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Herajy M, Liu F, Heiner M. Design patterns for the construction of computational biological models. Brief Bioinform 2024; 25:bbae318. [PMID: 38961813 PMCID: PMC11222664 DOI: 10.1093/bib/bbae318] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/15/2024] [Revised: 05/16/2024] [Accepted: 06/17/2024] [Indexed: 07/05/2024] Open
Abstract
Computational biological models have proven to be an invaluable tool for understanding and predicting the behaviour of many biological systems. While it may not be too challenging for experienced researchers to construct such models from scratch, it is not a straightforward task for early stage researchers. Design patterns are well-known techniques widely applied in software engineering as they provide a set of typical solutions to common problems in software design. In this paper, we collect and discuss common patterns that are usually used during the construction and execution of computational biological models. We adopt Petri nets as a modelling language to provide a visual illustration of each pattern; however, the ideas presented in this paper can also be implemented using other modelling formalisms. We provide two case studies for illustration purposes and show how these models can be built up from the presented smaller modules. We hope that the ideas discussed in this paper will help many researchers in building their own future models.
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Affiliation(s)
- Mostafa Herajy
- Department of Mathematics and Computer Science, Faculty of Science, Port Said University, 42521 Port Said, Egypt
| | - Fei Liu
- School of Software Engineering, South China University of Technology, 510006 Guangzhou, China
| | - Monika Heiner
- Computer Science Institute, Brandenburg University of Technology, 03013 Cottbus, Germany
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2
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Husar A, Ordyan M, Garcia GC, Yancey JG, Saglam AS, Faeder JR, Bartol TM, Kennedy MB, Sejnowski TJ. MCell4 with BioNetGen: A Monte Carlo simulator of rule-based reaction-diffusion systems with Python interface. PLoS Comput Biol 2024; 20:e1011800. [PMID: 38656994 PMCID: PMC11073787 DOI: 10.1371/journal.pcbi.1011800] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Revised: 05/06/2024] [Accepted: 01/03/2024] [Indexed: 04/26/2024] Open
Abstract
Biochemical signaling pathways in living cells are often highly organized into spatially segregated volumes, membranes, scaffolds, subcellular compartments, and organelles comprising small numbers of interacting molecules. At this level of granularity stochastic behavior dominates, well-mixed continuum approximations based on concentrations break down and a particle-based approach is more accurate and more efficient. We describe and validate a new version of the open-source MCell simulation program (MCell4), which supports generalized 3D Monte Carlo modeling of diffusion and chemical reaction of discrete molecules and macromolecular complexes in solution, on surfaces representing membranes, and combinations thereof. The main improvements in MCell4 compared to the previous versions, MCell3 and MCell3-R, include a Python interface and native BioNetGen reaction language (BNGL) support. MCell4's Python interface opens up completely new possibilities for interfacing with external simulators to allow creation of sophisticated event-driven multiscale/multiphysics simulations. The native BNGL support, implemented through a new open-source library libBNG (also introduced in this paper), provides the capability to run a given BNGL model spatially resolved in MCell4 and, with appropriate simplifying assumptions, also in the BioNetGen simulation environment, greatly accelerating and simplifying model validation and comparison.
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Affiliation(s)
- Adam Husar
- Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, California, United States of America
| | - Mariam Ordyan
- Institute for Neural Computations, University of California, San Diego, La Jolla, California, United States of America
| | - Guadalupe C. Garcia
- Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, California, United States of America
| | - Joel G. Yancey
- Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, California, United States of America
| | - Ali S. Saglam
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
| | - James R. Faeder
- Department of Computational and Systems Biology, University of Pittsburgh, Pittsburgh, Pennsylvania, United States of America
| | - Thomas M. Bartol
- Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, California, United States of America
| | - Mary B. Kennedy
- Division of Biology and Biological Engineering, California Institute of Technology, Pasadena, California, United States of America
| | - Terrence J. Sejnowski
- Computational Neurobiology Lab, Salk Institute for Biological Studies, La Jolla, California, United States of America
- Institute for Neural Computations, University of California, San Diego, La Jolla, California, United States of America
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Liu F, Heiner M, Gilbert D. Protocol for biomodel engineering of unilevel to multilevel biological models using colored Petri nets. STAR Protoc 2023; 4:102651. [PMID: 38103198 PMCID: PMC10751555 DOI: 10.1016/j.xpro.2023.102651] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/03/2023] [Revised: 07/26/2023] [Accepted: 09/27/2023] [Indexed: 12/18/2023] Open
Abstract
Biological systems inherently span multiple levels, which can pose challenges in spatial representation for modelers. We present a protocol that utilizes colored Petri nets to construct and analyze biological models of systems, encompassing both unilevel and multilevel scenarios. We detail a modeling workflow exploiting the PetriNuts platform comprising a set of tools linked together via common file formats. We describe steps for modeling preparation, component-level modeling and analysis, followed by system-level modeling and analysis, and model use.
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Affiliation(s)
- Fei Liu
- School of Software Engineering, South China University of Technology, Guangzhou, Guangdong 510006, P.R. China.
| | - Monika Heiner
- Department of Computing Science, Brandenburg University of Technology Cottbus-Senftenberg, D03013 Cottbus, Germany
| | - David Gilbert
- Department of Computing Science, Brunel University London, UB8 3PH London, UK
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Formal verification confirms the role of p53 protein in cell fate decision mechanism. Theory Biosci 2023; 142:29-45. [PMID: 36510032 PMCID: PMC9925526 DOI: 10.1007/s12064-022-00381-x] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/29/2022] [Accepted: 11/14/2022] [Indexed: 12/15/2022]
Abstract
The bio-cell cycle is controlled by a complex biochemical network of signaling pathways. Modeling such challenging networks accurately is imperative for the understanding of their detailed dynamical behavior. In this paper, we construct, analyze, and verify a hybrid Petri net (HPN) model of a complex biochemical network that captures the role of an important protein (namely p53) in deciding the fate of the cell. We model the behavior of the cell nucleus and cytoplasm as two stochastic and continuous Petri nets, respectively, combined together into a single HPN. We use simulative model checking to verify three different properties that capture the dynamical behavior of p53 protein with respect to the intensity of the ionizing radiation (IR) to which the cell is exposed. For each IR dose, 1000 simulation runs are carried out to verify each property. Our verification results showed that the fluctuations in p53, which relies on IR intensity, are compatible with the findings of the preceding simulation studies that have previously examined the role of p53 in cell fate decision.
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Liu F, Heiner M, Gilbert D. Hybrid modelling of biological systems: current progress and future prospects. Brief Bioinform 2022; 23:6555400. [PMID: 35352101 PMCID: PMC9116374 DOI: 10.1093/bib/bbac081] [Citation(s) in RCA: 5] [Impact Index Per Article: 2.5] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/17/2021] [Revised: 02/12/2022] [Accepted: 02/16/2022] [Indexed: 11/15/2022] Open
Abstract
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.
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Affiliation(s)
- Fei Liu
- School of Software Engineering, South China University of Technology, Guangzhou 510006, P.R. China
- Corresponding author: Fei Liu, School of Software Engineering, South China University of Technology, Guangzhou 510006, P.R. China. E-mail:
| | - Monika Heiner
- Department of Computer Science, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus 03046, Germany
| | - David Gilbert
- Department of Computer Science, Brunel University London, Middlesex UB8 3PH, UK
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Liu F, Yamamoto E, Shirahama K, Saitoh T, Aoyama S, Harada Y, Murakami R, Matsuno H. Analysis of Pattern Formation by Colored Petri Nets With Quantitative Regulation of Gene Expression Level. IEEE/ACM TRANSACTIONS ON COMPUTATIONAL BIOLOGY AND BIOINFORMATICS 2022; 19:317-327. [PMID: 32750877 DOI: 10.1109/tcbb.2020.3005392] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/11/2023]
Abstract
Modeling and simulation are becoming indispensable tools for studying multicellular events such as pattern formation during embryonic development. In this paper, we propose a new approach for analyzing multicellular biological phenomena by combining colored hybrid Petri nets (ColHPNs) with newly devised biological experiments that can control level of a gene quantitatively. With this approach, we analyzed patterning of the boundary cells in the Drosophila large intestine, where one-cell-wide domain of boundary cells differentiate through Delta-Notch signaling. Biological experiments regulating the level of Delta resulted in six distinct patterns of boundary cells correlating with the level of Delta. All these patterns were successfully reproduced by simulation based on ColHPN modeling only by changing the parameter related to the level of Delta. By monitoring the concentration of the active form of Notch in each cell during simulation, it was revealed that these distinct modes of patterning correlate with the fluctuation range of active Notch. Combination of simulation and quantitative manipulation of a gene activity described here is a reliable and powerful approach for analyzing and understanding the patterning process regulated by Notch signaling. This approach can be easily adapted to address other similar pattern formation issues in the systems biology area.
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Mc Auley MT. Modeling cholesterol metabolism and atherosclerosis. WIREs Mech Dis 2021; 14:e1546. [PMID: 34931487 DOI: 10.1002/wsbm.1546] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/23/2020] [Revised: 10/11/2021] [Accepted: 10/14/2021] [Indexed: 12/19/2022]
Abstract
Atherosclerotic cardiovascular disease (ASCVD) is the leading cause of morbidity and mortality among Western populations. Many risk factors have been identified for ASCVD; however, elevated low-density lipoprotein cholesterol (LDL-C) remains the gold standard. Cholesterol metabolism at the cellular and whole-body level is maintained by an array of interacting components. These regulatory mechanisms have complex behavior. Likewise, the mechanisms which underpin atherogenesis are nontrivial and multifaceted. To help overcome the challenge of investigating these processes mathematical modeling, which is a core constituent of the systems biology paradigm has played a pivotal role in deciphering their dynamics. In so doing models have revealed new insights about the key drivers of ASCVD. The aim of this review is fourfold; to provide an overview of cholesterol metabolism and atherosclerosis, to briefly introduce mathematical approaches used in this field, to critically discuss models of cholesterol metabolism and atherosclerosis, and to highlight areas where mathematical modeling could help to investigate in the future. This article is categorized under: Cardiovascular Diseases > Computational Models.
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Karagöz Z, Rijns L, Dankers PY, van Griensven M, Carlier A. Towards understanding the messengers of extracellular space: Computational models of outside-in integrin reaction networks. Comput Struct Biotechnol J 2020; 19:303-314. [PMID: 33425258 PMCID: PMC7779863 DOI: 10.1016/j.csbj.2020.12.025] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2020] [Revised: 12/15/2020] [Accepted: 12/16/2020] [Indexed: 02/06/2023] Open
Abstract
The interactions between cells and their extracellular matrix (ECM) are critically important for homeostatic control of cell growth, proliferation, differentiation and apoptosis. Transmembrane integrin molecules facilitate the communication between ECM and the cell. Since the characterization of integrins in the late 1980s, there has been great advancement in understanding the function of integrins at different subcellular levels. However, the versatility in molecular pathways integrins are involved in, the high diversity in their interaction partners both outside and inside the cell as well as on the cell membrane and the short lifetime of events happening at the cell-ECM interface make it difficult to elucidate all the details regarding integrin function experimentally. To overcome the experimental challenges and advance the understanding of integrin biology, computational modeling tools have been used extensively. In this review, we summarize the computational models of integrin signaling while we explain the function of integrins at three main subcellular levels (outside the cell, cell membrane, cytosol). We also discuss how these computational modeling efforts can be helpful in other disciplines such as biomaterial design. As such, this review is a didactic modeling summary for biomaterial researchers interested in complementing their experimental work with computational tools or for seasoned computational scientists that would like to advance current in silico integrin models.
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Affiliation(s)
- Zeynep Karagöz
- Department of Cell Biology-Inspired Tissue Engineering, MERLN Institute for Technology-Inspired Regenerative Medicine, Maastricht University, Universiteitssingel 40, 6229 ER Maastricht, the Netherlands
| | - Laura Rijns
- Department of Biomedical Engineering and Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, the Netherlands
| | - Patricia Y.W. Dankers
- Department of Biomedical Engineering and Institute for Complex Molecular Systems, Eindhoven University of Technology, PO Box 513, 5600 MB Eindhoven, the Netherlands
| | - Martijn van Griensven
- Department of Cell Biology-Inspired Tissue Engineering, MERLN Institute for Technology-Inspired Regenerative Medicine, Maastricht University, Universiteitssingel 40, 6229 ER Maastricht, the Netherlands
| | - Aurélie Carlier
- Department of Cell Biology-Inspired Tissue Engineering, MERLN Institute for Technology-Inspired Regenerative Medicine, Maastricht University, Universiteitssingel 40, 6229 ER Maastricht, the Netherlands
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Banwarth-Kuhn M, Sindi S. How and why to build a mathematical model: A case study using prion aggregation. J Biol Chem 2020; 295:5022-5035. [PMID: 32005659 PMCID: PMC7152750 DOI: 10.1074/jbc.rev119.009851] [Citation(s) in RCA: 11] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022] Open
Abstract
Biological systems are inherently complex, and the increasing level of detail with which we are able to experimentally probe such systems continually reveals new complexity. Fortunately, mathematical models are uniquely positioned to provide a tool suitable for rigorous analysis, hypothesis generation, and connecting results from isolated in vitro experiments with results from in vivo and whole-organism studies. However, developing useful mathematical models is challenging because of the often different domains of knowledge required in both math and biology. In this work, we endeavor to provide a useful guide for researchers interested in incorporating mathematical modeling into their scientific process. We advocate for the use of conceptual diagrams as a starting place to anchor researchers from both domains. These diagrams are useful for simplifying the biological process in question and distinguishing the essential components. Not only do they serve as the basis for developing a variety of mathematical models, but they ensure that any mathematical formulation of the biological system is led primarily by scientific questions. We provide a specific example of this process from our own work in studying prion aggregation to show the power of mathematical models to synergistically interact with experiments and push forward biological understanding. Choosing the most suitable model also depends on many different factors, and we consider how to make these choices based on different scales of biological organization and available data. We close by discussing the many opportunities that abound for both experimentalists and modelers to take advantage of collaborative work in this field.
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Affiliation(s)
- Mikahl Banwarth-Kuhn
- Department of Applied Mathematics, School of Natural Sciences, University of California, Merced, California 95343
| | - Suzanne Sindi
- Department of Applied Mathematics, School of Natural Sciences, University of California, Merced, California 95343
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Liu F, Heiner M, Gilbert D. Coloured Petri nets for multilevel, multiscale and multidimensional modelling of biological systems. Brief Bioinform 2019; 20:877-886. [PMID: 29112705 PMCID: PMC6585149 DOI: 10.1093/bib/bbx150] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/31/2017] [Revised: 09/22/2017] [Indexed: 01/25/2023] Open
Abstract
Owing to the availability of data of one biological phenomenon at different levels/scales, modelling of biological systems is moving from single level/scale to multiple levels/scales, which introduces a number of challenges. Coloured Petri nets (ColPNs) have been successfully applied to multilevel, multiscale and multidimensional modelling of some biological systems, addressing many of these challenges. In this article, we first review the basics of ColPNs and some popular extensions, and then their applications for multilevel, multiscale and multidimensional modelling of biological systems. This understanding of how to use ColPNs for modelling biological systems will assist readers in selecting appropriate ColPN classes for specific modelling circumstances.
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Affiliation(s)
- Fei Liu
- School of Software Engineering, South China University of Technology, Guangzhou, P.R. China
| | - Monika Heiner
- Department of Computer Science, Brandenburg University of Technology Cottbus-Senftenberg
| | - David Gilbert
- Department of Computer Science, Brunel University London
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Herajy M, Liu F, Rohr C, Heiner M. Coloured Hybrid Petri Nets: An adaptable modelling approach for multi-scale biological networks. Comput Biol Chem 2018; 76:87-100. [PMID: 29982167 DOI: 10.1016/j.compbiolchem.2018.05.023] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/17/2015] [Revised: 05/19/2018] [Accepted: 05/27/2018] [Indexed: 12/15/2022]
Abstract
Coloured Petri nets are an excellent choice for exploring large biological models, particularly when there are repetitions of components. Such models can be easily adapted by slight modifications of parameter values related to colours. Similarly, multi-scale models could involve multiple spatial scales in addition to multiple time scales. Thus, they require the full interplay between stochastic as well as deterministic processes. In this paper we take these two aspects into account and present a modelling and simulation approach for multi-scale biochemical networks using Coloured Generalised Hybrid Petri Nets (GHPNC). GHPNC are a Petri net class that associates colours to Generalised Hybrid Petri Nets (GHPN), which incorporate discrete and continuous places in addition to stochastic and continuous transitions. Moreover, we present two case studies to illustrate typical applications taking advantage of such a Petri net class.
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Affiliation(s)
- Mostafa Herajy
- Department of Mathematics and Computer Science, Faculty of Science, Port Said University, 42521 Port Said, Egypt.
| | - Fei Liu
- School of Software Engineering, South China University of Technology, 510006 Guangzhou, China.
| | - Christian Rohr
- Computer Science Institute, Brandenburg University of Technology, Postbox 10 13 44, 03013 Cottbus, Germany
| | - Monika Heiner
- Computer Science Institute, Brandenburg University of Technology, Postbox 10 13 44, 03013 Cottbus, Germany
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Widmer LA, Stelling J. Bridging intracellular scales by mechanistic computational models. Curr Opin Biotechnol 2018; 52:17-24. [PMID: 29486391 DOI: 10.1016/j.copbio.2018.02.005] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/18/2017] [Accepted: 02/11/2018] [Indexed: 12/31/2022]
Abstract
The impact of intracellular spatial organization beyond classical compartments on processes such as cell signaling is increasingly recognized. A quantitative, mechanistic understanding of cellular systems therefore needs to account for different scales in at least three coordinates: time, molecular abundances, and space. Mechanistic mathematical models may span all these scales, but corresponding multi-scale models need to resolve mechanistic details on small scales while maintaining computational tractability for larger ones. This typically results in models that combine different levels of description: from a microscopic representation of chemical reactions up to continuum dynamics in space and time. We highlight recent progress in bridging these model classes and outline current challenges in multi-scale models such as active transport and dynamic geometries.
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Affiliation(s)
- Lukas Andreas Widmer
- Department of Biosystems Science and Engineering and Swiss Institute of Bioinformatics, ETH Zürich, Basel, Switzerland; Systems Biology PhD Program, Life Science Zurich Graduate School, Zurich, Switzerland
| | - Jörg Stelling
- Department of Biosystems Science and Engineering and Swiss Institute of Bioinformatics, ETH Zürich, Basel, Switzerland.
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