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Konur S, Gheorghe M, Krasnogor N. Verifiable biology. J R Soc Interface 2023; 20:20230019. [PMID: 37160165 PMCID: PMC10169095 DOI: 10.1098/rsif.2023.0019] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/13/2023] [Accepted: 04/17/2023] [Indexed: 05/11/2023] Open
Abstract
The formalization of biological systems using computational modelling approaches as an alternative to mathematical-based methods has recently received much interest because computational models provide a deeper mechanistic understanding of biological systems. In particular, formal verification, complementary approach to standard computational techniques such as simulation, is used to validate the system correctness and obtain critical information about system behaviour. In this study, we survey the most frequently used computational modelling approaches and formal verification techniques for computational biology. We compare a number of verification tools and software suites used to analyse biological systems and biochemical networks, and to verify a wide range of biological properties. For users who have no expertise in formal verification, we present a novel methodology that allows them to easily apply formal verification techniques to analyse their biological or biochemical system of interest.
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Affiliation(s)
- Savas Konur
- Department of Computer Science, University of Bradford, Richmond Building, Bradford BD7 1DP, UK
| | - Marian Gheorghe
- Department of Computer Science, University of Bradford, Richmond Building, Bradford BD7 1DP, UK
| | - Natalio Krasnogor
- School of Computing Science, Newcastle University, Science Square, Newcastle upon Tyne NE4 5TG, UK
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2
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Santos-Buitrago B, Santos-García G, Hernández-Galilea E. Artificial intelligence for modeling uveal melanoma. Artif Intell Cancer 2020; 1:51-65. [DOI: 10.35713/aic.v1.i4.51] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Download PDF] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 09/26/2020] [Revised: 11/05/2020] [Accepted: 11/21/2020] [Indexed: 02/06/2023] Open
Affiliation(s)
| | - Gustavo Santos-García
- IME, University of Salamanca, Salamanca 37007, Spain
- FADoSS Research Unit, Universidad Complutense de Madrid, Madrid 28040, Spain
| | - Emiliano Hernández-Galilea
- Department of Ophthalmology, Institute of Biomedicine Investigation of Salamanca (IBSAL), University Hospital of Salamanca, University of Salamanca, Salamanca 37007, Spain
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3
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Riesco A, Santos-Buitrago B, De Las Rivas J, Knapp M, Santos-García G, Talcott C. Epidermal Growth Factor Signaling towards Proliferation: Modeling and Logic Inference Using Forward and Backward Search. BIOMED RESEARCH INTERNATIONAL 2017; 2017:1809513. [PMID: 28191459 PMCID: PMC5278199 DOI: 10.1155/2017/1809513] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/05/2016] [Accepted: 10/30/2016] [Indexed: 12/24/2022]
Abstract
In biological systems, pathways define complex interaction networks where multiple molecular elements are involved in a series of controlled reactions producing responses to specific biomolecular signals. These biosystems are dynamic and there is a need for mathematical and computational methods able to analyze the symbolic elements and the interactions between them and produce adequate readouts of such systems. In this work, we use rewriting logic to analyze the cellular signaling of epidermal growth factor (EGF) and its cell surface receptor (EGFR) in order to induce cellular proliferation. Signaling is initiated by binding the ligand protein EGF to the membrane-bound receptor EGFR so as to trigger a reactions path which have several linked elements through the cell from the membrane till the nucleus. We present two different types of search for analyzing the EGF/proliferation system with the help of Pathway Logic tool, which provides a knowledge-based development environment to carry out the modeling of the signaling. The first one is a standard (forward) search. The second one is a novel approach based on narrowing, which allows us to trace backwards the causes of a given final state. The analysis allows the identification of critical elements that have to be activated to provoke proliferation.
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Affiliation(s)
| | | | | | - Merrill Knapp
- Biosciences Division, SRI International, Menlo Park, CA, USA
| | | | - Carolyn Talcott
- Computer Science Laboratory, SRI International, Menlo Park, CA, USA
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Hall BA, Piterman N, Hajnal A, Fisher J. Emergent stem cell homeostasis in the C. elegans germline is revealed by hybrid modeling. Biophys J 2016. [PMID: 26200879 PMCID: PMC4621618 DOI: 10.1016/j.bpj.2015.06.007] [Citation(s) in RCA: 12] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/28/2022] Open
Abstract
The establishment of homeostasis among cell growth, differentiation, and apoptosis is of key importance for organogenesis. Stem cells respond to temporally and spatially regulated signals by switching from mitotic proliferation to asymmetric cell division and differentiation. Executable computer models of signaling pathways can accurately reproduce a wide range of biological phenomena by reducing detailed chemical kinetics to a discrete, finite form. Moreover, coordinated cell movements and physical cell-cell interactions are required for the formation of three-dimensional structures that are the building blocks of organs. To capture all these aspects, we have developed a hybrid executable/physical model describing stem cell proliferation, differentiation, and homeostasis in the Caenorhabditis elegans germline. Using this hybrid model, we are able to track cell lineages and dynamic cell movements during germ cell differentiation. We further show how apoptosis regulates germ cell homeostasis in the gonad, and propose a role for intercellular pressure in developmental control. Finally, we use the model to demonstrate how an executable model can be developed from the hybrid system, identifying a mechanism that ensures invariance in fate patterns in the presence of instability.
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Affiliation(s)
- Benjamin A Hall
- Medical Research Council Cancer Unit, Hutchison/Medical Research Council Research Centre, University of Cambridge, Cambridge, United Kingdom; Microsoft Research Cambridge, Cambridge, UK.
| | - Nir Piterman
- Department of Computer Science, University of Leicester, Leicester, UK
| | - Alex Hajnal
- Institute of Molecular Life Sciences, University of Zurich, Zurich, Switzerland
| | - Jasmin Fisher
- Microsoft Research Cambridge, Cambridge, UK; Department of Biochemistry, University of Cambridge, Cambridge, UK.
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5
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Read M, Andrews PS, Timmis J, Kumar V. Modelling biological behaviours with the unified modelling language: an immunological case study and critique. J R Soc Interface 2015; 11:rsif.2014.0704. [PMID: 25142524 PMCID: PMC4233755 DOI: 10.1098/rsif.2014.0704] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/15/2022] Open
Abstract
We present a framework to assist the diagrammatic modelling of complex biological systems using the unified modelling language (UML). The framework comprises three levels of modelling, ranging in scope from the dynamics of individual model entities to system-level emergent properties. By way of an immunological case study of the mouse disease experimental autoimmune encephalomyelitis, we show how the framework can be used to produce models that capture and communicate the biological system, detailing how biological entities, interactions and behaviours lead to higher-level emergent properties observed in the real world. We demonstrate how the UML can be successfully applied within our framework, and provide a critique of UML's ability to capture concepts fundamental to immunology and biology more generally. We show how specialized, well-explained diagrams with less formal semantics can be used where no suitable UML formalism exists. We highlight UML's lack of expressive ability concerning cyclic feedbacks in cellular networks, and the compounding concurrency arising from huge numbers of stochastic, interacting agents. To compensate for this, we propose several additional relationships for expressing these concepts in UML's activity diagram. We also demonstrate the ambiguous nature of class diagrams when applied to complex biology, and question their utility in modelling such dynamic systems. Models created through our framework are non-executable, and expressly free of simulation implementation concerns. They are a valuable complement and precursor to simulation specifications and implementations, focusing purely on thoroughly exploring the biology, recording hypotheses and assumptions, and serve as a communication medium detailing exactly how a simulation relates to the real biology.
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Affiliation(s)
- Mark Read
- Department of Electronics, University of York, York YO10 5GW, UK
| | - Paul S Andrews
- Department of Computer Science, University of York, York YO10 5GW, UK
| | - Jon Timmis
- Department of Electronics, University of York, York YO10 5GW, UK
| | - Vipin Kumar
- Torrey Pines Institute for Molecular Studies, San Diego, CA 92121, USA
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6
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Analysis of Cellular Proliferation and Survival Signaling by Using Two Ligand/Receptor Systems Modeled by Pathway Logic. HYBRID SYSTEMS BIOLOGY 2015. [DOI: 10.1007/978-3-319-26916-0_13] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/22/2023]
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Hall BA, Jackson E, Hajnal A, Fisher J. Logic programming to predict cell fate patterns and retrodict genotypes in organogenesis. J R Soc Interface 2014; 11:20140245. [PMID: 24966232 DOI: 10.1098/rsif.2014.0245] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Abstract
Caenorhabditis elegans vulval development is a paradigm system for understanding cell differentiation in the process of organogenesis. Through temporal and spatial controls, the fate pattern of six cells is determined by the competition of the LET-23 and the Notch signalling pathways. Modelling cell fate determination in vulval development using state-based models, coupled with formal analysis techniques, has been established as a powerful approach in predicting the outcome of combinations of mutations. However, computing the outcomes of complex and highly concurrent models can become prohibitive. Here, we show how logic programs derived from state machines describing the differentiation of C. elegans vulval precursor cells can increase the speed of prediction by four orders of magnitude relative to previous approaches. Moreover, this increase in speed allows us to infer, or 'retrodict', compatible genomes from cell fate patterns. We exploit this technique to predict highly variable cell fate patterns resulting from dig-1 reduced-function mutations and let-23 mosaics. In addition to the new insights offered, we propose our technique as a platform for aiding the design and analysis of experimental data.
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Affiliation(s)
| | - Ethan Jackson
- Microsoft Research, One Microsoft Way, Redmond, WA 98052, USA
| | - Alex Hajnal
- Institute of Molecular Life Sciences, University of Zurich, Zurich 8057, Switzerland
| | - Jasmin Fisher
- Microsoft Research, 21 Station Road, Cambridge CB1 2FB, UK Department of Biochemistry, University of Cambridge, Cambridge CB2 1QW, UK
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Buckler AJ, Paik D, Ouellette M, Danagoulian J, Wernsing G, Suzek BE. A novel knowledge representation framework for the statistical validation of quantitative imaging biomarkers. J Digit Imaging 2014; 26:614-29. [PMID: 23546775 DOI: 10.1007/s10278-013-9598-3] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/06/2023] Open
Abstract
Quantitative imaging biomarkers are of particular interest in drug development for their potential to accelerate the drug development pipeline. The lack of consensus methods and carefully characterized performance hampers the widespread availability of these quantitative measures. A framework to support collaborative work on quantitative imaging biomarkers would entail advanced statistical techniques, the development of controlled vocabularies, and a service-oriented architecture for processing large image archives. Until now, this framework has not been developed. With the availability of tools for automatic ontology-based annotation of datasets, coupled with image archives, and a means for batch selection and processing of image and clinical data, imaging will go through a similar increase in capability analogous to what advanced genetic profiling techniques have brought to molecular biology. We report on our current progress on developing an informatics infrastructure to store, query, and retrieve imaging biomarker data across a wide range of resources in a semantically meaningful way that facilitates the collaborative development and validation of potential imaging biomarkers by many stakeholders. Specifically, we describe the semantic components of our system, QI-Bench, that are used to specify and support experimental activities for statistical validation in quantitative imaging.
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Mol M, Patole MS, Singh S. Signaling networks in Leishmania macrophages deciphered through integrated systems biology: a mathematical modeling approach. SYSTEMS AND SYNTHETIC BIOLOGY 2013; 7:185-95. [PMID: 24432155 DOI: 10.1007/s11693-013-9111-9] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2013] [Accepted: 06/25/2013] [Indexed: 02/07/2023]
Abstract
Network of signaling proteins and functional interaction between the infected cell and the leishmanial parasite, though are not well understood, may be deciphered computationally by reconstructing the immune signaling network. As we all know signaling pathways are well-known abstractions that explain the mechanisms whereby cells respond to signals, collections of pathways form networks, and interactions between pathways in a network, known as cross-talk, enables further complex signaling behaviours. In silico perturbations can help identify sensitive crosstalk points in the network which can be pharmacologically tested. In this study, we have developed a model for immune signaling cascade in leishmaniasis and based upon the interaction analysis obtained through simulation, we have developed a model network, between four signaling pathways i.e., CD14, epidermal growth factor (EGF), tumor necrotic factor (TNF) and PI3 K mediated signaling. Principal component analysis of the signaling network showed that EGF and TNF pathways can be potent pharmacological targets to curb leishmaniasis. The approach is illustrated with a proposed workable model of epidermal growth factor receptor (EGFR) that modulates the immune response. EGFR signaling represents a critical junction between inflammation related signal and potent cell regulation machinery that modulates the expression of cytokines.
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Affiliation(s)
- Milsee Mol
- National Centre for Cell Science, NCCS Complex, Ganeshkhind, Pune University Campus, Pune, India
| | - Milind S Patole
- National Centre for Cell Science, NCCS Complex, Ganeshkhind, Pune University Campus, Pune, India
| | - Shailza Singh
- National Centre for Cell Science, NCCS Complex, Ganeshkhind, Pune University Campus, Pune, India
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Sadot A, Sarbu S, Kesseli J, Amir-Kroll H, Zhang W, Nykter M, Shmulevich I. Information-theoretic analysis of the dynamics of an executable biological model. PLoS One 2013; 8:e59303. [PMID: 23527156 PMCID: PMC3602105 DOI: 10.1371/journal.pone.0059303] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/01/2012] [Accepted: 02/14/2013] [Indexed: 12/16/2022] Open
Abstract
To facilitate analysis and understanding of biological systems, large-scale data are often integrated into models using a variety of mathematical and computational approaches. Such models describe the dynamics of the biological system and can be used to study the changes in the state of the system over time. For many model classes, such as discrete or continuous dynamical systems, there exist appropriate frameworks and tools for analyzing system dynamics. However, the heterogeneous information that encodes and bridges molecular and cellular dynamics, inherent to fine-grained molecular simulation models, presents significant challenges to the study of system dynamics. In this paper, we present an algorithmic information theory based approach for the analysis and interpretation of the dynamics of such executable models of biological systems. We apply a normalized compression distance (NCD) analysis to the state representations of a model that simulates the immune decision making and immune cell behavior. We show that this analysis successfully captures the essential information in the dynamics of the system, which results from a variety of events including proliferation, differentiation, or perturbations such as gene knock-outs. We demonstrate that this approach can be used for the analysis of executable models, regardless of the modeling framework, and for making experimentally quantifiable predictions.
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Affiliation(s)
- Avital Sadot
- Institute for Systems Biology, Seattle, Washington, United States of America
| | - Septimia Sarbu
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland
| | - Juha Kesseli
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland
| | - Hila Amir-Kroll
- Department of Medicine I, University Medical Centre Hamburg-Eppendorf, Hamburg, Germany
| | - Wei Zhang
- Department of Pathology, The University of Texas M. D. Anderson Cancer Center, Houston, Texas, United States of America
| | - Matti Nykter
- Department of Signal Processing, Tampere University of Technology, Tampere, Finland
- Institute of Biomedical Technology, University of Tampere, Tampere, Finland
- * E-mail: (MN); (IS)
| | - Ilya Shmulevich
- Institute for Systems Biology, Seattle, Washington, United States of America
- * E-mail: (MN); (IS)
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Somekh J, Choder M, Dori D. Conceptual Model-based Systems Biology: mapping knowledge and discovering gaps in the mRNA transcription cycle. PLoS One 2012; 7:e51430. [PMID: 23308089 PMCID: PMC3536069 DOI: 10.1371/journal.pone.0051430] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/10/2012] [Accepted: 11/01/2012] [Indexed: 01/17/2023] Open
Abstract
We propose a Conceptual Model-based Systems Biology framework for qualitative modeling, executing, and eliciting knowledge gaps in molecular biology systems. The framework is an adaptation of Object-Process Methodology (OPM), a graphical and textual executable modeling language. OPM enables concurrent representation of the system's structure-the objects that comprise the system, and behavior-how processes transform objects over time. Applying a top-down approach of recursively zooming into processes, we model a case in point-the mRNA transcription cycle. Starting with this high level cell function, we model increasingly detailed processes along with participating objects. Our modeling approach is capable of modeling molecular processes such as complex formation, localization and trafficking, molecular binding, enzymatic stimulation, and environmental intervention. At the lowest level, similar to the Gene Ontology, all biological processes boil down to three basic molecular functions: catalysis, binding/dissociation, and transporting. During modeling and execution of the mRNA transcription model, we discovered knowledge gaps, which we present and classify into various types. We also show how model execution enhances a coherent model construction. Identification and pinpointing knowledge gaps is an important feature of the framework, as it suggests where research should focus and whether conjectures about uncertain mechanisms fit into the already verified model.
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Affiliation(s)
- Judith Somekh
- Faculty of Industrial Engineering and Management, Technion, Israel Institute of Technology, Haifa, Israel.
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12
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Fertig EJ, Danilova LV, Favorov AV, Ochs MF. Hybrid Modeling of Cell Signaling and Transcriptional Reprogramming and Its Application in C. elegans Development. Front Genet 2011; 2:77. [PMID: 22303372 PMCID: PMC3268630 DOI: 10.3389/fgene.2011.00077] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/28/2011] [Accepted: 10/17/2011] [Indexed: 12/16/2022] Open
Abstract
Modeling of signal driven transcriptional reprogramming is critical for understanding of organism development, human disease, and cell biology. Many current modeling techniques discount key features of the biological sub-systems when modeling multiscale, organism-level processes. We present a mechanistic hybrid model, GESSA, which integrates a novel pooled probabilistic Boolean network model of cell signaling and a stochastic simulation of transcription and translation responding to a diffusion model of extracellular signals. We apply the model to simulate the well studied cell fate decision process of the vulval precursor cells (VPCs) in C. elegans, using experimentally derived rate constants wherever possible and shared parameters to avoid overfitting. We demonstrate that GESSA recovers (1) the effects of varying scaffold protein concentration on signal strength, (2) amplification of signals in expression, (3) the relative external ligand concentration in a known geometry, and (4) feedback in biochemical networks. We demonstrate that setting model parameters based on wild-type and LIN-12 loss-of-function mutants in C. elegans leads to correct prediction of a wide variety of mutants including partial penetrance of phenotypes. Moreover, the model is relatively insensitive to parameters, retaining the wild-type phenotype for a wide range of cell signaling rate parameters.
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Affiliation(s)
- Elana J. Fertig
- Division of Oncology Biostatistics and Bioinformatics, Department of Oncology, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins UniversityBaltimore, MD, USA
| | - Ludmila V. Danilova
- Division of Oncology Biostatistics and Bioinformatics, Department of Oncology, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins UniversityBaltimore, MD, USA
| | - Alexander V. Favorov
- Division of Oncology Biostatistics and Bioinformatics, Department of Oncology, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins UniversityBaltimore, MD, USA
- Scientific Center of RF GosNIIGenetikaMoscow, Russia
- Vavilov Institute of General Genetics of RASMoscow, Russia
| | - Michael F. Ochs
- Division of Oncology Biostatistics and Bioinformatics, Department of Oncology, Sidney Kimmel Comprehensive Cancer Center, Johns Hopkins UniversityBaltimore, MD, USA
- Department of Health Science Informatics, School of Medicine, Johns Hopkins UniversityBaltimore, MD, USA
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13
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Vainas O, Harel D, Cohen IR, Efroni S. Reactive animation: from piecemeal experimentation to reactive biological systems. Autoimmunity 2011; 44:271-81. [PMID: 21244340 DOI: 10.3109/08916934.2010.523260] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/16/2023]
Abstract
Over the past decade, multi-level complex behavior and reactive nature of biological systems, has been a focus point for the biomedical community. We have developed a computational approach, termed Reactive Animation (RA) for simulating such complex biological systems. RA is an approach for describing the dynamic characteristics of biological systems based on facts collected from experiments. These data are integrated bottom-up by computational tools and methods for reactive systems development and are simulated concomitantly to a front-end user friendly visualization and reporting systems. Using RA, the experimenter may intervene mid-simulation, suggest new hypotheses for cellular and molecular interactions, apply them to the simulation and observe their resulting outcomes "on-line". Several RA models have been developed including models of T cell activation, thymocyte development and pancreatic organogenesis, which are describe in the in this review.
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Affiliation(s)
- Oded Vainas
- The Mina & Everard Goodman Faculty of Life Sciences, Bar Ilan University Ramat Gan, Israel
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Evolving cell models for systems and synthetic biology. SYSTEMS AND SYNTHETIC BIOLOGY 2010; 4:55-84. [PMID: 20186253 PMCID: PMC2816226 DOI: 10.1007/s11693-009-9050-7] [Citation(s) in RCA: 19] [Impact Index Per Article: 1.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 08/27/2009] [Revised: 10/30/2009] [Accepted: 12/17/2009] [Indexed: 12/03/2022]
Abstract
This paper proposes a new methodology for the automated design of cell models for systems and synthetic biology. Our modelling framework is based on P systems, a discrete, stochastic and modular formal modelling language. The automated design of biological models comprising the optimization of the model structure and its stochastic kinetic constants is performed using an evolutionary algorithm. The evolutionary algorithm evolves model structures by combining different modules taken from a predefined module library and then it fine-tunes the associated stochastic kinetic constants. We investigate four alternative objective functions for the fitness calculation within the evolutionary algorithm: (1) equally weighted sum method, (2) normalization method, (3) randomly weighted sum method, and (4) equally weighted product method. The effectiveness of the methodology is tested on four case studies of increasing complexity including negative and positive autoregulation as well as two gene networks implementing a pulse generator and a bandwidth detector. We provide a systematic analysis of the evolutionary algorithm’s results as well as of the resulting evolved cell models.
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16
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Moya A, Krasnogor N, Peretó J, Latorre A. Goethe's dream. Challenges and opportunities for synthetic biology. EMBO Rep 2009; 10 Suppl 1:S28-S32. [PMID: 19636300 PMCID: PMC2726005 DOI: 10.1038/embor.2009.120] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [MESH Headings] [Grants] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/07/2023] Open
Affiliation(s)
- Andrés Moya
- Departament de Genètica and Institut Cavanilles de Biodiversitat i Biologia Evolutiva, University of València, Centro Superior de Investigación en Salud Pública (CSISP) and CIBER de Epidemiología y Salud Pública (CIBEResp), Spain.
E-mail:
| | - Natalio Krasnogor
- Natalio Krasnogor is at the School of Computer Science, University of Nottingham, UK.
E-mail:
| | - Juli Peretó
- Juli Peretó is at the Departament de Bioquímica i Biologia Molecular and Institut Cavanilles de Biodiversitat i Biologia Evolutiva, University of València and CIBER de Epidemiología y Salud Pública (CIBEResp), Spain.
E-mail:
| | - Amparo Latorre
- Amparo Latorre is at the Departament de Genètica and Institut Cavanilles de Biodiversitat i Biologia Evolutiva, University of València, Centro Superior de Investigación en Salud Pública (CSISP), and CIBER de Epidemiología y Salud Pública (CIBEResp), Spain.
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17
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A Bayesian Approach to Model Checking Biological Systems. COMPUTATIONAL METHODS IN SYSTEMS BIOLOGY 2009. [DOI: 10.1007/978-3-642-03845-7_15] [Citation(s) in RCA: 118] [Impact Index Per Article: 7.4] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
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