Mathematical modeling of microtubule dynamic instability: new insight into the link between gtp-hydrolysis and microtubule aging
ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2433-2456.

Microtubules (MTs) are protein polymers that exhibit a unique type of behavior referred to as dynamic instability. That is, they undergo periods of growth (through the addition of GTP-tubulin) and shortening (through the subtraction of GDP-tubulin). Shortening events are very fast, where this transition is referred to as a catastrophe. There are many processes that regulate MT dynamic instability, however, recent experiments show that MT dynamics may be highly regulated by a MTs age, where young MTs are less likely to undergo shortening events than older ones. In this paper, we develop a novel modeling approach to describe how the age of a MT affects its dynamic properties. In particular, we extend on a previously developed model that describes MT dynamics, by proposing a new concept for GTP-tubulin hydrolysis (the process by which newly incorporated GTP-tubulin is hydrolyzed to lower energy GDP-tubulin). In particular, we assume that hydrolysis is mainly vectorial, age-dependent and delayed according to the GTP-tubulin incorporation into the MT. Through numerical simulation, we are able to show how MT age affects certain properties that define MT dynamics. For example, simulations illustrate how the aging process leads to an increase in the rate of GTP-tubulin hydrolysis for older MTs, as well as increases in catastrophe frequency. Also, since it has been found that MT dynamic instability is affected by chemotherapy microtubule-targeting agents (MTAs), we highlight the fact that our model can be used to investigate the action of MTAs on MT dynamics by varying certain model parameters.

Reçu le :
Accepté le :
DOI : 10.1051/m2an/2017025
Classification : 92C50, 35Q80, 74S10
Mots-clés : Microtubules, Dynamic Instability, Microtubule Aging, Population Dynamics
Barlukova, Ayuna 1 ; White, Diana 1 ; Henry, Gérard 1 ; Honoré, Stéphane 1 ; Hubert, Florence 1

1
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     author = {Barlukova, Ayuna and White, Diana and Henry, G\'erard and Honor\'e, St\'ephane and Hubert, Florence},
     title = {Mathematical modeling of microtubule dynamic instability: new insight into the link between gtp-hydrolysis and microtubule aging},
     journal = {ESAIM: Mathematical Modelling and Numerical Analysis },
     pages = {2433--2456},
     publisher = {EDP-Sciences},
     volume = {52},
     number = {6},
     year = {2018},
     doi = {10.1051/m2an/2017025},
     zbl = {1415.92078},
     mrnumber = {3909806},
     language = {en},
     url = {http://archive.numdam.org/articles/10.1051/m2an/2017025/}
}
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Barlukova, Ayuna; White, Diana; Henry, Gérard; Honoré, Stéphane; Hubert, Florence. Mathematical modeling of microtubule dynamic instability: new insight into the link between gtp-hydrolysis and microtubule aging. ESAIM: Mathematical Modelling and Numerical Analysis , Tome 52 (2018) no. 6, pp. 2433-2456. doi : 10.1051/m2an/2017025. http://archive.numdam.org/articles/10.1051/m2an/2017025/

A. Akhmanova and M. Steinmetz, Microtubule end binding: Ebs sense the guanine nucleotide state. Curr. Biol. 21 (2011) R283–5. | DOI

T. Antal, P. Krapivsky, S. Redner, M. Mailman, B. Chakraborty, Dynamics of an idealized model of microtubule growth and catastrophe. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 76 (2007) 907. | DOI

I. Arnal, R. Wade, How does taxol stabilize microtubules?. Curr. Biol. 5 (1995) 900–908. | DOI

H. Bowne-Anderson, M. Zanic, M. Kauer, J. Howard, Microtubule dynamic instability: a new model with coupled gtp hydrolysis and multistep catastrophe. Bioessays 35 (2013) 579. | DOI

G. Brouhard, D. Sept, Microtubules: sizing up the gtp cap. Curr. Biol. 22 (2012) R802–3. | DOI

G. Buxton, S. Siedlak, G. Perry, S. Ma, Mathematical modeling of microtubule dynamics: insights into physiology and disease. Prog. Neurobiol. 92 (2010) 478–483. | DOI

Y. Chen, T. Hill, Monte Carlo study of the GTP cap in a five-start helix model of a microtubule. Proc. Natl. Acad. Sci. USA 82 (1985) 1131–1135. | DOI

C. Coombes, A. Yamamoto, M. Kenzie, D. Odde, M. Gardner, Evolving tip structures can explain age-dependent microtubule catastrophe. Curr. Biol. 23 (2013) 1342–1348. | DOI

A. Desai, T. Mitchison, Microtubule polymerization dynamics. Annu. Rev. Cell. Dev. Biol. 13 (1997) 83–117. | DOI

J. Daz, J. Andreu, J. Jiménez-Barbero, The Interaction of Microtubules with Stabilizers Characterized at Biochemical and Structural Levels . In Vol. 286 of Tubulin-Binding Agents (2008).

M. Dogterom, S. Leibler, Physical aspects of the growth and regulation of microtubule structures. Phys. Rev. Lett. 70 (1993) 1347–1350. | DOI

H. Flyvbjerg, T. Holy, S. Leibler, Stochastic dynamics of microtubules: a model for caps and catastrophes. Phys. Rev. Lett. 73 (1994) 2372–2375. | DOI

N. Galjart, Plus-end-tracking proteins and their review interactions at microtubule ends. Cur. Biol. 20 (2010) R528–R537. | DOI

M. Gardner, M. Zanic, C. Gell, V. Bormuth, J. Howard, Depolymerizing kinesins kip3 and mcak shape cellular microtubule architecture by differential control of catastrophe. cell 147 (2011) 1092–1103. | DOI

F. Hallett, Rapid estimation of length distributions of microtubule preparations by quasi-elastic light scattering. Biopolymers 24 (1985) 2403–2415. | DOI

P. Hinow, V. Rezania, M. Lopus, M. Jordan, J. Tuszyn'Ski, Modeling the effects of drug binding on the dynamic instability of microtubules. Phys. Biol. 8 (2011) 056004. | DOI

P. Hinow, V. Rezania, J. Tuszyn'Ski, Continuous model for microtubule dynamics with catastrophe, rescue, and nucleation processes. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 80 (2009) 031904. | DOI

S. Honoré, D. Braguer, Investigating microtubule dynamic instability using microtubule-targeting agents. Methods Mol. Biol. 777 (2011) 245–260. | DOI

S. Honoré, E. Pasquier, D. Braguer, Understanding microtubule dynamics for improved cancer therapy. Cell. Mol. Life Sci. 62 (2005) 3039–3056. | DOI

A. Janulevicius, J. Van Pelt and Van A. Ooyen, Compartment volume influences microtubule dynamic instability: a model study. Biophys. J. 90 (2006) 788–98. | DOI

V. Jemseena, M. Gopalakrishnan, Effects of aging in catastrophe on the steady state and dynamics of a microtubule population. Phys. Rev. E Stat. Nonlin. Soft. Matter Phys. 91 (2015) 052704. | DOI

X. Ji, X. Feng, Mechanochemical modeling of dynamic microtubule growth involving sheet-to-tube transition. PLoS One 6 (2011) e29049. | DOI

M. Le Grand, A. Rovini, V. Bourgarel-Rey, S. Honoré, S. Bastonero, D. Braguer, M. Carre, Ros-mediated eb1 phosphorylation through akt/gsk3β pathway: implication in cancer cell response to microtubule-targeting agents. Oncotarget 5 (2014) 3408–3423. | DOI

H. Lodish, A. Berk, S.L. Zipursky, P. Matsudaira, D. Baltimore, J. Darnell, Molecular cell biology, 4th edn. W.H. Freeman and Company, New York (2000).

Q. Lu, R. Luduena, In vitro analysis of microtubule assembly of isotypically pure tubulin dimers. intrinsic differences in the assembly properties of alpha beta ii, alpha beta iii, and alpha beta iv tubulin dimers in the absence of microtubule-associated proteins. J. Biol. Chem. 269 (1994) 2041–2047. | DOI

S. Martin, M. Schilstra, P. Bayley, Dynamic instability of microtubules: Monte carlo simulation and application to different types of microtubule lattice. Biophys. J. 65 (1993) 578–596. | DOI

S. Maurer, F. Fourniol, G. Bohner, C. Moores, T. Surrey, Ebs recognize a nucleotide-dependent structural cap at growing microtubule ends. Cell 149 (2012) 371–382. | DOI

M. Mirigian, K. Mukherejee, S.L. Bane, D.L. Sackett, Measurement of In vitro Microtubule polymerization by turbidity and fluorescence. Meth. Cell. Biol. 115 (2013) 215–228. | DOI

T. Mitchison, M. Kirschner, Dynamic instability of microtubule growth. Nature 312 (1984) 237–242. | DOI

R. Mohan, E. Katrukha, H. Doodhi, I. Smal, E. Meijering, L. Kapitein, M. Steinmetz, A. Akhmanova, End-binding proteins sensitize microtubules to the action of microtubule-targeting agents. Proc. Natl. Acad. Sci. USA 110 (2013) 8900–8905. | DOI

S. Montenegro Gouveia, K. Leslie, L. Kapitein, R. Buey, I. Grigoriev, M. Wagenbach, I. Smal, E. Meijering, C. Hoogenraad, L. Wordeman, M. Steinmetz, A. Akhmanova, In vitro reconstitution of the functional interplay between mcak and eb3 at microtubule plus ends. Curr. Biol. 20 (2010) 1717–1722. | DOI

N. Müller, J. Kierfeld, Effects of microtubule mechanics on hydrolysis and catastrophes. Phys. Biol. 11 (2014) 046001. | DOI

R. Padinhateeri, A. Kolomeisky, D. Lacoste, Random hydrolysis controls the dynamic instability of microtubules. Biophys. J. 102 (2012) 1274–1283. | DOI

A. Pagano, S. Honoré, R. Mohan, R. Berges, A. Akhmanova, D. Braguer, Epothilone b inhibits migration of glioblastoma cells by inducing microtubule catastrophes and affecting eb1 accumulation at microtubule plus ends. Biochem. Pharmacol. 84 (2012) 432–443. | DOI

D. Seetapun, B. Castle, A. Mcintyre, P. Tran, D. Odde, Estimating the microtubule gtp cap size in vivo. Curr. Biol. 22 (2012) 1681–1687. | DOI

V. Vanburen, L. Cassimeris, D. Odde, Mechanochemical model of microtubule structure and self-assembly kinetics. Biophys. J. 89 (2005) 2911–2926. | DOI

R. Walker, E. O’Brien, N. Pryer, M. Soboeiro, W. Voter, Erickson, H.E. Salmon, Dynamic instability of individual microtubules analyzed by video light microscopy: Rate constants and transition frequencies. J. Cell. Biol. 107 (1988) 1437–1448. | DOI

P. Zakharov, N. Gudimchuk, V. Voevodin, A. Tikhonravov, F. Ataullakhanov, E. Grishchuk, Molecular and mechanical causes of microtubule catastrophe and aging. Biophys. J. 109 (2015) 2574–2591. | DOI

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