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Numerical preservation issues in stochastic dynamical systems by $ \vartheta $-methods
A mathematical analysis of an activator-inhibitor Rho GTPase model
1. | University of Zaragoza, Department of Mechanical Engineering, Campus Rio Ebro, E-50018 Zaragoza, Spain |
2. | TU Dortmund University and Max-Planck-Institute of Molecular Physiology, Department of Chemistry and Chemical Biology and Department of Systemic Cell Biology, Otto-Hahn-Str. 4a, 44227, Dortmund, Germany |
3. | University of Manitoba, Department of Mathematics, 428 Machray Hall, Winnipeg, MB R3T 2N2 Canada |
4. | University of Sussex, Department of Mathematics, School of Mathematical and Physical Sciences, Pevensey 3 5C15, Brighton, BN1 9QH. UK |
Recent experimental observations reveal that local cellular contraction pulses emerge via a combination of fast positive and slow negative feedbacks based on a signal network composed of Rho, GEF and Myosin interactions [
References:
[1] |
E. Bodine, L. Deaett, J. McDonald, D. Olesky and P. van den Driessche,
Sign patterns that require or allow particular refined inertias, Linear Algebra Appl., 437 (2012), 2228-2242.
doi: 10.1016/j.laa.2012.05.014. |
[2] |
A. Bolado-Carrancio, O. S. Rukhlenko, E. Nikonova, M. A. Tsyganov, A. Wheeler, A. Garcia-Munoz, W. Kolch, A. von Kriegsheim and B. N. Kholodenko,
Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration, Elife, 9 (2020), e58165.
|
[3] |
A. Boureux, E. Vignal, S. Faure and P. Fort,
Evolution of the Rho family of ras-like GTPases in eukaryotes, Molecular Biology and Evolution, 24 (2006), 203-216.
doi: 10.1093/molbev/msl145. |
[4] |
E. Campillo-Funollet, C. Venkataraman and A. Madzvamuse,
Bayesian parameter identification for Turing systems on stationary and evolving domains, Bull. Math. Biol., 81 (2019), 81-104.
doi: 10.1007/s11538-018-0518-z. |
[5] |
G. Culos, D. Olesky and P. van den Driessche,
Using sign patterns to detect the possibility of periodicity in biological systems, J. Math. Biol., 72 (2016), 1281-1300.
doi: 10.1007/s00285-015-0906-z. |
[6] |
C. DerMardirossian and G. M. Bokoch,
GDIs: Central regulatory molecules in Rho GTPase activation, Trends in Cell Biology, 15 (2005), 356-363.
doi: 10.1016/j.tcb.2005.05.001. |
[7] |
A. Dhooge, W. Govaerts and Y. A. Kuznetsov,
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs, ACM Trans. Math. Software, 29 (2003), 141-164.
doi: 10.1145/779359.779362. |
[8] |
A. Dhooge, W. Govaerts, Y. A. Kuznetsov, H. Meijer and B. Sautois,
New features of the software Matcont for bifurcation analysis of dynamical systems, Math. Comput. Model. Dyn. Syst., 14 (2008), 147-175.
doi: 10.1080/13873950701742754. |
[9] |
J. Drew, C. Johnson and D. Olesky,
Spectrally arbitrary patterns, Linear Algebra Appl., 308 (2000), 121-137.
doi: 10.1016/S0024-3795(00)00026-4. |
[10] |
D. G. Drubin and W. J. Nelson,
Origins of cell polarity, Cell, 84 (1996), 335-344.
doi: 10.1016/S0092-8674(00)81278-7. |
[11] |
A. J. Engler, S. Sen, H. L. Sweeney and D. E. Discher,
Matrix elasticity directs stem cell lineage specification, Cell, 126 (2006), 677-689.
doi: 10.1016/j.cell.2006.06.044. |
[12] |
P. Friedl and S. Alexander,
Cancer invasion and the microenvironment: Plasticity and reciprocity, Cell, 147 (2011), 992-1009.
doi: 10.1016/j.cell.2011.11.016. |
[13] |
C. Garnett, D. Olesky and P. van den Driessche,
A note on sign patterns of order 3 that require particular refined inertias, Linear Algebra Appl., 450 (2014), 293-300.
doi: 10.1016/j.laa.2014.03.007. |
[14] |
A. Goldbeter and D. E. Koshland,
An amplified sensitivity arising from covalent modification in biological systems, Proc. Nat. Acad. Sci., 78 (1981), 6840-6844.
doi: 10.1073/pnas.78.11.6840. |
[15] |
M. Graessl, J. Koch, A. Calderon, D. Kamps, S. Banerjee, T. Mazel, N. Schulze, J. K. Jungkurth, R. Patwardhan and D. Solouk,
An excitable Rho GTPase signaling network generates dynamic subcellular contraction patterns, JCB, 216 (2017), 4271-4285.
doi: 10.1083/jcb.201706052. |
[16] |
C. Guilluy, R. Garcia-Mata and K. Burridge,
Rho protein crosstalk: Another social network?, Trends in Cell Biology, 21 (2011), 718-726.
doi: 10.1016/j.tcb.2011.08.002. |
[17] |
R. G. Hodge and A. J. Ridley,
Regulating Rho GTPases and their regulators, Nature Reviews Molecular Cell Biology, 17 (2016), 496-510.
doi: 10.1038/nrm.2016.67. |
[18] |
W. R. Holmes, M. A. Mata and L. Edelstein-Keshet,
Local perturbation analysis: A computational tool for biophysical reaction-diffusion models, Biophysical Journal, 108 (2015), 230-236.
doi: 10.1016/j.bpj.2014.11.3457. |
[19] |
M. Jacquier, S. Kuriakose, A. Bhardwaj, Y. Zhang, A. Shrivastav, S. Portet and S. V. Shrivastav,
Investigation of novel regulation of N-myristoyltransferase by mammalian target of rapamycin in breast cancer cells, Scientific reports, 8 (2018), 1-11.
doi: 10.1038/s41598-018-30447-0. |
[20] |
D. W. Jordan and P. Smith, Nonlinear ordinary differential equations: An introduction to dynamical systems, 3$^rd$ edition, Oxford University Press, USA, 1999.
![]() ![]() |
[21] |
V. O. Juma, Data-Driven Mathematical Modelling and Simulation of Rho-Myosin Dynamics, PhD thesis, University of Sussex, 2019. |
[22] |
D. Kamps, J. Koch, V. O. Juma, E. Campillo-Funollet, M. Graessl, S. Banerjee, T. Mazel, X. Chen, Y.-W. Wu and S. Portet,
Optogenetic tuning reveals rho amplification-dependent dynamics of a cell contraction signal network, Cell Reports, 33 (2020), 108467.
doi: 10.1016/j.celrep.2020.108467. |
[23] |
E. J. Y. Kim, E. Korotkevich and T. Hiiragi,
Coordination of cell polarity, mechanics and fate in tissue self-organization, Trends in Cell Biology, 28 (2018), 541-550.
doi: 10.1016/j.tcb.2018.02.008. |
[24] |
I.-J. Kim, D. D. Olesky, B. L. Shader, P. van den Driessche, H. van der Holst and K. N. Vander Meulen,
Generating potentially nilpotent full sign patterns, Electron. J. Linear Algebra, 18 (2009), 162-175.
doi: 10.13001/1081-3810.1302. |
[25] |
R. Larter,
Sensitivity analysis of autonomous oscillators. separation of secular terms and determination of structural stability, J. Phys. Chem., 87 (1983), 3114-3121.
doi: 10.1021/j100239a032. |
[26] |
D. Lee, A. Koul, N. Lubna, S. A. McKenna and S. Portet,
Mathematical modelling of OAS2 activation by dsRNA and effects of dsRNA lengths, AIMS Math., 6 (2021), 5924-5941.
doi: 10.3934/math.2021351. |
[27] |
B. Lu and H. Yue,
Sensitivity analysis of oscillatory biological systems with a SVD-based algorithm, Systemics and Informatics World Network, 10 (2010), 85-92.
|
[28] |
Y. Lu and H. Yue,
Objective sensitivity analysis of biological oscillatory systems, IFAC Proceedings Volumes, 44 (2011), 10466-10471.
doi: 10.3182/20110828-6-IT-1002.02967. |
[29] |
A. F. Marée, A. Jilkine, A. Dawes, V. A. Grieneisen and L. Edelstein-Keshet,
Polarization and movement of keratocytes: A multiscale modelling approach, Bulletin of Mathematical Biology, 68 (2006), 1169-1211.
|
[30] |
MATLAB, 9.7.0.1190202 (R2019b), The MathWorks Inc., Natick, Massachusetts, 2018. |
[31] |
J. D. Murray, Mathematical Biology I: An Introduction, 3$^{rd}$ edition, Interdisciplinary Applied Mathematics, 17. Springer-Verlag, New York, 2002. |
[32] |
P. Nalbant, Y.-C. Chang, J. Birkenfeld, Z.-F. Chang and G. M. Bokoch,
Guanine nucleotide exchange factor-H1 regulates cell migration via localized activation of Rhoa at the leading edge, Molecular Biology of the Cell, 20 (2009), 3985-4129.
doi: 10.1091/mbc.e09-01-0041. |
[33] |
S. Portet,
Dynamics of in vitro intermediate filament length distributions, Journal of Theoretical Biology, 332 (2013), 20-29.
doi: 10.1016/j.jtbi.2013.04.004. |
[34] |
S. Portet, A. Madzvamuse, A. Chung, R. E. Leube and R. Windoffer,
Keratin dynamics: Modeling the interplay between turnover and transport, PloS One, 10 (2015), 1-29.
doi: 10.1371/journal.pone.0121090. |
[35] |
H. Rabitz and D. Edelson,
Numerical techniques for modelling and analysis of oscillating chemical reactions, Oscillations and Traveling Waves in Chemical Systems, (1985), 193-222.
|
[36] |
M. Raftopoulou and A. Hall,
Cell migration: Rho GTPases lead the way, Developmental Biology, 265 (2004), 23-32.
doi: 10.1016/j.ydbio.2003.06.003. |
[37] |
A. J. Ridley,
Rho GTPase signalling in cell migration, Current Opinion in Cell Biology, 36 (2015), 103-112.
doi: 10.1016/j.ceb.2015.08.005. |
[38] |
A. J. Ridley, M. A. Schwartz, K. Burridge, R. A. Firtel, M. H. Ginsberg, G. Borisy, J. T. Parsons and A. R. Horwitz,
Cell migration: Integrating signals from front to back, Science, 302 (2003), 1704-1709.
doi: 10.1126/science.1092053. |
[39] |
S. Saha, T. L. Nagy and O. D. Weiner,
Joining forces: Crosstalk between biochemical signalling and physical forces orchestrates cellular polarity and dynamics, Philosophical Transactions of the Royal Society B: Biological Sciences, 373 (2018), 20170145.
doi: 10.1098/rstb.2017.0145. |
[40] |
L. F. Shampine and M. W. Reichelt,
The MATLAB ODE suite, SIAM J. Sci. Comput., 18 (1997), 1-22.
doi: 10.1137/S1064827594276424. |
[41] |
C. M. Simon, E. M. Vaughan, W. M. Bement and L. Edelstein-Keshet,
Pattern formation of Rho GTPases in single cell wound healing, Molecular Biology of the Cell, 24 (2013), 421-432.
doi: 10.1091/mbc.e12-08-0634. |
[42] |
R. Tomovic and M. Vukobratovic, General Sensitivity Theory, vol. 1 of Mod. Analytic Comput. Methods Sci. Math., 35, New York, NY: North-Holland, 1972. |
[43] |
J. J. Tyson, K. C. Chen and B. Novak,
Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell, Current Opinion in Cell Biology, 15 (2003), 221-231.
doi: 10.1016/S0955-0674(03)00017-6. |
[44] |
J. J. Tyson, K. Chen and B. Novak,
Network dynamics and cell physiology, Nature Reviews Molecular Cell Biology, 2 (2001), 908-916.
doi: 10.1038/35103078. |
[45] |
J. J. Tyson and B. Novak,
Temporal organization of the cell cycle, Current Biology, 18 (2008), 759-768.
doi: 10.1016/j.cub.2008.07.001. |
[46] |
K. Wolf, M. Te Lindert, M. Krause, S. Alexander, J. Te Riet, A. L. Willis, R. M. Hoffman, C. G. Figdor, S. J. Weiss and P. Friedl,
Physical limits of cell migration: Control by ECM space and nuclear deformation and tuning by proteolysis and traction force, Journal of Cell Biology, 201 (2013), 1069-1084.
doi: 10.1083/jcb.201210152. |
[47] |
D. E. Zak, J. Stelling and F. J. Doyle,
Sensitivity analysis of oscillatory (bio) chemical systems, Computers & Chemical Engineering, 29 (2005), 663-673.
doi: 10.1016/j.compchemeng.2004.08.021. |
show all references
References:
[1] |
E. Bodine, L. Deaett, J. McDonald, D. Olesky and P. van den Driessche,
Sign patterns that require or allow particular refined inertias, Linear Algebra Appl., 437 (2012), 2228-2242.
doi: 10.1016/j.laa.2012.05.014. |
[2] |
A. Bolado-Carrancio, O. S. Rukhlenko, E. Nikonova, M. A. Tsyganov, A. Wheeler, A. Garcia-Munoz, W. Kolch, A. von Kriegsheim and B. N. Kholodenko,
Periodic propagating waves coordinate RhoGTPase network dynamics at the leading and trailing edges during cell migration, Elife, 9 (2020), e58165.
|
[3] |
A. Boureux, E. Vignal, S. Faure and P. Fort,
Evolution of the Rho family of ras-like GTPases in eukaryotes, Molecular Biology and Evolution, 24 (2006), 203-216.
doi: 10.1093/molbev/msl145. |
[4] |
E. Campillo-Funollet, C. Venkataraman and A. Madzvamuse,
Bayesian parameter identification for Turing systems on stationary and evolving domains, Bull. Math. Biol., 81 (2019), 81-104.
doi: 10.1007/s11538-018-0518-z. |
[5] |
G. Culos, D. Olesky and P. van den Driessche,
Using sign patterns to detect the possibility of periodicity in biological systems, J. Math. Biol., 72 (2016), 1281-1300.
doi: 10.1007/s00285-015-0906-z. |
[6] |
C. DerMardirossian and G. M. Bokoch,
GDIs: Central regulatory molecules in Rho GTPase activation, Trends in Cell Biology, 15 (2005), 356-363.
doi: 10.1016/j.tcb.2005.05.001. |
[7] |
A. Dhooge, W. Govaerts and Y. A. Kuznetsov,
MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs, ACM Trans. Math. Software, 29 (2003), 141-164.
doi: 10.1145/779359.779362. |
[8] |
A. Dhooge, W. Govaerts, Y. A. Kuznetsov, H. Meijer and B. Sautois,
New features of the software Matcont for bifurcation analysis of dynamical systems, Math. Comput. Model. Dyn. Syst., 14 (2008), 147-175.
doi: 10.1080/13873950701742754. |
[9] |
J. Drew, C. Johnson and D. Olesky,
Spectrally arbitrary patterns, Linear Algebra Appl., 308 (2000), 121-137.
doi: 10.1016/S0024-3795(00)00026-4. |
[10] |
D. G. Drubin and W. J. Nelson,
Origins of cell polarity, Cell, 84 (1996), 335-344.
doi: 10.1016/S0092-8674(00)81278-7. |
[11] |
A. J. Engler, S. Sen, H. L. Sweeney and D. E. Discher,
Matrix elasticity directs stem cell lineage specification, Cell, 126 (2006), 677-689.
doi: 10.1016/j.cell.2006.06.044. |
[12] |
P. Friedl and S. Alexander,
Cancer invasion and the microenvironment: Plasticity and reciprocity, Cell, 147 (2011), 992-1009.
doi: 10.1016/j.cell.2011.11.016. |
[13] |
C. Garnett, D. Olesky and P. van den Driessche,
A note on sign patterns of order 3 that require particular refined inertias, Linear Algebra Appl., 450 (2014), 293-300.
doi: 10.1016/j.laa.2014.03.007. |
[14] |
A. Goldbeter and D. E. Koshland,
An amplified sensitivity arising from covalent modification in biological systems, Proc. Nat. Acad. Sci., 78 (1981), 6840-6844.
doi: 10.1073/pnas.78.11.6840. |
[15] |
M. Graessl, J. Koch, A. Calderon, D. Kamps, S. Banerjee, T. Mazel, N. Schulze, J. K. Jungkurth, R. Patwardhan and D. Solouk,
An excitable Rho GTPase signaling network generates dynamic subcellular contraction patterns, JCB, 216 (2017), 4271-4285.
doi: 10.1083/jcb.201706052. |
[16] |
C. Guilluy, R. Garcia-Mata and K. Burridge,
Rho protein crosstalk: Another social network?, Trends in Cell Biology, 21 (2011), 718-726.
doi: 10.1016/j.tcb.2011.08.002. |
[17] |
R. G. Hodge and A. J. Ridley,
Regulating Rho GTPases and their regulators, Nature Reviews Molecular Cell Biology, 17 (2016), 496-510.
doi: 10.1038/nrm.2016.67. |
[18] |
W. R. Holmes, M. A. Mata and L. Edelstein-Keshet,
Local perturbation analysis: A computational tool for biophysical reaction-diffusion models, Biophysical Journal, 108 (2015), 230-236.
doi: 10.1016/j.bpj.2014.11.3457. |
[19] |
M. Jacquier, S. Kuriakose, A. Bhardwaj, Y. Zhang, A. Shrivastav, S. Portet and S. V. Shrivastav,
Investigation of novel regulation of N-myristoyltransferase by mammalian target of rapamycin in breast cancer cells, Scientific reports, 8 (2018), 1-11.
doi: 10.1038/s41598-018-30447-0. |
[20] |
D. W. Jordan and P. Smith, Nonlinear ordinary differential equations: An introduction to dynamical systems, 3$^rd$ edition, Oxford University Press, USA, 1999.
![]() ![]() |
[21] |
V. O. Juma, Data-Driven Mathematical Modelling and Simulation of Rho-Myosin Dynamics, PhD thesis, University of Sussex, 2019. |
[22] |
D. Kamps, J. Koch, V. O. Juma, E. Campillo-Funollet, M. Graessl, S. Banerjee, T. Mazel, X. Chen, Y.-W. Wu and S. Portet,
Optogenetic tuning reveals rho amplification-dependent dynamics of a cell contraction signal network, Cell Reports, 33 (2020), 108467.
doi: 10.1016/j.celrep.2020.108467. |
[23] |
E. J. Y. Kim, E. Korotkevich and T. Hiiragi,
Coordination of cell polarity, mechanics and fate in tissue self-organization, Trends in Cell Biology, 28 (2018), 541-550.
doi: 10.1016/j.tcb.2018.02.008. |
[24] |
I.-J. Kim, D. D. Olesky, B. L. Shader, P. van den Driessche, H. van der Holst and K. N. Vander Meulen,
Generating potentially nilpotent full sign patterns, Electron. J. Linear Algebra, 18 (2009), 162-175.
doi: 10.13001/1081-3810.1302. |
[25] |
R. Larter,
Sensitivity analysis of autonomous oscillators. separation of secular terms and determination of structural stability, J. Phys. Chem., 87 (1983), 3114-3121.
doi: 10.1021/j100239a032. |
[26] |
D. Lee, A. Koul, N. Lubna, S. A. McKenna and S. Portet,
Mathematical modelling of OAS2 activation by dsRNA and effects of dsRNA lengths, AIMS Math., 6 (2021), 5924-5941.
doi: 10.3934/math.2021351. |
[27] |
B. Lu and H. Yue,
Sensitivity analysis of oscillatory biological systems with a SVD-based algorithm, Systemics and Informatics World Network, 10 (2010), 85-92.
|
[28] |
Y. Lu and H. Yue,
Objective sensitivity analysis of biological oscillatory systems, IFAC Proceedings Volumes, 44 (2011), 10466-10471.
doi: 10.3182/20110828-6-IT-1002.02967. |
[29] |
A. F. Marée, A. Jilkine, A. Dawes, V. A. Grieneisen and L. Edelstein-Keshet,
Polarization and movement of keratocytes: A multiscale modelling approach, Bulletin of Mathematical Biology, 68 (2006), 1169-1211.
|
[30] |
MATLAB, 9.7.0.1190202 (R2019b), The MathWorks Inc., Natick, Massachusetts, 2018. |
[31] |
J. D. Murray, Mathematical Biology I: An Introduction, 3$^{rd}$ edition, Interdisciplinary Applied Mathematics, 17. Springer-Verlag, New York, 2002. |
[32] |
P. Nalbant, Y.-C. Chang, J. Birkenfeld, Z.-F. Chang and G. M. Bokoch,
Guanine nucleotide exchange factor-H1 regulates cell migration via localized activation of Rhoa at the leading edge, Molecular Biology of the Cell, 20 (2009), 3985-4129.
doi: 10.1091/mbc.e09-01-0041. |
[33] |
S. Portet,
Dynamics of in vitro intermediate filament length distributions, Journal of Theoretical Biology, 332 (2013), 20-29.
doi: 10.1016/j.jtbi.2013.04.004. |
[34] |
S. Portet, A. Madzvamuse, A. Chung, R. E. Leube and R. Windoffer,
Keratin dynamics: Modeling the interplay between turnover and transport, PloS One, 10 (2015), 1-29.
doi: 10.1371/journal.pone.0121090. |
[35] |
H. Rabitz and D. Edelson,
Numerical techniques for modelling and analysis of oscillating chemical reactions, Oscillations and Traveling Waves in Chemical Systems, (1985), 193-222.
|
[36] |
M. Raftopoulou and A. Hall,
Cell migration: Rho GTPases lead the way, Developmental Biology, 265 (2004), 23-32.
doi: 10.1016/j.ydbio.2003.06.003. |
[37] |
A. J. Ridley,
Rho GTPase signalling in cell migration, Current Opinion in Cell Biology, 36 (2015), 103-112.
doi: 10.1016/j.ceb.2015.08.005. |
[38] |
A. J. Ridley, M. A. Schwartz, K. Burridge, R. A. Firtel, M. H. Ginsberg, G. Borisy, J. T. Parsons and A. R. Horwitz,
Cell migration: Integrating signals from front to back, Science, 302 (2003), 1704-1709.
doi: 10.1126/science.1092053. |
[39] |
S. Saha, T. L. Nagy and O. D. Weiner,
Joining forces: Crosstalk between biochemical signalling and physical forces orchestrates cellular polarity and dynamics, Philosophical Transactions of the Royal Society B: Biological Sciences, 373 (2018), 20170145.
doi: 10.1098/rstb.2017.0145. |
[40] |
L. F. Shampine and M. W. Reichelt,
The MATLAB ODE suite, SIAM J. Sci. Comput., 18 (1997), 1-22.
doi: 10.1137/S1064827594276424. |
[41] |
C. M. Simon, E. M. Vaughan, W. M. Bement and L. Edelstein-Keshet,
Pattern formation of Rho GTPases in single cell wound healing, Molecular Biology of the Cell, 24 (2013), 421-432.
doi: 10.1091/mbc.e12-08-0634. |
[42] |
R. Tomovic and M. Vukobratovic, General Sensitivity Theory, vol. 1 of Mod. Analytic Comput. Methods Sci. Math., 35, New York, NY: North-Holland, 1972. |
[43] |
J. J. Tyson, K. C. Chen and B. Novak,
Sniffers, buzzers, toggles and blinkers: Dynamics of regulatory and signaling pathways in the cell, Current Opinion in Cell Biology, 15 (2003), 221-231.
doi: 10.1016/S0955-0674(03)00017-6. |
[44] |
J. J. Tyson, K. Chen and B. Novak,
Network dynamics and cell physiology, Nature Reviews Molecular Cell Biology, 2 (2001), 908-916.
doi: 10.1038/35103078. |
[45] |
J. J. Tyson and B. Novak,
Temporal organization of the cell cycle, Current Biology, 18 (2008), 759-768.
doi: 10.1016/j.cub.2008.07.001. |
[46] |
K. Wolf, M. Te Lindert, M. Krause, S. Alexander, J. Te Riet, A. L. Willis, R. M. Hoffman, C. G. Figdor, S. J. Weiss and P. Friedl,
Physical limits of cell migration: Control by ECM space and nuclear deformation and tuning by proteolysis and traction force, Journal of Cell Biology, 201 (2013), 1069-1084.
doi: 10.1083/jcb.201210152. |
[47] |
D. E. Zak, J. Stelling and F. J. Doyle,
Sensitivity analysis of oscillatory (bio) chemical systems, Computers & Chemical Engineering, 29 (2005), 663-673.
doi: 10.1016/j.compchemeng.2004.08.021. |








Parameter | Description | Base value |
R activation by G per unit time | 4 | |
Rate of R baseline activation | 0.6 | |
R baseline inhibition per unit time | 1 | |
R inhibition by M per unit time | 1 | |
Rate of G activation by R | 1 | |
Rate of G inhibition by M | 1 | |
M activation rate | 0.035 | |
M decay rate | 0.01 | |
M baseline recruitment rate | 0.001 | |
Michaelis-Menten constant for R activation | 1 | |
Michaelis-Menten constant for R self inhibition | 1 | |
Michaelis-Menten constant for M activation | 1 | |
Michaelis-Menten constant for G activation | 0.12 | |
Michaelis-Menten constant for G inhibition | 0.075 | |
R total concentration | 1 | |
M total concentration | 1 | |
G total concentration | variable |
Parameter | Description | Base value |
R activation by G per unit time | 4 | |
Rate of R baseline activation | 0.6 | |
R baseline inhibition per unit time | 1 | |
R inhibition by M per unit time | 1 | |
Rate of G activation by R | 1 | |
Rate of G inhibition by M | 1 | |
M activation rate | 0.035 | |
M decay rate | 0.01 | |
M baseline recruitment rate | 0.001 | |
Michaelis-Menten constant for R activation | 1 | |
Michaelis-Menten constant for R self inhibition | 1 | |
Michaelis-Menten constant for M activation | 1 | |
Michaelis-Menten constant for G activation | 0.12 | |
Michaelis-Menten constant for G inhibition | 0.075 | |
R total concentration | 1 | |
M total concentration | 1 | |
G total concentration | variable |
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