Complexity and modularity of intracellular networks: a systematic approach for modelling and simulation

A Systems Biology Approach Towards a Comprehensive Understanding of Ferroptosis

Ferroptosis is a regulated cell death process characterized by iron ion catalysis and reactive oxygen species, leading to lipid peroxidation. This mechanism plays a crucial role in age-related diseases, including cancer and cardiovascular and neurological disorders. To better mimic iron-induced cell death, predict the effects of various elements, and identify drugs capable of regulating ferroptosis, it is essential to develop precise models of this process. Such drugs can be tested on cellular models. Systems biology offers a powerful approach to studying biological processes through modeling, which involves accumulating and analyzing comprehensive research data. Once a model is created, it allows for examining the system's response to various stimuli. Our goal is to develop a modular framework for ferroptosis, enabling the prediction and screening of compounds with geroprotective and antiferroptotic effects. For modeling and analysis, we utilized BioUML (Biological Universal Modeling Language), which supports key standards in systems biology, modular and visual modeling, rapid simulation, parameter estimation, and a variety of numerical methods. This combination fulfills the requirements for modeling complex biological systems. The integrated modular model was validated on diverse datasets, including original experimental data. This framework encompasses essential molecular genetic processes such as the Fenton reaction, iron metabolism, lipid synthesis, and the antioxidant system. We identified structural relationships between molecular agents within each module and compared them to our proposed system for regulating the initiation and progression of ferroptosis. Our research highlights that no current models comprehensively cover all regulatory mechanisms of ferroptosis. By integrating data on ferroptosis modules into an integrated modular model, we can enhance our understanding of its mechanisms and assist in the discovery of new treatment targets for age-related diseases. A computational model of ferroptosis was developed based on a modular modeling approach and included 73 differential equations and 93 species.

A framework for multi-scale intervention modeling: virtual cohorts, virtual clinical trials, and model-to-model comparisons

Computational models of disease progression have been constructed for a myriad of pathologies. Typically, the conceptual implementation for pathology-related in-silico intervention studies has been ad-hoc and similar in design to experimental studies. We introduce a multi-scale interventional design (MID) framework toward two key goals: tracking of disease dynamics from within-body to patient to population scale; and tracking impact(s) of interventions across these same spatial scales. Our MID framework prioritizes investigation of impact on individual patients within virtual pre-clinical trials, instead of replicating the design of experimental studies. We apply a MID framework to develop, organize, and analyze a cohort of virtual patients for the study of tuberculosis (TB) as an example disease. For this study, we use HostSim: our next-generation whole patient-scale computational model of individuals infected with Mycobacterium tuberculosis. HostSim captures infection within lungs by tracking multiple granulomas, together with dynamics occurring with blood and lymph node compartments, the compartments involved during pulmonary TB. We extend HostSim to include a simple drug intervention as an example of our approach and use our MID framework to quantify the impact of treatment at cellular and tissue (granuloma), patient (lungs, lymph nodes and blood), and population scales. Sensitivity analyses allow us to determine which features of virtual patients are the strongest predictors of intervention efficacy across scales. These insights allow us to identify patient-heterogeneous mechanisms that drive outcomes across scales.

Physiologically Based Pharmacokinetic Modeling of Nanoparticle Biodistribution: A Review of Existing Models, Simulation Software, and Data Analysis Tools

Cancer treatment and pharmaceutical development require targeted treatment and less toxic therapeutic intervention to achieve real progress against this disease. In this scenario, nanomedicine emerged as a reliable tool to improve drug pharmacokinetics and to translate to the clinical biologics based on large molecules. However, the ability of our body to recognize foreign objects together with carrier transport heterogeneity derived from the combination of particle physical and chemical properties, payload and surface modification, make the designing of effective carriers very difficult. In this scenario, physiologically based pharmacokinetic modeling can help to design the particles and eventually predict their ability to reach the target and treat the tumor. This effort is performed by scientists with specific expertise and skills and familiarity with artificial intelligence tools such as advanced software that are not usually in the "cords" of traditional medical or material researchers. The goal of this review was to highlight the advantages that computational modeling could provide to nanomedicine and bring together scientists with different background by portraying in the most simple way the work of computational developers through the description of the tools that they use to predict nanoparticle transport and tumor targeting in our body.

Modular Representation of Physiologically Based Pharmacokinetic Models: Nanoparticle Delivery to Solid Tumors in Mice as an Example

Here we describe a toolkit for presenting physiologically based pharmacokinetic (PBPK) models in a modular graphical view in the BioUML platform. Firstly, we demonstrate the BioUML capabilities for PBPK modeling tested on an existing model of nanoparticles delivery to solid tumors in mice. Secondly, we provide guidance on the conversion of the PBPK model code from a text modeling language like Berkeley Madonna to a visual modular diagram in the BioUML. We give step-by-step explanations of the model transformation and demonstrate that simulation results from the original model are exactly the same as numerical results obtained for the transformed model. The main advantage of the proposed approach is its clarity and ease of perception. Additionally, the modular representation serves as a simplified and convenient base for in silico investigation of the model and reduces the risk of technical errors during its reuse and extension by concomitant biochemical processes. In summary, this article demonstrates that BioUML can be used as an alternative and robust tool for PBPK modeling.

Rule-based epidemic models

Rule-based models generalise reaction-based models with reagents that have internal state and may be bound together to form complexes, as in chemistry. An important class of system that would be intractable if expressed as reactions or ordinary differential equations can be efficiently simulated when expressed as rules. In this paper we demonstrate the utility of the rule-based approach for epidemiological modelling presenting a suite of seven models illustrating the spread of infectious disease under different scenarios: wearing masks, infection via fomites and prevention by hand-washing, the concept of vector-borne diseases, testing and contact tracing interventions, disease propagation within motif-structured populations with shared environments such as schools, and superspreading events. Rule-based models allow to combine transparent modelling approach with scalability and compositionality and therefore can facilitate the study of aspects of infectious disease propagation in a richer context than would otherwise be feasible.

Thoroughly Calibrated Modular Agent-Based Model of the Human Cardiovascular and Renal Systems for Blood Pressure Regulation in Health and Disease

Here we present a modular agent-based mathematical model of the human cardiovascular and renal systems. It integrates the previous models primarily developed by A. C. Guyton, F. Karaaslan, K. M. Hallow, and Y. V. Solodyannikov. We performed the model calibration to find an equilibrium state within the normal vital sign ranges for a healthy adult. We verified the model's abilities to reproduce equilibrium states with abnormal physiological values related to different combinations of cardiovascular diseases (such as systemic hypertension, chronic heart failure, pulmonary hypertension, etc.). For the model creation and validation, we involved over 200 scientific studies covering known models of the human cardiovascular and renal functions, biosimulation platforms, and clinical measurements of physiological quantities in normal and pathological conditions. We compiled detailed documentation describing all equations, parameters and variables of the model with justification of all formulas and values. The model is implemented in BioUML and available in the web-version of the software.

A Modular Mathematical Model of Exercise-Induced Changes in Metabolism, Signaling, and Gene Expression in Human Skeletal Muscle

Skeletal muscle is the principal contributor to exercise-induced changes in human metabolism. Strikingly, although it has been demonstrated that a lot of metabolites accumulating in blood and human skeletal muscle during an exercise activate different signaling pathways and induce the expression of many genes in working muscle fibres, the systematic understanding of signaling-metabolic pathway interrelations with downstream genetic regulation in the skeletal muscle is still elusive. Herein, a physiologically based computational model of skeletal muscle comprising energy metabolism, Ca2+, and AMPK (AMP-dependent protein kinase) signaling pathways and the expression regulation of genes with early and delayed responses was developed based on a modular modeling approach and included 171 differential equations and more than 640 parameters. The integrated modular model validated on diverse including original experimental data and different exercise modes provides a comprehensive in silico platform in order to decipher and track cause-effect relationships between metabolic, signaling, and gene expression levels in skeletal muscle.

Model-driven engineering of supramolecular buffering by multivalency

The ability of chemists to regulate the concentration of molecules is extremely important. However, as reactions are slowly superseded by more complex reaction networks, new ways of regulating molecular concentrations are needed. Recently, we described a system in which the concentration of a monovalent molecule with catalytic activity was buffered over a wide concentration range by its binding to a divalent molecule. Guided by model predictions, we are able to experimentally optimize the system by increasing the valency of the buffer, with even-numbered valencies displaying superior buffering capabilities. These results allow us to understand and gain more control over the activities of molecules in complex molecular systems, thereby obtaining insights into natural systems as well as creating adaptive artificial systems.

A supramolecular system in which the concentration of a molecule is buffered over several orders of magnitude is presented. Molecular buffering is achieved as a result of competition in a ring–chain equilibrium of multivalent ureidopyrimidinone monomers and a monovalent naphthyridine molecule which acts as an end-capper. While we previously only considered divalent ureidopyrimidinone monomers we now present a model-driven engineering approach to improve molecular buffering using multivalent ring–chain systems. Our theoretical models reveal an odd–even effect where even-valent molecules show superior buffering capabilities. Furthermore, we predict that supramolecular buffering can be significantly improved using a tetravalent instead of a divalent molecule, since the tetravalent molecule can form two intramolecular rings with different “stabilities” due to statistical effects. Our model predictions are validated against experimental ¹H NMR data, demonstrating that model-driven engineering has considerable potential in supramolecular chemistry.

Annotation of rule-based models with formal semantics to enable creation, analysis, reuse and visualization

MOTIVATION

Biological systems are complex and challenging to model and therefore model reuse is highly desirable. To promote model reuse, models should include both information about the specifics of simulations and the underlying biology in the form of metadata. The availability of computationally tractable metadata is especially important for the effective automated interpretation and processing of models. Metadata are typically represented as machine-readable annotations which enhance programmatic access to information about models. Rule-based languages have emerged as a modelling framework to represent the complexity of biological systems. Annotation approaches have been widely used for reaction-based formalisms such as SBML. However, rule-based languages still lack a rich annotation framework to add semantic information, such as machine-readable descriptions, to the components of a model.

RESULTS

We present an annotation framework and guidelines for annotating rule-based models, encoded in the commonly used Kappa and BioNetGen languages. We adapt widely adopted annotation approaches to rule-based models. We initially propose a syntax to store machine-readable annotations and describe a mapping between rule-based modelling entities, such as agents and rules, and their annotations. We then describe an ontology to both annotate these models and capture the information contained therein, and demonstrate annotating these models using examples. Finally, we present a proof of concept tool for extracting annotations from a model that can be queried and analyzed in a uniform way. The uniform representation of the annotations can be used to facilitate the creation, analysis, reuse and visualization of rule-based models. Although examples are given, using specific implementations the proposed techniques can be applied to rule-based models in general.

AVAILABILITY AND IMPLEMENTATION

The annotation ontology for rule-based models can be found at http://purl.org/rbm/rbmo The krdf tool and associated executable examples are available at http://purl.org/rbm/rbmo/krdf

CONTACT

anil.wipat@newcastle.ac.uk or vdanos@inf.ed.ac.uk.

Toward modular biological models: defining analog modules based on referent physiological mechanisms

Background

Currently, most biomedical models exist in isolation. It is often difficult to reuse or integrate models or their components, in part because they are not modular. Modular components allow the modeler to think more deeply about the role of the model and to more completely address a modeling project’s requirements. In particular, modularity facilitates component reuse and model integration for models with different use cases, including the ability to exchange modules during or between simulations. The heterogeneous nature of biology and vast range of wet-lab experimental platforms call for modular models designed to satisfy a variety of use cases. We argue that software analogs of biological mechanisms are reasonable candidates for modularization. Biomimetic software mechanisms comprised of physiomimetic mechanism modules offer benefits that are unique or especially important to multi-scale, biomedical modeling and simulation.

Results

We present a general, scientific method of modularizing mechanisms into reusable software components that we call physiomimetic mechanism modules (PMMs). PMMs utilize parametric containers that partition and expose state information into physiologically meaningful groupings. To demonstrate, we modularize four pharmacodynamic response mechanisms adapted from an in silico liver (ISL). We verified the modularization process by showing that drug clearance results from in silico experiments are identical before and after modularization. The modularized ISL achieves validation targets drawn from propranolol outflow profile data. In addition, an in silico hepatocyte culture (ISHC) is created. The ISHC uses the same PMMs and required no refactoring. The ISHC achieves validation targets drawn from propranolol intrinsic clearance data exhibiting considerable between-lab variability. The data used as validation targets for PMMs originate from both in vitro to in vivo experiments exhibiting large fold differences in time scale.

Conclusions

This report demonstrates the feasibility of PMMs and their usefulness across multiple model use cases. The pharmacodynamic response module developed here is robust to changes in model context and flexible in its ability to achieve validation targets in the face of considerable experimental uncertainty. Adopting the modularization methods presented here is expected to facilitate model reuse and integration, thereby accelerating the pace of biomedical research.

CaMKII activation and dynamics are independent of the holoenzyme structure: an infinite subunit holoenzyme approximation

The combinatorial explosion produced by the multi-state, multi-subunit character of CaMKII has made analysis and modeling of this key signaling protein a significant challenge. Using rule-based and particle-based approaches, we construct exact models of CaMKII holoenzyme dynamics and study these models as a function of the number of subunits per holoenzyme, N. Without phosphatases the dynamics of activation are independent of the holoenzyme structure unless phosphorylation significantly alters the kinase activity of a subunit. With phosphatases the model is independent of holoenzyme size for N > 6. We introduce an infinite subunit holoenzyme approximation (ISHA), which simplifies the modeling by eliminating the combinatorial complexities encountered in any finite holoenzyme model. The ISHA is an excellent approximation to the full system over a broad range of physiologically relevant parameters. Finally, we demonstrate that the ISHA reproduces the behavior of exact models during synaptic plasticity protocols, which justifies its use as a module in large models of synaptic plasticity.

Using views of Systems Biology Cloud: application for model building

A large and growing network ("cloud") of interlinked terms and records of items of Systems Biology knowledge is available from the web. These items include pathways, reactions, substances, literature references, organisms, and anatomy, all described in different data sets. Here, we discuss how the knowledge from the cloud can be molded into representations (views) useful for data visualization and modeling. We discuss methods to create and use various views relevant for visualization, modeling, and model annotations, while hiding irrelevant details without unacceptable loss or distortion. We show that views are compatible with understanding substances and processes as sets of microscopic compounds and events respectively, which allows the representation of specializations and generalizations as subsets and supersets respectively. We explain how these methods can be implemented based on the bridging ontology Systems Biological Pathway Exchange (SBPAX) in the Systems Biology Linker (SyBiL) we have developed.

Annotation of SBML models through rule-based semantic integration

BACKGROUND

The creation of accurate quantitative Systems Biology Markup Language (SBML) models is a time-intensive, manual process often complicated by the many data sources and formats required to annotate even a small and well-scoped model. Ideally, the retrieval and integration of biological knowledge for model annotation should be performed quickly, precisely, and with a minimum of manual effort.

RESULTS

Here we present rule-based mediation, a method of semantic data integration applied to systems biology model annotation. The heterogeneous data sources are first syntactically converted into ontologies, which are then aligned to a small domain ontology by applying a rule base. We demonstrate proof-of-principle of this application of rule-based mediation using off-the-shelf semantic web technology through two use cases for SBML model annotation. Existing tools and technology provide a framework around which the system is built, reducing development time and increasing usability.

CONCLUSIONS

Integrating resources in this way accommodates multiple formats with different semantics, and provides richly-modelled biological knowledge suitable for annotation of SBML models. This initial work establishes the feasibility of rule-based mediation as part of an automated SBML model annotation system.

AVAILABILITY

Detailed information on the project files as well as further information on and comparisons with similar projects is available from the project page at http://cisban-silico.cs.ncl.ac.uk/RBM/.

The natural and engineered 3D microenvironment as a regulatory cue during stem cell fate determination

The concept of using stem cells as self-renewing sources of healthy cells in regenerative medicine has existed for decades, but most applications have yet to achieve clinical success. A main reason for the lack of successful stem cell therapies is the difficulty in fully recreating the maintenance and control of the native stem cell niche. Improving the performance of transplanted stem cells therefore requires a better understanding of the cellular mechanisms guiding stem cell behavior in both native and engineered three-dimensional (3D) microenvironments. Most techniques, however, for uncovering mechanisms controlling cell behavior in vitro have been developed using 2D cell cultures and are of limited use in 3D environments such as engineered tissue constructs. Deciphering the mechanisms controlling stem cell fate in native and engineered 3D environments, therefore, requires rigorous quantitative techniques that permit mechanistic, hypothesis-driven studies of cell-microenvironment interactions. Here, we review the current understanding of 2D and 3D stem cell control mechanisms and propose an approach to uncovering the mechanisms that govern stem cell behavior in 3D.

Molecular machines or pleiomorphic ensembles: signaling complexes revisited

Signaling complexes typically consist of highly dynamic molecular ensembles that are challenging to study and to describe accurately. Conventional mechanical descriptions misrepresent this reality and can be actively counterproductive by misdirecting us away from investigating critical issues.