Hybrid modelling of biological systems: current progress and future prospects

Copyright © 2022 The Author(s). 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.National Natural Science Foundation of China (61873094)

Modeling of dynamic systems with Petri nets and fuzzy logic

Aktuelle Methoden zur dynamischen Modellierung von biologischen Systemen sind für Benutzer ohne mathematische Ausbildung oft wenig verständlich. Des Weiteren fehlen sehr oft genaue Daten und detailliertes Wissen über Konzentrationen, Reaktionskinetiken oder regulatorische Effekte. Daher erfordert eine computergestützte Modellierung eines biologischen Systems, mit Unsicherheiten und grober Information umzugehen, die durch qualitatives Wissen und natürlichsprachliche Beschreibungen zur Verfügung gestellt wird. Der Autor schlägt einen neuen Ansatz vor, mit dem solche Beschränkungen überwunden werden können. Dazu wird eine Petri-Netz-basierte graphische Darstellung von Systemen mit einer leistungsstarken und dennoch intuitiven Fuzzy-Logik-basierten Modellierung verknüpft. Der Petri Netz und Fuzzy Logik (PNFL) Ansatz erlaubt eine natürlichsprachlich-basierte Beschreibung von biologischen Entitäten sowie eine Wenn-Dann-Regel-basierte Definition von Reaktionen. Beides kann einfach und direkt aus qualitativem Wissen abgeleitet werden. PNFL verbindet damit qualitatives Wissen und quantitative Modellierung.Current approaches in dynamic modeling of biological systems often lack comprehensibility,n especially for users without mathematical background. Additionally, exact data or detailed knowledge about concentrations, reaction kinetics or regulatory effects is missing. Thus, computational modeling of a biological system requires dealing with uncertainty and rough information provided by qualitative knowledge and linguistic descriptions. The author proposes a new approach to overcome such limitations by combining the graphical representation provided by Petri nets with the modeling of dynamics by powerful yet intuitive fuzzy logic based systems. The Petri net and fuzzy logic (PNFL) approach allows natural language based descriptions of biological entities as well as if-then rule based definitions of reactions, both of which can be easily and directly derived from qualitative knowledge. PNFL bridges the gap between qualitative knowledge and quantitative modeling

Hybrid modelling of biological systems using fuzzy continuous Petri nets

Copyright © The Author(s) 2019. 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.National Key R&D Program of China (2018YFC0830900); National Natural Science Foundation of China (61873094); Science and Technology Program of Guangzhou, China (201804010246); Natural Science Foundation of Guangdong Province of China (2018A030313338)

A systems biology approach to multi-scale modelling and analysis of planar cell polarity in drosophila melanogaster wing

This thesis was submitted for the degree of Doctor of Philosophy and awarded by Brunel University.Systems biology aims to describe and understand biology at a global scale where biological systems function as a result of complex mechanisms that happen at several scales. Modelling and simulation are computational tools that are invaluable for description, understanding and prediction these mechanisms in a quantitative and integrative way. Thus multi-scale methods that couple the design, simulation and analysis of models spanning several spatial and temporal scales is becoming a new emerging focus of systems biology. This thesis uses an exemplar – Planar cell polarity (PCP) signalling – to illustrate a generic approach to model biological systems at different spatial scales, using the new concept of Hierarchically Coloured Petri Nets (HCPN). PCP signalling refers to the coordinated polarisation of cells within the plane of various epithelial tissues to generate sub-cellular asymmetry along an axis orthogonal to their apical-basal axes. This polarisation is required for many developmental events in both vertebrates and non-vertebrates. Defects in PCP in vertebrates are responsible for developmental abnormalities in multiple tissues including the neural tube, the kidney and the inner ear. In Drosophila wing, PCP is seen in the parallel orientation of hairs that protrude from each of the approximately 30,000 epithelial cells to robustly point toward the wing tip. This work applies HCPN to model a tissue comprising multiple cells hexagonally packed in a honeycomb formation in order to describe the phenomenon of Planar Cell Polarity (PCP) in Drosophila wing. HCPN facilitate the construction of mathematically tractable, compact and parameterised large-scale models. Different levels of abstraction that can be used in order to simplify such a complex system are first illustrated. The PCP system is first represented at an abstract level without modelling details of the cell. Each cell is then sub-divided into seven virtual compartments with adjacent cells being coupled via the formation of intercellular complexes. A more detailed model is later developed, describing the intra- and inter-cellular signalling mechanisms involved in PCP signalling. The initial model is for a wild-type organism, and then a family of related models, permitting different hypotheses to be explored regarding the mechanisms underlying PCP, are constructed. Among them, the largest model consists of 800 cells which when unfolded yields 164,000 places (each of which is described by an ordinary differential equation). This thesis illustrates the power and validity of the approach by showing how the models can be easily adapted to describe well-documented genetic mutations in the Drosophila wing using the proposed approach including clustering and model checking over time series of primary and secondary data, which can be employed to analyse and check such multi-scale models similar to the case of PCP. The HCPN models support the interpretation of biological observations reported in literature and are able to make sensible predictions. As HCPN model multi-scale systems in a compact, parameterised and scalable way, this modelling approach can be applied to other large-scale or multi-scale systems.This study was funded by Brunel University

A diversity-aware computational framework for systems biology

L'abstract è presente nell'allegato / the abstract is in the attachmen

Computational Modeling and Reverse Engineering to Reveal Dominant Regulatory Interactions Controlling Osteochondral Differentiation: Potential for Regenerative Medicine

The specialization of cartilage cells, or chondrogenic differentiation, is an intricate and meticulously regulated process that plays a vital role in both bone formation and cartilage regeneration. Understanding the molecular regulation of this process might help to identify key regulatory factors that can serve as potential therapeutic targets, or that might improve the development of qualitative and robust skeletal tissue engineering approaches. However, each gene involved in this process is influenced by a myriad of feedback mechanisms that keep its expression in a desirable range, making the prediction of what will happen if one of these genes defaults or is targeted with drugs, challenging. Computer modeling provides a tool to simulate this intricate interplay from a network perspective. This paper aims to give an overview of the current methodologies employed to analyze cell differentiation in the context of skeletal tissue engineering in general and osteochondral differentiation in particular. In network modeling, a network can either be derived from mechanisms and pathways that have been reported in the literature (knowledge-based approach) or it can be inferred directly from the data (data-driven approach). Combinatory approaches allow further optimization of the network. Once a network is established, several modeling technologies are available to interpret dynamically the relationships that have been put forward in the network graph (implication of the activation or inhibition of certain pathways on the evolution of the system over time) and to simulate the possible outcomes of the established network such as a given cell state. This review provides for each of the aforementioned steps (building, optimizing, and modeling the network) a brief theoretical perspective, followed by a concise overview of published works, focusing solely on applications related to cell fate decisions, cartilage differentiation and growth plate biology. Particular attention is paid to an in-house developed example of gene regulatory network modeling of growth plate chondrocyte differentiation as all the aforementioned steps can be illustrated. In summary, this paper discusses and explores a series of tools that form a first step toward a rigorous and systems-level modeling of osteochondral differentiation in the context of regenerative medicine

In-silico-Systemanalyse von Biopathways

Chen M. In silico systems analysis of biopathways. Bielefeld (Germany): Bielefeld University; 2004.In the past decade with the advent of high-throughput technologies, biology has migrated from a descriptive science to a predictive one. A vast amount of information on the metabolism have been produced; a number of specific genetic/metabolic databases and computational systems have been developed, which makes it possible for biologists to perform in silico analysis of metabolism. With experimental data from laboratory, biologists wish to systematically conduct their analysis with an easy-to-use computational system. One major task is to implement molecular information systems that will allow to integrate different molecular database systems, and to design analysis tools (e.g. simulators of complex metabolic reactions). Three key problems are involved: 1) Modeling and simulation of biological processes; 2) Reconstruction of metabolic pathways, leading to predictions about the integrated function of the network; and 3) Comparison of metabolism, providing an important way to reveal the functional relationship between a set of metabolic pathways. This dissertation addresses these problems of in silico systems analysis of biopathways. We developed a software system to integrate the access to different databases, and exploited the Petri net methodology to model and simulate metabolic networks in cells. It develops a computer modeling and simulation technique based on Petri net methodology; investigates metabolic networks at a system level; proposes a markup language for biological data interchange among diverse biological simulators and Petri net tools; establishes a web-based information retrieval system for metabolic pathway prediction; presents an algorithm for metabolic pathway alignment; recommends a nomenclature of cellular signal transduction; and attempts to standardize the representation of biological pathways. Hybrid Petri net methodology is exploited to model metabolic networks. Kinetic modeling strategy and Petri net modeling algorithm are applied to perform the processes of elements functioning and model analysis. The proposed methodology can be used for all other metabolic networks or the virtual cell metabolism. Moreover, perspectives of Petri net modeling and simulation of metabolic networks are outlined. A proposal for the Biology Petri Net Markup Language (BioPNML) is presented. The concepts and terminology of the interchange format, as well as its syntax (which is based on XML) are introduced. BioPNML is designed to provide a starting point for the development of a standard interchange format for Bioinformatics and Petri nets. The language makes it possible to exchange biology Petri net diagrams between all supported hardware platforms and versions. It is also designed to associate Petri net models and other known metabolic simulators. A web-based metabolic information retrieval system, PathAligner, is developed in order to predict metabolic pathways from rudimentary elements of pathways. It extracts metabolic information from biological databases via the Internet, and builds metabolic pathways with data sources of genes, sequences, enzymes, metabolites, etc. The system also provides a navigation platform to investigate metabolic related information, and transforms the output data into XML files for further modeling and simulation of the reconstructed pathway. An alignment algorithm to compare the similarity between metabolic pathways is presented. A new definition of the metabolic pathway is proposed. The pathway defined as a linear event sequence is practical for our alignment algorithm. The algorithm is based on strip scoring the similarity of 4-hierarchical EC numbers involved in the pathways. The algorithm described has been implemented and is in current use in the context of the PathAligner system. Furthermore, new methods for the classification and nomenclature of cellular signal transductions are recommended. For each type of characterized signal transduction, a unique ST number is provided. The Signal Transduction Classification Database (STCDB), based on the proposed classification and nomenclature, has been established. By merging the ST numbers with EC numbers, alignments of biopathways are possible. Finally, a detailed model of urea cycle that includes gene regulatory networks, metabolic pathways and signal transduction is demonstrated by using our approaches. A system biological interpretation of the observed behavior of the urea cycle and its related transcriptomics information is proposed to provide new insights for metabolic engineering and medical care

The application of agent-based modeling and fuzzy-logic controllers for the study of magnesium biomaterials

Agent-based modeling (ABM) is a powerful approach for studying complex systems and their underlying properties by explicitly modeling the actions and interactions of individual agents. Over the past decade, numerous software programs have been developed to address the needs of the ABM community. However, these solutions often suffer from limitations in design, a lack of comprehensive documentation, or poor performance. As the first objective of this thesis, we introduce CppyABM-a general-purpose software for ABM that provides simulation tools in both Python and C++. CppyABM also enables ABM development using a combination of C++ and Python, taking advantage of the computational performance of C++ and the data analysis and visualization tools of Python. We demonstrate the capabilities of CppyABM through its application to various problems in ecology, virology, and computational biology. As the second objective of this thesis, we use ABM and fuzzy logic controllers (FLCs) to numerically study the effects of magnesium (Mg2+) ions on osteogenesis. Mg-based materials have emerged as the next generation of biomaterials that degrade in the body after implantation and eliminate the need for secondary surgery. We develop two computer models using ABM and FLC and calibrate them based on cell culture experiments. The models were able to capture the regulatory effects of Mg2+ ions and other important factors such as inflammatory cytokines on mesenchymal stem cells (MSC) activities. The models were also able to shed light on the fundamental differences in the cells cultured in different experiments such as proliferation capacity and sensitivity to environmental factors

Dépliages et interprétation abstraite pour réseaux de régulation biologiques paramétrés

The analysis of dynamics of biological regulatory networks, notably signalling and gene regulatory networks, faces the uncertainty of the exact computational model. Indeed, most of the knowledge available concerns the existence of (possibly indirect) interactions between biological entities (species), e.g. proteins, RNAs, genes, etc. The details on how different regulators of a same target cooperate, and even more so on consistent rates for those interactions, however, are rarely available. In this regard, qualitative modelling approaches in the form of discrete regulatory networks, such as Boolean and Thomas networks, offer an appropriate level of abstraction for the biological regulatory network dynamics. As discrete regulatory networks are based on an influence graph, they require few additional parameters compared to classical quantitative models. Nevertheless, determining the discrete parameters is a well known challenge, and a major bottleneck for providing robust predictions from computational models.The influence graph of a regulatory network establishes dependencies for the evolution of each specie, specified by the directed edges of the graph. The dependencies alone, however, do not suffice to specify the logical function governing the evolution of a specie. Instead the logical functions associated to each specie, constrained by the influence graph, are encoded within the parameters of a discrete regulatory network. The space of admissible logical functions is then represented by a parametric regulatory network. On the one hand, parametric regulatory networks can be used for identification of parameter values for which the resulting discrete regulatory network satisfies given (dynamical) properties. Parameter identification of regulatory networks can thus be seen as a particular instance of model synthesis, in the constrained setting of the underlying influence graph. On the other hand, parametric regulatory networks may be analysed as a stand-alone model, for making predictions that are robust with respect to variability in the network.The analysis of parametric regulatory network dynamics is hampered by dual combinatorial explosion, of the state space and of the parameter space. In this thesis, we develop novel methods of parametric regulatory network analysis, in the form of specialised semantics, aimed at alleviating the combinatorial explosion. First, we introduce abstract interpretation for the set of admissible parameter evaluations (parametrisations).The abstraction allows us to represent any set of parametrisations by a constant size encoding, at the cost of a conservative over-approximation. Second, we lift partial order semantics in the form of unfolding from Petri nets to parametric regulatory networks. The influence graphs of biological regulatory networks tend to be relatively sparse, allowing for a lot of concurrency. This can be harnessed by partial order reduction methods to produce concise state space representations.The two approaches are aimed at tackling both aspects of the dual combinatorial explosion and are introduced in a compatible manner, allowing one to employ them simultaneously. Such application is supported by a prototype implementation used to conduct experiments on various parametric regulatory networks. We further consider refinements of the methods, such as an on-the-run model reduction method lifted to parametric regulatory networks from automata networks.L'analyse de la dynamique des réseaux de régulation biologique, notamment des réseaux de signalisation et de régulation génique, fait face à l'incertitude du modèle de calcul exact. En effet, la plupart des connaissances disponibles concernent l'existence d'interactions (éventuellement indirectes) entre des entités biologiques (espèces), par ex. protéines, ARN, gènes, etc. Les détails sur la manière dont les différents régulateurs d'une même cible coopèrent, et plus encore sur les taux cohérents pour ces interactions, sont cependant rarement disponibles. A cet égard, des approches de modélisation qualitative sous forme de réseaux de régulation discrets, tels que les réseaux booléens et Thomas, offrir un niveau d'abstraction approprié pour la dynamique du réseau de régulation biologique. Les réseaux de régulation discrets étant basés sur un graphe d'influence, ils nécessitent peu de paramètres supplémentaires par rapport aux modèles quantitatifs classiques. Néanmoins, la détermination des paramètres discrets est un défi bien connu et un goulot d'étranglement majeur pour fournir des prédictions robustes à partir de modèles informatiques.Le graphe d'influence d'un réseau de régulation établit des dépendances pour l'évolution de chaque espèce, spécifiées par les arêtes dirigées du graphe. Les dépendances seules, cependant, ne suffisent pas pour spécifier la fonction logique régissant l'évolution d'une espèce. Au lieu de cela, les fonctions logiques associées à chaque espèce, contraintes par le graphe d'influence, sont codées dans les paramètres d'un réseau de régulation discret. L'espace des fonctions logiques admissibles est alors représenté par un réseau de régulation paramétrique. D'une part, les réseaux de régulation paramétriques peuvent être utilisés pour l'identification de valeurs de paramètres pour lesquelles le réseau de régulation discret résultant satisfait des propriétés (dynamiques) données. L'identification des paramètres des réseaux de régulation peut ainsi être vue comme un exemple particulier de synthèse de modèle, dans le cadre contraint du graphe d'influence sous-jacent. D'autre part, les réseaux de régulation paramétriques peuvent être analysés comme un modèle autonome, pour faire des prédictions robustes vis-à-vis de la variabilité du réseau.L'analyse de la dynamique du réseau de régulation paramétrique est entravée par la double explosion combinatoire, de l'espace d'états et de l'espace des paramètres. Dans cette thèse, nous développons de nouvelles méthodes d'analyse de réseau de régulation paramétrique, sous forme de sémantique spécialisée, visant à atténuer l'explosion combinatoire. Tout d'abord, nous introduisons une interprétation abstraite de l'ensemble des évaluations de paramètres admissibles (paramétrisations). L'abstraction permet de représenter n'importe quel ensemble de paramétrisations par un encodage de taille constante, au prix d'une sur-approximation conservatrice. Deuxièmement, nous élevons la sémantique d'ordre partiel sous la forme d'un déploiement des réseaux de Petri vers des réseaux de régulation paramétriques. Les graphiques d'influence des réseaux de régulation biologique ont tendance à être relativement clairsemés, ce qui permet une grande concurrence. Cela peut être exploité par des méthodes de réduction d'ordre partiel pour produire des représentations d'espace d'état concises.Les deux approches visent à aborder les deux aspects de la double explosion combinatoire et sont introduites de manière compatible, ce qui permet de les utiliser simultanément. Une telle application est soutenue par une implémentation prototype utilisée pour mener des expériences sur divers réseaux de régulation paramétriques. Nous considérons en outre des raffinements des méthodes, comme une méthode de réduction de modèle à la volée portée aux réseaux de régulation paramétriques à partir de réseaux d'automates

Reconstruction And Analysis Of The Molecular Programs Involved In Deciding Mammalian Cell Fate

Cellular function hinges on the ability to process information from the outside environment into specific decisions. Ultimately these processes decide cell fate, whether it be to undergo proliferation, apoptosis, differentiation, migration and other cellular functions. These processes can be thought of as finely tuned programs evolved to maintain robust function in spite of environmental perturbations. Malfunctions in these programs can lead to improper cellular function and various disease states. To develop more effective, personalized and even preventative therapeutics we must attain a better, more detailed, understanding of the programs involved. To this end we have employed mechanistic mathematical modeling to a variety of complex cellular programs. In Chapter 1, we review a variety of computational methods have have been used successfully in different areas of biotechnology. In Chapter 2, we present the software platform UNIVERSAL, which was developed in our lab. UNIVERSAL is an extensible code generation framework for Mac OS X which produces editable, fully commented platform-independent physiochemical model code in several common programming languages from a variety of inputs. UNIVERSAL generates mass-action ODE models of intracellular signal transduction processes and model analysis code, such as adjoint sensitivity balances. We employed the mass-action ODE framework, as generated by UNIVERSAL, commonly throughout the studies presented here. In Chapter 3, we introduce a variety of modeling strategies in the context of EGF-induced Eukaryotic transcription. We demon- strated the ability to make meaningful and statistically consistent model predictions despite considerable parametric uncertainty. In Chapter 4, we constructed a mathematical model to study a mechanism for androgen independent proliferation in prostate cancer. Analysis of the model provided insight into the importance of network components as a function of androgen dependence. Translation became progressively more important in androgen independent cells. Moreover, the analysis suggested that direct targeting of the translational machinery, specifically eIF4E, could be efficacious in androgen independent prostate cancers. In Chapter 5, A mathematical model of RA-induced cell-cycle arrest and differentiation was formulated and tested against BLR1 wild-type (wt) knock-out and knock-in HL-60 cell lines with and without RA. The ensemble of HL-60 models recapitulated the positive feedback between BLR1 and MAPK signaling. We investigated the robustness of the HL-60 network architecture to structural perturbations and generated experimentally testable hypotheses for future study. In Chapter 6, we carried out experimental studies to reduce the structural uncertainty of the HL60 model. Result from the HL-60 model cRaf as the most critical component of the MAPK cascade. To investigate the role of cRaf in RA-induced differentiation we observed the effect of cRaf kinase inhibition. Furthermore, we interrogated a panel of proteins to identify RA responsive cRaf binding partner. We found that cRaf kinase activity was necessary for functional ROS response, but not for RA-induced growth arrest. Based on our findings, we proposed a simplified ontrol architecture for sustained MAPK activation. Computational modeling identified a bistability suggesting that the MAPK activation was self-sustaining. This result was experimentally validated, and could explain previously observed cellular memory effects. Taken together, the results of these studies demonstrated that computational modeling can identify therapeutically relevant targets for human disease such as cancer. Furthermore, we demonstrated the ability of an iterative strategy between computational and experimental analysis to provide insight on key regulator circuits for complex programs involved in deciding cell fate