51
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Shitiri E, Vasilakos AV, Cho HS. Biological Oscillators in Nanonetworks-Opportunities and Challenges. SENSORS 2018; 18:s18051544. [PMID: 29757252 PMCID: PMC5982695 DOI: 10.3390/s18051544] [Citation(s) in RCA: 13] [Impact Index Per Article: 2.2] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/20/2018] [Revised: 04/26/2018] [Accepted: 05/09/2018] [Indexed: 01/07/2023]
Abstract
One of the major issues in molecular communication-based nanonetworks is the provision and maintenance of a common time knowledge. To stay true to the definition of molecular communication, biological oscillators are the potential solutions to achieve that goal as they generate oscillations through periodic fluctuations in the concentrations of molecules. Through the lens of a communication systems engineer, the scope of this survey is to explicitly classify, for the first time, existing biological oscillators based on whether they are found in nature or not, to discuss, in a tutorial fashion, the main principles that govern the oscillations in each oscillator, and to analyze oscillator parameters that are most relevant to communication engineer researchers. In addition, the survey highlights and addresses the key open research issues pertaining to several physical aspects of the oscillators and the adoption and implementation of the oscillators to nanonetworks. Moreover, key research directions are discussed.
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Affiliation(s)
- Ethungshan Shitiri
- School of Electronics, Kyungpook National University, Daegu 41566, Korea.
| | - Athanasios V Vasilakos
- Department of Computer Science, Electrical and Space Engineering, Lulea University of Technology, 93187 Lulea, Sweden.
| | - Ho-Shin Cho
- School of Electronics, Kyungpook National University, Daegu 41566, Korea.
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52
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Gonze D, Gérard C, Wacquier B, Woller A, Tosenberger A, Goldbeter A, Dupont G. Modeling-Based Investigation of the Effect of Noise in Cellular Systems. Front Mol Biosci 2018; 5:34. [PMID: 29707543 PMCID: PMC5907451 DOI: 10.3389/fmolb.2018.00034] [Citation(s) in RCA: 22] [Impact Index Per Article: 3.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/02/2018] [Accepted: 03/26/2018] [Indexed: 12/14/2022] Open
Abstract
Noise is pervasive in cellular biology and inevitably affects the dynamics of cellular processes. Biological systems have developed regulatory mechanisms to ensure robustness with respect to noise or to take advantage of stochasticity. We review here, through a couple of selected examples, some insights on possible robustness factors and constructive roles of noise provided by computational modeling. In particular, we focus on (1) factors that likely contribute to the robustness of oscillatory processes such as the circadian clocks and the cell cycle, (2) how reliable coding/decoding of calcium-mediated signaling could be achieved in presence of noise and, in some cases, enhanced through stochastic resonance, and (3) how embryonic cell differentiation processes can exploit stochasticity to create heterogeneity in a population of identical cells.
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Affiliation(s)
- Didier Gonze
- Unité de Chronobiologie Théorique, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium
| | - Claude Gérard
- de Duve Institute (LPAD Group), Université Catholique de Louvain, Brussels, Belgium
| | - Benjamin Wacquier
- Unité de Chronobiologie Théorique, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium
| | - Aurore Woller
- Unité de Chronobiologie Théorique, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium
| | - Alen Tosenberger
- Unité de Chronobiologie Théorique, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium
| | - Albert Goldbeter
- Unité de Chronobiologie Théorique, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium
| | - Geneviève Dupont
- Unité de Chronobiologie Théorique, Faculté des Sciences, Université Libre de Bruxelles, Brussels, Belgium
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53
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de la Cruz R, Perez-Carrasco R, Guerrero P, Alarcon T, Page KM. Minimum Action Path Theory Reveals the Details of Stochastic Transitions Out of Oscillatory States. PHYSICAL REVIEW LETTERS 2018; 120:128102. [PMID: 29694079 DOI: 10.1103/physrevlett.120.128102] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/21/2017] [Revised: 12/13/2017] [Indexed: 06/08/2023]
Abstract
Cell state determination is the outcome of intrinsically stochastic biochemical reactions. Transitions between such states are studied as noise-driven escape problems in the chemical species space. Escape can occur via multiple possible multidimensional paths, with probabilities depending nonlocally on the noise. Here we characterize the escape from an oscillatory biochemical state by minimizing the Freidlin-Wentzell action, deriving from it the stochastic spiral exit path from the limit cycle. We also use the minimized action to infer the escape time probability density function.
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Affiliation(s)
- Roberto de la Cruz
- Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain and Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain
| | - Ruben Perez-Carrasco
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Pilar Guerrero
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
| | - Tomas Alarcon
- ICREA, Pg. Lluís Companys 23, 08010 Barcelona, Spain
- Centre de Recerca Matemàtica, Edifici C, Campus de Bellaterra, 08193 Bellaterra (Barcelona), Spain
- Departament de Matemàtiques, Universitat Autònoma de Barcelona, 08193 Bellaterra (Barcelona), Spain and Barcelona Graduate School of Mathematics (BGSMath), Barcelona, Spain
| | - Karen M Page
- Department of Mathematics, University College London, Gower Street, London WC1E 6BT, United Kingdom
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54
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Abstract
The ability of bacterial cells to adjust their gene expression program in response to environmental perturbation is often critical for their survival. Recent experimental advances allowing us to quantitatively record gene expression dynamics in single cells and in populations coupled with mathematical modeling enable mechanistic understanding on how these responses are shaped by the underlying regulatory networks. Here, we review how the combination of local and global factors affect dynamical responses of gene regulatory networks. Our goal is to discuss the general principles that allow extrapolation from a few model bacteria to less understood microbes. We emphasize that, in addition to well-studied effects of network architecture, network dynamics are shaped by global pleiotropic effects and cell physiology.
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Affiliation(s)
- David L Shis
- Department of Biosciences, Rice University, Houston, Texas 77005, USA;
| | - Matthew R Bennett
- Department of Biosciences, Rice University, Houston, Texas 77005, USA; .,Department of Bioengineering, Rice University, Houston, Texas 77005, USA
| | - Oleg A Igoshin
- Department of Biosciences, Rice University, Houston, Texas 77005, USA; .,Department of Bioengineering, Rice University, Houston, Texas 77005, USA.,Center for Theoretical Biological Physics, Rice University, Houston, Texas 77005, USA
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55
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Maeda K, Kurata H. Long negative feedback loop enhances period tunability of biological oscillators. J Theor Biol 2018; 440:21-31. [PMID: 29253507 DOI: 10.1016/j.jtbi.2017.12.014] [Citation(s) in RCA: 6] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/07/2017] [Revised: 12/08/2017] [Accepted: 12/14/2017] [Indexed: 11/18/2022]
Abstract
Oscillatory phenomena play a major role in organisms. In some biological oscillations such as cell cycles and heartbeats, the period can be tuned without significant changes in the amplitude. This property is called (period) tunability, one of the prominent features of biological oscillations. However, how biological oscillators produce tunable oscillations remains largely unexplored. We tackle this question using computational experiments. It has been reported that positive-plus-negative feedback oscillators produce tunable oscillations through the hysteresis-based mechanism. First, in this study, we confirmed that positive-plus-negative feedback oscillators generate tunable oscillations. Second, we found that tunability is positively correlated with the dynamic range of oscillations. Third, we showed that long negative feedback oscillators without any additional positive feedback loops can produce tunable oscillations. Finally, we computationally demonstrated that by lengthening the negative feedback loop, the Repressilator, known as a non-tunable synthetic gene oscillator, can be converted into a tunable oscillator. This work provides synthetic biologists with clues to design tunable gene oscillators.
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Affiliation(s)
- Kazuhiro Maeda
- Frontier Research Academy for Young Researchers, Kyushu Institute of Technology, 1-1 Sensui-cho, Tobata, Kitakyushu, Fukuoka 804-8550, Japan; Department of Bioscience and Bioinformatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka 820-8502, Japan.
| | - Hiroyuki Kurata
- Department of Bioscience and Bioinformatics, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka 820-8502, Japan; Biomedical Informatics R&D Center, Kyushu Institute of Technology, 680-4 Kawazu, Iizuka, Fukuoka 820-8502, Japan.
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56
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Letellier C, Sendiña-Nadal I, Bianco-Martinez E, Baptista MS. A symbolic network-based nonlinear theory for dynamical systems observability. Sci Rep 2018; 8:3785. [PMID: 29491432 PMCID: PMC5830642 DOI: 10.1038/s41598-018-21967-w] [Citation(s) in RCA: 17] [Impact Index Per Article: 2.8] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/06/2017] [Accepted: 02/06/2018] [Indexed: 11/23/2022] Open
Abstract
When the state of the whole reaction network can be inferred by just measuring the dynamics of a limited set of nodes the system is said to be fully observable. However, as the number of all possible combinations of measured variables and time derivatives spanning the reconstructed state of the system exponentially increases with its dimension, the observability becomes a computationally prohibitive task. Our approach consists in computing the observability coefficients from a symbolic Jacobian matrix whose elements encode the linear, nonlinear polynomial or rational nature of the interaction among the variables. The novelty we introduce in this paper, required for treating large-dimensional systems, is to identify from the symbolic Jacobian matrix the minimal set of variables (together with their time derivatives) candidate to be measured for completing the state space reconstruction. Then symbolic observability coefficients are computed from the symbolic observability matrix. Our results are in agreement with the analytical computations, evidencing the correctness of our approach. Its application to efficiently exploring the dynamics of real world complex systems such as power grids, socioeconomic networks or biological networks is quite promising.
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Affiliation(s)
- Christophe Letellier
- CORIA-UMR 6614 Normandie Université, Campus Universitaire du Madrillet, F-76800, Saint-Etienne du Rouvray, France.
| | - Irene Sendiña-Nadal
- Complex Systems Group, Universidad Rey Juan Carlos, 28933, Móstoles, Madrid, Spain
- Center for Biomedical Technology, Universidad Politécnica de Madrid, 28223, Pozuelo de Alarcón, Madrid, Spain
| | - Ezequiel Bianco-Martinez
- Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Old Aberdeen, AB24 3UE, United Kingdom
| | - Murilo S Baptista
- Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Old Aberdeen, AB24 3UE, United Kingdom
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57
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CLOCKΔ19 mutation modifies the manner of synchrony among oscillation neurons in the suprachiasmatic nucleus. Sci Rep 2018; 8:854. [PMID: 29339832 PMCID: PMC5770461 DOI: 10.1038/s41598-018-19224-1] [Citation(s) in RCA: 12] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2017] [Accepted: 12/28/2017] [Indexed: 01/05/2023] Open
Abstract
In mammals, the principal circadian oscillator exists in the hypothalamic suprachiasmatic nucleus (SCN). In the SCN, CLOCK works as an essential component of molecular circadian oscillation, and ClockΔ19 mutant mice show unique characteristics of circadian rhythms such as extended free running periods, amplitude attenuation, and high-magnitude phase-resetting responses. Here we investigated what modifications occur in the spatiotemporal organization of clock gene expression in the SCN of ClockΔ19 mutants. The cultured SCN, sampled from neonatal homozygous ClockΔ19 mice on an ICR strain comprising PERIOD2::LUCIFERASE, demonstrated that the Clock gene mutation not only extends the circadian period, but also affects the spatial phase and period distribution of circadian oscillations in the SCN. In addition, disruption of the synchronization among neurons markedly attenuated the amplitude of the circadian rhythm of individual oscillating neurons in the mutant SCN. Further, with numerical simulations based on the present studies, the findings suggested that, in the SCN of the ClockΔ19 mutant mice, stable oscillation was preserved by the interaction among oscillating neurons, and that the orderly phase and period distribution that makes a phase wave are dependent on the functionality of CLOCK.
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58
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Bae SA, Acevedo A, Androulakis IP. Asymmetry in Signal Oscillations Contributes to Efficiency of Periodic Systems. Crit Rev Biomed Eng 2017; 44:193-211. [PMID: 28605352 DOI: 10.1615/critrevbiomedeng.2017019658] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/12/2022]
Abstract
Oscillations are an important feature of cellular signaling that result from complex combinations of positive- and negative-feedback loops. The encoding and decoding mechanisms of oscillations based on amplitude and frequency have been extensively discussed in the literature in the context of intercellular and intracellular signaling. However, the fundamental questions of whether and how oscillatory signals offer any competitive advantages-and, if so, what-have not been fully answered. We investigated established oscillatory mechanisms and designed a study to analyze the oscillatory characteristics of signaling molecules and system output in an effort to answer these questions. Two classic oscillators, Goodwin and PER, were selected as the model systems, and corresponding no-feedback models were created for each oscillator to discover the advantage of oscillating signals. Through simulating the original oscillators and the matching no-feedback models, we show that oscillating systems have the capability to achieve better resource-to-output efficiency, and we identify oscillatory characteristics that lead to improved efficiency.
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Affiliation(s)
- Seul-A Bae
- Chemical and Biochemical Engineering Department, Rutgers University, Piscataway, New Jersey
| | - Alison Acevedo
- Biomedical Engineering Department, Rutgers University, Piscataway, New Jersey
| | - Ioannis P Androulakis
- Chemical and Biochemical Engineering Department, Rutgers University, Piscataway, New Jersey; Biomedical Engineering Department, Rutgers University, Piscataway, New Jersey; Department of Surgery, Rutgers Robert Wood Johnson Medical School, New Brunswick, New Jersey
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59
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Constantino PH, Kaznessis YN. Maximum Entropy Prediction of Non-Equilibrium Stationary Distributions for Stochastic Reaction Networks with Oscillatory Dynamics. Chem Eng Sci 2017; 171:139-148. [PMID: 30899124 DOI: 10.1016/j.ces.2017.05.029] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
Abstract
Many chemical reaction networks in biological systems present complex oscillatory dynamics. In systems such as regulatory gene networks, cell cycle, and enzymatic processes, the number of molecules involved is often far from the thermodynamic limit. Although stochastic models based on the probabilistic approach of the Chemical Master Equation (CME) have been proposed, studies in the literature have been limited by the challenges of solving the CME and the lack of computational power to perform large-scale stochastic simulations. In this paper, we show that the infinite set of stationary moment equations describing the stochastic Brusselator and Schnakenberg oscillatory reactions networks can be truncated and solved using maximization of the entropy of the distributions. The results from our numerical experiments compare with the distributions obtained from well-established kinetic Monte Carlo methods and suggest that the accuracy of the prediction increases exponentially with the closure order chosen for the system. We conclude that maximum entropy models can be used as an efficient closure scheme alternative for moment equations to predict the non-equilibrium stationary distributions of stochastic chemical reactions with oscillatory dynamics. This prediction is accomplished without any prior knowledge of the system dynamics and without imposing any biased assumptions on the mathematical relations among species involved.
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Affiliation(s)
- Pedro H Constantino
- Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. SE, Minneapolis, MN 55455, USA.
| | - Yiannis N Kaznessis
- Department of Chemical Engineering and Materials Science, University of Minnesota, 421 Washington Ave. SE, Minneapolis, MN 55455, USA.
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60
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Kang JH, Cho KH. A novel interaction perturbation analysis reveals a comprehensive regulatory principle underlying various biochemical oscillators. BMC SYSTEMS BIOLOGY 2017; 11:95. [PMID: 29017496 PMCID: PMC5635494 DOI: 10.1186/s12918-017-0472-7] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 03/06/2017] [Accepted: 10/02/2017] [Indexed: 02/05/2023]
Abstract
Background Biochemical oscillations play an important role in maintaining physiological and cellular homeostasis in biological systems. The frequency and amplitude of oscillations are regulated to properly adapt to environments by numerous interactions within biomolecular networks. Despite the advances in our understanding of biochemical oscillators, the relationship between the network structure of an oscillator and its regulatory function still remains unclear. To investigate such a relationship in a systematic way, we have developed a novel analysis method called interaction perturbation analysis that enables direct modulation of the strength of every interaction and evaluates its consequence on the regulatory function. We have applied this new method to the analysis of three representative types of oscillators. Results The results of interaction perturbation analysis showed different regulatory features according to the network structure of the oscillator: (1) both frequency and amplitude were seldom modulated in simple negative feedback oscillators; (2) frequency could be tuned in amplified negative feedback oscillators; (3) amplitude could be modulated in the incoherently amplified negative feedback oscillators. A further analysis of naturally-occurring biochemical oscillator models supported such different regulatory features according to their network structures. Conclusions Our results provide a clear evidence that different network structures have different regulatory features in modulating the oscillation frequency and amplitude. Our findings may help to elucidate the fundamental regulatory roles of network structures in biochemical oscillations. Electronic supplementary material The online version of this article (10.1186/s12918-017-0472-7) contains supplementary material, which is available to authorized users.
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Affiliation(s)
- Jun Hyuk Kang
- Laboratory for Systems Biology and Bio-inspired Engineering, Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea.,Graduate School of Medical Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea
| | - Kwang-Hyun Cho
- Laboratory for Systems Biology and Bio-inspired Engineering, Department of Bio and Brain Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea. .,Graduate School of Medical Science and Engineering, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 34141, Republic of Korea.
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61
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Abstract
Sustained oscillations abound in biological systems. They occur at all levels of biological organization over a wide range of periods, from a fraction of a second to years, and with a variety of underlying mechanisms. They control major physiological functions, and their dysfunction is associated with a variety of physiological disorders. The goal of this review is (i) to give an overview of the main rhythms observed at the cellular and supracellular levels, (ii) to briefly describe how the study of biological rhythms unfolded in the course of time, in parallel with studies on chemical oscillations, (iii) to present the major roles of biological rhythms in the control of physiological functions, and (iv) the pathologies associated with the alteration, disappearance, or spurious occurrence of biological rhythms. Two tables present the main examples of cellular and supracellular rhythms ordered according to their period, and their role in physiology and pathophysiology. Among the rhythms discussed are neural and cardiac rhythms, metabolic oscillations such as those occurring in glycolysis in yeast, intracellular Ca++ oscillations, cyclic AMP oscillations in Dictyostelium amoebae, the segmentation clock that controls somitogenesis, pulsatile hormone secretion, circadian rhythms which occur in all eukaryotes and some bacteria with a period close to 24 h, the oscillatory dynamics of the enzymatic network driving the cell cycle, and oscillations in transcription factors such as NF-ΚB and tumor suppressors such as p53. Ilya Prigogine's concept of dissipative structures applies to temporal oscillations and allows us to unify within a common framework the various rhythms observed at different levels of biological organization, regardless of their period and underlying mechanism.
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Affiliation(s)
- Albert Goldbeter
- Unité de Chronobiologie théorique, Service de Chimie physique et Biologie théorique, Faculté des Sciences, Université Libre de Bruxelles (ULB), Campus Plaine, CP 231, B-1050 Brussels, Belgium
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62
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Modeling and simulation of biological systems using SPICE language. PLoS One 2017; 12:e0182385. [PMID: 28787027 PMCID: PMC5546598 DOI: 10.1371/journal.pone.0182385] [Citation(s) in RCA: 11] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/18/2017] [Accepted: 07/17/2017] [Indexed: 11/19/2022] Open
Abstract
The article deals with BB-SPICE (SPICE for Biochemical and Biological Systems), an extension of the famous Simulation Program with Integrated Circuit Emphasis (SPICE). BB-SPICE environment is composed of three modules: a new textual and compact description formalism for biological systems, a converter that handles this description and generates the SPICE netlist of the equivalent electronic circuit and NGSPICE which is an open-source SPICE simulator. In addition, the environment provides back and forth interfaces with SBML (System Biology Markup Language), a very common description language used in systems biology. BB-SPICE has been developed in order to bridge the gap between the simulation of biological systems on the one hand and electronics circuits on the other hand. Thus, it is suitable for applications at the interface between both domains, such as development of design tools for synthetic biology and for the virtual prototyping of biosensors and lab-on-chip. Simulation results obtained with BB-SPICE and COPASI (an open-source software used for the simulation of biochemical systems) have been compared on a benchmark of models commonly used in systems biology. Results are in accordance from a quantitative viewpoint but BB-SPICE outclasses COPASI by 1 to 3 orders of magnitude regarding the computation time. Moreover, as our software is based on NGSPICE, it could take profit of incoming updates such as the GPU implementation, of the coupling with powerful analysis and verification tools or of the integration in design automation tools (synthetic biology).
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63
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Koinuma S, Kori H, Tokuda IT, Yagita K, Shigeyoshi Y. Transition of phase response properties and singularity in the circadian limit cycle of cultured cells. PLoS One 2017; 12:e0181223. [PMID: 28715496 PMCID: PMC5513448 DOI: 10.1371/journal.pone.0181223] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/28/2015] [Accepted: 06/28/2017] [Indexed: 11/21/2022] Open
Abstract
The circadian system has been regarded as a limit cycle oscillator constructed by the integrated interaction of clock genes and proteins. Here, we investigated a mammalian circadian oscillation geometrically before and after a perturbation. We detected the singular point and transition from a type 1 to type 0 phase response curve (PRC) and determined the embedding dimension to show how many variables are needed to describe the limit cycle oscillation and relaxation process after a perturbation. As a perturbation, forskolin (FK) was administered to Rat-1 cells expressing the Per2::luc gene. By broadly and finely changing the phase and strength of the perturbation, we detected the transition of the PRC from type 1 to type 0 and a possible singular transition point, the property of which agreed quite well with our numerical simulation of the noisy Goodwin model, a simple yet canonical model for the transcription-translation feedback loop of the core clock genes. Furthermore, we estimated the embedding dimension of the limit cycle before and after the perturbation. The trajectory of the limit cycle was embedded in two dimensions but with the perturbation of the state point moved out of the trajectory, the relaxation process was generally embedded in higher dimensions. The average number of embedding dimensions at each dose of FK increased as the FK dose increased but most of the relaxation process was generally embedded within four dimensions. These findings support the existence of a circadian limit cycle oscillator in mammalian cells and suggest that a small number of variables determine the relaxation process after a perturbation.
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Affiliation(s)
- Satoshi Koinuma
- Department of Anatomy and Neurobiology, Kindai University Faculty of Medicine, Osakasayama, Osaka, Japan
- * E-mail: (SK); (YS)
| | - Hiroshi Kori
- Department of Information Sciences, Ochanomizu University, Bunkyo-ku, Tokyo, Japan
| | - Isao T. Tokuda
- Department of Mechanical Engineering, Ritsumeikan University, Kusatsu, Shiga, Japan
| | - Kazuhiro Yagita
- Department of Neuroscience and Cell Biology, Kyoto Prefectural University of Medicine, Kamigyo-ku, Kyoto, Japan
| | - Yasufumi Shigeyoshi
- Department of Anatomy and Neurobiology, Kindai University Faculty of Medicine, Osakasayama, Osaka, Japan
- * E-mail: (SK); (YS)
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64
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Almeira N, Risau-Gusman S. Role of transcriptional bursts in cellular oscillations. J Theor Biol 2017; 426:49-56. [PMID: 28549618 DOI: 10.1016/j.jtbi.2017.05.029] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/27/2017] [Revised: 05/19/2017] [Accepted: 05/23/2017] [Indexed: 11/30/2022]
Abstract
Genetic oscillators are present in the cells of many organisms and control several biological processes. The common feature of such oscillators is the presence of a protein which represses the transcription of its own gene. Recently, it has been shown that for many genes transcription is not a continuous process, but that it proceeds in bursts. We study here the relationship between bursty transcription and the robustness of protein oscillations. We concentrate on the temporal profile of mRNA production by studying regimes where this profile changes but the amount of mRNA produced is kept fixed. For systems with different degrees of cooperativity we show that in general bursts are associated with more robust oscillations, but when they are too short and intense they can have the opposite effect. In other words, we show that, in terms of the regularity of the oscillations generated, there is an optimal value for the intensity of the bursts.
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Affiliation(s)
- N Almeira
- Facultad de Matemática, Astronomía, Física y Computación, Universidad Nacional de Córdoba, Ciudad Universitaria, Córdoba, Argentina; Instituto de Física Enrique Gaviola (IFEG-ConICET), Ciudad Universitaria, 5000 Córdoba, Argentina
| | - S Risau-Gusman
- Centro Atómico Bariloche, 8400 S. C. de Bariloche, Argentina; Consejo Nacional de Investigaciones Científicas y Técnicas, Argentina.
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65
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Millius A, Ueda HR. Systems Biology-Derived Discoveries of Intrinsic Clocks. Front Neurol 2017; 8:25. [PMID: 28220104 PMCID: PMC5292584 DOI: 10.3389/fneur.2017.00025] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/25/2016] [Accepted: 01/17/2017] [Indexed: 12/19/2022] Open
Abstract
A systems approach to studying biology uses a variety of mathematical, computational, and engineering tools to holistically understand and model properties of cells, tissues, and organisms. Building from early biochemical, genetic, and physiological studies, systems biology became established through the development of genome-wide methods, high-throughput procedures, modern computational processing power, and bioinformatics. Here, we highlight a variety of systems approaches to the study of biological rhythms that occur with a 24-h period-circadian rhythms. We review how systems methods have helped to elucidate complex behaviors of the circadian clock including temperature compensation, rhythmicity, and robustness. Finally, we explain the contribution of systems biology to the transcription-translation feedback loop and posttranslational oscillator models of circadian rhythms and describe new technologies and "-omics" approaches to understand circadian timekeeping and neurophysiology.
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Affiliation(s)
- Arthur Millius
- Laboratory for Synthetic Biology, RIKEN Quantitative Biology Center, Suita, Osaka, Japan
| | - Hiroki R. Ueda
- Laboratory for Synthetic Biology, RIKEN Quantitative Biology Center, Suita, Osaka, Japan
- Department of Systems Pharmacology, Graduate School of Medicine, The University of Tokyo, Tokyo, Japan
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66
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Feedback, Mass Conservation and Reaction Kinetics Impact the Robustness of Cellular Oscillations. PLoS Comput Biol 2016; 12:e1005298. [PMID: 28027301 PMCID: PMC5226835 DOI: 10.1371/journal.pcbi.1005298] [Citation(s) in RCA: 14] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/20/2016] [Revised: 01/11/2017] [Accepted: 12/07/2016] [Indexed: 12/20/2022] Open
Abstract
Oscillations occur in a wide variety of cellular processes, for example in calcium and p53 signaling responses, in metabolic pathways or within gene-regulatory networks, e.g. the circadian system. Since it is of central importance to understand the influence of perturbations on the dynamics of these systems a number of experimental and theoretical studies have examined their robustness. The period of circadian oscillations has been found to be very robust and to provide reliable timing. For intracellular calcium oscillations the period has been shown to be very sensitive and to allow for frequency-encoded signaling. We here apply a comprehensive computational approach to study the robustness of period and amplitude of oscillatory systems. We employ different prototype oscillator models and a large number of parameter sets obtained by random sampling. This framework is used to examine the effect of three design principles on the sensitivities towards perturbations of the kinetic parameters. We find that a prototype oscillator with negative feedback has lower period sensitivities than a prototype oscillator relying on positive feedback, but on average higher amplitude sensitivities. For both oscillator types, the use of Michaelis-Menten instead of mass action kinetics in all degradation and conversion reactions leads to an increase in period as well as amplitude sensitivities. We observe moderate changes in sensitivities if replacing mass conversion reactions by purely regulatory reactions. These insights are validated for a set of established models of various cellular rhythms. Overall, our work highlights the importance of reaction kinetics and feedback type for the variability of period and amplitude and therefore for the establishment of predictive models. Rhythmic behavior is omnipresent in biology and has many crucial functions. In cells the activation levels and abundances of signaling molecules such as NF-κB, p53, EGFR or calcium repeatedly increase and decrease in response to stimuli. Such a dynamic behavior can also be observed monitoring the concentrations of mRNAs and proteins in the circadian clock and the cell cycle. Period and amplitude which are the time span between peaks and the peak height, respectively, as well as their variabilities are important features of oscillations. The circadian period is very stable allowing for proper time keeping, whereas in calcium signaling the period is very variable encoding different stimulation strengths. Our goal is to examine the origin of differences in sensitivities of periods and amplitudes using a computational approach. We use prototype oscillators and demonstrate that they can be used to derive general principles that explain the degree of robustness in period and amplitude for a set of commonly used models of cellular oscillators. Our findings imply that the robustness of oscillating systems can be influenced by feedback type and kinetic properties to which special attention should be paid when designing mathematical models of cellular rhythms.
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Bechtel W. Mechanists Must be Holists Too! Perspectives from Circadian Biology. JOURNAL OF THE HISTORY OF BIOLOGY 2016; 49:705-731. [PMID: 26966017 DOI: 10.1007/s10739-016-9439-6] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/05/2023]
Abstract
The pursuit of mechanistic explanations in biology has produced a great deal of knowledge about the parts, operations, and organization of mechanisms taken to be responsible for biological phenomena. Holist critics have often raised important criticisms of proposed mechanistic explanations, but until recently holists have not had alternative research strategies through which to advance explanations. This paper argues both that the results of mechanistic strategies has forced mechanists to confront ways in which whole systems affect their components and that new representational and modeling strategies are providing tools for understanding these effects of whole systems upon components. Drawing from research on the mechanism responsible for circadian rhythms in mammals, I develop two examples in which mechanistic analysis is being integrated into a more holist perspective: research revealing intercellular integration of circadian mechanisms with those involved in cell metabolism and research revealing that stable␣rhythms are dependent on how individual cells in the suprachiasmatic nucleus synchronize with each other to generate regular rhythms. Tools such as network diagramming and computational modeling are providing means to integrate mechanistic models into accounts of whole systems.
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Affiliation(s)
- William Bechtel
- Department of Philosophy and Center for Circadian Biology, University of California, San Diego, La Jolla, CA, USA.
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68
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Zhao B, Diraviyam T, Zhang X. Biomathematical modeling on chronobiological rhythms of antibody- exemplified through chicken IgY. BIOL RHYTHM RES 2016. [DOI: 10.1080/09291016.2016.1197520] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/21/2022]
Affiliation(s)
- Bin Zhao
- College of Veterinary Medicine, Northwest A&F University, Yangling, China
- College of Science, Northwest A&F University, Yangling, China
| | | | - Xiaoying Zhang
- College of Veterinary Medicine, Northwest A&F University, Yangling, China
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69
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Semenov SN, Kraft LJ, Ainla A, Zhao M, Baghbanzadeh M, Campbell VE, Kang K, Fox JM, Whitesides GM. Autocatalytic, bistable, oscillatory networks of biologically relevant organic reactions. Nature 2016; 537:656-60. [DOI: 10.1038/nature19776] [Citation(s) in RCA: 196] [Impact Index Per Article: 24.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/04/2016] [Accepted: 08/12/2016] [Indexed: 02/07/2023]
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70
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Gomez MM, Murray RM, Bennett MR. The effects of time-varying temperature on delays in genetic networks. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS 2016; 15:1734-1752. [PMID: 29081723 PMCID: PMC5656297 DOI: 10.1137/15m1040979] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 06/07/2023]
Abstract
Delays in gene networks result from the sequential nature of protein assembly. However, it is unclear how models of gene networks that use delays should be modified when considering time-dependent changes in temperature. This is important, as delay is often used in models of genetic oscillators that can be entrained by periodic fluctuations in temperature. Here, we analytically derive the time dependence of delay distributions in response to time-varying temperature changes. We find that the resulting time-varying delay is nonlinearly dependent on parameters of the time-varying temperature such as amplitude and frequency, therefore, applying an Arrhenius scaling may result in erroneous conclusions. We use these results to examine a model of a synthetic gene oscillator with temperature compensation. We show that temperature entrainment follows from the same mechanism that results in temperature compensation. Under a common Arrhenius scaling alone, the frequency of the oscillator is sensitive to changes in the mean temperature but robust to changes in the frequency of a periodically time-varying temperature. When a mechanism for temperature compensation is included in the model, however, we show that the oscillator is entrained by periodically varying temperature even when maintaining insensitivity to the mean temperature.
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Affiliation(s)
- Marcella M Gomez
- Electrical Engineering and Computer Science, UC Berkeley, CA 94720, USA
| | | | - Matthew R Bennett
- Department of Bioengineering and Department of Biosciences, Rice University, Houston, TX 77005, USA
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71
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Martin O, Krzywicki A, Zagorski M. Drivers of structural features in gene regulatory networks: From biophysical constraints to biological function. Phys Life Rev 2016; 17:124-58. [DOI: 10.1016/j.plrev.2016.06.002] [Citation(s) in RCA: 8] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/21/2015] [Revised: 03/25/2016] [Accepted: 04/20/2016] [Indexed: 12/23/2022]
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72
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Abstract
The authors examine collective rhythms in a general multicell system with both linearly diffusive and nondiffusive couplings. The effect of coupling on synchronization through intercellular signaling in a population of Escherichia coli cells is studied. In particular, a synchronization solution is given through the auxiliary individual system for 2 types of couplings. The sufficient conditions for the global synchronization of such a coupled system are derived based on the Lyapunov function method. The authors show that an appropriate design of the coupling and the inner-linking matrix can ensure global synchronization of the coupled synthetic biological system. Moreover, they demonstrate that the dynamics of an individual cell with coupling and without coupling may be qualitatively different; one is oscillatory, and the other is steady state. The change from a nonoscillatory state to an oscillatory one is induced by appropriate coupling, which also entrains all cells to synchronization. These results establish not only a theoretical foundation but also a quantitative basis for understanding the essential cooperative dynamics, such as collective rhythms or synchronization, in a population of cells.
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Affiliation(s)
- Ruiqi Wang
- Department of Electrical Engineering and Electronics, Osaka Sangyo University, Osaka, Japan
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73
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Leloup JC, Goldbeter A. Modelling the dual role of Per phosphorylation and its effect on the period and phase of the mammalian circadian clock. IET Syst Biol 2016; 5:44. [PMID: 21261401 DOI: 10.1049/iet-syb.2009.0068] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022] Open
Abstract
Circadian clocks are regulated at the post-translational level by a variety of processes among which protein phosphorylation plays a prominent, although complex, role. Thus, the phosphorylation of different sites on the clock protein PER by casein kinase I (CKI) can lead to opposite effects on the stability of the protein and on the period of circadian oscillations. Here the authors extend a computational model previously proposed for the mammalian circadian clock by incorporating two distinct phosphorylations of PER by CKI. On the basis of experimental observations the authors consider that phosphorylation at one site (denoted here PER-P1) enhances the rate of degradation of the protein and decreases the period, while phosphorylation at another site (PER-P2) stabilises the protein, enhances the transcription of the Per gene, and increases the period. The model also incorporates an additional phosphorylation of PER by the Glycogen Synthase Kinase 3 (GSK3). The authors show that the extended model incorporating the antagonistic effects of PER phosphorylations by CKI can account for observations pertaining to (i) the decrease in period in the Tau mutant, because of an increase in phosphorylation by CKI leading to PER-P1, and (ii) the familial advanced sleep phase syndrome (FASPS) in which the period is shortened and the phase of the oscillations is advanced when the rate of phosphorylation leading to PER-P2 is decreased. The model further accounts for the increase in period observed in the presence of CKI inhibitors that decrease the rate of phosphorylation leading to both PER-P1 and PER-P2. A similar increase in period results from inhibition of GSK3. [Includes supplementary material].
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Affiliation(s)
- J-C Leloup
- Université Libre de Bruxelles, Unité de Chronobiologie théorique, Faculté des Sciences, Brussels, Belgium
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74
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Pauls SD, Honma KI, Honma S, Silver R. Deconstructing Circadian Rhythmicity with Models and Manipulations. Trends Neurosci 2016; 39:405-419. [PMID: 27090429 DOI: 10.1016/j.tins.2016.03.006] [Citation(s) in RCA: 18] [Impact Index Per Article: 2.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 12/28/2015] [Revised: 03/15/2016] [Accepted: 03/18/2016] [Indexed: 01/15/2023]
Abstract
A master brain clock, localized to the hypothalamic suprachiasmatic nucleus (SCN), coordinates daily rhythms of physiology and behavior. Within the SCN, interconnected individual neurons are oscillators that, as an ensemble, function to send a coherent timing signal to the brain and body. However, individually, these neurons display different amplitudes, periods, and phases of oscillation. The dynamic properties of the SCN have been characterized over several spatial levels of analysis, from proteins to cells to tissues, and over several temporal ranges, from milliseconds to weeks. Modeling tools guide empirical research in this complex and multiscale spatiotemporal environment. Given that the SCN is a prototypical example of oscillating neural systems, principles of its organization hold promise as general prototypes of rhythms in other frequencies.
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Affiliation(s)
- Scott D Pauls
- Mathematics Department, Dartmouth College, Hanover, NH, USA
| | - Ken-Ichi Honma
- Department of Chronomedicine, Hokkaido University Graduate School of Medicine, Sapporo, Hokkaido, Japan
| | - Sato Honma
- Department of Chronomedicine, Hokkaido University Graduate School of Medicine, Sapporo, Hokkaido, Japan
| | - Rae Silver
- Neuroscience Program, Barnard College, New York, NY, USA; Department of Psychology, Columbia University, New York, NY, USA; Department of Pathology and Cell Biology, Columbia University Medical Center, New York, NY, USA.
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75
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Bechtel W. Using computational models to discover and understand mechanisms. STUDIES IN HISTORY AND PHILOSOPHY OF SCIENCE 2016; 56:113-121. [PMID: 27083091 DOI: 10.1016/j.shpsa.2015.10.004] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 01/09/2015] [Revised: 07/02/2015] [Accepted: 10/08/2015] [Indexed: 06/05/2023]
Abstract
Areas of biology such as cell and molecular biology have been dominated by research directed at constructing mechanistic explanations that identify parts and operations that when organized appropriately are responsible for the various phenomena they investigate. Increasingly the mechanisms hypothesized involve non-sequential organization of non-linear operations and so exceed the ability of researchers to mentally rehearse their behavior. Accordingly, scientists rely on tools of computational modeling and dynamical systems theory in advancing dynamic mechanistic explanations. Using circadian rhythm research as an exemplar, this paper explores the variety of roles computational modeling is playing. They serve not just to determine whether the mechanism will produce the desired behavior, but in the discovery process of hypothesizing mechanisms and in understanding why proposed mechanisms behave as they do.
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Affiliation(s)
- William Bechtel
- Department of Philosophy and Center for Circadian Biology, University of California, La Jolla, CA 92093-0119, United States.
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76
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Sarode KD, Kumar VR, Kulkarni BD. Inverse problem studies of biochemical systems with structure identification of S-systems by embedding training functions in a genetic algorithm. Math Biosci 2016; 275:93-106. [PMID: 26968929 DOI: 10.1016/j.mbs.2016.02.014] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/06/2015] [Revised: 02/03/2016] [Accepted: 02/26/2016] [Indexed: 10/22/2022]
Abstract
An efficient inverse problem approach for parameter estimation, state and structure identification from dynamic data by embedding training functions in a genetic algorithm methodology (ETFGA) is proposed for nonlinear dynamical biosystems using S-system canonical models. Use of multiple shooting and decomposition approach as training functions has been shown for handling of noisy datasets and computational efficiency in studying the inverse problem. The advantages of the methodology are brought out systematically by studying it for three biochemical model systems of interest. By studying a small-scale gene regulatory system described by a S-system model, the first example demonstrates the use of ETFGA for the multifold aims of the inverse problem. The estimation of a large number of parameters with simultaneous state and network identification is shown by training a generalized S-system canonical model with noisy datasets. The results of this study bring out the superior performance of ETFGA on comparison with other metaheuristic approaches. The second example studies the regulation of cAMP oscillations in Dictyostelium cells now assuming limited availability of noisy data. Here, flexibility of the approach to incorporate partial system information in the identification process is shown and its effect on accuracy and predictive ability of the estimated model are studied. The third example studies the phenomenological toy model of the regulation of circadian oscillations in Drosophila that follows rate laws different from S-system power-law. For the limited noisy data, using a priori information about properties of the system, we could estimate an alternate S-system model that showed robust oscillatory behavior with predictive abilities.
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Affiliation(s)
- Ketan Dinkar Sarode
- Chemical Engineering and Process Development Division, CSIR-National Chemical Laboratory (CSIR-NCL), Pune 411008, India; Centre of Excellence in Scientific Computing, (CoESC), CSIR-NCL, Pune, India; Academy of Scientific and Innovative Research (AcSIR), CSIR-NCL Campus, Pune, India.
| | - V Ravi Kumar
- Chemical Engineering and Process Development Division, CSIR-National Chemical Laboratory (CSIR-NCL), Pune 411008, India; Centre of Excellence in Scientific Computing, (CoESC), CSIR-NCL, Pune, India; Academy of Scientific and Innovative Research (AcSIR), CSIR-NCL Campus, Pune, India.
| | - B D Kulkarni
- Chemical Engineering and Process Development Division, CSIR-National Chemical Laboratory (CSIR-NCL), Pune 411008, India; Centre of Excellence in Scientific Computing, (CoESC), CSIR-NCL, Pune, India; Academy of Scientific and Innovative Research (AcSIR), CSIR-NCL Campus, Pune, India.
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77
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Exponentially Fitted Two-Derivative Runge-Kutta Methods for Simulation of Oscillatory Genetic Regulatory Systems. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2015; 2015:689137. [PMID: 26633991 PMCID: PMC4645493 DOI: 10.1155/2015/689137] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 04/16/2015] [Revised: 08/02/2015] [Accepted: 08/25/2015] [Indexed: 11/18/2022]
Abstract
Oscillation is one of the most important phenomena in the chemical reaction systems in
living cells. The general purpose simulation algorithms fail to take into account this special
character and produce unsatisfying results. In order to enhance the accuracy of the integrator,
the second-order derivative is incorporated in the scheme. The oscillatory feature of the solution
is captured by the integrators with an exponential fitting property. Three practical exponentially
fitted TDRK (EFTDRK) methods are derived. To test the effectiveness of the new EFTDRK
methods, the two-gene system with cross-regulation and the circadian oscillation of the period
protein in Drosophila are simulated. Each EFTDRK method has the best fitting frequency
which minimizes the global error. The numerical results show that the new EFTDRK methods
are more accurate and more efficient than their prototype TDRK methods or RK methods of
the same order and the traditional exponentially fitted RK method in the literature.
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78
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A tunable artificial circadian clock in clock-defective mice. Nat Commun 2015; 6:8587. [PMID: 26617050 PMCID: PMC4674671 DOI: 10.1038/ncomms9587] [Citation(s) in RCA: 40] [Impact Index Per Article: 4.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/06/2015] [Accepted: 09/09/2015] [Indexed: 12/17/2022] Open
Abstract
Self-sustaining oscillations are essential for diverse physiological functions such as the cell cycle, insulin secretion and circadian rhythms. Synthetic oscillators using biochemical feedback circuits have been generated in cell culture. These synthetic systems provide important insight into design principles for biological oscillators, but have limited similarity to physiological pathways. Here we report the generation of an artificial, mammalian circadian clock in vivo, capable of generating robust, tunable circadian rhythms. In mice deficient in Per1 and Per2 genes (thus lacking circadian rhythms), we artificially generate PER2 rhythms and restore circadian sleep/wake cycles with an inducible Per2 transgene. Our artificial clock is tunable as the period and phase of the rhythms can be modulated predictably. This feature, and other design principles of our work, might enhance the study and treatment of circadian dysfunction and broader aspects of physiology involving biological oscillators. Circadian rhythms are central to health and disease and there is renewed interest in chronotherapy. Here, the authors present a mouse with an artificial circadian clock that can be pharmacologically tuned, providing a tool for future studies of circadian biology and therapy.
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79
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Wang G, Peskin CS. Stochastic entrainment of a stochastic oscillator. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 92:052718. [PMID: 26651734 DOI: 10.1103/physreve.92.052718] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Subscribe] [Scholar Register] [Received: 04/17/2015] [Indexed: 06/05/2023]
Abstract
In this work, we consider a stochastic oscillator described by a discrete-state continuous-time Markov chain, in which the states are arranged in a circle, and there is a constant probability per unit time of jumping from one state to the next in a specified direction around the circle. At each of a sequence of equally spaced times, the oscillator has a specified probability of being reset to a particular state. The focus of this work is the entrainment of the oscillator by this periodic but stochastic stimulus. We consider a distinguished limit, in which (i) the number of states of the oscillator approaches infinity, as does the probability per unit time of jumping from one state to the next, so that the natural mean period of the oscillator remains constant, (ii) the resetting probability approaches zero, and (iii) the period of the resetting signal approaches a multiple, by a ratio of small integers, of the natural mean period of the oscillator. In this distinguished limit, we use analytic and numerical methods to study the extent to which entrainment occurs.
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Affiliation(s)
- Guanyu Wang
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
| | - Charles S Peskin
- Courant Institute of Mathematical Sciences, New York University, New York, New York 10012, USA
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80
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Rajesh D, Muthukumar S, Siva D, Saibaba G, Dhanasekaran D, Archunan G. Examining and elucidation of human weight cycle model adopting e-cell simulation system. Bioinformation 2015; 11:336-42. [PMID: 26339149 PMCID: PMC4546992 DOI: 10.6026/97320630011336] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/15/2014] [Accepted: 11/12/2014] [Indexed: 11/23/2022] Open
Abstract
Cellular rhythms regulate various physiological functions in circadian oscillatory mechanisms. Weight cycling or 'yo-yo' dieting is an evitable process in human, because of subsequent loss and regain of body weight due to irregular diet. Human weight cycle (HWC) is the major factor for causing global epidemic diseases in human beings. Understanding the HWC process would provide potent additional knowledge to prevent obesity. However till date, there is no study dealing with examine the HWC model using virtual cell simulation based on system biological approach. Therefore, the present study was designed to develop a computational HWC model, which was simulated using E-cell system v3.0. The developed model has the cyclic feedback reactions of three significant variables (the consecutive cycles of weight loss in continuous food intake (Q) and regain of body weight (P) at highest threshold point of cognitive restraint (R)) which are obtained by mathematical modelling. The dynamic plot results supported that the PQR variables depicted sustained oscillation with reversible modification due to protein diet. By contrast, the virtual model simulation would provide extensive information on HWC, which might provide knowledge to develop HWC linked with obesity pathway. The presents study concludes that optimization of body weight is essential to prevent the obesity based diseases.
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Affiliation(s)
- Durairaj Rajesh
- Centre for Pheromone Technology, Department of Animal Science, School of Life Sciences, Bharathidasan University, Tiruchirappalli-620024, Tamil Nadu, India
| | - Subramanian Muthukumar
- Centre for Pheromone Technology, Department of Animal Science, School of Life Sciences, Bharathidasan University, Tiruchirappalli-620024, Tamil Nadu, India
| | - Durairaj Siva
- Department of Environmental Biotechnology, Bharathidasan University, Tiruchirappalli-620024; Tamil Nadu, India
| | - Ganesan Saibaba
- Centre for Pheromone Technology, Department of Animal Science, School of Life Sciences, Bharathidasan University, Tiruchirappalli-620024, Tamil Nadu, India
| | | | - Govindaraju Archunan
- Centre for Pheromone Technology, Department of Animal Science, School of Life Sciences, Bharathidasan University, Tiruchirappalli-620024, Tamil Nadu, India
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81
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Caicedo-Casso A, Kang HW, Lim S, Hong CI. Robustness and period sensitivity analysis of minimal models for biochemical oscillators. Sci Rep 2015; 5:13161. [PMID: 26267886 PMCID: PMC4542697 DOI: 10.1038/srep13161] [Citation(s) in RCA: 9] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2015] [Accepted: 07/20/2015] [Indexed: 11/24/2022] Open
Abstract
Biological systems exhibit numerous oscillatory behaviors from calcium oscillations to circadian rhythms that recur daily. These autonomous oscillators contain complex feedbacks with nonlinear dynamics that enable spontaneous oscillations. The detailed nonlinear dynamics of such systems remains largely unknown. In this paper, we investigate robustness and dynamical differences of five minimal systems that may underlie fundamental molecular processes in biological oscillatory systems. Bifurcation analyses of these five models demonstrate an increase of oscillatory domains with a positive feedback mechanism that incorporates a reversible reaction, and dramatic changes in dynamics with small modifications in the wiring. Furthermore, our parameter sensitivity analysis and stochastic simulations reveal different rankings of hierarchy of period robustness that are determined by the number of sensitive parameters or network topology. In addition, systems with autocatalytic positive feedback loop are shown to be more robust than those with positive feedback via inhibitory degradation regardless of noise type. We demonstrate that robustness has to be comprehensively assessed with both parameter sensitivity analysis and stochastic simulations.
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Affiliation(s)
- Angélica Caicedo-Casso
- 1] Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA [2] Departamento de Matemáticas, Universidad del Valle, Cali, Valle, COL
| | - Hye-Won Kang
- Department of Mathematics and Statistics, University of Maryland at Baltimore County, Baltimore, MD 21250, USA
| | - Sookkyung Lim
- Department of Mathematical Sciences, University of Cincinnati, Cincinnati, OH 45221, USA
| | - Christian I Hong
- Department of Molecular and Cellular Physiology, University of Cincinnati, Cincinnati, OH 45267, USA
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82
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Chowdhury AR, Chetty M, Evans R. Stochastic S-system modeling of gene regulatory network. Cogn Neurodyn 2015; 9:535-47. [PMID: 26379803 DOI: 10.1007/s11571-015-9346-0] [Citation(s) in RCA: 19] [Impact Index Per Article: 2.1] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 11/12/2014] [Revised: 04/14/2015] [Accepted: 05/30/2015] [Indexed: 02/06/2023] Open
Abstract
Microarray gene expression data can provide insights into biological processes at a system-wide level and is commonly used for reverse engineering gene regulatory networks (GRN). Due to the amalgamation of noise from different sources, microarray expression profiles become inherently noisy leading to significant impact on the GRN reconstruction process. Microarray replicates (both biological and technical), generated to increase the reliability of data obtained under noisy conditions, have limited influence in enhancing the accuracy of reconstruction . Therefore, instead of the conventional GRN modeling approaches which are deterministic, stochastic techniques are becoming increasingly necessary for inferring GRN from noisy microarray data. In this paper, we propose a new stochastic GRN model by investigating incorporation of various standard noise measurements in the deterministic S-system model. Experimental evaluations performed for varying sizes of synthetic network, representing different stochastic processes, demonstrate the effect of noise on the accuracy of genetic network modeling and the significance of stochastic modeling for GRN reconstruction . The proposed stochastic model is subsequently applied to infer the regulations among genes in two real life networks: (1) the well-studied IRMA network, a real-life in-vivo synthetic network constructed within the Saccharomyces cerevisiae yeast, and (2) the SOS DNA repair network in Escherichia coli.
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Affiliation(s)
- Ahsan Raja Chowdhury
- School of Engineering and Information Technology, Federation University Australia, Churchill, Australia ; Department of Computer Science and Engineering, University of Dhaka, Dhaka, Bangladesh
| | - Madhu Chetty
- School of Engineering and Information Technology, Federation University Australia, Churchill, Australia
| | - Rob Evans
- Department of Electrical and Electronics Engineering, University of Melbourne, Parkville, Australia
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83
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Bianco-Martinez E, Baptista MS, Letellier C. Symbolic computations of nonlinear observability. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2015; 91:062912. [PMID: 26172777 DOI: 10.1103/physreve.91.062912] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 12/22/2014] [Indexed: 06/04/2023]
Abstract
Observability is a very useful concept for determining whether the dynamics of complicated systems can be correctly reconstructed from a single (univariate or multivariate) time series. When the governing equations of dynamical systems are high-dimensional and/or rational, analytical computations of observability coefficients produce large polynomial functions with a number of terms that become exponentially large with the dimension and the nature of the system. In order to overcome this difficulty, we introduce here a symbolic observability coefficient based on a symbolic computation of the determinant of the observability matrix. The computation of such coefficients is straightforward and can be easily analytically carried out, as demonstrated in this paper for a five-dimensional rational system.
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Affiliation(s)
- Ezequiel Bianco-Martinez
- Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Old Aberdeen AB24 3UE, United Kingdom
| | - Murilo S Baptista
- Institute for Complex Systems and Mathematical Biology, SUPA, University of Aberdeen, Old Aberdeen AB24 3UE, United Kingdom
| | - Christophe Letellier
- CORIA-UMR 6614 Normandie Université, CNRS-Université et INSA de Rouen, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France
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84
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Luna A, McFadden GB, Aladjem MI, Kohn KW. Predicted Role of NAD Utilization in the Control of Circadian Rhythms during DNA Damage Response. PLoS Comput Biol 2015; 11:e1004144. [PMID: 26020938 PMCID: PMC4462596 DOI: 10.1371/journal.pcbi.1004144] [Citation(s) in RCA: 13] [Impact Index Per Article: 1.4] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/21/2014] [Accepted: 01/20/2015] [Indexed: 02/06/2023] Open
Abstract
The circadian clock is a set of regulatory steps that oscillate with a period of approximately 24 hours influencing many biological processes. These oscillations are robust to external stresses, and in the case of genotoxic stress (i.e. DNA damage), the circadian clock responds through phase shifting with primarily phase advancements. The effect of DNA damage on the circadian clock and the mechanism through which this effect operates remains to be thoroughly investigated. Here we build an in silico model to examine damage-induced circadian phase shifts by investigating a possible mechanism linking circadian rhythms to metabolism. The proposed model involves two DNA damage response proteins, SIRT1 and PARP1, that are each consumers of nicotinamide adenine dinucleotide (NAD), a metabolite involved in oxidation-reduction reactions and in ATP synthesis. This model builds on two key findings: 1) that SIRT1 (a protein deacetylase) is involved in both the positive (i.e. transcriptional activation) and negative (i.e. transcriptional repression) arms of the circadian regulation and 2) that PARP1 is a major consumer of NAD during the DNA damage response. In our simulations, we observe that increased PARP1 activity may be able to trigger SIRT1-induced circadian phase advancements by decreasing SIRT1 activity through competition for NAD supplies. We show how this competitive inhibition may operate through protein acetylation in conjunction with phosphorylation, consistent with reported observations. These findings suggest a possible mechanism through which multiple perturbations, each dominant during different points of the circadian cycle, may result in the phase advancement of the circadian clock seen during DNA damage. Many physiological processes are regulated by the circadian clock, and we are continuing to learn about the role of the circadian clock in disease. Research in recent years has begun to shed light on the feedback mechanisms that exist between circadian regulation and other processes, including metabolism and the response to DNA damage. A challenge has been to understand the dynamic nature of the protein interactions of these processes, which often involve protein modification as a means of communicating cellular states, such as damaged DNA. Here we have devised a model that simulates an alteration of the circadian clock that is observed during DNA damage response. A novel aspect of this model is the inclusion of SIRT1, a protein that regulates core circadian proteins through modification and helps to repress gene expression. SIRT1 is dependent on a metabolite regulated by the circadian clock and is depleted during DNA damage. In conjunction with a second form of protein modification, our results suggest that multiple forms of protein modification may contribute to the experimentally observed alterations to circadian function.
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Affiliation(s)
- Augustin Luna
- Laboratory of Molecular Pharmacology, National Cancer Institute, Bethesda, Maryland, United States of America
- Department of Bioinformatics, Boston University, Boston, Massachusetts, United States of America
- * E-mail:
| | - Geoffrey B. McFadden
- Applied and Computational Mathematics Division, National Institute of Standards and Technology, Gaithersburg, Maryland, United States of America
| | - Mirit I. Aladjem
- Laboratory of Molecular Pharmacology, National Cancer Institute, Bethesda, Maryland, United States of America
| | - Kurt W. Kohn
- Laboratory of Molecular Pharmacology, National Cancer Institute, Bethesda, Maryland, United States of America
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85
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Nieto PS, Revelli JA, Garbarino-Pico E, Condat CA, Guido ME, Tamarit FA. Effects of different per translational kinetics on the dynamics of a core circadian clock model. PLoS One 2015; 10:e0115067. [PMID: 25607544 PMCID: PMC4301915 DOI: 10.1371/journal.pone.0115067] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/10/2014] [Accepted: 11/18/2014] [Indexed: 11/19/2022] Open
Abstract
Living beings display self-sustained daily rhythms in multiple biological processes, which persist in the absence of external cues since they are generated by endogenous circadian clocks. The period (per) gene is a central player within the core molecular mechanism for keeping circadian time in most animals. Recently, the modulation PER translation has been reported, both in mammals and flies, suggesting that translational regulation of clock components is important for the proper clock gene expression and molecular clock performance. Because translational regulation ultimately implies changes in the kinetics of translation and, therefore, in the circadian clock dynamics, we sought to study how and to what extent the molecular clock dynamics is affected by the kinetics of PER translation. With this objective, we used a minimal mathematical model of the molecular circadian clock to qualitatively characterize the dynamical changes derived from kinetically different PER translational mechanisms. We found that the emergence of self-sustained oscillations with characteristic period, amplitude, and phase lag (time delays) between per mRNA and protein expression depends on the kinetic parameters related to PER translation. Interestingly, under certain conditions, a PER translation mechanism with saturable kinetics introduces longer time delays than a mechanism ruled by a first-order kinetics. In addition, the kinetic laws of PER translation significantly changed the sensitivity of our model to parameters related to the synthesis and degradation of per mRNA and PER degradation. Lastly, we found a set of parameters, with realistic values, for which our model reproduces some experimental results reported recently for Drosophila melanogaster and we present some predictions derived from our analysis.
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Affiliation(s)
- Paula S. Nieto
- Instituto de Física Enrique Gaviola (IFEG-CONICET) and Facultad de Matemática, Astronomía y Física (FaMAF), Universidad Nacional de Córdoba (UNC). Ciudad Universitaria, CP:X5000HUA Córdoba, Argentina
| | - Jorge A. Revelli
- Instituto de Física Enrique Gaviola (IFEG-CONICET) and Facultad de Matemática, Astronomía y Física (FaMAF), Universidad Nacional de Córdoba (UNC). Ciudad Universitaria, CP:X5000HUA Córdoba, Argentina
| | - Eduardo Garbarino-Pico
- Centro de Investigaciones en Química Biológica de Córdoba (CIQUIBIC-CONICET) and Departamento de Química Biológica, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba (UNC). Ciudad Universitaria, CP:X5000HUA Córdoba, Argentina
| | - Carlos A. Condat
- Instituto de Física Enrique Gaviola (IFEG-CONICET) and Facultad de Matemática, Astronomía y Física (FaMAF), Universidad Nacional de Córdoba (UNC). Ciudad Universitaria, CP:X5000HUA Córdoba, Argentina
| | - Mario E. Guido
- Centro de Investigaciones en Química Biológica de Córdoba (CIQUIBIC-CONICET) and Departamento de Química Biológica, Facultad de Ciencias Químicas, Universidad Nacional de Córdoba (UNC). Ciudad Universitaria, CP:X5000HUA Córdoba, Argentina
| | - Francisco A. Tamarit
- Instituto de Física Enrique Gaviola (IFEG-CONICET) and Facultad de Matemática, Astronomía y Física (FaMAF), Universidad Nacional de Córdoba (UNC). Ciudad Universitaria, CP:X5000HUA Córdoba, Argentina
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86
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Generalizing Mechanistic Explanations Using Graph-Theoretic Representations. HISTORY, PHILOSOPHY AND THEORY OF THE LIFE SCIENCES 2015. [DOI: 10.1007/978-94-017-9822-8_9] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
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87
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Leedale J, Herrmann A, Bagnall J, Fercher A, Papkovsky D, Sée V, Bearon RN. Modeling the dynamics of hypoxia inducible factor-1α (HIF-1α) within single cells and 3D cell culture systems. Math Biosci 2014; 258:33-43. [DOI: 10.1016/j.mbs.2014.09.007] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 04/02/2014] [Revised: 07/28/2014] [Accepted: 09/13/2014] [Indexed: 11/27/2022]
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88
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Risau-Gusman S, Gleiser PM. A mathematical model of communication between groups of circadian neurons in Drosophila melanogaster. J Biol Rhythms 2014; 29:401-10. [PMID: 25416595 DOI: 10.1177/0748730414557865] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/25/2023]
Abstract
In the fruit fly, circadian behavior is controlled by a small number of specialized neurons, whose molecular clocks are relatively well known. However, much less is known about how these neurons communicate among themselves. In particular, only 1 circadian neuropeptide, pigment-dispersing factor (PDF), has been identified, and most aspects of its interaction with the molecular clock remain to be elucidated. Furthermore, it is speculated that many other peptides should contribute to circadian communication. We have developed a relatively detailed model of the 2 main groups of circadian pacemaker neurons (sLNvs and LNds) to investigate these issues. We have proposed many possible mechanisms for the interaction between the synchronization factors and the molecular clock, and we have compared the outputs with the experimental results reported in the literature both for the wild-type and PDF-null mutant. We have studied how different the properties of each neuron should be to account for the observations reported for the sLNvs in the mutant. We have found that only a few mechanisms, mostly related to the slowing down of nuclear entry of a circadian protein, can synchronize neurons that present these differences. Detailed immunofluorescent recordings have suggested that, whereas in the mutant, LNd neurons are synchronized, in the wild-type, a subset of the LNds oscillate faster than the rest. With our model, we find that a more likely explanation for the same observations is that this subset is being driven outside its synchronization range and displays therefore a complex pattern of oscillation.
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89
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Wang J, Lefranc M, Thommen Q. Stochastic oscillations induced by intrinsic fluctuations in a self-repressing gene. Biophys J 2014; 107:2403-16. [PMID: 25418309 PMCID: PMC4241447 DOI: 10.1016/j.bpj.2014.09.042] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/05/2013] [Revised: 09/25/2014] [Accepted: 09/30/2014] [Indexed: 10/24/2022] Open
Abstract
Biochemical reaction networks are subjected to large fluctuations attributable to small molecule numbers, yet underlie reliable biological functions. Thus, it is important to understand how regularity can emerge from noise. Here, we study the stochastic dynamics of a self-repressing gene with arbitrarily long or short response time. We find that when the mRNA and protein half-lives are approximately equal to the gene response time, fluctuations can induce relatively regular oscillations in the protein concentration. To gain insight into this phenomenon at the crossroads of determinism and stochasticity, we use an intermediate theoretical approach, based on a moment-closure approximation of the master equation, which allows us to take into account the binary character of gene activity. We thereby obtain differential equations that describe how nonlinearity can feed-back fluctuations into the mean-field equations to trigger oscillations. Finally, our results suggest that the self-repressing Hes1 gene circuit exploits this phenomenon to generate robust oscillations, inasmuch as its time constants satisfy precisely the conditions we have identified.
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Affiliation(s)
- Jingkui Wang
- Laboratoire de Physique des Lasers, Atomes, et Molécules, Centre National de la Recherche Scientifique, UMR8523, Université Lille 1, Villeneuve d'Ascq, France
| | - Marc Lefranc
- Laboratoire de Physique des Lasers, Atomes, et Molécules, Centre National de la Recherche Scientifique, UMR8523, Université Lille 1, Villeneuve d'Ascq, France
| | - Quentin Thommen
- Laboratoire de Physique des Lasers, Atomes, et Molécules, Centre National de la Recherche Scientifique, UMR8523, Université Lille 1, Villeneuve d'Ascq, France.
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90
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Gennemark P, Hjorth S, Gabrielsson J. Modeling energy intake by adding homeostatic feedback and drug intervention. J Pharmacokinet Pharmacodyn 2014; 42:79-96. [PMID: 25388764 DOI: 10.1007/s10928-014-9399-4] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/08/2014] [Accepted: 11/03/2014] [Indexed: 12/19/2022]
Abstract
Energy intake (EI) is a pivotal biomarker used in quantification approaches to metabolic disease processes such as obesity, diabetes, and growth disorders. Eating behavior is however under both short-term and long-term control. This control system manifests itself as tolerance and rebound phenomena in EI, when challenged by drug treatment or diet restriction. The paper describes a model with the capability to capture physiological counter-regulatory feedback actions triggered by energy imbalances. This feedback is general as it handles tolerance to both increases and decreases in EI, and works in both acute and chronic settings. A drug mechanism function inhibits (or stimulates) EI. The deviation of EI relative to a reference level (set-point) serves as input to a non-linear appetite control signal which in turn impacts EI in parallel to the drug intervention. Three examples demonstrate the potential usefulness of the model in both acute and chronic dosing situations. The model shifts the predicted concentration-response relationship rightwardly at lower concentrations, in contrast to models that do not handle functional adaptation. A fourth example further shows that the model may qualitatively explain differences in rate and extent of adaptation in observed EI and its concomitants in both rodents and humans.
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91
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Ramkisoensing A, Gu C, van Engeldorp Gastelaars HMD, Michel S, Deboer T, Rohling JHT, Meijer JH. Enhanced phase resetting in the synchronized suprachiasmatic nucleus network. J Biol Rhythms 2014; 29:4-15. [PMID: 24492878 DOI: 10.1177/0748730413516750] [Citation(s) in RCA: 15] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/09/2023]
Abstract
The suprachiasmatic nucleus (SCN) adapts to both the external light-dark (LD) cycle and seasonal changes in day length. In short photoperiods, single-cell activity patterns are tightly synchronized (i.e., in phase); in long photoperiods, these patterns are relatively dispersed, causing lower amplitude rhythms. The limit cycle oscillator has been used to describe the SCN's circadian rhythmicity and predicts that following a given perturbation, high-amplitude SCN rhythms will shift less than low-amplitude rhythms. Some studies reported, however, that phase delays are larger when animals are entrained to a short photoperiod. Because phase advances and delays are mediated by partially distinct (i.e., nonoverlapping) biochemical pathways, we investigated the effect of a 4-h phase advance of the LD cycle in mice housed in either short (LD 8:16) or long (LD 16:8) photoperiods. In vitro recordings revealed a significantly larger phase advance in the SCN of mice entrained to short as compared to long photoperiods (4.2 ± 0.3 h v. 1.4 ± 0.9 h, respectively). Surprisingly, in mice with long photoperiods, the behavioral phase shift was larger than the phase shift of the SCN (3.7 ± 0.4 h v. 1.4 ± 0.9 h, respectively). To exclude a confounding influence of running-wheel activity on the magnitude of the shifts of the SCN, we repeated the experiments in the absence of running wheels and found similar shifts in the SCN in vitro in short and long days (3.0 ± 0.5 h v. 0.4 ± 0.9 h, respectively). Interestingly, removal of the running wheel reduced the phase-shifting capacity of mice in long days, leading to similar behavioral shifts in short and long photoperiods (1.0 ± 0.1 h v. 1.0 ± 0.4 h). As the behavioral shifts in the presence of wheels were larger than the shift of the SCN, it is suggested that additional, non-SCN neuronal networks in the brain are involved in regulating the timing of behavioral activity. On the basis of the phase shifts observed in vitro, we conclude that highly synchronized SCN networks with high-amplitude rhythms show a larger phase-shifting capacity than desynchronized networks of low amplitude.
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Affiliation(s)
- Ashna Ramkisoensing
- Laboratory for Neurophysiology, Department of Molecular Cell Biology, Leiden University Medical Center, Leiden, the Netherlands
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92
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Miro-Bueno J, Sosík P. Brain clock driven by neuropeptides and second messengers. PHYSICAL REVIEW. E, STATISTICAL, NONLINEAR, AND SOFT MATTER PHYSICS 2014; 90:032705. [PMID: 25314471 DOI: 10.1103/physreve.90.032705] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 02/18/2014] [Indexed: 06/04/2023]
Abstract
The master circadian pacemaker in mammals is localized in a small portion of the brain called the suprachiasmatic nucleus (SCN). It is unclear how the SCN produces circadian rhythms. A common interpretation is that the SCN produces oscillations through the coupling of genetic oscillators in the neurons. The coupling is effected by a network of neuropeptides and second messengers. This network is crucial for the correct function of the SCN. However, models that study a possible oscillatory behavior of the network itself have received little attention. Here we propose and analyze a model to examine this oscillatory potential. We show that an intercellular oscillator emerges in the SCN as a result of the neuropeptide and second messenger dynamics. We find that this intercellular clock can produce circadian rhythms by itself with and without genetic clocks. We also found that the model is robust to perturbation of parameters and can be entrained by light-dark cycles.
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Affiliation(s)
- Jesus Miro-Bueno
- Research Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601 Opava, Czech Republic
| | - Petr Sosík
- Research Institute of the IT4Innovations Centre of Excellence, Faculty of Philosophy and Science, Silesian University in Opava, 74601 Opava, Czech Republic and Departamento de Inteligencia Artificial, Escuela Técnica Superior de Ingenieros Informáticos, Universidad Politécnica de Madrid, Madrid, Spain
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93
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Observer design for a core circadian rhythm network. ScientificWorldJournal 2014; 2014:476912. [PMID: 25121122 PMCID: PMC4121104 DOI: 10.1155/2014/476912] [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: 06/08/2014] [Accepted: 06/15/2014] [Indexed: 11/18/2022] Open
Abstract
The paper investigates the observer design for a core circadian rhythm network in Drosophila and Neurospora. Based on the constructed highly nonlinear differential equation model and the recently proposed graphical approach, we design a rather simple observer for the circadian rhythm oscillator, which can well track the state of the original system for various input signals. Numerical simulations show the effectiveness of the designed observer. Potential applications of the related investigations include the real-world control and experimental design of the related biological networks.
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94
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Yan J, Shi G, Zhang Z, Wu X, Liu Z, Xing L, Qu Z, Dong Z, Yang L, Xu Y. An intensity ratio of interlocking loops determines circadian period length. Nucleic Acids Res 2014; 42:10278-87. [PMID: 25122753 PMCID: PMC4176327 DOI: 10.1093/nar/gku701] [Citation(s) in RCA: 20] [Impact Index Per Article: 2.0] [Reference Citation Analysis] [Abstract] [MESH Headings] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 03/11/2014] [Revised: 07/20/2014] [Accepted: 07/21/2014] [Indexed: 11/14/2022] Open
Abstract
Circadian clocks allow organisms to orchestrate the daily rhythms in physiology and behaviors, and disruption of circadian rhythmicity can profoundly affect fitness. The mammalian circadian oscillator consists of a negative primary feedback loop and is associated with some 'auxiliary' loops. This raises the questions of how these interlocking loops coordinate to regulate the period and maintain its robustness. Here, we focused on the REV-ERBα/Cry1 auxiliary loop, consisting of Rev-Erbα/ROR-binding elements (RORE) mediated Cry1 transcription, coordinates with the negative primary feedback loop to modulate the mammalian circadian period. The silicon simulation revealed an unexpected rule: the intensity ratio of the primary loop to the auxiliary loop is inversely related to the period length, even when post-translational feedback is fixed. Then we measured the mRNA levels from two loops in 10-mutant mice and observed the similar monotonic relationship. Additionally, our simulation and the experimental results in human osteosarcoma cells suggest that a coupling effect between the numerator and denominator of this intensity ratio ensures the robustness of circadian period and, therefore, provides an efficient means of correcting circadian disorders. This ratio rule highlights the contribution of the transcriptional architecture to the period dynamics and might be helpful in the construction of synthetic oscillators.
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Affiliation(s)
- Jie Yan
- Center for Systems Biology, Soochow University, Suzhou 215006, China MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China
| | - Guangsen Shi
- MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China
| | - Zhihui Zhang
- MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China
| | - Xi Wu
- MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China
| | - Zhiwei Liu
- MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China
| | - Lijuan Xing
- MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China
| | - Zhipeng Qu
- MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China
| | - Zhen Dong
- MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China
| | - Ling Yang
- Center for Systems Biology, Soochow University, Suzhou 215006, China School of Mathematical Sciences, Soochow University, Suzhou 215006, China
| | - Ying Xu
- Center for Systems Biology, Soochow University, Suzhou 215006, China MOE Key Laboratory of Model Animal for Disease Study, Model Animal Research Center, Medical School of Nanjing University, Nanjing 210061, China Collaborative Innovation Center for Genetics and Development, Fudan University, Shanghai 200433, China
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95
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Xing J, Mather W, Hong C. Computational cell biology: past, present and future. Interface Focus 2014. [DOI: 10.1098/rsfs.2014.0027] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/12/2022] Open
Affiliation(s)
- Jianhua Xing
- Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
- Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
| | - William Mather
- Department of Biological Sciences, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
- Department of Physics, Virginia Polytechnic Institute and State University, Blacksburg, VA 24061, USA
| | - Christian Hong
- Department of Molecular and Cellular Physiology, University of Cincinnati, Cincinnati, OH 45267, USA
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96
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Splitting strategy for simulating genetic regulatory networks. COMPUTATIONAL AND MATHEMATICAL METHODS IN MEDICINE 2014; 2014:683235. [PMID: 24624223 PMCID: PMC3929534 DOI: 10.1155/2014/683235] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Subscribe] [Scholar Register] [Received: 05/30/2013] [Accepted: 10/24/2013] [Indexed: 11/30/2022]
Abstract
The splitting approach is developed for the numerical simulation of genetic regulatory networks with a stable steady-state structure. The numerical results of the simulation of a one-gene network, a two-gene network, and a p53-mdm2 network show that the new splitting methods constructed in this paper are remarkably more effective and more suitable for long-term computation with large steps than the traditional general-purpose Runge-Kutta methods. The new methods have no restriction on the choice of stepsize due to their infinitely large stability regions.
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97
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Sandefur CI, Mincheva M, Schnell S. Network representations and methods for the analysis of chemical and biochemical pathways. MOLECULAR BIOSYSTEMS 2014; 9:2189-200. [PMID: 23857078 DOI: 10.1039/c3mb70052f] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.8] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/21/2022]
Abstract
Systems biologists increasingly use network representations to investigate biochemical pathways and their dynamic behaviours. In this critical review, we discuss four commonly used network representations of chemical and biochemical pathways. We illustrate how some of these representations reduce network complexity but result in the ambiguous representation of biochemical pathways. We also examine the current theoretical approaches available to investigate the dynamic behaviour of chemical and biochemical networks. Finally, we describe how the critical chemical and biochemical pathways responsible for emergent dynamic behaviour can be identified using network mining and functional mapping approaches.
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Affiliation(s)
- Conner I Sandefur
- Cystic Fibrosis and Pulmonary Diseases Research and Treatment Center and Department of Pharmacology, University of North Carolina at Chapel Hill, Chapel Hill, North Carolina, USA
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98
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Amin MR, Roussel MR. Graph-theoretic analysis of a model for the coupling between photosynthesis and photorespiration. CAN J CHEM 2014. [DOI: 10.1139/cjc-2013-0315] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 02/04/2023]
Abstract
We develop and analyze a mathematical model based on a previously enunciated hypothesis regarding the origin of rapid, irregular oscillations observed in photosynthetic variables when a leaf is transferred to a low-CO2atmosphere. This model takes the form of a set of differential equations with two delays. We review graph-theoretical methods of analysis based on the bipartite graph representation of mass-action models, including models with delays. We illustrate the use of these methods by showing that our model is capable of delay-induced oscillations. We present some numerical examples confirming this possibility, including the possibility of complex transient oscillations. We then use the structure of the identified oscillophore, the part of the reaction network responsible for the oscillations, along with our knowledge of the plausible range of values for one of the delays, to rule out this hypothetical mechanism.
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Affiliation(s)
- Md. Ruhul Amin
- Department of Chemistry and Biochemistry, University Hall, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada
| | - Marc R. Roussel
- Department of Chemistry and Biochemistry, University Hall, University of Lethbridge, Lethbridge, AB T1K 3M4, Canada
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99
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Tsai TYC, Theriot JA, Ferrell JE. Changes in oscillatory dynamics in the cell cycle of early Xenopus laevis embryos. PLoS Biol 2014; 12:e1001788. [PMID: 24523664 PMCID: PMC3921120 DOI: 10.1371/journal.pbio.1001788] [Citation(s) in RCA: 61] [Impact Index Per Article: 6.1] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 05/02/2013] [Accepted: 12/31/2013] [Indexed: 11/19/2022] Open
Abstract
During the early development of Xenopus laevis embryos, the first mitotic cell cycle is long (∼85 min) and the subsequent 11 cycles are short (∼30 min) and clock-like. Here we address the question of how the Cdk1 cell cycle oscillator changes between these two modes of operation. We found that the change can be attributed to an alteration in the balance between Wee1/Myt1 and Cdc25. The change in balance converts a circuit that acts like a positive-plus-negative feedback oscillator, with spikes of Cdk1 activation, to one that acts like a negative-feedback-only oscillator, with a shorter period and smoothly varying Cdk1 activity. Shortening the first cycle, by treating embryos with the Wee1A/Myt1 inhibitor PD0166285, resulted in a dramatic reduction in embryo viability, and restoring the length of the first cycle in inhibitor-treated embryos with low doses of cycloheximide partially rescued viability. Computations with an experimentally parameterized mathematical model show that modest changes in the Wee1/Cdc25 ratio can account for the observed qualitative changes in the cell cycle. The high ratio in the first cycle allows the period to be long and tunable, and decreasing the ratio in the subsequent cycles allows the oscillator to run at a maximal speed. Thus, the embryo rewires its feedback regulation to meet two different developmental requirements during early development.
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Affiliation(s)
- Tony Y.-C. Tsai
- Department of Chemical and Systems Biology, Stanford University School of Medicine, Stanford, California, United States of America
- Department of Biochemistry, Stanford University School of Medicine, Stanford, California, United States of America
- Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford, California, United States of America
| | - Julie A. Theriot
- Department of Biochemistry, Stanford University School of Medicine, Stanford, California, United States of America
- Howard Hughes Medical Institute, Stanford University School of Medicine, Stanford, California, United States of America
| | - James E. Ferrell
- Department of Chemical and Systems Biology, Stanford University School of Medicine, Stanford, California, United States of America
- Department of Biochemistry, Stanford University School of Medicine, Stanford, California, United States of America
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Varma V, Mukherjee N, Kannan NN, Sharma VK. Strong (type 0) phase resetting of activity-rest rhythm in fruit flies, Drosophila melanogaster, at low temperature. J Biol Rhythms 2013; 28:380-9. [PMID: 24336416 DOI: 10.1177/0748730413508922] [Citation(s) in RCA: 8] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 01/21/2023]
Abstract
Amplitude modulation in limit cycle models of circadian clocks has been previously formulated to explain the phenomenon of temperature compensation. These models propose that invariance of clock period (τ) with changing temperature is a result of the system traversing small or large limit cycles such that despite a decrease or an increase in the linear velocity of the clock owing to slowing down or speeding up of the underlying biochemical reactions, respectively, the angular velocity and, thus, the clock period remain constant. In addition, these models predict that phase resetting behavior of circadian clocks described by limit cycles of different amplitudes at low or high temperatures will be drastically different. More specifically, this class of models predicts that at low temperatures, circadian clocks will respond to perturbations by eliciting larger phase shifts by virtue of their smaller amplitude and vice versa. Here, we present the results of our tests of this prediction: We examined the nature of photic phase response curves (PRCs) and phase transition curves (PTCs) for the circadian clocks of 4 wild-type fruit fly Drosophila melanogaster populations at 3 different ambient temperatures (18, 25, and 29 °C). Interestingly, we observed that at the low temperature of 18 °C, fly clocks respond to light perturbations more strongly, eliciting strong (type 0) PRCs and PTCs, while at moderate (25 °C) and high (29 °C) temperatures the same stimuli evoke weak (type 1) responses. This pattern of strong and weak phase resetting at low and high temperatures, respectively, renders support for the limit cycle amplitude modulation model for temperature compensation of circadian clocks.
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Affiliation(s)
- Vishwanath Varma
- Chronobiology Laboratory, Evolutionary and Organismal Biology Unit, Jawaharlal Nehru Centre for Advanced Scientific Research, Bangalore, India
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