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Junior MGV, Côrtes AMDA, Carneiro FRG, Carels N, da Silva FAB. Unveiling the Dynamics behind Glioblastoma Multiforme Single-Cell Data Heterogeneity. Int J Mol Sci 2024; 25:4894. [PMID: 38732140 PMCID: PMC11084314 DOI: 10.3390/ijms25094894] [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: 03/08/2024] [Revised: 04/02/2024] [Accepted: 04/03/2024] [Indexed: 05/13/2024] Open
Abstract
Glioblastoma Multiforme is a brain tumor distinguished by its aggressiveness. We suggested that this aggressiveness leads single-cell RNA-sequence data (scRNA-seq) to span a representative portion of the cancer attractors domain. This conjecture allowed us to interpret the scRNA-seq heterogeneity as reflecting a representative trajectory within the attractor's domain. We considered factors such as genomic instability to characterize the cancer dynamics through stochastic fixed points. The fixed points were derived from centroids obtained through various clustering methods to verify our method sensitivity. This methodological foundation is based upon sample and time average equivalence, assigning an interpretative value to the data cluster centroids and supporting parameters estimation. We used stochastic simulations to reproduce the dynamics, and our results showed an alignment between experimental and simulated dataset centroids. We also computed the Waddington landscape, which provided a visual framework for validating the centroids and standard deviations as characterizations of cancer attractors. Additionally, we examined the stability and transitions between attractors and revealed a potential interplay between subtypes. These transitions might be related to cancer recurrence and progression, connecting the molecular mechanisms of cancer heterogeneity with statistical properties of gene expression dynamics. Our work advances the modeling of gene expression dynamics and paves the way for personalized therapeutic interventions.
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Affiliation(s)
- Marcos Guilherme Vieira Junior
- Graduate Program in Computational and Systems Biology, Oswaldo Cruz Institute (IOC), Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040-900, Brazil;
| | - Adriano Maurício de Almeida Côrtes
- Department of Applied Mathematics, Institute of Mathematics, Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro 21941-909, Brazil;
- Systems Engineering and Computer Science Program, Coordination of Postgraduate Programs in Engineering (COPPE), Federal University of Rio de Janeiro (UFRJ), Rio de Janeiro 21941-972, Brazil
| | - Flávia Raquel Gonçalves Carneiro
- Center of Technological Development in Health (CDTS), Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040-361, Brazil;
- Laboratório Interdisciplinar de Pesquisas Médicas, Oswaldo Cruz Institute (IOC), Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040-900, Brazil
- Program of Immunology and Tumor Biology, Brazilian National Cancer Institute (INCA), Rio de Janeiro 20231-050, Brazil
| | - Nicolas Carels
- Laboratory of Biological System Modeling, Center of Technological Development in Health (CDTS), Oswaldo Cruz Foundation (FIOCRUZ), Rio de Janeiro 21040-361, Brazil
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Madec M, Rosati E, Lallement C. Feasibility and reliability of sequential logic with gene regulatory networks. PLoS One 2021; 16:e0249234. [PMID: 33784367 PMCID: PMC8009411 DOI: 10.1371/journal.pone.0249234] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/26/2020] [Accepted: 03/14/2021] [Indexed: 11/19/2022] Open
Abstract
Gene regulatory networks exhibiting Boolean behaviour, e.g. AND, OR or XOR, have been routinely designed for years. However, achieving more sophisticated functions, such as control or computation, usually requires sequential circuits or so-called state machines. For such a circuit, outputs depend both on inputs and the current state of the system. Although it is still possible to design such circuits by analogy with digital electronics, some particularities of biology make the task trickier. The impact of two of them, namely the stochasticity of biological processes and the inhomogeneity in the response of regulation mechanisms, are assessed in this paper. Numerical simulations performed in two use cases point out high risks of malfunctions even for designed GRNs functional from a theoretical point of view. Several solutions to improve reliability of such systems are also discussed.
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Affiliation(s)
- Morgan Madec
- Laboratory of Engineering Sciences, Computer Sciences and Imaging, UMR 7357 (University of Strasbourg / CNRS), Illkirch, France
- * E-mail:
| | - Elise Rosati
- Laboratory of Engineering Sciences, Computer Sciences and Imaging, UMR 7357 (University of Strasbourg / CNRS), Illkirch, France
| | - Christophe Lallement
- Laboratory of Engineering Sciences, Computer Sciences and Imaging, UMR 7357 (University of Strasbourg / CNRS), Illkirch, France
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Hortsch SK, Kremling A. Stochastic Models for Studying the Role of Cellular Noise and Heterogeneity. SYSTEMS MEDICINE 2021. [DOI: 10.1016/b978-0-12-801238-3.11466-7] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/28/2022] Open
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Zacchetti B, Wösten HA, Claessen D. Multiscale heterogeneity in filamentous microbes. Biotechnol Adv 2018; 36:2138-2149. [DOI: 10.1016/j.biotechadv.2018.10.002] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/11/2018] [Revised: 09/15/2018] [Accepted: 10/01/2018] [Indexed: 12/20/2022]
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External Noise and External Signal Induced Transition of Gene Switch and Coherence Resonance in the Genetic Regulatory System. Acta Biotheor 2017; 65:135-150. [PMID: 28315023 DOI: 10.1007/s10441-017-9307-6] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/14/2015] [Accepted: 03/10/2017] [Indexed: 10/19/2022]
Abstract
The transition of gene switch induced by external noises (multiplicative external noise and additive external noise) and external signals is investigated in the genetic regulatory system. Results show that the state-to-state transition of gene switch as well as resonant behaviors, such as the explicit coherence resonance (ECR), implicit coherence resonance (ICR) and control parameter coherence biresonance (CPCBR), can appear when noises are injected into the genetic regulatory system. The ECR is increased with the increase of the control parameter value when starting from the supercritical Hopf bifurcation parameter point, and there exists a critical control parameter value for the occurrence of ECR. However, the ICR is decreased as the control parameter value is increased when starting from the subcritical Hopf bifurcation point. In particular, the coherence of ECR is higher and more sensitive to noise than that of ICR. When an external signal is introduced into the system, the enhancement or suppression of the CPCBR and the number of peaks strongly depend on the frequency and amplitude of the external signal. Furthermore, the gene regulation system can selectively enhance or decrease the noise-induced oscillation signals at preferred frequency and amplitude of an external signal.
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Ferwerda C, Lipan O. Splitting nodes and linking channels: A method for assembling biocircuits from stochastic elementary units. Phys Rev E 2016; 94:052404. [PMID: 27967020 DOI: 10.1103/physreve.94.052404] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/14/2016] [Indexed: 11/07/2022]
Abstract
Akin to electric circuits, we construct biocircuits that are manipulated by cutting and assembling channels through which stochastic information flows. This diagrammatic manipulation allows us to create a method which constructs networks by joining building blocks selected so that (a) they cover only basic processes; (b) it is scalable to large networks; (c) the mean and variance-covariance from the Pauli master equation form a closed system; and (d) given the initial probability distribution, no special boundary conditions are necessary to solve the master equation. The method aims to help with both designing new synthetic signaling pathways and quantifying naturally existing regulatory networks.
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Affiliation(s)
- Cameron Ferwerda
- School of Physics and Astronomy, University of St Andrews, North Haugh, KY16 9SS, Scotland, United Kingdom
| | - Ovidiu Lipan
- Department of Physics, University of Richmond, 28 Westhampton Way, Richmond, Virginia 23173, USA
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Sun X, Zhang J, Zhao Q, Chen X, Zhu W, Yan G, Zhou T. Stochastic modeling suggests that noise reduces differentiation efficiency by inducing a heterogeneous drug response in glioma differentiation therapy. BMC SYSTEMS BIOLOGY 2016; 10:73. [PMID: 27515956 PMCID: PMC4982223 DOI: 10.1186/s12918-016-0316-x] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/14/2016] [Accepted: 07/06/2016] [Indexed: 12/23/2022]
Abstract
Background Glioma differentiation therapy is a novel strategy that has been used to induce glioma cells to differentiate into glia-like cells. Although some advances in experimental methods for exploring the molecular mechanisms involved in differentiation therapy have been made, a model-based comprehensive analysis is still needed to understand these differentiation mechanisms and improve the effects of anti-cancer therapeutics. This type of analysis becomes necessary in stochastic cases for two main reasons: stochastic noise inherently exists in signal transduction and phenotypic regulation during targeted therapy and chemotherapy, and the relationship between this noise and drug efficacy in differentiation therapy is largely unknown. Results In this study, we developed both an additive noise model and a Chemical-Langenvin-Equation model for the signaling pathways involved in glioma differentiation therapy to investigate the functional role of noise in the drug response. Our model analysis revealed an ultrasensitive mechanism of cyclin D1 degradation that controls the glioma differentiation induced by the cAMP inducer cholera toxin (CT). The role of cyclin D1 degradation in human glioblastoma cell differentiation was then experimentally verified. Our stochastic simulation demonstrated that noise not only renders some glioma cells insensitive to cyclin D1 degradation during drug treatment but also induce heterogeneous differentiation responses among individual glioma cells by modulating the ultrasensitive response of cyclin D1. As such, the noise can reduce the differentiation efficiency in drug-treated glioma cells, which was verified by the decreased evolution of differentiation potential, which quantified the impact of noise on the dynamics of the drug-treated glioma cell population. Conclusion Our results demonstrated that targeting the noise-induced dynamics of cyclin D1 during glioma differentiation therapy can increase anti-glioma effects, implying that noise is a considerable factor in assessing and optimizing anti-cancer drug interventions. Electronic supplementary material The online version of this article (doi:10.1186/s12918-016-0316-x) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Xiaoqiang Sun
- Zhong-shan School of Medicine, Sun Yat-Sen University, Guangzhou, 510089, China. .,School of Mathematical and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China.
| | - Jiajun Zhang
- School of Mathematical and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China
| | - Qi Zhao
- School of Mathematics, Liaoning University, Shenyang, 110036, China.,Research Center for Computer Simulating and Information Processing of Bio-macromolecules of Liaoning Province, Shenyang, 110036, China
| | - Xing Chen
- School of Information and Electrical Engineering, China University of Mining and Technology, Xuzhou, Jiangsu, 221116, China
| | - Wenbo Zhu
- Zhong-shan School of Medicine, Sun Yat-Sen University, Guangzhou, 510089, China.
| | - Guangmei Yan
- Zhong-shan School of Medicine, Sun Yat-Sen University, Guangzhou, 510089, China
| | - Tianshou Zhou
- School of Mathematical and Computational Science, Sun Yat-Sen University, Guangzhou, 510275, China.
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Liu F, Heiner M, Yang M. Fuzzy Stochastic Petri Nets for Modeling Biological Systems with Uncertain Kinetic Parameters. PLoS One 2016; 11:e0149674. [PMID: 26910830 PMCID: PMC4766190 DOI: 10.1371/journal.pone.0149674] [Citation(s) in RCA: 26] [Impact Index Per Article: 3.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/11/2015] [Accepted: 01/29/2016] [Indexed: 12/27/2022] Open
Abstract
Stochastic Petri nets (SPNs) have been widely used to model randomness which is an inherent feature of biological systems. However, for many biological systems, some kinetic parameters may be uncertain due to incomplete, vague or missing kinetic data (often called fuzzy uncertainty), or naturally vary, e.g., between different individuals, experimental conditions, etc. (often called variability), which has prevented a wider application of SPNs that require accurate parameters. Considering the strength of fuzzy sets to deal with uncertain information, we apply a specific type of stochastic Petri nets, fuzzy stochastic Petri nets (FSPNs), to model and analyze biological systems with uncertain kinetic parameters. FSPNs combine SPNs and fuzzy sets, thereby taking into account both randomness and fuzziness of biological systems. For a biological system, SPNs model the randomness, while fuzzy sets model kinetic parameters with fuzzy uncertainty or variability by associating each parameter with a fuzzy number instead of a crisp real value. We introduce a simulation-based analysis method for FSPNs to explore the uncertainties of outputs resulting from the uncertainties associated with input parameters, which works equally well for bounded and unbounded models. We illustrate our approach using a yeast polarization model having an infinite state space, which shows the appropriateness of FSPNs in combination with simulation-based analysis for modeling and analyzing biological systems with uncertain information.
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Affiliation(s)
- Fei Liu
- Control and Simulation Center, Harbin Institute of Technology, Harbin, 150080 China
- * E-mail: (FL); (MY)
| | - Monika Heiner
- Department of Computer Science, Brandenburg University of Technology Cottbus-Senftenberg, Cottbus, 03013 Germany
| | - Ming Yang
- Control and Simulation Center, Harbin Institute of Technology, Harbin, 150080 China
- * E-mail: (FL); (MY)
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Jia C, Qian M, Kang Y, Jiang D. Modeling stochastic phenotype switching and bet-hedging in bacteria: stochastic nonlinear dynamics and critical state identification. QUANTITATIVE BIOLOGY 2015. [DOI: 10.1007/s40484-014-0035-5] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/24/2022]
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