as glucose, PVD, and QS signal molecules. The CCBM1146 model showed that the QS phenomenon directly influences the P. aeruginosa metabolism to PVD biosynthesis as a function of the change in QS signal intensity. The CCBM1146 model made it possible to characterize and explain the complex and emergent behavior generated by the interactions between the two networks, which would have been impossible to do by studying each system’s individual components or scales separately. This work is the first in silico report of an integrative model comprising the QS gene regulatory network and the metabolic network of P. aeruginosa.

Network architecture plays a crucial role in governing the dynamics of any biological network. Further, network structures have been shown to remain conserved across organisms for a given phenotype. Therefore, the mapping between network structures and the output functionality not only aids in understanding of biological systems but also finds application in synthetic biology and therapeutics. Based on the approaches involved, most of the efforts hitherto invested in this field can be classified into three broad categories, namely, computational efforts, rule-based methods and systems-theoretic approaches. The present review provides a qualitative and quantitative study of all three approaches in the light of three well-researched biological phenotypes, namely, oscillation, toggle switching, and adaptation. We also discuss the advantages, limitations, and future research scope for all three approaches along with their possible applications to other emergent properties of biological relevance.

The discrete chemical master equation (dCME) provides a general framework for studying stochasticity in mesoscopic reaction networks. Since its direct solution rapidly becomes intractable due to the increasing size of the state space, truncation of the state space is necessary for solving most dCMEs. It is therefore important to assess the consequences of state space truncations so errors can be quantified and minimized. Here we describe a novel method for state space truncation. By partitioning a reaction network into multiple molecular equivalence groups (MEGs), we truncate the state space by limiting the total molecular copy numbers in each MEG. We further describe a theoretical framework for analysis of the truncation error in the steady-state probability landscape using reflecting boundaries. By aggregating the state space based on the usage of a MEG and constructing an aggregated Markov process, we show that the truncation error of a MEG can be asymptotically bounded by the probability of states on the reflecting boundary of the MEG. Furthermore, truncating states of an arbitrary MEG will not undermine the estimated error of truncating any other MEGs. We then provide an overall error estimate for networks with multiple MEGs. To rapidly determine the appropriate size of an arbitrary MEG, we also introduce an a priori method to estimate the upper bound of its truncation error. This a priori estimate can be rapidly computed from reaction rates of the network, without the need of costly trial solutions of the dCME. As examples, we show results of applying our methods to the four stochastic networks of (1) the birth and death model, (2) the single gene expression model, (3) the genetic toggle switch model, and (4) the phage lambda bistable epigenetic switch model. We demonstrate how truncation errors and steady-state probability landscapes can be computed using different sizes of the MEG(s) and how the results validate our theories. Overall, the novel state space truncation and error analysis methods developed here can be used to ensure accurate direct solutions to the dCME for a large number of stochastic networks.

Background Molecular biology knowledge can be formalized and systematically represented in a computer-readable form as a comprehensive map of molecular interactions. There exist an increasing number of maps of molecular interactions containing detailed and step-wise description of various cell mechanisms. It is difficult to explore these large maps, to organize discussion of their content and to maintain them. Several efforts were recently made to combine these capabilities together in one environment, and NaviCell is one of them. Results NaviCell is a web-based environment for exploiting large maps of molecular interactions, created in CellDesigner, allowing their easy exploration, curation and maintenance. It is characterized by a combination of three essential features: (1) efficient map browsing based on Google Maps; (2) semantic zooming for viewing different levels of details or of abstraction of the map and (3) integrated web-based blog for collecting community feedback. NaviCell can be easily used by experts in the field of molecular biology for studying molecular entities of interest in the context of signaling pathways and crosstalk between pathways within a global signaling network. NaviCell allows both exploration of detailed molecular mechanisms represented on the map and a more abstract view of the map up to a top-level modular representation. NaviCell greatly facilitates curation, maintenance and updating the comprehensive maps of molecular interactions in an interactive and user-friendly fashion due to an imbedded blogging system. Conclusions NaviCell provides user-friendly exploration of large-scale maps of molecular interactions, thanks to Google Maps and WordPress interfaces, with which many users are already familiar. Semantic zooming which is used for navigating geographical maps is adopted for molecular maps in NaviCell, making any level of visualization readable. In addition, NaviCell provides a framework for community-based curation of maps.

What can we learn about controlling a system solely from its underlying network structure? Here we adapt a recently developed framework for control of networks governed by a broad class of nonlinear dynamics that includes the major dynamic models of biological, technological, and social processes. This feedback-based framework provides realizable node overrides that steer a system toward any of its natural long-term dynamic behaviors, regardless of the specific functional forms and system parameters. We use this framework on several real networks, identify the topological characteristics that underlie the predicted node overrides, and compare its predictions to those of structural controllability in control theory. Finally, we demonstrate this framework’s applicability in dynamic models of gene regulatory networks and identify nodes whose override is necessary for control in the general case but not in specific model instances.

High-throughput technologies, offering an unprecedented wealth of quantitative data underlying the makeup of living systems, are changing biology. Notably, the systematic mapping of the relationships between biochemical entities has fueled the rapid development of network biology, offering a suitable framework to describe disease phenotypes and predict potential drug targets. However, our ability to develop accurate dynamical models remains limited, due in part to the limited knowledge of the kinetic parameters underlying these interactions. Here,we explore the degree to which we can make reasonably accurate predictions in the absence of the kinetic parameters. We find that simple dynamically agnostic models are sufficient to recover the strength and sign of the biochemical perturbation patterns observed in 87 biological models for which the underlying kinetics are known. Surprisingly, a simple distance-based model achieves 65% accuracy. We show that this predictive power is robust to topological and kinetic parameter perturbations, and we identify key network properties that can increase up to 80% the recovery rate of the true perturbation patterns. We validate our approach using experimental data on the chemotactic pathway in bacteria, finding that a network model of perturbation spreading predicts with ∼80% accuracy the directionality of gene expression and phenotype changes in knock-out and overproduction experiments. These findings show that the steady advances in mapping out the topology of biochemical interaction networks opens avenues for accurate perturbation spread modeling, with direct implications for medicine and drug development.

• Leaf vein network geometry can predict levels of resource transport, defence and mechanical support that operate at different spatial scales. However, it is challenging to quantify network architecture across scales due to the difficulties both in segmenting networks from images and in extracting multiscale statistics from subsequent network graph representations. • Here we developed deep learning algorithms using convolutional neural networks (CNNs) to automatically segment leaf vein networks. Thirty-eight CNNs were trained on subsets of manually defined ground-truth regions from >700 leaves representing 50 southeast Asian plant families. Ensembles of six independently trained CNNs were used to segment networks from larger leaf regions (c. 100 mm²). Segmented networks were analysed using hierarchical loop decomposition to extract a range of statistics describing scale transitions in vein and areole geometry. • The CNN approach gave a precision-recall harmonic mean of 94.5% ± 6%, outperforming other current network extraction methods, and accurately described the widths, angles and connectivity of veins. Multiscale statistics then enabled the identification of previously undescribed variation in network architecture across species. • We provide a LeafVeinCNN software package to enable multiscale quantification of leaf vein networks, facilitating the comparison across species and the exploration of the functional significance of different leaf vein architectures.

Background The complexity of biological systems has increasingly been unraveled through computational methods, with biological network analysis now focusing on the construction and exploration of well-defined interaction networks. Traditional graph-theoretical approaches have been instrumental in mapping key biological processes using high-confidence interaction data. However, these methods often struggle with incomplete or/and heterogeneous datasets. In this study, we extend beyond conventional bipartite models by integrating attribute-driven knowledge from the Molecular Signatures Database (MSigDB) using the node2vec algorithm. Results Our approach explores unsupervised biological relationships and uncovers potential associations between genes and biological terms through network connectivity analysis. By embedding both human and mouse data into a shared vector space, we validate our findings cross-species, further strengthening the robustness of our method. Conclusions This integrative framework reveals both expected and novel biological insights, offering a comprehensive perspective that complements traditional biological network analysis and paves the way for deeper understanding of complex biological processes and diseases.

Hepatocellular carcinoma (HCC) is one of the most frequent forms of liver cancer, and effective treatment methods are limited due to tumor heterogeneity. There is a great need for comprehensive approaches to stratify HCC patients, gain biological insights into subtypes, and ultimately identify effective therapeutic targets. We stratified HCC patients and characterized each subtype using transcriptomics data, genome-scale metabolic networks and network topology/controllability analysis. This comprehensive systems-level analysis identified three distinct subtypes with substantial differences in metabolic and signaling pathways reflecting at genomic, transcriptomic, and proteomic levels. These subtypes showed large differences in clinical survival associated with altered kynurenine metabolism, WNT/β-catenin–associated lipid metabolism, and PI3K/AKT/mTOR signaling. Integrative analyses indicated that the three subtypes rely on alternative enzymes (e.g., ACSS1/ACSS2/ACSS3, PKM/PKLR, ALDOB/ALDOA, MTHFD1L/MTHFD2/MTHFD1) to catalyze the same reactions. Based on systems-level analysis, we identified 8 to 28 subtype-specific genes with pivotal roles in controlling the metabolic network and predicted that these genes may be targeted for development of treatment strategies for HCC subtypes by performing in silico analysis. To validate our predictions, we performed experiments using HepG2 cells under normoxic and hypoxic conditions and observed opposite expression patterns between genes expressed in high/moderate/low-survival tumor groups in response to hypoxia, reflecting activated hypoxic behavior in patients with poor survival. In conclusion, our analyses showed that the heterogeneous HCC tumors can be stratified using a metabolic network-driven approach, which may also be applied to other cancer types, and this stratification may have clinical implications to drive the development of precision medicine.