Mathematical and Computational Modeling in Complex Biological Systems

In this article I address the interactions between biological knowledge and ideas about the kinds of entity that are suited to appropriation. I start by arguing that commodification and reductionism are closely linked, and that patenting suits entities that are discrete and isolable, such as those that are the focus of molecular biology. I then turn to the new field of systems biology, which recognizes that traditional reductionist approaches to biology are no longer adequate and attempts to provide a more integrative understanding of biological systems. In doing this, systems biology has to deal with emergent phenomena. But patenting does not suit the dynamic and interactive complexity that is the object of study in systems biology. If systems biology rejects reductionism where does that leave commodification? I examine attempts to commodify predictive computational models in systems biology. I then turn to systems biology's sister discipline, synthetic biology, which deals with emergence by reducing the complexity of biological systems. By factoring out messy contingencies, synthetic biology is, in theory, well suited to commodification. Drawing on both these examples I explore how ideas about appropriation, including open source, are influencing the nature and course of research in biology.

BACKGROUND: The Ayurvedic concept of Ama refers to the accumulation of incompletely digested or metabolized substances in the body due to impaired Agni (digestive fire). Ama is described as a pathological entity that disrupts systemic homeostasis, leading to chronic metabolic and immune disorders. Modern medical science recognizes similar pathological processes, such as endotoxin accumulation, gut dysbiosis, metabolic endotoxemia, and inflammatory responses driven by advanced glycation end-products (AGEs), damage-associated molecular patterns, and oxidative stress. Despite advances in research and clinical interventions, metabolic and immune disorders like diabetes, metabolic dysfunction-associated fatty liver disease, inflammatory bowel disease, and autoimmune conditions continue to rise globally. Expanding the scope of Ama and its subtypes in relation to these disorders may provide novel insights for disease prevention, diagnostics, and therapeutic approaches. EXISTING KNOWLEDGE AND GAP: Ayurvedic texts elaborate on Ama as a primary etiological factor in disease progression, classifying it based on its origins, affinity, and systemic translocation. However, there is a lack of standardized clinical assessment tools to evaluate Ama in the context of modern disease models. Current biomedical research highlights the crucial role of gut health, intestinal permeability, microbial dysbiosis, and metabolic endotoxemia in the development of chronic diseases. Despite these parallels, there is minimal integrative research correlating Ama with measurable biochemical or molecular markers. Moreover, the role of Ama in immune activation and inflammatory disorders remains largely unexplored within a scientific framework. PROPOSED CONCEPT: This paper proposes an expanded classification of Ama , integrating Ayurvedic epistemology with modern biomedical understanding. Ama can be characterized as a gut-derived response antigen complex or gut-associated molecular complex, which includes toxic metabolites, undigested peptides, microbial toxins, and inflammatory mediators resulting from impaired digestion and absorption. The subtypes of Ama can be categorized based on the site of expression, cause of origin, specificity or affinity, Kaal , and its movement or translocation. Modern tools such as metabolomics, proteomics, transcriptomics, and computational systems biology models can be employed to validate Ama and its subtypes. Biomarkers such as HbA1c (paralleling Ama in diabetes), lipid oxidation markers, gut microbiome alterations, and inflammatory cytokines may serve as objective correlates of Ama . WAY FORWARD: Future research should focus on developing standardized clinical scales for Ama assessment, incorporating radiological, biochemical, molecular, and genetic markers. Systems biology approaches, such as network pharmacology and artificial intelligence-based predictive models, should be utilized to map the progression of Ama in metabolic and immune disorders. Ayurvedic interventions, such as Deepana, Pachana , and Shodhana therapies, should be studied for their impact on gut barrier function, microbiome modulation, and immune homeostasis. Bridging Ayurvedic concepts with modern scientific methodologies will enable the development of personalized diagnostic and therapeutic strategies for chronic diseases.

A cornerstone of systems biology is the use of computational modeling, by which hypotheses can be cast into a quantitative form that can be tested systematically. The use of computational modeling by biologists promises to pave the way for more rigorous analyses of biological functions, and ultimately will lead to new and better treatments for disease.A crucial enabler for more widespread use of computational modeling in biology is reaching agreement on how to represent, store, and communicate models between software tools. The Systems Biology Markup Language (SBML) project is an effort to create a machine-readable format for representing computational models in biology. By supporting SBML as an input and output format, different software tools can operate on the same representation of a model, removing chances for errors in translation and assuring a common starting point for analyses and simulations. SBML has become the most successful effort in this direction so far, with over 100 software systems supporting it today.In this presentation, I will discuss the current state of SBML, including recent developments such as this year's finalization of Version 2 of SBML Level 2. I will also survey some of the software tools that support SBML, and related projects that have arisen to support more effective use of computational models. Lastly, I will discuss expected future developments in SBML.

Correction to: Addressing barriers in comprehensiveness, accessibility, reusability, interoperability and reproducibility of computational models in systems biology.

Mathematical modeling is key for systems level understanding of cellular processes. The development of mathematical models demands advanced computational tools that keep track of heterogeneous data of molecules and their interactions. Especially the integration of experimental data and pre-existing knowledge into computational models of biological systems is of considerable importance. In silico simulations of model behavior under similar conditions as in the experiment give the possibility for model validation regarding specific experimental data. Such an integrative approach leads eventually to a more accurate and consistent description of the observed biological system. We review several resources and computational tools which support the investigation of biological networks and describe several resources and methods for integrative modeling.

Systems biology has arisen through the convergence of theoretical, computational, and mathematical modeling of systems and the need to understand the wealth of information being rapidly generated in biology. Systems biology by its nature requires collaborations between scientists with expertise in biology, chemistry, computer sciences, engineering, mathematics, and physics. Successful integration of these disciplines depends on bringing to bear both social and technological tools: namely, consortia that help forge collaborations and common understanding, software tools that permit analysis of vast and complex data, and agreed-upon standards that enable researchers to communicate and reuse each other's results in practical and unambiguous ways. In this presentation, I will discuss several international projects (SBML, SBGN, and BioModels.net) aimed at addressing the last issue.An important prerequisite for effective sharing of computational models is reaching agreement on how to communicate them, both between software and between humans. The Systems Biology Markup Language (SBML) project is an effort to create a machine-readable format for representing computational models at the biochemical reaction level. By supporting SBML as an input and output format, different software tools can operate on the same representation of a model, removing chance for errors in translation and assuring a common starting point for analyses and simulations. SBML has become the most successful effort in this direction so far, with nearly 100 software tools supporting it today.A recently-created sister project is the Systems Biology Graphical Notation (SBGN) project. It addresses the issue of consistent human communication, by attempting to add more rigor and consistency to the graphical network diagrams that often accompany published research on models of biological reaction systems. The real payoff will come when more people and software adopt such a common visual notation and it becomes as familiar to them as circuit schematics are to electronics engineers.Finally, when developing and publishing computational models, it is only natural to want to put them into a database. The BioModels.net project is an effort to (1) provide a free, centralized, publicly-accessible database of human-curated computational models in SBML and other structured formats; (2) define agreed-upon standards for model curation; and (2) define agreed-upon vocabularies for annotating models with connections to biological data resources.

Computational modeling of biological systems is becoming increasingly important in the endeavors to better understand complex biological behavior. It enables researchers to perform computerized simulations using a systems biology approach, in order to understand the underlying mechanisms of certain biological phenomena. It provides an opportunity to perform experiments that are otherwise impractical or infeasible in vivo/vitro experiments. In our approach we propose to model and simulate the pathogenesis ofMycobacterium marinum using Petri Net formalism based on data obtained from analysis of microscope images and to provide a three dimensional visualization of the whole infection process and granuloma formation. Image analysis will provide an accurate estimation of the infection in a structured database which will be used for the construction of the Petri Net model. The results of the simulation and analysis of the infection behavior will be visualized in 3D.

Standardised management of tuberculosis may soon be replaced by individualised, precision medicine-guided therapies informed with knowledge provided by the field of systems biology. Systems biology is a rapidly expanding field of computational and mathematical analysis and modelling of complex biological systems that can provide insights into mechanisms underlying tuberculosis, identify novel biomarkers, and help to optimise prevention, diagnosis and treatment of disease. These advances are critically important in the context of the evolving epidemic of drug-resistant tuberculosis. Here, we review the available evidence on the role of systems biology approaches – human and mycobacterial genomics and transcriptomics, proteomics, lipidomics/metabolomics, immunophenotyping, systems pharmacology and gut microbiomes – in the management of tuberculosis including prediction of risk for disease progression, severity of mycobacterial virulence and drug resistance, adverse events, comorbidities, response to therapy and treatment outcomes. Application of the Grading of Recommendations, Assessment, Development and Evaluation (GRADE) approach demonstrated that at present most of the studies provide “very low” certainty of evidence for answering clinically relevant questions. Further studies in large prospective cohorts of patients, including randomised clinical trials, are necessary to assess the applicability of the findings in tuberculosis prevention and more efficient clinical management of patients.

In his famous essay, Lazebnik [1] discussed whether a biologist can fix a broken radio and suggested that applying the ‘biologist approach’ to a broken radio will likely not lead to a successful end, while any engineer or even a trained repairman evidently could fix the radio. In biology, the study of molecules one by one is fine for gathering information on how molecules work, but deciphering biological mechanisms, or the function of biological systems, is a different story. One difference between an engineer and a biologist, according to Lazebnik, lies in the language: in biology, language is oftentimes vague and nonquantitative which limits the possibility of making predictions [1]. In systems biology, a quantitative and predictive language is adopted to describe biological knowledge in order to understand how molecules act together within the network of interactions that makes up a living system. Systems biology, in other words, is the holistic analysis of complex systems. Indeed, systems biology can be defined as the computational and mathematical modeling of complex biological systems, in contrast to the traditional, reductionist approach to biology. Common technology platforms that are deployed to obtain complex datasets are transcriptomics, proteomics, metabolomics and epigenomics. However, systems biology should not be seen merely as the generation of lists of genes, proteins or metabolites using such omics platforms; the objective is to exploit these data and to develop quantitative models that describe the biological system and its response to individual perturbations (see [2] for an excellent introduction to this subject). Furthermore, systems biology can be seen as an iterative interplay between discoveryand hypothesis-driven science: “global observations (discoveries) are matched against model predictions (hypotheses) in an iterative manner, leading to the formation of new models, new predictions, and new experiments to test them” [2]. Systems toxicology, in turn, has been described as “the integration of classical toxicology with quantitative analysis of large networks of molecular and functional changes occurring across multiple levels of biological organization”, and it has been suggested that its application could be part of a new and improved risk assessment [3]. This is nothing less than a paradigm shift in the way that toxicology is conducted. Importantly, systems toxicology – and systems biology in general – relies heavily on computational approaches to manage, analyze and interpret the data generated by large-scale experiments, and computer databases are thus an integral feature of this approach [2]. To this end, commonly accepted repositories and software environments are crucially important [4]. This does not mean that the introduction of systems toxicology approaches is breaking the rice bowl of the classically trained toxicologist. Instead, the ‘new’ toxicology is Systems biology in nanosafety research

With the release of the landmark report Toxicity Testing in the 21st Century: A Vision and a Strategy, the U.S. National Academy of Sciences, in 2007, precipitated a major change in the way toxicity testing is conducted. It envisions increased efficiency in toxicity testing and decreased animal usage by transitioning from current expensive and lengthy in vivo testing with qualitative endpoints to in vitro toxicity pathway assays on human cells or cell lines using robotic high-throughput screening with mechanistic quantitative parameters. Risk assessment in the exposed human population would focus on avoiding significant perturbations in these toxicity pathways. Computational systems biology models would be implemented to determine the dose-response models of perturbations of pathway function. Extrapolation of in vitro results to in vivo human blood and tissue concentrations would be based on pharmacokinetic models for the given exposure condition. This practice would enhance human relevance of test results, and would cover several test agents, compared to traditional toxicological testing strategies. As all the tools that are necessary to implement the vision are currently available or in an advanced stage of development, the key prerequisites to achieving this paradigm shift are a commitment to change in the scientific community, which could be facilitated by a broad discussion of the vision, and obtaining necessary resources to enhance current knowledge of pathway perturbations and pathway assays in humans and to implement computational systems biology models. Implementation of these strategies would result in a new toxicity testing paradigm firmly based on human biology.

Computational models are becoming more and more the central scientific paradigm for understanding the complexity of living systems. With the increasing number and size of these models there is a growing need for model reuse and exchange. Furthermore, detailed models are not manageable without computer support. There are efforts to formalise the mathematical structure of models (e.g. SBML) and to standardise the kinetic and biological meaning of model components (e.g. SBO, GO, UniProt). However, formalising only the structure of computational models is not sufficient to easily exchange and reuse models and to achieve full computer support for modelling. We also need to formalise the pragmatical and dynamical aspects of models.For this purpose we propose two ontologies: The Kinetic Simulation Algorithm Ontology (KiSAO) and the TErminology for the Description of DYnamics (TEDDY). KiSAO covers algorithms used for simulation of computational models. The ontology classifies and puts into context existing simulation algorithms. For the classification, it uses several criteria such as deterministic/stochastic or spatial/nonspatial. The aim of TEDDY is to provide terms for describing and characterising dynamical behaviours, observable dynamical phenomena, and control elements of biological models and biological systems in Systems Biology and Synthetic Biology.We demonstrate how these new ontologies can extend the formalisation of models beyond structure, using the well-known repressilator model as an example. The simulation results depend pragmatically on the used algorithm: We compare the simulation results of the deterministic Livermore solver for ordinary differential equations (KiSAO:0000071) to the simulation results of the stochastic Gibson and Bruck’s next reaction method (KiSAO:0000027). The simulation results depend dynamically on the parameter setting: While parameter * (maximum number of produced proteins per promotor) is increased the modelled dynamical system undergoes a Supercritical Hopf Bifurcation (TEDDY_0000074). Below the critical value of * the system exhibits _Damped Oscillation_ (TEDDY_0000063) converging to a Stable Spiral Point (TEDDY_0000126). Above the bifurcation the system possesses a Stable _Limit Cycle_ (TEDDY_0000114), i.e. it shows Sustained Oscillation. The Negative Feedback (TEDDY_0000034) of the system is a necessary precondition for the ability of the system to oscillate.For details on KiSAO see the "MIASE project page":http://sourceforge.net/projects/miase, for details on TEDDY see the "project page":http://sourceforge.net/projects/teddyontology.

In this poster, we present our experience with techniques for the management of bio-models (i.e. XML-encoded computational models of biological systems) in repositories. These techniques support users to find, access, adapt and then re-submit models - tasks which are essential for the reuse of models in systems biology. Here, we focus on model retrieval, the ranking of search results and concepts to track the history of a model through version control. These concepts have so far not been sufficiently addressed in existing systems.To validate our techniques, we have been implemented a framework called Sombi. The underlying database called mDB is tailored towards a fine-grained storage of the model and its annotations. The design is applicable to different representation formats but, to begin with, has been tested with SBML models (Köhn et al., 2009).We furthermore present a retrieval algorithm for bio-model repositories (Henkel et al., 2010). The algorithm has been implemented and validated with mDB and the BioModels Database (www.ebi.ac.uk/biomodels-main/). The ranked retrieval enhances the result set by incorporating expert knowledge in the annotations. In contrast to existing systems, our approach provides a ranked result which is justified and explains the ordering of retrieved models to the users. The mDB design furthermore enables the application of structured queries on the stored model data.Finally, the poster proposes a solution to model version control. We introduce a library called BiVeS for tracking a model’s history in a diff tree; i.e. a tree-like storage of changes between model versions. These changes are additionally classified into modifications to XML structure, biology and mathematics. This information helps to understand existing models.All approaches are independent of the SBML format and can therefore be applied to other XML based exchange formats. All code is freely available on Sourceforge from http://bives.sourceforge.net/ and http://sombi.sourceforge.net/.

SummaryThe Computational Modelling of Systems Biology (SysMod) Community of Special Interest (COSI) convenes annually at the Intelligent Systems for Molecular Biology (ISMB) conference to facilitate knowledge dissemination and exchange of research findings on systems modelling from interdisciplinary domains. The SysMod meeting 2022 was held in a hybrid mode in Madison, Wisconsin, spanning a 1-day duration centred on modelling techniques, applications, and single-cell technology implementations. The meeting showcased innovative approaches to modelling biological systems using cell-specific and multiscale modelling, multiomics data integration, and novel tools to develop systems models using single-cell and multiomics technology. The meeting also recognized outstanding research by awarding the three best posters. This report summarizes the key highlights and outcomes of the meeting.Availability and implementationAll resources and further information are freely accessible at https://sysmod.info.

Computational Modeling of Protein Networks Predicts Treatment Outcomes in Multiple Myeloma (MM)

The exploding number of computational models produced by Systems Biologists over the last years is an invitation to structure and exploit this new wealth of information. Researchers would like to trace models relevant to specific scientific questions, to explore their biological content, to align and combine them, and to match them with experimental data. To automate these processes, it is essential to consider semantic annotations, which describe their biological meaning. As a prerequisite for a wide range of computational methods, we propose general and flexible similarity measures for Systems Biology models computed from semantic annotations. By using these measures and a large extensible ontology, we implement a platform that can retrieve, cluster, and align Systems Biology models and experimental data sets. At present, its major application is the search for relevant models in the BioModels Database, starting from initial models, data sets, or lists of biological concepts. Beyond similarity searches, the representation of models by semantic feature vectors may pave the way for visualisation, exploration, and statistical analysis of large collections of models and corresponding data.