Modeling formalisms in Systems Biology

Microbiome modeling: a beginner's guide

Microbiomes, comprised of diverse microbial species and viruses, play pivotal roles in human health, environmental processes, and biotechnological applications and interact with each other, their environment, and hosts via ecological interactions. Our understanding of microbiomes is still limited and hampered by their complexity. A concept improving this understanding is systems biology, which focuses on the holistic description of biological systems utilizing experimental and computational methods. An important set of such experimental methods are metaomics methods which analyze microbiomes and output lists of molecular features. These lists of data are integrated, interpreted, and compiled into computational microbiome models, to predict, optimize, and control microbiome behavior. There exists a gap in understanding between microbiologists and modelers/bioinformaticians, stemming from a lack of interdisciplinary knowledge. This knowledge gap hinders the establishment of computational models in microbiome analysis. This review aims to bridge this gap and is tailored for microbiologists, researchers new to microbiome modeling, and bioinformaticians. To achieve this goal, it provides an interdisciplinary overview of microbiome modeling, starting with fundamental knowledge of microbiomes, metaomics methods, common modeling formalisms, and how models facilitate microbiome control. It concludes with guidelines and repositories for modeling. Each section provides entry-level information, example applications, and important references, serving as a valuable resource for comprehending and navigating the complex landscape of microbiome research and modeling.

Maboss for HPC environments: implementations of the continuous time Boolean model simulator for large CPU clusters and GPU accelerators

BACKGROUND

Computational models in systems biology are becoming more important with the advancement of experimental techniques to query the mechanistic details responsible for leading to phenotypes of interest. In particular, Boolean models are well fit to describe the complexity of signaling networks while being simple enough to scale to a very large number of components. With the advance of Boolean model inference techniques, the field is transforming from an artisanal way of building models of moderate size to a more automatized one, leading to very large models. In this context, adapting the simulation software for such increases in complexity is crucial.

RESULTS

We present two new developments in the continuous time Boolean simulators: MaBoSS.MPI, a parallel implementation of MaBoSS which can exploit the computational power of very large CPU clusters, and MaBoSS.GPU, which can use GPU accelerators to perform these simulations.

CONCLUSION

These implementations enable simulation and exploration of the behavior of very large models, thus becoming a valuable analysis tool for the systems biology community.

Combined mechanistic modeling and machine-learning approaches in systems biology - A systematic literature review

BACKGROUND AND OBJECTIVE

Mechanistic-based Model simulations (MM) are an effective approach commonly employed, for research and learning purposes, to better investigate and understand the inherent behavior of biological systems. Recent advancements in modern technologies and the large availability of omics data allowed the application of Machine Learning (ML) techniques to different research fields, including systems biology. However, the availability of information regarding the analyzed biological context, sufficient experimental data, as well as the degree of computational complexity, represent some of the issues that both MMs and ML techniques could present individually. For this reason, recently, several studies suggest overcoming or significantly reducing these drawbacks by combining the above-mentioned two methods. In the wake of the growing interest in this hybrid analysis approach, with the present review, we want to systematically investigate the studies available in the scientific literature in which both MMs and ML have been combined to explain biological processes at genomics, proteomics, and metabolomics levels, or the behavior of entire cellular populations.

METHODS

Elsevier Scopus®, Clarivate Web of Science™ and National Library of Medicine PubMed® databases were enquired using the queries reported in Table 1, resulting in 350 scientific articles.

RESULTS

Only 14 of the 350 documents returned by the comprehensive search conducted on the three major online databases met our search criteria, i.e. present a hybrid approach consisting of the synergistic combination of MMs and ML to treat a particular aspect of systems biology.

CONCLUSIONS

Despite the recent interest in this methodology, from a careful analysis of the selected papers, it emerged how examples of integration between MMs and ML are already present in systems biology, highlighting the great potential of this hybrid approach to both at micro and macro biological scales.

Adapting modeling and simulation credibility standards to computational systems biology

Computational models are increasingly used in high-impact decision making in science, engineering, and medicine. The National Aeronautics and Space Administration (NASA) uses computational models to perform complex experiments that are otherwise prohibitively expensive or require a microgravity environment. Similarly, the Food and Drug Administration (FDA) and European Medicines Agency (EMA) have began accepting models and simulations as forms of evidence for pharmaceutical and medical device approval. It is crucial that computational models meet a standard of credibility when using them in high-stakes decision making. For this reason, institutes including NASA, the FDA, and the EMA have developed standards to promote and assess the credibility of computational models and simulations. However, due to the breadth of models these institutes assess, these credibility standards are mostly qualitative and avoid making specific recommendations. On the other hand, modeling and simulation in systems biology is a narrower domain and several standards are already in place. As systems biology models increase in complexity and influence, the development of a credibility assessment system is crucial. Here we review existing standards in systems biology, credibility standards in other science, engineering, and medical fields, and propose the development of a credibility standard for systems biology models.

New perspectives into the vaginal microbiome with systems biology

The vaginal microbiome (VMB) is critical to female reproductive health; however, the mechanisms associated with optimal and non-optimal states remain poorly understood due to the complex community structure and dynamic nature. Quantitative systems biology techniques applied to the VMB have improved understanding of community composition and function using primarily statistical methods. In contrast, fewer mechanistic models that use a priori knowledge of VMB features to develop predictive models have been implemented despite their use for microbiomes at other sites, including the gastrointestinal tract. Here, we explore systems biology approaches that have been applied in the VMB, highlighting successful techniques and discussing new directions that hold promise for improving understanding of health and disease.

Leveraging quantum computing for dynamic analyses of logical networks in systems biology

The dynamics of cellular mechanisms can be investigated through the analysis of networks. One of the simplest but most popular modeling strategies involves logic-based models. However, these models still face exponential growth in simulation complexity compared with a linear increase in nodes. We transfer this modeling approach to quantum computing and use the upcoming technique in the field to simulate the resulting networks. Leveraging logic modeling in quantum computing has many benefits, including complexity reduction and quantum algorithms for systems biology tasks. To showcase the applicability of our approach to systems biology tasks, we implemented a model of mammalian cortical development. Here, we applied a quantum algorithm to estimate the tendency of the model to reach particular stable conditions and further revert dynamics. Results from two actual quantum processing units and a noisy simulator are presented, and current technical challenges are discussed.

Comparison of rule- and ordinary differential equation-based dynamic model of DARPP-32 signalling network

Dynamic modelling has considerably improved our understanding of complex molecular mechanisms. Ordinary differential equations (ODEs) are the most detailed and popular approach to modelling the dynamics of molecular systems. However, their application in signalling networks, characterised by multi-state molecular complexes, can be prohibitive. Contemporary modelling methods, such as rule- based (RB) modelling, have addressed these issues. The advantages of RB modelling over ODEs have been presented and discussed in numerous reviews. In this study, we conduct a direct comparison of the time courses of a molecular system founded on the same reaction network but encoded in the two frameworks. To make such a comparison, a set of reactions that underlie an ODE model was manually encoded in the Kappa language, one of the RB implementations. A comparison of the models was performed at the level of model specification and dynamics, acquired through model simulations. In line with previous reports, we confirm that the Kappa model recapitulates the general dynamics of its ODE counterpart with minor differences. These occur when molecules have multiple sites binding the same interactor. Furthermore, activation of these molecules in the RB model is slower than in the ODE one. As reported for other molecular systems, we find that, also for the DARPP-32 reaction network, the RB representation offers a more expressive and flexible syntax that facilitates access to fine details of the model, easing model reuse. In parallel with these analyses, we report a refactored model of the DARPP-32 interaction network that can serve as a canvas for the development of more complex dynamic models to study this important molecular system.

Monitoring and modelling the dynamics of the cellular glycolysis pathway: A review and future perspectives

BACKGROUND

The dynamics of the cellular glycolysis pathway underpin cellular function and dysfunction, and therefore ultimately health, disease, diagnostic and therapeutic strategies. Evolving our understanding of this fundamental process and its dynamics remains critical.

SCOPE OF REVIEW

This paper reviews the medical relevance of glycolytic pathway in depth and explores the current state of the art for monitoring and modelling the dynamics of the process. The future perspectives of label free, vibrational microspectroscopic techniques to overcome the limitations of the current approaches are considered.

MAJOR CONCLUSIONS

Vibrational microspectroscopic techniques can potentially operate in the niche area of limitations of other omics technologies for non-destructive, real-time, in vivo label-free monitoring of glycolysis dynamics at a cellular and subcellular level.

Network thermodynamics of biological systems: A bond graph approach

Edmund Crampin (1973-2021) was at the forefront of Systems Biology research and his work will influence the field for years to come. This paper brings together and summarises the seminal work of his group in applying energy-based bond graph methods to biological systems. In particular, this paper: (a) motivates the need to consider energy in modelling biology; (b) introduces bond graphs as a methodology for achieving this; (c) describes extensions to modelling electrochemical transduction; (d) outlines how bond graph models can be constructed in a modular manner and (e) describes stoichiometric approaches to deriving fundamental properties of reaction networks. These concepts are illustrated using a new bond graph model of photosynthesis in chloroplasts.

Towards a comprehensive assessment of QSP models: what would it take?

Quantitative Systems Pharmacology (QSP) has emerged as a powerful ensemble of approaches aiming at developing integrated mathematical and computational models elucidating the complex interactions between pharmacology, physiology, and disease. As the field grows and matures its applications expand beyond the boundaries of research and development and slowly enter the decision making and regulatory arenas. However, widespread acceptance and eventual adoption of a new modeling approach requires assessment criteria and quantifiable metrics that establish credibility and increase confidence in model predictions. QSP aims to provide an integrated understanding of pathology in the context of therapeutic interventions. Because of its ambitious nature and the fact that QSP emerged in an uncoordinated manner as a result of activities distributed across organizations and academic institutions, high entropy characterizes the tools, methods, and computational methodologies and approaches used. The eventual acceptance of QSP model predictions as supporting material for an application to a regulatory agency will require that two key aspects are considered: (1) increase confidence in the QSP framework, which drives standardization and assessment; and (2) careful articulation of the expectations. Both rely heavily on our ability to rigorously and consistently assess QSP models. In this manuscript, we wish to discuss the meaning and purpose of such an assessment in the context of QSP model development and elaborate on the differentiating features of QSP that render such an endeavor challenging. We argue that QSP establishes a conceptual, integrative framework rather than a specific and well-defined computational methodology. QSP elicits the use of a wide variety of modeling and computational methodologies optimized with respect to specific applications and available data modalities, which exceed the data structures employed by chemometrics and PK/PD models. While the range of options fosters creativity and promises to substantially advance our ability to design pharmaceutical interventions rationally and optimally, our expectations of QSP models need to be clearly articulated and agreed on, with assessment emphasizing the scope of QSP studies rather than the methods used. Nevertheless, QSP should not be considered an independent approach, rather one of many in the broader continuum of computational models.

Addressing barriers in comprehensiveness, accessibility, reusability, interoperability and reproducibility of computational models in systems biology

Computational models are often employed in systems biology to study the dynamic behaviours of complex systems. With the rise in the number of computational models, finding ways to improve the reusability of these models and their ability to reproduce virtual experiments becomes critical. Correct and effective model annotation in community-supported and standardised formats is necessary for this improvement. Here, we present recent efforts toward a common framework for annotated, accessible, reproducible and interoperable computational models in biology, and discuss key challenges of the field.

Modeling and Simulation of Cell Signaling Networks for Subsequent Analytics Processes Using Big Data and Machine Learning

This work explores how much the traditional approach to modeling and simulation of biological systems, specifically cell signaling networks, can be increased and improved by integrating big data, data mining, and machine learning techniques. Specifically, we first model, simulate, validate, and calibrate the behavior of the PI3K/AKT/mTOR cancer-related signaling pathway. Subsequently, once the behavior of the simulated signaling network matches the expected behavior, the capacity of the computational simulation is increased to grow data (data farming). First, we use big data techniques to extract, collect, filter, and store large volumes of data describing all the interactions among the simulated cell signaling system components over time. Afterward, we apply data mining and machine learning techniques-specifically, exploratory data analysis, feature selection techniques, and supervised neural network models-to the resulting biological dataset to obtain new inferences and knowledge about this biological system. The results showed how the traditional approach to the simulation of biological systems could be enhanced and improved by incorporating big data, data mining, and machine learning techniques, which significantly contributed to increasing the predictive power of the simulation.

Hybrid modelling of biological systems: current progress and future prospects

Integrated modelling of biological systems is becoming a necessity for constructing models containing the major biochemical processes of such systems in order to obtain a holistic understanding of their dynamics and to elucidate emergent behaviours. Hybrid modelling methods are crucial to achieve integrated modelling of biological systems. This paper reviews currently popular hybrid modelling methods, developed for systems biology, mainly revealing why they are proposed, how they are formed from single modelling formalisms and how to simulate them. By doing this, we identify future research requirements regarding hybrid approaches for further promoting integrated modelling of biological systems.

Homology of process: developmental dynamics in comparative biology

Comparative biology builds up systematic knowledge of the diversity of life, across evolutionary lineages and levels of organization, starting with evidence from a sparse sample of model organisms. In developmental biology, a key obstacle to the growth of comparative approaches is that the concept of homology is not very well defined for levels of organization that are intermediate between individual genes and morphological characters. In this paper, we investigate what it means for ontogenetic processes to be homologous, focusing specifically on the examples of insect segmentation and vertebrate somitogenesis. These processes can be homologous without homology of the underlying genes or gene networks, since the latter can diverge over evolutionary time, while the dynamics of the process remain the same. Ontogenetic processes like these therefore constitute a dissociable level and distinctive unit of comparison requiring their own specific criteria of homology. In addition, such processes are typically complex and nonlinear, such that their rigorous description and comparison requires not only observation and experimentation, but also dynamical modelling. We propose six criteria of process homology, combining recognized indicators (sameness of parts, morphological outcome and topological position) with novel ones derived from dynamical systems modelling (sameness of dynamical properties, dynamical complexity and evidence for transitional forms). We show how these criteria apply to animal segmentation and other ontogenetic processes. We conclude by situating our proposed dynamical framework for homology of process in relation to similar research programmes, such as process structuralism and developmental approaches to morphological homology.

Integration of temporal single cell cellular stress response activity with logic-ODE modeling reveals activation of ATF4-CHOP axis as a critical predictor of drug-induced liver injury

Drug-induced liver injury (DILI) is the most prevalent adversity encountered in drug development and clinical settings leading to urgent needs to understand the underlying mechanisms. In this study, we have systematically investigated the dynamics of the activation of cellular stress response pathways and cell death outcomes upon exposure of a panel of liver toxicants using live cell imaging of fluorescent reporter cell lines. We established a comprehensive temporal dynamic response profile of a large set of BAC-GFP HepG2 cell lines representing the following components of stress signaling: i) unfolded protein response (UPR) [ATF4, XBP1, BIP and CHOP]; ii) oxidative stress [NRF2, SRXN1, HMOX1]; iii) DNA damage [P53, P21, BTG2, MDM2]; and iv) NF-κB pathway [A20, ICAM1]. We quantified the single cell GFP expression as a surrogate for endogenous protein expression using live cell imaging over > 60 h upon exposure to 14 DILI compounds at multiple concentrations. Using logic-based ordinary differential equation (Logic-ODE), we modelled the dynamic profiles of the different stress responses and extracted specific descriptors potentially predicting the progressive outcomes. We identified the activation of ATF4-CHOP axis of the UPR as the key pathway showing the highest correlation with cell death upon DILI compound perturbation. Knocking down main components of the UPR provided partial protection from compound-induced cytotoxicity, indicating a complex interplay among UPR components as well as other stress pathways. Our results suggest that a systematic analysis of the temporal dynamics of ATF4-CHOP axis activation can support the identification of DILI risk for new candidate drugs.

Biosensors: A Sneak Peek into Plant Cell's Immunity

Biosensors are indispensable tools to understand a plant’s immunity as its spatiotemporal dimension is key in withstanding complex plant immune signaling. The diversity of genetically encoded biosensors in plants is expanding, covering new analytes with ever higher sensitivity and robustness, but their assortment is limited in some respects, such as their use in following biotic stress response, employing more than one biosensor in the same chassis, and their implementation into crops. In this review, we focused on the available biosensors that encompass these aspects. We show that in vivo imaging of calcium and reactive oxygen species is satisfactorily covered with the available genetically encoded biosensors, while on the other hand they are still underrepresented when it comes to imaging of the main three hormonal players in the immune response: salicylic acid, ethylene and jasmonic acid. Following more than one analyte in the same chassis, upon one or more conditions, has so far been possible by using the most advanced genetically encoded biosensors in plants which allow the monitoring of calcium and the two main hormonal pathways involved in plant development, auxin and cytokinin. These kinds of biosensor are also the most evolved in crops. In the last section, we examine the challenges in the use of biosensors and demonstrate some strategies to overcome them.

Multiscale Regulation of the Intervertebral Disc: Achievements in Experimental, In Silico, and Regenerative Research

Intervertebral disc (IVD) degeneration is a major risk factor of low back pain. It is defined by a progressive loss of the IVD structure and functionality, leading to severe impairments with restricted treatment options due to the highly demanding mechanical exposure of the IVD. Degenerative changes in the IVD usually increase with age but at an accelerated rate in some individuals. To understand the initiation and progression of this disease, it is crucial to identify key top-down and bottom-up regulations' processes, across the cell, tissue, and organ levels, in health and disease. Owing to unremitting investigation of experimental research, the comprehension of detailed cell signaling pathways and their effect on matrix turnover significantly rose. Likewise, in silico research substantially contributed to a holistic understanding of spatiotemporal effects and complex, multifactorial interactions within the IVD. Together with important achievements in the research of biomaterials, manifold promising approaches for regenerative treatment options were presented over the last years. This review provides an integrative analysis of the current knowledge about (1) the multiscale function and regulation of the IVD in health and disease, (2) the possible regenerative strategies, and (3) the in silico models that shall eventually support the development of advanced therapies.

KiMoSys 2.0: an upgraded database for submitting, storing and accessing experimental data for kinetic modeling

The KiMoSys (https://kimosys.org), launched in 2014, is a public repository of published experimental data, which contains concentration data of metabolites, protein abundances and flux data. It offers a web-based interface and upload facility to share data, making it accessible in structured formats, while also integrating associated kinetic models related to the data. In addition, it also supplies tools to simplify the construction process of ODE (Ordinary Differential Equations)-based models of metabolic networks. In this release, we present an update of KiMoSys with new data and several new features, including (i) an improved web interface, (ii) a new multi-filter mechanism, (iii) introduction of data visualization tools, (iv) the addition of downloadable data in machine-readable formats, (v) an improved data submission tool, (vi) the integration of a kinetic model simulation environment and (vii) the introduction of a unique persistent identifier system. We believe that this new version will improve its role as a valuable resource for the systems biology community. Database URL:  www.kimosys.org.

A unifying modelling formalism for the integration of stoichiometric and kinetic models

Current research on systems and synthetic biology relies heavily on mathematical models of the systems under study. The usefulness of such models depends on the quantity and quality of biological data, and on the availability of appropriate modelling formalisms that can gather and accommodate such data so that they can be exploited properly. Given our incomplete knowledge of biological systems and the fact that they consist of many subsystems, biological data are usually uncertain and heterogeneous. These facts hinder the use of mathematical models and computational methods. In the scope of dynamic biological systems, e.g. metabolic networks, this difficulty can be overcome by the novel modelling formalism of flexible nets (FNs). We show that an FN can combine, in a natural way, a stoichiometric model and a kinetic model. Moreover, the resulting net admits nonlinear dynamics and can be analysed in both transient and steady states.

SBML Level 3: an extensible format for the exchange and reuse of biological models

Systems biology has experienced dramatic growth in the number, size, and complexity of computational models. To reproduce simulation results and reuse models, researchers must exchange unambiguous model descriptions. We review the latest edition of the Systems Biology Markup Language (SBML), a format designed for this purpose. A community of modelers and software authors developed SBML Level 3 over the past decade. Its modular form consists of a core suited to representing reaction-based models and packages that extend the core with features suited to other model types including constraint-based models, reaction-diffusion models, logical network models, and rule-based models. The format leverages two decades of SBML and a rich software ecosystem that transformed how systems biologists build and interact with models. More recently, the rise of multiscale models of whole cells and organs, and new data sources such as single-cell measurements and live imaging, has precipitated new ways of integrating data with models. We provide our perspectives on the challenges presented by these developments and how SBML Level 3 provides the foundation needed to support this evolution.

Cancer systems immunology

Tumor immunology is undergoing a renaissance due to the recent profound clinical successes of tumor immunotherapy. These advances have coincided with an exponential growth in the development of -omics technologies. Armed with these technologies and their associated computational and modeling toolsets, systems biologists have turned their attention to tumor immunology in an effort to understand the precise nature and consequences of interactions between tumors and the immune system. Such interactions are inherently multivariate, spanning multiple time and size scales, cell types, and organ systems, rendering systems biology approaches particularly amenable to their interrogation. While in its infancy, the field of 'Cancer Systems Immunology' has already influenced our understanding of tumor immunology and immunotherapy. As the field matures, studies will move beyond descriptive characterizations toward functional investigations of the emergent behavior that govern tumor-immune responses. Thus, Cancer Systems Immunology holds incredible promise to advance our ability to fight this disease.

Applications of personalised signalling network models in precision oncology

As our ability to provide in-depth, patient-specific characterisation of the molecular alterations within tumours rapidly improves, it is becoming apparent that new approaches will be required to leverage the power of this data and derive the full benefit for each individual patient. Systems biology approaches are beginning to emerge within this field as a potential method of incorporating large volumes of network level data and distilling a coherent, clinically-relevant prediction of drug response. However, the initial promise of this developing field is yet to be realised. Here we argue that in order to develop these precise models of individual drug response and tailor treatment accordingly, we will need to develop mathematical models capable of capturing both the dynamic nature of drug-response signalling networks and key patient-specific information such as mutation status or expression profiles. We also review the modelling approaches commonly utilised within this field, and outline recent examples of their use in furthering the application of systems biology for a precision medicine approach to cancer treatment.

Harnessing the Potential of Stem Cells for Disease Modeling: Progress and Promises

Ex vivo cell/tissue-based models are an essential step in the workflow of pathophysiology studies, assay development, disease modeling, drug discovery, and development of personalized therapeutic strategies. For these purposes, both scientific and pharmaceutical research have adopted ex vivo stem cell models because of their better predictive power. As matter of a fact, the advancing in isolation and in vitro expansion protocols for culturing autologous human stem cells, and the standardization of methods for generating patient-derived induced pluripotent stem cells has made feasible to generate and investigate human cellular disease models with even greater speed and efficiency. Furthermore, the potential of stem cells on generating more complex systems, such as scaffold-cell models, organoids, or organ-on-a-chip, allowed to overcome the limitations of the two-dimensional culture systems as well as to better mimic tissues structures and functions. Finally, the advent of genome-editing/gene therapy technologies had a great impact on the generation of more proficient stem cell-disease models and on establishing an effective therapeutic treatment. In this review, we discuss important breakthroughs of stem cell-based models highlighting current directions, advantages, and limitations and point out the need to combine experimental biology with computational tools able to describe complex biological systems and deliver results or predictions in the context of personalized medicine.

A scalable method for parameter-free simulation and validation of mechanistic cellular signal transduction network models

The metabolic modelling community has established the gold standard for bottom-up systems biology with reconstruction, validation and simulation of mechanistic genome-scale models. Similar methods have not been established for signal transduction networks, where the representation of complexes and internal states leads to scalability issues in both model formulation and execution. While rule- and agent-based methods allow efficient model definition and execution, respectively, model parametrisation introduces an additional layer of uncertainty due to the sparsity of reliably measured parameters. Here, we present a scalable method for parameter-free simulation of mechanistic signal transduction networks. It is based on rxncon and uses a bipartite Boolean logic with separate update rules for reactions and states. Using two generic update rules, we enable translation of any rxncon model into a unique Boolean model, which can be used for network validation and simulation-allowing the prediction of system-level function directly from molecular mechanistic data. Through scalable model definition and simulation, and the independence of quantitative parameters, it opens up for simulation and validation of mechanistic genome-scale models of signal transduction networks.

Hybrid modelling of biological systems using fuzzy continuous Petri nets

Integrated modelling of biological systems is challenged by composing components with sufficient kinetic data and components with insufficient kinetic data or components built only using experts’ experience and knowledge. Fuzzy continuous Petri nets (FCPNs) combine continuous Petri nets with fuzzy inference systems, and thus offer an hybrid uncertain/certain approach to integrated modelling of such biological systems with uncertainties. In this paper, we give a formal definition and a corresponding simulation algorithm of FCPNs, and briefly introduce the FCPN tool that we have developed for implementing FCPNs. We then present a methodology and workflow utilizing FCPNs to achieve hybrid (uncertain/certain) modelling of biological systems illustrated with a case study of the Mercaptopurine metabolic pathway. We hope this research will promote the wider application of FCPNs and address the uncertain/certain integrated modelling challenge in the systems biology area.

Multiscale Multiobjective Systems Analysis (MiMoSA): an advanced metabolic modeling framework for complex systems

In natural environments, cells live in complex communities and experience a high degree of heterogeneity internally and in the environment. Even in 'ideal' laboratory environments, cells can experience a high degree of heterogeneity in their environments. Unfortunately, most of the metabolic modeling approaches that are currently used assume ideal conditions and that each cell is identical, limiting their application to pure cultures in well-mixed vessels. Here we describe our development of Multiscale Multiobjective Systems Analysis (MiMoSA), a metabolic modeling approach that can track individual cells in both space and time, track the diffusion of nutrients and light and the interaction of cells with each other and the environment. As a proof-of concept study, we used MiMoSA to model the growth of Trichodesmium erythraeum, a filamentous diazotrophic cyanobacterium which has cells with two distinct metabolic modes. The use of MiMoSA significantly improves our ability to predictively model metabolic changes and phenotype in more complex cell cultures.

Dynamic modeling and network approaches for omics time course data: overview of computational approaches and applications

Inferring networks and dynamics of genes, proteins, cells and other biological entities from high-throughput biological omics data is a central and challenging issue in computational and systems biology. This is essential for understanding the complexity of human health, disease susceptibility and pathogenesis for Predictive, Preventive, Personalized and Participatory (P4) system and precision medicine. The delineation of the possible interactions of all genes/proteins in a genome/proteome is a task for which conventional experimental techniques are ill suited. Urgently needed are rapid and inexpensive computational and statistical methods that can identify interacting candidate disease genes or drug targets out of thousands that can be further investigated or validated by experimentations. Moreover, identifying biological dynamic systems, and simultaneously estimating the important kinetic structural and functional parameters, which may not be experimentally accessible could be important directions for drug-disease-gene network studies. In this article, we present an overview and comparison of recent developments of dynamic modeling and network approaches for time-course omics data, and their applications to various biological systems, health conditions and disease statuses. Moreover, various data reduction and analytical schemes ranging from mathematical to computational to statistical methods are compared including their merits, drawbacks and limitations. The most recent software, associated web resources and other potentials for the compared methods are also presented and discussed in detail.

Modelling the role of redox-related mechanisms in musculoskeletal ageing

The decline in the musculoskeletal system with age is driven at the cellular level by random molecular damage. Cells possess mechanisms to repair or remove damage and many of the pathways involved in this response are regulated by redox signals. However, with ageing there is an increase in oxidative stress which can lead to chronic inflammation and disruption of redox signalling pathways. The complexity of the processes involved has led to the use of computational modelling to help increase our understanding of the system, test hypotheses and make testable predictions. This paper will give a brief background of the biological systems that have been modelled, an introduction to computational modelling, a review of models that involve redox-related mechanisms that are applicable to musculoskeletal ageing, and finally a discussion of the future potential for modelling in this field.

Visualization and Analysis of Epiproteome Dynamics

The epiproteome describes the set of all post-translational modifications (PTMs) made to the proteins comprising a cell or organism. The extent of the epiproteome is still largely unknown; however, advances in experimental techniques are beginning to produce a deluge of data, tracking dynamic changes to the epiproteome in response to cellular stimuli. These data have potential to revolutionize our understanding of biology and disease. This review covers a range of recent visualization methods and tools developed specifically for dynamic epiproteome data sets. These methods have been designed primarily for data sets on phosphorylation, as this the most studied PTM; however, most of these methods are also applicable to other types of PTMs. Unfortunately, the currently available methods are often inadequate for existing data sets; thus, realizing the potential buried in epiproteome data sets will require new, tailored bioinformatics methods that will help researchers analyze, visualize, and interactively explore these complex data sets.

Quantifying the relative importance of experimental data points in parameter estimation

BACKGROUND

Ordinary differential equations (ODEs) are often used to understand biological processes. Since ODE-based models usually contain many unknown parameters, parameter estimation is an important step toward deeper understanding of the process. Parameter estimation is often formulated as a least squares optimization problem, where all experimental data points are considered as equally important. However, this equal-weight formulation ignores the possibility of existence of relative importance among different data points, and may lead to misleading parameter estimation results. Therefore, we propose to introduce weights to account for the relative importance of different data points when formulating the least squares optimization problem. Each weight is defined by the uncertainty of one data point given the other data points. If one data point can be accurately inferred given the other data, the uncertainty of this data point is low and the importance of this data point is low. Whereas, if inferring one data point from the other data is almost impossible, it contains a huge uncertainty and carries more information for estimating parameters.

RESULTS

G1/S transition model with 6 parameters and 12 parameters, and MAPK module with 14 parameters were used to test the weighted formulation. In each case, evenly spaced experimental data points were used. Weights calculated in these models showed similar patterns: high weights for data points in dynamic regions and low weights for data points in flat regions. We developed a sampling algorithm to evaluate the weighted formulation, and demonstrated that the weighted formulation reduced the redundancy in the data. For G1/S transition model with 12 parameters, we examined unevenly spaced experimental data points, strategically sampled to have more measurement points where the weights were relatively high, and fewer measurement points where the weights were relatively low. This analysis showed that the proposed weights can be used for designing measurement time points.

CONCLUSIONS

Giving a different weight to each data point according to its relative importance compared to other data points is an effective method for improving robustness of parameter estimation by reducing the redundancy in the experimental data.

Modernizing the Bradford Hill criteria for assessing causal relationships in observational data

Perhaps no other topic in risk analysis is more difficult, more controversial, or more important to risk management policy analysts and decision-makers than how to draw valid, correctly qualified causal conclusions from observational data. Statistical methods can readily quantify associations between observed variables using measures such as relative risk (RR) ratios, odds ratios (OR), slope coefficients for exposure or treatment variables in regression models, and quantities derived from these measures. Textbooks of epidemiology explain how to calculate population attributable fractions, attributable risks, burden-of-disease estimates, and probabilities of causation from relative risk (RR) ratios. Despite their suggestive names, these association-based measures have no necessary connection to causation if the associations on which they are based arise from bias, confounding, p-hacking, coincident historical trends, or other noncausal sources. But policy analysts and decision makers need something more: trustworthy predictions - and, later, evaluations - of the changes in outcomes caused by changes in policy variables. This concept of manipulative causation differs from the more familiar concepts of associational and attributive causation most widely used in epidemiology. Drawing on modern literature on causal discovery and inference principles and algorithms for drawing limited but useful causal conclusions from observational data, we propose seven criteria for assessing consistency of data with a manipulative causal exposure-response relationship - mutual information, directed dependence, internal and external consistency, coherent causal explanation of biological plausibility, causal mediation confirmation, and refutation of non-causal explanations - and discuss to what extent it is now possible to automate discovery of manipulative causal dependencies and quantification of causal effects from observational data. We compare our proposed principles for causal discovery and inference to the traditional Bradford Hill considerations from 1965. Understanding how old and new principles are related can clarify and enrich both.

From systems to biology: A computational analysis of the research articles on systems biology from 1992 to 2013

Systems biology is a discipline that studies biological systems from a holistic and interdisciplinary perspective. It brings together biologists, mathematicians, computer scientists, physicists, and engineers, so it has both biology-oriented components and systems-oriented components. We applied several computational tools to analyze the bibliographic information of published articles in systems biology to answer the question: Did the research topics of systems biology become more biology-oriented or more systems-oriented from 1992 to 2013? We analyzed the metadata of 9923 articles on systems biology from the Web of Science database. We identified the most highly cited 330 references using computational tools and through close reading we divided them into nine categories of research types in systems biology. Interestingly, we found that articles in one category, namely, systems biology’s applications in medical research, increased tremendously. This finding was corroborated by computational analysis of the abstracts, which also suggested that the percentages of topics on vaccines, diseases, drugs and cancers increased over time. In addition, we analyzed the institutional backgrounds of the corresponding authors of those 9923 articles and identified the most highly cited 330 authors over time. We found that before the mid-1990s, systems-oriented scientists had made the most referenced contributions. However, in recent years, researchers from biology-oriented institutions not only represented a huge percentage of the total number of researchers, but also had made the most referenced contributions. Notably, interdisciplinary institutions only produced a small percentage of researchers, but had made disproportionate contributions to this field.

In Silico Prediction of Large-Scale Microbial Production Performance: Constraints for Getting Proper Data-Driven Models

Industrial bioreactors range from 10.000 to 700.000 L and characteristically show different zones of substrate availabilities, dissolved gas concentrations and pH values reflecting physical, technical and economic constraints of scale-up. Microbial producers are fluctuating inside the bioreactors thereby experiencing frequently changing micro-environmental conditions. The external stimuli induce responses on microbial metabolism and on transcriptional regulation programs. Both may deteriorate the expected microbial production performance in large scale compared to expectations deduced from ideal, well-mixed lab-scale conditions. Accordingly, predictive tools are needed to quantify large-scale impacts considering bioreactor heterogeneities. The review shows that the time is right to combine simulations of microbial kinetics with calculations of large-scale environmental conditions to predict the bioreactor performance. Accordingly, basic experimental procedures and computational tools are presented to derive proper microbial models and hydrodynamic conditions, and to link both for bioreactor modeling. Particular emphasis is laid on the identification of gene regulatory networks as the implementation of such models will surely gain momentum in future studies.

In silico prediction of ErbB signal activation from receptor expression profiles through a data analytics pipeline

The ErbB signalling pathway has been studied extensively owing to its role in normal physiology and its dysregulation in cancer. Reverse engineering by mathematical models use the reductionist approach to characterize the network components. For an emergent, system-level view of the network, we propose a data analytics pipeline that can learn from the data generated by reverse engineering and use it to re-engineer the system with an agent-based approach. Data from a kinetic model that estimates the parameters by fitting to experiments on cell lines, were encoded into rules, for the interactions of the molecular species (agents) involved in biochemical reactions. The agent model, a digital representation of the cell line system, tracks the activation of ErbB1-3 receptors on binding with ligands, resulting in their dimerization, phosphorylation, trafficking and stimulation of downstream signalling through P13-Akt and Erk pathways. The analytics pipeline has been used to mechanistically link HER expression profile to receptor dimerization and activation of downstream signalling pathways. When applied to drug studies, the efficacy of a drug can be investigated in silico. The anti-tumour activity of Pertuzumab, a monoclonal antibody that inhibits HER2 dimerization, was simulated by blocking 80% of the cellular HER2 available, to observe the effect on signal activation.

DSGRN: Examining the Dynamics of Families of Logical Models

We present a computational tool DSGRN for exploring the dynamics of a network by computing summaries of the dynamics of switching models compatible with the network across all parameters. The network can arise directly from a biological problem, or indirectly as the interaction graph of a Boolean model. This tool computes a finite decomposition of parameter space such that for each region, the state transition graph that describes the coarse dynamical behavior of a network is the same. Each of these parameter regions corresponds to a different logical description of the network dynamics. The comparison of dynamics across parameters with experimental data allows the rejection of parameter regimes or entire networks as viable models for representing the underlying regulatory mechanisms. This in turn allows a search through the space of perturbations of a given network for networks that robustly fit the data. These are the first steps toward discovering a network that optimally matches the observed dynamics by searching through the space of networks.

Petri net siphon analysis and graph theoretic measures for identifying combination therapies in cancer

Epidermal Growth Factor Receptor (EGFR) signaling to the Ras-MAPK pathway is implicated in the development and progression of cancer and is a major focus of targeted combination therapies. Physiochemical models have been used for identifying and testing the signal-inhibiting potential of targeted therapies, however, their application to larger multi-pathway networks is limited by the availability of experimentally-determined rate and concentration parameters. An alternate strategy for identifying and evaluating drug-targetable nodes is proposed. A physiochemical model of EGFR-Ras-MAPK signaling is implemented and calibrated to experimental data. Essential topological features of the model are converted into a Petri net and nodes that behave as siphons-a structural property of Petri nets-are identified. Siphons represent potential drug-targets since they are unrecoverable if their values fall below a threshold. Centrality measures are then used to prioritize siphons identified as candidate drug-targets. Single and multiple drug-target combinations are identified which correspond to clinically relevant drug targets and exhibit inhibition synergy in physiochemical simulations of EGF-induced EGFR-Ras-MAPK signaling. Taken together, these studies suggest that siphons and centrality analyses are a promising computational strategy to identify and rank drug-targetable nodes in larger networks as they do not require knowledge of the dynamics of the system, but rely solely on topology.

The best models of metabolism

Biochemical systems are among of the oldest application areas of mathematical modeling. Spanning a time period of over one hundred years, the repertoire of options for structuring a model and for formulating reactions has been constantly growing, and yet, it is still unclear whether or to what degree some models are better than others and how the modeler is to choose among them. In fact, the variety of options has become overwhelming and difficult to maneuver for novices and experts alike. This review outlines the metabolic model design process and discusses the numerous choices for modeling frameworks and mathematical representations. It tries to be inclusive, even though it cannot be complete, and introduces the various modeling options in a manner that is as unbiased as that is feasible. However, the review does end with personal recommendations for the choices of default models. WIREs Syst Biol Med 2017, 9:e1391. doi: 10.1002/wsbm.1391 For further resources related to this article, please visit the WIREs website.

ML-Space: Hybrid Spatial Gillespie and Particle Simulation of Multi-Level Rule-Based Models in Cell Biology

Spatio-temporal dynamics of cellular processes can be simulated at different levels of detail, from (deterministic) partial differential equations via the spatial Stochastic Simulation algorithm to tracking Brownian trajectories of individual particles. We present a spatial simulation approach for multi-level rule-based models, which includes dynamically hierarchically nested cellular compartments and entities. Our approach ML-Space combines discrete compartmental dynamics, stochastic spatial approaches in discrete space, and particles moving in continuous space. The rule-based specification language of ML-Space supports concise and compact descriptions of models and to adapt the spatial resolution of models easily.

MicroRNA pharmacogenomics based integrated model of miR-17-92 cluster in sorafenib resistant HCC cells reveals a strategy to forestall drug resistance

Among solid tumors, hepatocellular carcinoma (HCC) emerges as a prototypical therapy-resistant tumor. Considering the emerging sorafenib resistance crisis in HCC, future studies are urgently required to overcome resistance. Recently noncoding RNAs (ncRNAs) have emerged as significant regulators in signalling pathways involved in cancer drug resistance and pharmacologically targeting these ncRNAs might be a novel stratagem to reverse drug resistance. In the current study, using a hybrid Petri net based computational model, we have investigated the harmonious effect of miR-17-92 cluster inhibitors/mimics and circular RNAs on sorafenib resistant HCC cells in order to explore potential resistance mechanisms and to identify putative targets for sorafenib-resistant HCC cells. An integrated model was developed that incorporates seven miRNAs belonging to miR-17-92 cluster (hsa-miR-17-5p, hsa-miR-17-3p, hsa-miR-19a, hsa-miR-19b, hsa-miR-18a, hsa-miR-20a and hsa-miR-92) and crosstalk of two signaling pathways (EGFR and IL-6) that are differentially regulated by these miRNAs. The mechanistic connection was proposed by the correlation between members belonging to miR-17-92 cluster and corresponding changes in the protein levels of their targets in HCC, specifically those targets that have verified importance in sorafenib resistance. Current findings uncovered potential pathway features, underlining the significance of developing modulators of this cluster to combat drug resistance in HCC.

Pathway Analysis with Signaling Hypergraphs

Signaling pathways play an important role in the cell's response to its environment. Signaling pathways are often represented as directed graphs, which are not adequate for modeling reactions such as complex assembly and dissociation, combinatorial regulation, and protein activation/inactivation. More accurate representations such as directed hypergraphs remain underutilized. In this paper, we present an extension of a directed hypergraph that we call a signaling hypergraph. We formulate a problem that asks what proteins and interactions must be involved in order to stimulate a specific response downstream of a signaling pathway. We relate this problem to computing the shortest acyclic B-hyperpath in a signaling hypergraph-an NP-hard problem-and present a mixed integer linear program to solve it. We demonstrate that the shortest hyperpaths computed in signaling hypergraphs are far more informative than shortest paths, Steiner trees, and subnetworks containing many short paths found in corresponding graph representations. Our results illustrate the potential of signaling hypergraphs as an improved representation of signaling pathways and motivate the development of novel hypergraph algorithms.

Multi-level and hybrid modelling approaches for systems biology

During the last decades, high-throughput techniques allowed for the extraction of a huge amount of data from biological systems, unveiling more of their underling complexity. Biological systems encompass a wide range of space and time scales, functioning according to flexible hierarchies of mechanisms making an intertwined and dynamic interplay of regulations. This becomes particularly evident in processes such as ontogenesis, where regulative assets change according to process context and timing, making structural phenotype and architectural complexities emerge from a single cell, through local interactions. The information collected from biological systems are naturally organized according to the functional levels composing the system itself. In systems biology, biological information often comes from overlapping but different scientific domains, each one having its own way of representing phenomena under study. That is, the different parts of the system to be modelled may be described with different formalisms. For a model to have improved accuracy and capability for making a good knowledge base, it is good to comprise different system levels, suitably handling the relative formalisms. Models which are both multi-level and hybrid satisfy both these requirements, making a very useful tool in computational systems biology. This paper reviews some of the main contributions in this field.

Systems modelling ageing: from single senescent cells to simple multi-cellular models

Systems modelling has been successfully used to investigate several key molecular mechanisms of ageing. Modelling frameworks to allow integration of models and methods to enhance confidence in models are now well established. In this article, we discuss these issues and work through the process of building an integrated model for cellular senescence as a single cell and in a simple tissue context.

Computational dynamic approaches for temporal omics data with applications to systems medicine

Modeling and predicting biological dynamic systems and simultaneously estimating the kinetic structural and functional parameters are extremely important in systems and computational biology. This is key for understanding the complexity of the human health, drug response, disease susceptibility and pathogenesis for systems medicine. Temporal omics data used to measure the dynamic biological systems are essentials to discover complex biological interactions and clinical mechanism and causations. However, the delineation of the possible associations and causalities of genes, proteins, metabolites, cells and other biological entities from high throughput time course omics data is challenging for which conventional experimental techniques are not suited in the big omics era. In this paper, we present various recently developed dynamic trajectory and causal network approaches for temporal omics data, which are extremely useful for those researchers who want to start working in this challenging research area. Moreover, applications to various biological systems, health conditions and disease status, and examples that summarize the state-of-the art performances depending on different specific mining tasks are presented. We critically discuss the merits, drawbacks and limitations of the approaches, and the associated main challenges for the years ahead. The most recent computing tools and software to analyze specific problem type, associated platform resources, and other potentials for the dynamic trajectory and interaction methods are also presented and discussed in detail.

Agent-based re-engineering of ErbB signaling: a modeling pipeline for integrative systems biology

Motivation

Experiments in systems biology are generally supported by a computational model which quantitatively estimates the parameters of the system by finding the best fit to the experiment. Mathematical models have proved to be successful in reverse engineering the system. The data generated is interpreted to understand the dynamics of the underlying phenomena. The question we have sought to answer is that - is it possible to use an agent-based approach to re-engineer a biological process, making use of the available knowledge from experimental and modelling efforts? Can the bottom-up approach benefit from the top-down exercise so as to create an integrated modelling formalism for systems biology? We propose a modelling pipeline that learns from the data given by reverse engineering, and uses it for re-engineering the system, to carry out in-silico experiments.

Results

A mathematical model that quantitatively predicts co-expression of EGFR-HER2 receptors in activation and trafficking has been taken for this study. The pipeline architecture takes cues from the population model that gives the rates of biochemical reactions, to formulate knowledge-based rules for the particle model. Agent-based simulations using these rules, support the existing facts on EGFR-HER2 dynamics. We conclude that, re-engineering models, built using the results of reverse engineering, opens up the possibility of harnessing the power pack of data which now lies scattered in literature. Virtual experiments could then become more realistic when empowered with the findings of empirical cell biology and modelling studies.

Availability and Implementation

Implemented on the Agent Modelling Framework developed in-house. C ++ code templates available in Supplementary material .

Contact

liz.csir@gmail.com.

Supplementary information

Supplementary data are available at Bioinformatics online.

Modelling the molecular mechanisms of aging

The aging process is driven at the cellular level by random molecular damage that slowly accumulates with age. Although cells possess mechanisms to repair or remove damage, they are not 100% efficient and their efficiency declines with age. There are many molecular mechanisms involved and exogenous factors such as stress also contribute to the aging process. The complexity of the aging process has stimulated the use of computational modelling in order to increase our understanding of the system, test hypotheses and make testable predictions. As many different mechanisms are involved, a wide range of models have been developed. This paper gives an overview of the types of models that have been developed, the range of tools used, modelling standards and discusses many specific examples of models that have been grouped according to the main mechanisms that they address. We conclude by discussing the opportunities and challenges for future modelling in this field.