Oscillator model reduction preserving the phase response: Application to the circadian clock
Open accessAbstract
Mathematical model reduction is a long-standing technique used both to gain insight into model subprocesses and to reduce the computational costs of simulation and analysis. A reduced model must retain essential features of the full model, which, traditionally, have been the trajectories of certain state variables. For biological clocks, timing, or phase, characteristics must be preserved. A key performance criterion for a clock is the ability to adjust its phase correctly in response to external signals. We present a novel model reduction technique that removes components from a single-oscillator clock model and discover that four feedback loops are redundant with respect to its phase response behavior. Using a coupled multioscillator model of a circadian clock, we demonstrate that by preserving the phase response behavior of a single oscillator, we preserve timing behavior at the multioscillator level.
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Weekend oversleep compounds the phase delay in the circadian clock, making it more difficult to get up on Monday morning.
“Weekend oversleep compounds the phase delay in the clock (46,47), making it even more difficult to get up on Monday morning.”
From Impact of Sleep and Circadian Rhythms on Addiction Vulnerability in Adolescents (2018) · cites this paper as [47]
Cites
Genetic algorithms in search, optimization, and machine learning
(1989) · Choice Reviews Online · doi:10.5860/choice.27-0936 · Cited by 49,169 · see citing works
Genetic Algorithms in Search, Optimization and Machine Learning
Goldberg, D. E., & Robson, D. (1988) · Cited by 18,391 · see citing works
Goldberg, D. E., & Shakespeare, W. (2002) · Cited by 16,077 · see citing works
Genetic Algorithms + Data Structures = Evolution Programs
Michalewicz, Z. (1992) · Artificial intelligence · doi:10.1007/978-3-662-02830-8 · Cited by 11,581 · see citing works
Handbook of Genetic Algorithms
Davis, L. D. (1991) · Cumulative Index of Computer Aided Architectural Design · Cited by 7,297 · see citing works
Chemical Oscillations, Waves, and Turbulence
Kuramoto, Y. (1984) · Springer series in synergetics · doi:10.1007/978-3-642-69689-3 · Cited by 7,242 · see citing works
The Geometry of Biological Time
Winfree, A. T. (1980) · doi:10.1007/978-3-662-22492-2 · Cited by 3,613 · see citing works
Strogatz, S. H. (2000) · Physica D Nonlinear Phenomena · doi:10.1016/s0167-2789(00)00094-4 · Cited by 3,094 · see citing works
Simplifying chemical kinetics: Intrinsic low-dimensional manifolds in composition space
Maas, U., & Pope, S. B. (1992) · Combustion and Flame · doi:10.1016/0010-2180(92)90034-m · Cited by 1,554 · see citing works
A Note on the Kinetics of Enzyme Action
Briggs, G. E., & Haldane, J. B. S. (1925) · Biochemical Journal · doi:10.1042/bj0190338 · Cited by 1,338 · see citing works
The Geometry of Biological Time
Winfree, A. T. (2001) · Interdisciplinary applied mathematics · doi:10.1007/978-1-4757-3484-3 · Cited by 1,242 · see citing works
The CSP method for simplifying kinetics
Lam, S. H., & Goussis, D. A. (1994) · International Journal of Chemical Kinetics · doi:10.1002/kin.550260408 · Cited by 768 · see citing works
Aton, S. J., Colwell, C. S., Harmar, A. J., Waschek, J. A., & Herzog, E. D. (2005) · Nature Neuroscience · doi:10.1038/nn1419 · Cited by 764 · see citing works
Genetic algorithms + data structures = evolution programs
Bousonville, T. (1997) · Computational Statistics & Data Analysis · doi:10.1016/s0167-9473(97)87028-4 · Cited by 665 · see citing works
Evolution and Optimum Seeking: The Sixth Generation
Schwefel, H. (1993) · John Wiley & Sons, Inc. eBooks · Cited by 653 · see citing works
Biegler, L. T., & Grossmann, I. E. (2004) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2003.11.003 · Cited by 594 · see citing works
Sensitivity analysis of complex kinetic systems. Tools and applications
Tur�nyi, T. (1990) · Journal of Mathematical Chemistry · doi:10.1007/bf01166355 · Cited by 582 · see citing works
Toward a detailed computational model for the mammalian circadian clock
Leloup, J., & Goldbeter, A. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.1132112100 · Cited by 535 · see citing works
On the Phase Reduction and Response Dynamics of Neural Oscillator Populations
Brown, E., Moehlis, J., & Holmes, P. J. (2004) · Neural Computation · doi:10.1162/089976604322860668 · Cited by 499 · see citing works
Parametric Sensitivity in Chemical Systems
Varma, A., Morbidelli, M., & Wu, H. (1999) · Cambridge University Press eBooks · doi:10.1017/cbo9780511721779 · Cited by 472 · see citing works
Spontaneous Synchronization of Coupled Circadian Oscillators
Gonze, D., Bernard, S., Waltermann, C., Kramer, A., & Herzel, H. (2005) · Biophysical Journal · doi:10.1529/biophysj.104.058388 · Cited by 465 · see citing works
Locke, J. C. W., Kozma‐Bognár, L., Gould, P. D., et al. (2006) · Molecular Systems Biology · doi:10.1038/msb4100102 · Cited by 431 · see citing works
Extension of a genetic network model by iterative experimentation and mathematical analysis
Locke, J. C. W., Southern, M. M., Kozma‐Bognár, L., Hibberd, V., Brown, P. E., Turner, M. S., & Millar, A. J. (2005) · Molecular Systems Biology · doi:10.1038/msb4100018 · Cited by 381 · see citing works
Genetic and evolutionary algorithms come of age
Goldberg, D. E. (1994) · Communications of the ACM · doi:10.1145/175247.175259 · Cited by 371 · see citing works
A detailed predictive model of the mammalian circadian clock
Forger, D. B., & Peskin, C. S. (2003) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.2036281100 · Cited by 354 · see citing works
Simplification of Mathematical Models of Chemical Reaction Systems
Okino, M. S., & Mavrovouniotis, M. L. (1998) · Chemical Reviews · doi:10.1021/cr950223l · Cited by 345 · see citing works
Temporal Precision in the Mammalian Circadian System: A Reliable Clock from Less Reliable Neurons
Herzog, E. D., Aton, S. J., Numano, R., Sakaki, Y., & Tei, H. (2004) · Journal of Biological Rhythms · doi:10.1177/0748730403260776 · Cited by 281 · see citing works
Locke, J. C. W., Millar, A. J., & Turner, M. S. (2005) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2004.11.038 · Cited by 238 · see citing works
A novel computational model of the circadian clock in Arabidopsis that incorporates PRR7 and PRR9
Zeilinger, M. N., Farré, E. M., Taylor, S. R., Kay, S. A., & Doyle, F. J. (2006) · Molecular Systems Biology · doi:10.1038/msb4100101 · Cited by 232 · see citing works
Self-citationSynchronization-Induced Rhythmicity of Circadian Oscillators in the Suprachiasmatic Nucleus
Bernard, S., Gonze, D., Čajavec, B., Herzel, H., & Kramer, A. (2007) · PLoS Computational Biology · doi:10.1371/journal.pcbi.0030068 · Cited by 229 · see citing works
Neuropeptides phase shift the mammalian circadian pacemaker
Piggins, H. D., Antle, M. C., & Rusak, B. (1995) · Journal of Neuroscience · doi:10.1523/jneurosci.15-08-05612.1995 · Cited by 219 · see citing works
Part II. Future perspective on optimization
Grossmann, I. E., & Biegler, L. T. (2004) · Computers & Chemical Engineering · doi:10.1016/j.compchemeng.2003.11.006 · Cited by 190 · see citing works
A Simple Model of Circadian Rhythms Based on Dimerization and Proteolysis of PER and TIM
Tyson, J. J., Hong, C. I., Thron, C. D., & Novák, B. (1999) · Biophysical Journal · doi:10.1016/s0006-3495(99)77078-5 · Cited by 190 · see citing works
The steady state and equilibrium approximations: A geometrical picture
Fraser, S. J. (1988) · The Journal of Chemical Physics · doi:10.1063/1.454686 · Cited by 175 · see citing works
A Molecular Model for Intercellular Synchronization in the Mammalian Circadian Clock
To, T., Henson, M. A., Herzog, E. D., & Doyle, F. J. (2007) · Biophysical Journal · doi:10.1529/biophysj.106.094086 · Cited by 158 · see citing works
Self-citationGABA and G i/o differentially control circadian rhythms and synchrony in clock neurons
Aton, S. J., Huettner, J. E., Straume, M., & Herzog, E. D. (2006) · Proceedings of the National Academy of Sciences · doi:10.1073/pnas.0607466103 · Cited by 156 · see citing works
Reduction of conductance-based neuron models
Kepler, T. B., Abbott, L. F., & Marder, E. E. (1992) · Biological Cybernetics · doi:10.1007/bf00197717 · Cited by 154 · see citing works
Model reduction for chemical kinetics: An optimization approach
Petzold, L. R., & Zhu, W. (1999) · AIChE Journal · doi:10.1002/aic.690450418 · Cited by 146 · see citing works
Self-citationGeometry of the steady-state approximation: Perturbation and accelerated convergence methods
Roussel, M. R., & Fraser, S. J. (1990) · The Journal of Chemical Physics · doi:10.1063/1.459171 · Cited by 136 · see citing works
Kinetic mechanism reduction based on an integer programming approach
Androulakis, I. P. (2000) · AIChE Journal · doi:10.1002/aic.690460214 · Cited by 97 · see citing works
Kinetic model reduction using genetic algorithms
Edwards, K., Edgar, T. F., & Manousiouthakis, V. I. (1998) · Computers & Chemical Engineering · doi:10.1016/s0098-1354(96)00362-6 · Cited by 84 · see citing works
Model Reduction and Physical Understanding of Slowly Oscillating Processes: The Circadian Cycle
Goussis, D. A., & Najm, H. N. (2006) · Multiscale Modeling and Simulation · doi:10.1137/060649768 · Cited by 78 · see citing works
Starting, stopping, and resetting biological oscillators: in search of optimum perturbations
Forger, D. B., & Paydarfar, D. (2004) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2004.04.043 · Cited by 72 · see citing works
Conzelmann, H., Sauter, T., Gilles, E. D., Allgöwer, F., Sáez-Rodríguez, J., & Bullinger, E. (2004) · Systems Biology · doi:10.1049/sb:20045011 · Cited by 71 · see citing works
Sensitivity Measures for Oscillating Systems: Application to Mammalian Circadian Gene Network
Taylor, S. R., Gunawan, R., Petzold, L. R., & Doyle, F. J. (2008) · IEEE Transactions on Automatic Control · doi:10.1109/tac.2007.911364 · Cited by 63 · see citing works
Self-citationDurkin, J. (2002) · Elsevier eBooks · doi:10.1016/b978-012443880-4/50046-6 · Cited by 57 · see citing works
Reconciling Mathematical Models of Biological Clocks by Averaging on Approximate Manifolds
Forger, D. B., & Kronauer, R. E. (2002) · SIAM Journal on Applied Mathematics · doi:10.1137/s0036139900373587 · Cited by 45 · see citing works
Sensitivity analysis of oscillatory systems
Kramer, M. A. M., RABITZ, H. A., & CALO, J. M. (1984) · Applied Mathematical Modelling · doi:10.1016/0307-904x(84)90146-x · Cited by 43 · see citing works
Isochron-Based Phase Response Analysis of Circadian Rhythms
Gunawan, R., & Doyle, F. J. (2006) · Biophysical Journal · doi:10.1529/biophysj.105.078006 · Cited by 28 · see citing works
Self-citationDesign of flexible reduced kinetic mechanisms
Sirdeshpande, A. R., Ierapetritou, M., & Androulakis, I. P. (2001) · AIChE Journal · doi:10.1002/aic.690471110 · Cited by 26 · see citing works
Model based conjectures on mammalian clock controversies
Forger, D. B., & Peskin, C. S. (2004) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2004.04.041 · Cited by 25 · see citing works
Indic, P., Gurdziel, K., Kronauer, R. E., et al. (2006) · Journal of Biological Rhythms · doi:10.1177/0748730406287357 · Cited by 23 · see citing works
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Impact of Sleep and Circadian Rhythms on Addiction Vulnerability in Adolescents
Logan, R. W., Hasler, B. P., Forbes, E. E., Franzen, P. L., Torregrossa, M. M., Huang, Y. H., Buysse, D. J., Clark, D. B., & McClung, C. A. (2018) · Biological Psychiatry · doi:10.1016/j.biopsych.2017.11.035 · Cited by 194 · see citing works
- Authors
- Taylor, S. R., Doyle, F. J., & Petzold, L. R.
- Affiliations
- University of California, Santa Barbara (US)
- Corresponding author
- Petzold, Linda R.
- Venue
- Biophysical Journal
- Publisher
- Elsevier BV
- Published
- 2008-08
- Volume
- 95
- Issue
- 4
- Pages
- 1658-1673
- ISSN
- 0006-3495 (ISSN-L)
- PMC
- PMC2483761
- OpenAlex
- W2093549234
- Cited by
- 37
- References
- 52
- Citations by year
- 2026: 2 · 2023: 1 · 2022: 2 · 2021: 4 · 2020: 3 · 2018: 2 · 2017: 4 · 2015: 1 · 2014: 4 · 2013: 1 · 2012: 2
- FWCI
- 1.63
- Type
- journal article
- Language
- en
- Open access
- bronze
- doi.org
- Licence
- Locations
- Biophysical Journal (publishedVersion)
- PubMed Central (publishedVersion)
- PubMed (publishedVersion)
- Funders
- National Science Foundation
- National Institutes of Health (EB007511)
- National Institute of General Medical Sciences (GM078993)
- Army Research Office (W911NF-07-1-0279)
- Institute for Collaborative Biotechnologies (DAAD19-03-D-0004)
- Topics
- Life Sciences › Neuroscience › Endocrine and Autonomic Systems › Circadian rhythm and melatonin
- Physical Sciences › Computer Science › Computer Networks and Communications › Nonlinear Dynamics and Pattern Formation
- Life Sciences › Biochemistry, Genetics and Molecular Biology › Molecular Biology › Gene Regulatory Network Analysis
- Keywords
- model reduction, phase response, circadian clock, biological clock, timing behavior, coupled oscillators
- MeSH terms
- Algorithms, Biological Clocks, Cell Cycle, Circadian Rhythm, Computer Simulation, Models, Biological, Cell Cycle Proteins
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