[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, et al., 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, et al., 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, et al., 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.
|