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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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2
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Shafiekhani S, Jafari A, Jafarzadeh L, Sadeghi V, Gheibi N. Predicting efficacy of 5-fluorouracil therapy via a mathematical model with fuzzy uncertain parameters. JOURNAL OF MEDICAL SIGNALS & SENSORS 2022; 12:202-218. [PMID: 36120402 PMCID: PMC9480509 DOI: 10.4103/jmss.jmss_92_21] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/21/2021] [Revised: 11/12/2021] [Accepted: 01/21/2022] [Indexed: 11/08/2022]
Abstract
Background: Due to imprecise/missing data used for parameterization of ordinary differential equations (ODEs), model parameters are uncertain. Uncertainty of parameters has hindered the application of ODEs that require accurate parameters. Methods: We extended an available ODE model of tumor-immune system interactions via fuzzy logic to illustrate the fuzzification procedure of an ODE model. The fuzzy ODE (FODE) model assigns a fuzzy number to the parameters, to capture parametric uncertainty. We used the FODE model to predict tumor and immune cell dynamics and to assess the efficacy of 5-fluorouracil (5-FU) chemotherapy. Result: FODE model investigates how parametric uncertainty affects the uncertainty band of cell dynamics in the presence and absence of 5-FU treatment. In silico experiments revealed that the frequent 5-FU injection created a beneficial tumor microenvironment that exerted detrimental effects on tumor cells by enhancing the infiltration of CD8+ T cells, and natural killer cells, and decreasing that of myeloid-derived suppressor cells. The global sensitivity analysis was proved model robustness against random perturbation to parameters. Conclusion: ODE models with fuzzy uncertain kinetic parameters cope with insufficient/imprecise experimental data in the field of mathematical oncology and can predict cell dynamics uncertainty band.
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3
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Jung Y, Kraikivski P, Shafiekhani S, Terhune SS, Dash RK. Crosstalk between Plk1, p53, cell cycle, and G2/M DNA damage checkpoint regulation in cancer: computational modeling and analysis. NPJ Syst Biol Appl 2021; 7:46. [PMID: 34887439 PMCID: PMC8660825 DOI: 10.1038/s41540-021-00203-8] [Citation(s) in RCA: 21] [Impact Index Per Article: 7.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/17/2020] [Accepted: 11/03/2021] [Indexed: 12/21/2022] Open
Abstract
Different cancer cell lines can have varying responses to the same perturbations or stressful conditions. Cancer cells that have DNA damage checkpoint-related mutations are often more sensitive to gene perturbations including altered Plk1 and p53 activities than cancer cells without these mutations. The perturbations often induce a cell cycle arrest in the former cancer, whereas they only delay the cell cycle progression in the latter cancer. To study crosstalk between Plk1, p53, and G2/M DNA damage checkpoint leading to differential cell cycle regulations, we developed a computational model by extending our recently developed model of mitotic cell cycle and including these key interactions. We have used the model to analyze the cancer cell cycle progression under various gene perturbations including Plk1-depletion conditions. We also analyzed mutations and perturbations in approximately 1800 different cell lines available in the Cancer Dependency Map and grouped lines by genes that are represented in our model. Our model successfully explained phenotypes of various cancer cell lines under different gene perturbations. Several sensitivity analysis approaches were used to identify the range of key parameter values that lead to the cell cycle arrest in cancer cells. Our resulting model can be used to predict the effect of potential treatments targeting key mitotic and DNA damage checkpoint regulators on cell cycle progression of different types of cancer cells.
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Affiliation(s)
- Yongwoon Jung
- grid.30760.320000 0001 2111 8460Department of Biomedical Engineering, Medical College of Wisconsin, Milwaukee, WI 53226 USA
| | - Pavel Kraikivski
- Academy of Integrated Science, Division of Systems Biology, Virginia Tech, Blacksburg, VA, 24061, USA.
| | - Sajad Shafiekhani
- grid.411705.60000 0001 0166 0922Department of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
| | - Scott S. Terhune
- grid.30760.320000 0001 2111 8460Departments of Microbiology and Immunology, Medical College of Wisconsin, Milwaukee, WI 53226 USA ,grid.30760.320000 0001 2111 8460Center of Systems and Molecular Medicine, Medical College of Wisconsin, Milwaukee, WI 53226 USA
| | - Ranjan K. Dash
- grid.30760.320000 0001 2111 8460Department of Biomedical Engineering, Medical College of Wisconsin, Milwaukee, WI 53226 USA ,grid.30760.320000 0001 2111 8460Center of Systems and Molecular Medicine, Medical College of Wisconsin, Milwaukee, WI 53226 USA ,grid.30760.320000 0001 2111 8460Department of Physiology, Medical College of Wisconsin, Milwaukee, WI 53226 USA
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Shafiekhani S, Dehghanbanadaki H, Fatemi AS, Rahbar S, Hadjati J, Jafari AH. Prediction of anti-CD25 and 5-FU treatments efficacy for pancreatic cancer using a mathematical model. BMC Cancer 2021; 21:1226. [PMID: 34781899 PMCID: PMC8594222 DOI: 10.1186/s12885-021-08770-z] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/13/2021] [Accepted: 09/09/2021] [Indexed: 02/18/2023] Open
Abstract
BACKGROUND Pancreatic ductal adenocarcinoma (PDAC) is a highly lethal disease with rising incidence and with 5-years overall survival of less than 8%. PDAC creates an immune-suppressive tumor microenvironment to escape immune-mediated eradication. Regulatory T (Treg) cells and myeloid-derived suppressor cells (MDSC) are critical components of the immune-suppressive tumor microenvironment. Shifting from tumor escape or tolerance to elimination is the major challenge in the treatment of PDAC. RESULTS In a mathematical model, we combine distinct treatment modalities for PDAC, including 5-FU chemotherapy and anti- CD25 immunotherapy to improve clinical outcome and therapeutic efficacy. To address and optimize 5-FU and anti- CD25 treatment (to suppress MDSCs and Tregs, respectively) schedule in-silico and simultaneously unravel the processes driving therapeutic responses, we designed an in vivo calibrated mathematical model of tumor-immune system (TIS) interactions. We designed a user-friendly graphical user interface (GUI) unit which is configurable for treatment timings to implement an in-silico clinical trial to test different timings of both 5-FU and anti- CD25 therapies. By optimizing combination regimens, we improved treatment efficacy. In-silico assessment of 5-FU and anti- CD25 combination therapy for PDAC significantly showed better treatment outcomes when compared to 5-FU and anti- CD25 therapies separately. Due to imprecise, missing, or incomplete experimental data, the kinetic parameters of the TIS model are uncertain that this can be captured by the fuzzy theorem. We have predicted the uncertainty band of cell/cytokines dynamics based on the parametric uncertainty, and we have shown the effect of the treatments on the displacement of the uncertainty band of the cells/cytokines. We performed global sensitivity analysis methods to identify the most influential kinetic parameters and simulate the effect of the perturbation on kinetic parameters on the dynamics of cells/cytokines. CONCLUSION Our findings outline a rational approach to therapy optimization with meaningful consequences for how we effectively design treatment schedules (timing) to maximize their success, and how we treat PDAC with combined 5-FU and anti- CD25 therapies. Our data revealed that a synergistic combinatorial regimen targeting the Tregs and MDSCs in both crisp and fuzzy settings of model parameters can lead to tumor eradication.
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Affiliation(s)
- Sajad Shafiekhani
- Departments of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran, Iran.,Students' Scientific Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Hojat Dehghanbanadaki
- Students' Scientific Research Center, Tehran University of Medical Sciences, Tehran, Iran.,Metabolic Disorders Research Center, Endocrinology and Metabolism Molecular-Cellular Sciences Institute, Tehran University of Medical Sciences, Tehran, Iran
| | - Azam Sadat Fatemi
- Departments of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran, Iran
| | - Sara Rahbar
- Departments of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran, Iran
| | - Jamshid Hadjati
- Departments of Medical Immunology, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
| | - Amir Homayoun Jafari
- Departments of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran. .,Research Center for Biomedical Technologies and Robotics, Tehran, Iran.
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Bardini R, Benso A, Politano G, Di Carlo S. Nets-within-nets for modeling emergent patterns in ontogenetic processes. Comput Struct Biotechnol J 2021; 19:5701-5721. [PMID: 34765090 PMCID: PMC8554175 DOI: 10.1016/j.csbj.2021.10.008] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2021] [Revised: 10/05/2021] [Accepted: 10/05/2021] [Indexed: 11/16/2022] Open
Abstract
Ontogenesis is the development of an organism from its earliest stage to maturity, including homeostasis maintenance throughout adulthood despite environmental perturbations. Almost all cells of a multicellular organism share the same genomic information. Nevertheless, phenotypic diversity and complex supra-cellular architectures emerge at every level, starting from tissues and organs. This is possible thanks to a robust and dynamic interplay of regulative mechanisms. To study ontogenesis, it is necessary to consider different levels of regulation, both genetic and epigenetic. Each cell undergoes a specific path across a landscape of possible regulative states affecting both its structure and its functions during development. This paper proposes using the Nets-Within-Nets formalism, which combines Petri Nets' simplicity with the capability to represent and simulate the interplay between different layers of regulation connected by non-trivial and context-dependent hierarchical relations. In particular, this work introduces a modeling strategy based on Nets-Within-Nets that can model several critical processes involved in ontogenesis. Moreover, it presents a case study focusing on the first phase of Vulval Precursor Cells specification in C.Elegans. The case study shows that the proposed model can simulate the emergent morphogenetic pattern corresponding to the observed developmental outcome of that phase, in both the physiological case and different mutations. The model presented in the results section is available online at https://github.com/sysbio-polito/NWN_CElegans_VPC_model/.
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Affiliation(s)
- Roberta Bardini
- Politecnico di Torino, Control and Computer Engineering Department, Corso Duca degli Abruzzi 24, Torino 10129, Italy
| | - Alfredo Benso
- Politecnico di Torino, Control and Computer Engineering Department, Corso Duca degli Abruzzi 24, Torino 10129, Italy
| | - Gianfranco Politano
- Politecnico di Torino, Control and Computer Engineering Department, Corso Duca degli Abruzzi 24, Torino 10129, Italy
| | - Stefano Di Carlo
- Politecnico di Torino, Control and Computer Engineering Department, Corso Duca degli Abruzzi 24, Torino 10129, Italy
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6
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Nourisa J, Zeller-Plumhoff B, Helmholz H, Luthringer-Feyerabend B, Ivannikov V, Willumeit-Römer R. Magnesium ions regulate mesenchymal stem cells population and osteogenic differentiation: A fuzzy agent-based modeling approach. Comput Struct Biotechnol J 2021; 19:4110-4122. [PMID: 34527185 PMCID: PMC8346546 DOI: 10.1016/j.csbj.2021.07.005] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/09/2021] [Revised: 07/05/2021] [Accepted: 07/07/2021] [Indexed: 12/17/2022] Open
Abstract
Mesenchymal stem cells (MSCs) are proliferative and multipotent cells that play a key role in the bone regeneration process. Empirical data have repeatedly shown the bioregulatory importance of magnesium (Mg) ions in MSC growth and osteogenesis. In this study, we propose an agent-based model to predict the spatiotemporal dynamics of the MSC population and osteogenic differentiation in response to Mg2+ ions. A fuzzy-logic controller was designed to govern the decision-making process of cells by predicting four cellular processes of proliferation, differentiation, migration, and mortality in response to several important bioregulatory factors such as Mg2+ ions, pH, BMP2, and TGF-β1. The model was calibrated using the empirical data obtained from three sets of cell culture experiments. The model successfully reproduced the empirical observations regarding live cell count, viability, DNA content, and the differentiation-related markers of alkaline phosphate (ALP) and osteocalcin (OC). The simulation results, in agreement with the empirical data, showed that Mg2+ ions within 3-6 mM concentration have the highest stimulation effect on cell population growth. The model also correctly reproduced the stimulatory effect of Mg2+ ions on ALP and its inhibitory effect on OC as the early and late differentiation markers, respectively. Besides, the numerical simulation shed light on the innate cellular differences of the cells cultured in different experiments in terms of the proliferative capacity as well as sensitivity to Mg2+ ions. The proposed model can be adopted in the study of the osteogenesis around Mg-based implants where ions released due to degradation interact with local cells and regulate bone regeneration.
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Affiliation(s)
- Jalil Nourisa
- Helmholtz Zentrum Hereon, Institute of Metallic Biomaterials, Max-Planck-Straße 1, 21502 Geesthacht, Germany
| | - Berit Zeller-Plumhoff
- Helmholtz Zentrum Hereon, Institute of Metallic Biomaterials, Max-Planck-Straße 1, 21502 Geesthacht, Germany
| | - Heike Helmholz
- Helmholtz Zentrum Hereon, Institute of Metallic Biomaterials, Max-Planck-Straße 1, 21502 Geesthacht, Germany
| | | | - Vladimir Ivannikov
- Helmholtz Zentrum Hereon, Institute of Metallic Biomaterials, Max-Planck-Straße 1, 21502 Geesthacht, Germany
| | - Regine Willumeit-Römer
- Helmholtz Zentrum Hereon, Institute of Metallic Biomaterials, Max-Planck-Straße 1, 21502 Geesthacht, Germany
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7
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Shafiekhani S, Poursheykhani A, Rahbar S, Jafari AH. Simulating ATO Mechanism and EGFR Signaling with Fuzzy Logic and Petri Net. J Biomed Phys Eng 2021; 11:325-336. [PMID: 34189121 PMCID: PMC8236109 DOI: 10.31661/jbpe.v0i0.796] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2017] [Accepted: 11/05/2017] [Indexed: 12/04/2022]
Abstract
BACKGROUND Interactions of many key proteins or genes in signalling pathway have been studied qualitatively in the literature, but only little quantitative information is available. OBJECTIVE Although much has been done to clarify the biochemistry of transcriptional dynamics in signalling pathway, it remains difficult to find out and predict quantitative responses. The aim of this study is to construct a computational model of epidermal growth factor receptor (EGFR) signalling pathway as one of hallmarks of cancer so as to predict quantitative responses. MATERIAL AND METHODS In this analytical study, we presented a computational model to investigate EGFR signalling pathway. Interaction of Arsenic trioxide (ATO) with EGFR signalling pathway factors has been elicited by systematic search in data bases, as ATO is one of the mysterious chemotherapy agents that control EGFR expression in cancer. ATO has dichotomous manner in vivo, dependent on its concentration. According to fuzzy rules based upon qualitative knowledge and Petri Net, we can construct a quantitative model to describe ATO mechanism in EGFR signalling pathway. RESULTS By Fuzzy Logic models that have the potential to trade with the loss of quantitative information on how different species interact, along with Petri net quantitatively describe the dynamics of EGFR signalling pathway. By this model the dynamic of different factors in EGFR signalling pathway is achieved. CONCLUSION The use of Fuzzy Logic and PNs in biological network modelling causes a deeper understanding and comprehensive analysis of the biological networks.
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Affiliation(s)
- Sajad Shafiekhani
- PhD Candidate, Department of Biophysics & Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
- PhD Candidate, Research Center for Science and Technology in Medicine (RCSTIM), Tehran University of Medical Sciences, Tehran, Iran
| | - Arash Poursheykhani
- PhD Candidate, Department of Medical Genetics, School of Medicine, Mashhad University of Medical Science, Mashhad, Iran
| | - Sara Rahbar
- PhD Candidate, Department of Biophysics & Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
- PhD Candidate, Research Center for Science and Technology in Medicine (RCSTIM), Tehran University of Medical Sciences, Tehran, Iran
| | - Amir Homayoun Jafari
- PhD, Department of Biophysics & Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran
- PhD, Research Center for Science and Technology in Medicine (RCSTIM), Tehran University of Medical Sciences, Tehran, Iran
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8
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Nobile MS, Votta G, Palorini R, Spolaor S, De Vitto H, Cazzaniga P, Ricciardiello F, Mauri G, Alberghina L, Chiaradonna F, Besozzi D. Fuzzy modeling and global optimization to predict novel therapeutic targets in cancer cells. Bioinformatics 2020; 36:2181-2188. [PMID: 31750879 PMCID: PMC7141866 DOI: 10.1093/bioinformatics/btz868] [Citation(s) in RCA: 8] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/13/2019] [Revised: 09/13/2019] [Accepted: 11/20/2019] [Indexed: 12/18/2022] Open
Abstract
Motivation The elucidation of dysfunctional cellular processes that can induce the onset of a disease is a challenging issue from both the experimental and computational perspectives. Here we introduce a novel computational method based on the coupling between fuzzy logic modeling and a global optimization algorithm, whose aims are to (1) predict the emergent dynamical behaviors of highly heterogeneous systems in unperturbed and perturbed conditions, regardless of the availability of quantitative parameters, and (2) determine a minimal set of system components whose perturbation can lead to a desired system response, therefore facilitating the design of a more appropriate experimental strategy. Results We applied this method to investigate what drives K-ras-induced cancer cells, displaying the typical Warburg effect, to death or survival upon progressive glucose depletion. The optimization analysis allowed to identify new combinations of stimuli that maximize pro-apoptotic processes. Namely, our results provide different evidences of an important protective role for protein kinase A in cancer cells under several cellular stress conditions mimicking tumor behavior. The predictive power of this method could facilitate the assessment of the response of other complex heterogeneous systems to drugs or mutations in fields as medicine and pharmacology, therefore paving the way for the development of novel therapeutic treatments. Availability and implementation The source code of FUMOSO is available under the GPL 2.0 license on GitHub at the following URL: https://github.com/aresio/FUMOSO Supplementary information Supplementary data are available at Bioinformatics online.
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Affiliation(s)
- Marco S Nobile
- Department of Informatics, Systems and Communication, University of Milano-Bicocca, Milano 20126, Italy.,SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy.,Department of Industrial Engineering and Innovation Sciences, Eindhoven University of Technology, Eindhoven 5612 AZ, The Netherlands
| | - Giuseppina Votta
- SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy.,Department of Biotechnology and Biosciences, University of Milano-Bicocca, Milano 20126, Italy
| | - Roberta Palorini
- SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy.,Department of Biotechnology and Biosciences, University of Milano-Bicocca, Milano 20126, Italy
| | - Simone Spolaor
- Department of Informatics, Systems and Communication, University of Milano-Bicocca, Milano 20126, Italy.,SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy
| | - Humberto De Vitto
- SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy.,Hormel Institute, University of Minnesota, Austin, MN 55912, USA
| | - Paolo Cazzaniga
- SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy.,Department of Human and Social Sciences, University of Bergamo, Bergamo 24129, Italy
| | - Francesca Ricciardiello
- SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy.,Department of Biotechnology and Biosciences, University of Milano-Bicocca, Milano 20126, Italy
| | - Giancarlo Mauri
- Department of Informatics, Systems and Communication, University of Milano-Bicocca, Milano 20126, Italy.,SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy
| | - Lilia Alberghina
- SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy.,Department of Biotechnology and Biosciences, University of Milano-Bicocca, Milano 20126, Italy
| | - Ferdinando Chiaradonna
- SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy.,Department of Biotechnology and Biosciences, University of Milano-Bicocca, Milano 20126, Italy
| | - Daniela Besozzi
- Department of Informatics, Systems and Communication, University of Milano-Bicocca, Milano 20126, Italy.,SYSBIO.IT Centre for Systems Biology, Milano 20126, Italy
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9
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Shafiekhani S, Shafiekhani M, Rahbar S, Jafari AH. Extended Robust Boolean Network of Budding Yeast Cell Cycle. JOURNAL OF MEDICAL SIGNALS & SENSORS 2020; 10:94-104. [PMID: 32676445 PMCID: PMC7359953 DOI: 10.4103/jmss.jmss_40_19] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/14/2019] [Revised: 10/22/2019] [Accepted: 10/20/2019] [Indexed: 11/17/2022]
Abstract
Background: How to explore the dynamics of transition probabilities between phases of budding yeast cell cycle (BYCC) network based on the dynamics of protein activities that control this network? How to identify the robust structure of protein interactions of BYCC Boolean network (BN)? Budding yeast allows scientists to put experiments into effect in order to discover the intracellular cell cycle regulating structures which are well simulated by mathematical modeling. Methods: We extended an available deterministic BN of proteins responsible for the cell cycle to a Markov chain model containing apoptosis besides G1, S, G2, M, and stationary G1. Using genetic algorithm (GA), we estimated the kinetic parameters of the extended BN model so that the subsequent transition probabilities derived using Markov chain model of cell states as normal cell cycle becomes the maximum while the structure of chemical interactions of extended BN of cell cycle becomes more stable. Results: Using kinetic parameters optimized by GA, the probability of the subsequent transitions between cell cycle phases is maximized. The relative basin size of stationary G1 increased from 86% to 96.48% while the number of attractors decreased from 7 in the original model to 5 in the extended one. Hence, an increase in the robustness of the system has been achieved. Conclusion: The structure of interacting proteins in cell cycle network affects its robustness and probabilities of transitions between different cell cycle phases. Markov chain and BN are good approaches to study the stability and dynamics of the cell cycle network.
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Affiliation(s)
- Sajad Shafiekhani
- Department of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran University of Medical Sciences, Tehran, Iran.,Students' Scientific Research Center, Tehran University of Medical Sciences, Tehran, Iran
| | - Mojtaba Shafiekhani
- Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran
| | - Sara Rahbar
- Department of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran University of Medical Sciences, Tehran, Iran
| | - Amir Homayoun Jafari
- Department of Biomedical Engineering, School of Medicine, Tehran University of Medical Sciences, Tehran, Iran.,Research Center for Biomedical Technologies and Robotics, Tehran University of Medical Sciences, Tehran, Iran
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10
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Symmetric Fuzzy Stochastic Differential Equations with Generalized Global Lipschitz Condition. Symmetry (Basel) 2020. [DOI: 10.3390/sym12050819] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/16/2022] Open
Abstract
The paper contains a discussion on solutions to symmetric type of fuzzy stochastic differential equations. The symmetric equations under study have drift and diffusion terms symmetrically on both sides of equations. We claim that such symmetric equations have unique solutions in the case that equations’ coefficients satisfy a certain generalized Lipschitz condition. To show this, we prove that an approximation sequence converges to the solution. Then, a study on stability of solution is given. Some inferences for symmetric set-valued stochastic differential equations end the paper.
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11
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Ilan Y. Order Through Disorder: The Characteristic Variability of Systems. Front Cell Dev Biol 2020; 8:186. [PMID: 32266266 PMCID: PMC7098948 DOI: 10.3389/fcell.2020.00186] [Citation(s) in RCA: 32] [Impact Index Per Article: 8.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/02/2019] [Accepted: 03/05/2020] [Indexed: 12/17/2022] Open
Abstract
Randomness characterizes many processes in nature, and therefore its importance cannot be overstated. In the present study, we investigate examples of randomness found in various fields, to underlie its fundamental processes. The fields we address include physics, chemistry, biology (biological systems from genes to whole organs), medicine, and environmental science. Through the chosen examples, we explore the seemingly paradoxical nature of life and demonstrate that randomness is preferred under specific conditions. Furthermore, under certain conditions, promoting or making use of variability-associated parameters may be necessary for improving the function of processes and systems.
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Affiliation(s)
- Yaron Ilan
- Department of Medicine, Hadassah-Hebrew University Medical Center, Jerusalem, Israel
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12
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Liu F, Heiner M, Gilbert D. Fuzzy Petri nets for modelling of uncertain biological systems. Brief Bioinform 2018; 21:198-210. [PMID: 30590430 DOI: 10.1093/bib/bby118] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 08/21/2018] [Revised: 10/09/2018] [Accepted: 11/16/2018] [Indexed: 12/28/2022] Open
Abstract
The modelling of biological systems is accompanied with epistemic uncertainties that range from structural uncertainty to parametric uncertainty due to such limitations as insufficient understanding of the underlying mechanism and incomplete measurement data of a system. Fuzzy logic approaches such as fuzzy Petri nets (FPNs) are effective in addressing these issues. In this paper, we review FPNs that have been used for modelling uncertain biological systems, which we classify in three categories: basic fuzzy Petri nets, fuzzy quantitative Petri nets and Petri nets with fuzzy kinetic parameters. For each category of these FPNs, we summarize its modelling capabilities and current applications, discuss its merits and drawbacks and give suggestions for further research. This understanding on how to use FPNs for modelling uncertain biological systems will assist readers in selecting appropriate FPN classes for specific modelling circumstances. This review may also promote the extensive research and application of FPNs in the systems biology area.
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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, Cottbus, Germany
| | - David Gilbert
- Department of Computer Science, Brunel University London, Middlesex, UK
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13
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Ashraf J, Ahmad J, Ali A, Ul-Haq Z. Analyzing the Behavior of Neuronal Pathways in Alzheimer's Disease Using Petri Net Modeling Approach. Front Neuroinform 2018; 12:26. [PMID: 29875647 PMCID: PMC5974338 DOI: 10.3389/fninf.2018.00026] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/11/2017] [Accepted: 04/30/2018] [Indexed: 11/13/2022] Open
Abstract
Alzheimer's Disease (AD) is the most common neuro-degenerative disorder in the elderly that leads to dementia. The hallmark of AD is senile lesions made by abnormal aggregation of amyloid beta in extracellular space of brain. One of the challenges in AD treatment is to better understand the mechanism of action of key proteins and their related pathways involved in neuronal cell death in order to identify adequate therapeutic targets. This study focuses on the phenomenon of aggregation of amyloid beta into plaques by considering the signal transduction pathways of Calpain-Calpastatin (CAST) regulation system and Amyloid Precursor Protein (APP) processing pathways along with Ca2+ channels. These pathways are modeled and analyzed individually as well as collectively through Stochastic Petri Nets for comprehensive analysis and thorough understating of AD. The model predicts that the deregulation of Calpain activity, disruption of Calcium homeostasis, inhibition of CAST and elevation of abnormal APP processing are key cytotoxic events resulting in an early AD onset and progression. Interestingly, the model also reveals that plaques accumulation start early (at the age of 40) in life but symptoms appear late. These results suggest that the process of neuro-degeneration can be slowed down or paused by slowing down the degradation rate of Calpain-CAST Complex. In the light of this study, the suggestive therapeutic strategy might be the prevention of the degradation of Calpain-CAST complexes and the inhibition of Calpain for the treatment of neurodegenerative diseases such as AD.
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Affiliation(s)
- Javaria Ashraf
- Research Center for Modeling and Simulation, National University of Sciences and Technology, Islamabad, Pakistan
| | - Jamil Ahmad
- Research Center for Modeling and Simulation, National University of Sciences and Technology, Islamabad, Pakistan
| | - Amjad Ali
- Atta-Ur-Rahman School of Applied Biosciences, National University of Sciences and Technology, Islamabad, Pakistan
| | - Zaheer Ul-Haq
- Dr. Panjwani Center for Molecular Medicine and Drug Research, International Center for Chemical Sciences, University of Karachi, Karachi, Pakistan
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14
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Liu F, Chen S, Heiner M, Song H. Modeling biological systems with uncertain kinetic data using fuzzy continuous Petri nets. BMC SYSTEMS BIOLOGY 2018; 12:42. [PMID: 29745860 PMCID: PMC5998910 DOI: 10.1186/s12918-018-0568-8] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Indexed: 11/10/2022]
Abstract
BACKGROUND Uncertainties exist in many biological systems, which can be classified as random uncertainties and fuzzy uncertainties. The former can usually be dealt with using stochastic methods, while the latter have to be handled with such approaches as fuzzy methods. RESULTS In this paper, we focus on a special type of biological systems that can be described using ordinary differential equations or continuous Petri nets (CPNs), but some kinetic parameters are missing or inaccurate. For this, we propose a class of fuzzy continuous Petri nets (FCPNs) by combining CPNs and fuzzy logics. We also present and implement a simulation algorithm for FCPNs, and illustrate our method with the heat shock response system. CONCLUSIONS This approach can be used to model biological systems where some kinetic parameters are not available or their values vary due to some environmental factors.
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Affiliation(s)
- Fei Liu
- School of Software Engineering, South China University of Technology, Guangzhou, 510006, People's Republic of China.
| | - Siyuan Chen
- Control and simulation center, Harbin Institute of Technology, Harbin, 150080, China
| | - Monika Heiner
- Computer Science Institute, Brandenburg University of Technology, Cottbus, 10 13 44, Germany
| | - Hengjie Song
- School of Software Engineering, South China University of Technology, Guangzhou, 510006, People's Republic of China.
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15
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Handling variability and incompleteness of biological data by flexible nets: a case study for Wilson disease. NPJ Syst Biol Appl 2018; 4:7. [PMID: 29354285 PMCID: PMC5765040 DOI: 10.1038/s41540-017-0044-x] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/19/2017] [Revised: 12/05/2017] [Accepted: 12/12/2017] [Indexed: 12/22/2022] Open
Abstract
Mathematical models that combine predictive accuracy with explanatory power are central to the progress of systems and synthetic biology, but the heterogeneity and incompleteness of biological data impede our ability to construct such models. Furthermore, the robustness displayed by many biological systems means that they have the flexibility to operate under a range of physiological conditions and this is difficult for many modeling formalisms to handle. Flexible nets (FNs) address these challenges and represent a paradigm shift in model-based analysis of biological systems. FNs can: (i) handle uncertainties, ranges and missing information in concentrations, stoichiometry, network topology, and transition rates without having to resort to statistical approaches; (ii) accommodate different types of data in a unified model that integrates various cellular mechanisms; and (iii) be employed for system optimization and model predictive control. We present FNs and illustrate their capabilities by modeling a well-established system, the dynamics of glucose consumption by a microbial population. We further demonstrate the ability of FNs to take control actions in response to genetic or metabolic perturbations. Having bench-marked the system, we then construct the first quantitative model for Wilson disease—a rare genetic disorder that impairs copper utilization in the liver. We used this model to investigate the feasibility of using vitamin E supplementation therapy for symptomatic improvement. Our results indicate that hepatocytic inflammation caused by copper accumulation was not aggravated by limitations on endogenous antioxidant supplies, which means that treating patients with antioxidants is unlikely to be effective. In order to study complex dynamical systems, appropriate mathematical models that capture the system features are necessary. Biological systems, in particular, require flexible modeling approaches for their study since they exhibit variable quantifiable responses under different conditions. Moreover, data about a given biological system are often uncertain or unavailable. Here, a group of scientists from the University of Cambridge introduce Flexible Nets (FNs), a novel approach for the modeling, analysis, and control of biological systems. After presenting the FN approach, they show how a well-known system of glucose consumption and utilization by yeast can be modeled, analyzed and controlled. Then, FNs are used to build and analyze the first quantitative and predictive model of Wilson disease (a heritable defect in copper utilization). They demonstrate that FN simulations permit an evaluation of the relative efficacy of different therapeutic options.
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