1,245
Views
1
CrossRef citations to date
0
Altmetric
Original Articles

Existence and uniqueness for a coupled PDE model for motor-induced microtubule organization

, , &
Pages 294-315 | Received 24 Apr 2016, Accepted 25 Feb 2017, Published online: 20 Apr 2017

References

  • I. Aranson and L. Tsimring, Pattern formation of microtubules and motors: Inelastic interaction of polar rods, Phys. Rev. 71 (2005), pp. 050901.
  • I. Aranson and L. Tsimring, Theory of self-assembly of microtubule and motors, Phys. Rev. E74 (2006), pp. 031915. 1–15.
  • A. Bressan, Hyperbolic Systems of Conservation Laws, Oxford University Press, Oxford, 2000.
  • L.C. Evans, Partial Differential Equations, AMS Press, Rhodes Island, 1998.
  • F. Golse, P.L. Lions, B. Perthame, and R. Sentis, Regularity of the moments of the solution of a transport equation, J. Funct. Anal. 76 (1988), pp. 110–125. doi: 10.1016/0022-1236(88)90051-1
  • T. Hillen, P. Hinow, and Z. Wang, Mathematical analysis of a kinetic model for cell movement in tissue networks, Discr. Contin. Dyn. Syst. Ser. B 14(3) (2010), pp. 1055–1080. doi: 10.3934/dcdsb.2010.14.1055
  • J. Howard, Mechanics of Motor Proteins and the Cytoskeleton, Sinauer Associates Inc., Sunderland, MA, 2001.
  • D. Humphrey, C. Duggan, D. Saha, D. Smith, and J. Ka, Active fluidization of polymer networks through molecular motors, Lett. Nat. 416 (2002), pp. 413–416. doi: 10.1038/416413a
  • Z. Jia, D. Karpeev, I. Aranson, and P. Bates, Simulation studies of self-organization of microtubules and molecular motors, Phys. Rev. E77 (2008), pp. 051905, 1–8.
  • N. Johnson and L. Kotz, Distributions in Statistics-Continuous Univariate Distributions, 2nd ed., John Wiley and Sons, Hoboken, 1970.
  • G. Karp, Cell and Molecular Biology, 1st ed., John Wiley and Sons, Inc., Hoboken, 1996.
  • J. Kim, Y. Park, B. Kahng, and H. Y. Lee, Self-organized patterns in mixtures of microtubules and motor proteins, J. Kor. Phys. Soc. 42(1) (2003), pp. 162–166.
  • M. Kirschner and K. Mitchison, Dynamic instability of microtubule growth, Nature 312 (1984), pp. 237–242. doi: 10.1038/312237a0
  • H.Y. Lee, Macroscopic equations for pattern formation in mixtures of microtubules and molecular motors, Phys. Rev. 64 (2001), pp. 056113, 1–8.
  • W. Luo, C.H. Yu, Z. Lieu, J. Allard, A. Mogilner, M. Sheetz, and A. Bershadsky, Analysis of the local organization and dynamics of cellular actin networks, J. Cell Biol. 202 (2013), pp. 1057–1073. doi: 10.1083/jcb.201210123
  • C. Miller, G. Ermentrout, and L. Davidson, Rotational model for actin filament alignment by myosin, J. Theor. Biol. 300 (2012), pp. 344–359. doi: 10.1016/j.jtbi.2012.01.036
  • K. Mitchison and M. Kirschner, Beyond self-assembly: From microtubules to morphogenesis, Cell 45 (1986), pp. 329–342. doi: 10.1016/0092-8674(86)90283-7
  • F. Nedelec and T. Surrey, Dynamics of microtubule aster formation by motor complexes, Phys. Scale Cell 4 (2001), pp. 841–847.
  • F. Nedelec, T. Surrey, A.C. Maggs, and S. Leibler, Self-organization of microtubules and motors, Nature 389 (1997), pp. 305–308. doi: 10.1038/38532
  • H. Othmer, S. Dunbar, and W. Alt, Models of dispersal in biological systems, J. Math. Biol. 26 (1988), pp. 263–298. doi: 10.1007/BF00277392
  • A. Pazy, Semigroups of Linear Operators and Applications to Partial Differential Equations, Springer-Verlag, New York, 1983.
  • A.C. Reymann, J.L. Martiel, T. Cambier, L. Blanchoin, R. Boujemaa-Paterski, and M. Théry, Nucleation geometry governs ordered actin network structures, Nat. Mater. 9 (2010), pp. 827–832. doi: 10.1038/nmat2855
  • J. Robinson, Infinite-Dimensional Dynamical Systems, 1st ed., Ordinary Differential Equations, Cambridge University Press, Cambridge, 2001.
  • V. Rodionov, E. Nadezhdina, and G. Borisy, Centrosomal control of microtubule dynamics, Proc. Natl. Acad. Sci. 96 (1999), pp. 115–120. doi: 10.1073/pnas.96.1.115
  • D. Smith, F. Ziebert, D. Humphrey, C. Duggan, M. Steinbeck, W. Zimmermann, and J. Ka, Molecular motor-induced instabilities and cross linkers determine biopolymer organization, Biophys. J. 93 (2007), pp. 4445–4452. doi: 10.1529/biophysj.106.095919
  • T. Surrey, F. Nedelec, S. Leibler, and E. Karsenti, Physical properties determining self-organization of motors and microtubules, Science 292 (2001), pp. 1167–1171. doi: 10.1126/science.1059758
  • L. Tao, A. Mogliner, G. Civelekoglu-Scholey, R. Wollman, J. Evans, H. Stahlberg, and J. Scholey, A homotetrameric kinesin-5, klp61f, bundles microtubules and antagonizes Ncd in motility assays, Curr. Biol. 16 (2006), pp. 2293–2302. doi: 10.1016/j.cub.2006.09.064
  • M. Taylor, Partial Differential Equations 3, Springer-Verlag, New York, 1996.
  • R. Vale, F. Malik, and D. Brown, Directional instability of microtubule transport in the presence of kinesin and dynein, two opposite polarity motor proteins, J. Cell Biol. 119 (1992), pp. 1589–1596. doi: 10.1083/jcb.119.6.1589
  • R.H. Wade, On and around microtubules: an overview, Mol. Biotechnol. 43 (2009), pp. 177–191. doi: 10.1007/s12033-009-9193-5
  • C.M. Waterman-Storer and E.D. Salmon, Microtubule dynamics: treadmilling comes around again, Curr. Biol. 7 (1997), pp. 369–372. doi: 10.1016/S0960-9822(06)00177-1
  • C.M. Waterman-Storer and E.D. Salmon, Microtubules: strange polymers inside the cell, Bioelectro-Chem. Bioenerget. 48 (1999), pp. 285–295. doi: 10.1016/S0302-4598(99)00011-2
  • D. White, Microtubule organization in the presence of motor proteins. Ph.D. thesis, University of Alberta, 2013.
  • D. White, G. de Vries, and A. Dawes, Microtubule patterning in the presence of stationary motor distributions, Bull. Math. Biol. 76(8) (2014), pp. 1917–1940. doi: 10.1007/s11538-014-9991-1
  • D. White, G. de Vries, J. Martin, and A. Dawes, Microtubule patterning in the presence of moving motors, J. Theor. Biol. 382 (2015), pp. 81–90. doi: 10.1016/j.jtbi.2015.06.040