1
|
Sarkar M. Synchronization transition in the two-dimensional Kuramoto model with dichotomous noise. CHAOS (WOODBURY, N.Y.) 2021; 31:083102. [PMID: 34470227 DOI: 10.1063/5.0056001] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 05/05/2021] [Accepted: 07/16/2021] [Indexed: 06/13/2023]
Abstract
We numerically study the celebrated Kuramoto model of identical oscillators arranged on the sites of a two-dimensional periodic square lattice and subject to nearest-neighbor interactions and dichotomous noise. In the nonequilibrium stationary state attained after a long time, the model exhibits a Berezinskii-Kosterlitz-Thouless (BKT)-like transition between a phase at a low noise amplitude characterized by quasi long-range order (critically ordered phase) and an algebraic decay of correlations and a phase at a high noise amplitude that is characterized by complete disorder and an exponential decay of correlations. The interplay between the noise amplitude and the noise-correlation time is investigated, and the complete, nonequilibrium stationary-state phase diagram of the model is obtained. We further study the dynamics of a single topological defect for various amplitudes and correlation time of the noise. Our analysis reveals that a finite correlation time promotes vortex excitations, thereby lowering the critical noise amplitude of the transition with an increase in correlation time. In the suitable limit, the resulting phase diagram allows one to estimate the critical temperature of the equilibrium BKT transition, which is consistent with that obtained from the study of the dynamics in the Gaussian white noise limit.
Collapse
Affiliation(s)
- Mrinal Sarkar
- Department of Physics, Indian Institute of Technology Madras, Chennai 600036, India
| |
Collapse
|
2
|
Yin H, Liu S, Wen X. Optimal transition paths of phenotypic switching in a non-Markovian self-regulation gene expression. Phys Rev E 2021; 103:022409. [PMID: 33736096 DOI: 10.1103/physreve.103.022409] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/23/2020] [Accepted: 01/06/2021] [Indexed: 11/07/2022]
Abstract
Gene expression is a complex biochemical process involving multiple reaction steps, creating molecular memory because the probability of waiting time between consecutive reaction steps no longer follows exponential distributions. What effect the molecular memory has on metastable states in gene expression remains not fully understood. Here, we study transition paths of switching between bistable states for a non-Markovian model of gene expression equipped with a self-regulation. Employing the large deviation theory for this model, we analyze the optimal transition paths of switching between bistable states in gene expression, interestingly finding that dynamic behaviors in gene expression along the optimal transition paths significantly depend on the molecular memory. Moreover, we discover that the molecular memory can prolong the time of switching between bistable states in gene expression along the optimal transition paths. Our results imply that the molecular memory may be an unneglectable factor to affect switching between metastable states in gene expression.
Collapse
Affiliation(s)
- Hongwei Yin
- School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221111, People's Republic of China
- School of Science, Nanchang University, Nanchang 330031, People's Republic of China
| | - Shuqin Liu
- School of Science, Nanchang University, Nanchang 330031, People's Republic of China
| | - Xiaoqing Wen
- School of Mathematics and Statistics, Xuzhou University of Technology, Xuzhou 221111, People's Republic of China
- School of Science, Nanchang University, Nanchang 330031, People's Republic of China
| |
Collapse
|
3
|
Laghmach R, Potoyan DA. Liquid-liquid phase separation driven compartmentalization of reactive nucleoplasm. Phys Biol 2021; 18:015001. [PMID: 33113512 PMCID: PMC8201646 DOI: 10.1088/1478-3975/abc5ad] [Citation(s) in RCA: 6] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/11/2022]
Abstract
The nucleus of eukaryotic cells harbors active and out of equilibrium environments conducive to diverse gene regulatory processes. On a molecular scale, gene regulatory processes take place within hierarchically compartmentalized sub-nuclear bodies. While the impact of nuclear structure on gene regulation is widely appreciated, it has remained much less clear whether and how gene regulation is impacting nuclear order itself. Recently, the liquid-liquid phase separation emerged as a fundamental mechanism driving the formation of biomolecular condensates, including membrane-less organelles, chromatin territories, and transcriptional domains. The transience and environmental sensitivity of biomolecular condensation are strongly suggestive of kinetic gene-regulatory control of phase separation. To better understand kinetic aspects controlling biomolecular phase-separation, we have constructed a minimalist model of the reactive nucleoplasm. The model is based on the Cahn-Hilliard formulation of ternary protein-RNA-nucleoplasm components coupled to non-equilibrium and spatially dependent gene expression. We find a broad range of kinetic regimes through an extensive set of simulations where the interplay of phase separation and reactive timescales can generate heterogeneous multi-modal gene expression patterns. Furthermore, the significance of this finding is that heterogeneity of gene expression is linked directly with the heterogeneity of length-scales in phase-separated condensates.
Collapse
Affiliation(s)
- Rabia Laghmach
- Department of Chemistry, Iowa State University, Ames, IA 50011, United States of America. Department of Biochemistry, Biophysics and Molecular Biology, Iowa State University, Ames, IA 50011, United States of America. Bioinformatics and Computational Biology program, Iowa State University, Ames, IA 50011, United States of America
| | | |
Collapse
|
4
|
Jia C, Wang LY, Yin GG, Zhang MQ. Single-cell stochastic gene expression kinetics with coupled positive-plus-negative feedback. Phys Rev E 2019; 100:052406. [PMID: 31869986 DOI: 10.1103/physreve.100.052406] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/24/2019] [Indexed: 06/10/2023]
Abstract
Here we investigate single-cell stochastic gene expression kinetics in a minimal coupled gene circuit with positive-plus-negative feedback. A triphasic stochastic bifurcation is observed upon increasing the ratio of the positive and negative feedback strengths, which reveals a strong synergistic interaction between positive and negative feedback loops. We discover that coupled positive-plus-negative feedback amplifies gene expression mean but reduces gene expression noise over a wide range of feedback strengths when promoter switching is relatively slow, stabilizing gene expression around a relatively high level. In addition, we study two types of macroscopic limits of the discrete chemical master equation model: the Kurtz limit applies to proteins with large burst frequencies and the Lévy limit applies to proteins with large burst sizes. We derive the analytic steady-state distributions of the protein abundance in a coupled gene circuit for both the discrete model and its two macroscopic limits, generalizing the results obtained by Liu et al. [Chaos 26, 043108 (2016)CHAOEH1054-150010.1063/1.4947202]. We also obtain the analytic time-dependent protein distribution for the classical Friedman-Cai-Xie random bursting model [Friedman, Cai, and Xie, Phys. Rev. Lett. 97, 168302 (2006)PRLTAO0031-900710.1103/PhysRevLett.97.168302]. Our analytic results are further applied to study the structure of gene expression noise in a coupled gene circuit, and a complete decomposition of noise in terms of five different biophysical origins is provided.
Collapse
Affiliation(s)
- Chen Jia
- Division of Applied and Computational Mathematics, Beijing Computational Science Research Center, Beijing 100193, China
- Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA
| | - Le Yi Wang
- Department of Electrical and Computer Engineering, Wayne State University, Detroit, Michigan 48202, USA
| | - George G Yin
- Department of Mathematics, Wayne State University, Detroit, Michigan 48202, USA
| | - Michael Q Zhang
- Department of Biological Sciences, Center for Systems Biology, University of Texas at Dallas, Richardson, Texas 75080, USA
- MOE Key Laboratory of Bioinformatics, Center for Synthetic and Systems Biology, Tsinghua University, Beijing 100084, China
| |
Collapse
|
5
|
Hufton PG, Lin YT, Galla T. Model reduction methods for population dynamics with fast-switching environments: Reduced master equations, stochastic differential equations, and applications. Phys Rev E 2019; 99:032122. [PMID: 30999395 DOI: 10.1103/physreve.99.032122] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/14/2019] [Indexed: 11/07/2022]
Abstract
We study stochastic population dynamics coupled to fast external environments and combine expansions in the inverse switching rate of the environment and a Kramers-Moyal expansion in the inverse size of the population. This leads to a series of approximation schemes, capturing both intrinsic and environmental noise. These methods provide a means of efficient simulation and we show how they can be used to obtain analytical results for the fluctuations of population dynamics in switching environments. We place the approximations in relation to existing work on piecewise-deterministic and piecewise-diffusive Markov processes. Finally, we demonstrate the accuracy and efficiency of these model-reduction methods in different research fields, including systems in biology and a model of crack propagation.
Collapse
Affiliation(s)
- Peter G Hufton
- Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| | - Yen Ting Lin
- Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom.,Center for Nonlinear Studies and Theoretical and Biophysics Group, Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
| | - Tobias Galla
- Theoretical Physics, School of Physics and Astronomy, University of Manchester, Manchester M13 9PL, United Kingdom
| |
Collapse
|
6
|
Ali Al-Radhawi M, Del Vecchio D, Sontag ED. Multi-modality in gene regulatory networks with slow promoter kinetics. PLoS Comput Biol 2019; 15:e1006784. [PMID: 30779734 PMCID: PMC6396950 DOI: 10.1371/journal.pcbi.1006784] [Citation(s) in RCA: 20] [Impact Index Per Article: 4.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 09/27/2018] [Revised: 03/01/2019] [Accepted: 01/14/2019] [Indexed: 12/27/2022] Open
Abstract
Phenotypical variability in the absence of genetic variation often reflects complex energetic landscapes associated with underlying gene regulatory networks (GRNs). In this view, different phenotypes are associated with alternative states of complex nonlinear systems: stable attractors in deterministic models or modes of stationary distributions in stochastic descriptions. We provide theoretical and practical characterizations of these landscapes, specifically focusing on stochastic Slow Promoter Kinetics (SPK), a time scale relevant when transcription factor binding and unbinding are affected by epigenetic processes like DNA methylation and chromatin remodeling. In this case, largely unexplored except for numerical simulations, adiabatic approximations of promoter kinetics are not appropriate. In contrast to the existing literature, we provide rigorous analytic characterizations of multiple modes. A general formal approach gives insight into the influence of parameters and the prediction of how changes in GRN wiring, for example through mutations or artificial interventions, impact the possible number, location, and likelihood of alternative states. We adapt tools from the mathematical field of singular perturbation theory to represent stationary distributions of Chemical Master Equations for GRNs as mixtures of Poisson distributions and obtain explicit formulas for the locations and probabilities of metastable states as a function of the parameters describing the system. As illustrations, the theory is used to tease out the role of cooperative binding in stochastic models in comparison to deterministic models, and applications are given to various model systems, such as toggle switches in isolation or in communicating populations, a synthetic oscillator, and a trans-differentiation network.
Collapse
Affiliation(s)
- M. Ali Al-Radhawi
- Departments of Electrical and Computer Engineering and of Bioengineering, Northeastern University, Boston, Massachusetts, United States of America
| | - Domitilla Del Vecchio
- Department of Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, Massachusetts, United States of America
| | - Eduardo D. Sontag
- Departments of Electrical and Computer Engineering and of Bioengineering, Northeastern University, Boston, Massachusetts, United States of America
- Laboratory of Systems Pharmacology, Harvard Medical School, Boston, Massachusetts, United States of America
| |
Collapse
|
7
|
Role of noise and parametric variation in the dynamics of gene regulatory circuits. NPJ Syst Biol Appl 2018; 4:40. [PMID: 30416751 PMCID: PMC6218471 DOI: 10.1038/s41540-018-0076-x] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/20/2018] [Revised: 10/14/2018] [Accepted: 10/16/2018] [Indexed: 12/21/2022] Open
Abstract
Stochasticity in gene expression impacts the dynamics and functions of gene regulatory circuits. Intrinsic noises, including those that are caused by low copy number of molecules and transcriptional bursting, are usually studied by stochastic simulations. However, the role of extrinsic factors, such as cell-to-cell variability and heterogeneity in the microenvironment, is still elusive. To evaluate the effects of both the intrinsic and extrinsic noises, we develop a method, named sRACIPE, by integrating stochastic analysis with random circuit perturbation (RACIPE) method. RACIPE uniquely generates and analyzes an ensemble of models with random kinetic parameters. Previously, we have shown that the gene expression from random models form robust and functionally related clusters. In sRACIPE we further develop two stochastic simulation schemes, aiming to reduce the computational cost without sacrificing the convergence of statistics. One scheme uses constant noise to capture the basins of attraction, and the other one uses simulated annealing to detect the stability of states. By testing the methods on several synthetic gene regulatory circuits and an epithelial-mesenchymal transition network in squamous cell carcinoma, we demonstrate that sRACIPE can interpret the experimental observations from single-cell gene expression data. We observe that parametric variation (the spread of parameters around a median value) increases the spread of the gene expression clusters, whereas high noise merges the states. Our approach quantifies the robustness of a gene circuit in the presence of noise and sheds light on a new mechanism of noise-induced hybrid states. We have implemented sRACIPE as an R package.
Collapse
|
8
|
Lineage marker synchrony in hematopoietic genealogies refutes the PU.1/GATA1 toggle switch paradigm. Nat Commun 2018; 9:2697. [PMID: 30002371 PMCID: PMC6043612 DOI: 10.1038/s41467-018-05037-3] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/30/2017] [Accepted: 05/25/2018] [Indexed: 01/21/2023] Open
Abstract
Molecular regulation of cell fate decisions underlies health and disease. To identify molecules that are active or regulated during a decision, and not before or after, the decision time point is crucial. However, cell fate markers are usually delayed and the time of decision therefore unknown. Fortunately, dividing cells induce temporal correlations in their progeny, which allow for retrospective inference of the decision time point. We present a computational method to infer decision time points from correlated marker signals in genealogies and apply it to differentiating hematopoietic stem cells. We find that myeloid lineage decisions happen generations before lineage marker onsets. Inferred decision time points are in agreement with data from colony assay experiments. The levels of the myeloid transcription factor PU.1 do not change during, but long after the predicted lineage decision event, indicating that the PU.1/GATA1 toggle switch paradigm cannot explain the initiation of early myeloid lineage choice.
Collapse
|
9
|
Jia C, Qian H, Chen M, Zhang MQ. Relaxation rates of gene expression kinetics reveal the feedback signs of autoregulatory gene networks. J Chem Phys 2018. [DOI: 10.1063/1.5009749] [Citation(s) in RCA: 18] [Impact Index Per Article: 3.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023] Open
Affiliation(s)
- Chen Jia
- Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Hong Qian
- Department of Applied Mathematics, University of Washington, Seattle, Washington 98195, USA
| | - Min Chen
- Department of Mathematical Sciences, University of Texas at Dallas, Richardson, Texas 75080, USA
| | - Michael Q. Zhang
- Department of Biological Sciences, Center for Systems Biology, University of Texas at Dallas, Richardson, Texas 75080, USA
- MOE Key Lab and Division of Bioinformatics, CSSB, TNLIST, Tsinghua University, Beijing 100084, China
| |
Collapse
|
10
|
Lin YT, Hufton PG, Lee EJ, Potoyan DA. A stochastic and dynamical view of pluripotency in mouse embryonic stem cells. PLoS Comput Biol 2018; 14:e1006000. [PMID: 29451874 PMCID: PMC5833290 DOI: 10.1371/journal.pcbi.1006000] [Citation(s) in RCA: 32] [Impact Index Per Article: 5.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2017] [Revised: 03/01/2018] [Accepted: 01/19/2018] [Indexed: 12/26/2022] Open
Abstract
Pluripotent embryonic stem cells are of paramount importance for biomedical sciences because of their innate ability for self-renewal and differentiation into all major cell lines. The fateful decision to exit or remain in the pluripotent state is regulated by complex genetic regulatory networks. The rapid growth of single-cell sequencing data has greatly stimulated applications of statistical and machine learning methods for inferring topologies of pluripotency regulating genetic networks. The inferred network topologies, however, often only encode Boolean information while remaining silent about the roles of dynamics and molecular stochasticity inherent in gene expression. Herein we develop a framework for systematically extending Boolean-level network topologies into higher resolution models of networks which explicitly account for the promoter architectures and gene state switching dynamics. We show the framework to be useful for disentangling the various contributions that gene switching, external signaling, and network topology make to the global heterogeneity and dynamics of transcription factor populations. We find the pluripotent state of the network to be a steady state which is robust to global variations of gene switching rates which we argue are a good proxy for epigenetic states of individual promoters. The temporal dynamics of exiting the pluripotent state, on the other hand, is significantly influenced by the rates of genetic switching which makes cells more responsive to changes in extracellular signals.
Collapse
Affiliation(s)
- Yen Ting Lin
- Theoretical Division and Center for Nonlinear Studies, Los Alamos National Laboratory, Los Alamos, New Mexico, United States of America
- School of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
| | - Peter G. Hufton
- School of Physics and Astronomy, The University of Manchester, Manchester, United Kingdom
| | - Esther J. Lee
- Department of Bioengineering, Rice University, Houston, Texas, United States of America
| | - Davit A. Potoyan
- Department of Chemistry, Iowa State University, Ames, Iowa, United States of America
| |
Collapse
|
11
|
Wang Z, Potoyan DA, Wolynes PG. Modeling the therapeutic efficacy of NFκB synthetic decoy oligodeoxynucleotides (ODNs). BMC SYSTEMS BIOLOGY 2018; 12:4. [PMID: 29382384 PMCID: PMC5791368 DOI: 10.1186/s12918-018-0525-6] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Abstract] [Key Words] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 06/12/2017] [Accepted: 01/04/2018] [Indexed: 01/24/2023]
Abstract
BACKGROUND Transfection of NF κB synthetic decoy Oligodeoxynucleotides (ODNs) has been proposed as a promising therapeutic strategy for a variety of diseases arising from constitutive activation of the eukaryotic transcription factor NF κB. The decoy approach faces some limitations under physiological conditions notably nuclease-induced degradation. RESULTS In this work, we show how a systems pharmacology model of NF κB regulatory networks displaying oscillatory temporal dynamics, can be used to predict quantitatively the dependence of therapeutic efficacy of NF κB synthetic decoy ODNs on dose, unbinding kinetic rates and nuclease-induced degradation rates. Both deterministic mass action simulations and stochastic simulations of the systems biology model show that the therapeutic efficacy of synthetic decoy ODNs is inversely correlated with unbinding kinetic rates, nuclease-induced degradation rates and molecular stripping rates, but is positively correlated with dose. We show that the temporal coherence of the stochastic dynamics of NF κB regulatory networks is most sensitive to adding NF κB synthetic decoy ODNs having unbinding time-scales that are in-resonance with the time-scale of the limit cycle of the network. CONCLUSIONS The pharmacokinetics/pharmacodynamics (PK/PD) predicted by the systems-level model should provide quantitative guidance for in-depth translational research of optimizing the thermodynamics/kinetic properties of synthetic decoy ODNs.
Collapse
Affiliation(s)
- Zhipeng Wang
- Center for Theoretical Biological Physics, Rice University, Houston, 77005, TX, USA.,Department of Chemistry, Rice University, Houston, 77005, TX, USA.,Present Address: Genentech Inc. 350 DNA Way, South San Francisco, 94080, CA, USA
| | - Davit A Potoyan
- Center for Theoretical Biological Physics, Rice University, Houston, 77005, TX, USA.,Department of Chemistry, Rice University, Houston, 77005, TX, USA.,Present Address: Department of Chemistry, Iowa State University, Ames, 50011, IA, USA
| | - Peter G Wolynes
- Center for Theoretical Biological Physics, Rice University, Houston, 77005, TX, USA. .,Department of Chemistry, Rice University, Houston, 77005, TX, USA. .,Department of Physics and Astronomy, Rice University, Houston, 77005, TX, USA.
| |
Collapse
|
12
|
Herbach U, Bonnaffoux A, Espinasse T, Gandrillon O. Inferring gene regulatory networks from single-cell data: a mechanistic approach. BMC SYSTEMS BIOLOGY 2017; 11:105. [PMID: 29157246 PMCID: PMC5697158 DOI: 10.1186/s12918-017-0487-0] [Citation(s) in RCA: 25] [Impact Index Per Article: 3.6] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/12/2017] [Accepted: 11/09/2017] [Indexed: 01/13/2023]
Abstract
Background The recent development of single-cell transcriptomics has enabled gene expression to be measured in individual cells instead of being population-averaged. Despite this considerable precision improvement, inferring regulatory networks remains challenging because stochasticity now proves to play a fundamental role in gene expression. In particular, mRNA synthesis is now acknowledged to occur in a highly bursty manner. Results We propose to view the inference problem as a fitting procedure for a mechanistic gene network model that is inherently stochastic and takes not only protein, but also mRNA levels into account. We first explain how to build and simulate this network model based upon the coupling of genes that are described as piecewise-deterministic Markov processes. Our model is modular and can be used to implement various biochemical hypotheses including causal interactions between genes. However, a naive fitting procedure would be intractable. By performing a relevant approximation of the stationary distribution, we derive a tractable procedure that corresponds to a statistical hidden Markov model with interpretable parameters. This approximation turns out to be extremely close to the theoretical distribution in the case of a simple toggle-switch, and we show that it can indeed fit real single-cell data. As a first step toward inference, our approach was applied to a number of simple two-gene networks simulated in silico from the mechanistic model and satisfactorily recovered the original networks. Conclusions Our results demonstrate that functional interactions between genes can be inferred from the distribution of a mechanistic, dynamical stochastic model that is able to describe gene expression in individual cells. This approach seems promising in relation to the current explosion of single-cell expression data. Electronic supplementary material The online version of this article (doi:10.1186/s12918-017-0487-0) contains supplementary material, which is available to authorized users.
Collapse
Affiliation(s)
- Ulysse Herbach
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d'Italie Site Jacques Monod, Lyon, F-69007, France.,Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, Lyon, France.,Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, Villeurbanne Cedex, F-6962, France
| | - Arnaud Bonnaffoux
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d'Italie Site Jacques Monod, Lyon, F-69007, France.,Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, Lyon, France.,The CoSMo company, 5 passage du Vercors, Lyon, 69007, France
| | - Thibault Espinasse
- Univ Lyon, Université Claude Bernard Lyon 1, CNRS UMR 5208, Institut Camille Jordan, 43 blvd. du 11 novembre 1918, Villeurbanne Cedex, F-6962, France
| | - Olivier Gandrillon
- Univ Lyon, ENS de Lyon, Univ Claude Bernard, CNRS UMR 5239, INSERM U1210, Laboratory of Biology and Modelling of the Cell, 46 allée d'Italie Site Jacques Monod, Lyon, F-69007, France. .,Inria Team Dracula, Inria Center Grenoble Rhône-Alpes, Lyon, France.
| |
Collapse
|
13
|
Paul S, Ghosh S, Ray DS. Noisy-flow-induced instability in a reaction-diffusion system. Phys Rev E 2017; 94:062217. [PMID: 28085378 DOI: 10.1103/physreve.94.062217] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/05/2016] [Indexed: 11/07/2022]
Abstract
We consider a generic reaction-diffusion-advection system where the flow velocity of the advection term is subjected to dichotomous noise with zero mean and Ornstein-Zernike correlation. A general condition for noisy-flow-induced instability is derived in the flow velocity-correlation rate parameter plane. Full numerical simulations on Gierer-Meinhardt model with activator-inhibitor kinetics have been performed to show how noisy differential flow can lead to symmetry breaking of a homogeneous stable state in the presence of noise resulting in traveling waves.
Collapse
Affiliation(s)
- Shibashis Paul
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Shyamolina Ghosh
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| | - Deb Shankar Ray
- Indian Association for the Cultivation of Science, Jadavpur, Kolkata-700032, India
| |
Collapse
|
14
|
Innocentini GCP, Guiziou S, Bonnet J, Radulescu O. Analytic framework for a stochastic binary biological switch. Phys Rev E 2017; 94:062413. [PMID: 28085300 DOI: 10.1103/physreve.94.062413] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/15/2016] [Indexed: 11/07/2022]
Abstract
We propose and solve analytically a stochastic model for the dynamics of a binary biological switch, defined as a DNA unit with two mutually exclusive configurations, each one triggering the expression of a different gene. Such a device has the potential to be used as a memory unit for biological computing systems designed to operate in noisy environments. We discuss a recent implementation of this switch in living cells, the recombinase addressable data (RAD) module. In order to understand the behavior of a RAD module we compute the exact time-dependent joint distribution of the two expressed genes starting in one state and evolving to another asymptotic state. We consider two operating regimes of the RAD module, a fast and a slow stochastic switching regime. The fast regime is aggregative and produces unimodal distributions, whereas the slow regime is separative and produces bimodal distributions. Both regimes can serve to prepare pure memory states when all cells are expressing the same gene. The slow regime can also separate mixed states by producing two subpopulations, each one expressing a different gene. Compared to the genetic toggle switch based on positive feedback, the RAD module ensures more rapid memory operations for the same quality of the separation between binary states. Our model provides a simplified phenomenological framework for studying RAD memory devices and our analytic solution can be further used to clarify theoretical concepts in biocomputation and for optimal design in synthetic biology.
Collapse
Affiliation(s)
| | - Sarah Guiziou
- CBS, CNRS UMR 5048 - UM - INSERM U 1054, Montpellier, France
| | - Jerome Bonnet
- CBS, CNRS UMR 5048 - UM - INSERM U 1054, Montpellier, France
| | - Ovidiu Radulescu
- DIMNP, UMR CNRS 5235, University of Montpellier, Montpellier, France
| |
Collapse
|
15
|
Hufton PG, Lin YT, Galla T, McKane AJ. Intrinsic noise in systems with switching environments. Phys Rev E 2016; 93:052119. [PMID: 27300842 DOI: 10.1103/physreve.93.052119] [Citation(s) in RCA: 60] [Impact Index Per Article: 7.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/02/2015] [Indexed: 11/07/2022]
Abstract
We study individual-based dynamics in finite populations, subject to randomly switching environmental conditions. These are inspired by models in which genes transition between on and off states, regulating underlying protein dynamics. Similarly, switches between environmental states are relevant in bacterial populations and in models of epidemic spread. Existing piecewise-deterministic Markov process approaches focus on the deterministic limit of the population dynamics while retaining the randomness of the switching. Here we go beyond this approximation and explicitly include effects of intrinsic stochasticity at the level of the linear-noise approximation. Specifically, we derive the stationary distributions of a number of model systems, in good agreement with simulations. This improves existing approaches which are limited to the regimes of fast and slow switching.
Collapse
Affiliation(s)
- Peter G Hufton
- Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Yen Ting Lin
- Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Tobias Galla
- Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| | - Alan J McKane
- Theoretical Physics, School of Physics and Astronomy, The University of Manchester, Manchester M13 9PL, United Kingdom
| |
Collapse
|