Several independent observations have suggested that catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent in vitro {\it  observations by Gardner et al.[  Cell {\bf147}, 1092 (2011)] showed that microtubule catastrophe takes place via multiple steps , and the frequency increases with the "age " of the filament. Here, we investigate, via numerical simulations and mathematical calculations, some of the consequences of age-dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: (a) exponential growth, but saturating asymptotically and (b) purely linear growth. The boundary demarcating the steady state and non-steady state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to non-exponential length distributions in steady state , as well as oscillations in microtubule length . The oscillations are reduced and eventually eliminated by increasing the frequency of rescue events. Our study shows that age-dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.
Several independent observations have suggested that catastrophe transition in microtubules is not a first-order process, as is usually assumed. Recent {\it in vitro observations by Gardner et al.[ M. K. Gardner et al., Cell {\bf147}, 1092 (2011)] showed that microtubule catastrophe takes place via multiple steps and the frequency increases with the age of the filament. Here, we investigate, via numerical simulations and mathematical calculations, some of the consequences of age dependence of catastrophe on the dynamics of microtubules as a function of the aging rate, for two different models of aging: exponential growth, but saturating asymptotically and purely linear growth. The boundary demarcating the steady state and non-steady state regimes in the dynamics is derived analytically in both cases. Numerical simulations, supported by analytical calculations in the linear model, show that aging leads to non-exponential length distributions in steady state . More importantly, oscillations ensue in microtubule length and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced by increasing the frequency of rescue events. Our study shows that age dependence of catastrophe could function as an intrinsic mechanism to generate oscillatory dynamics in a microtubule population, distinct from hitherto identified ones.
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in vitro
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in vitro
A
M. K. Gardner et al.,
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,
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"age "
age
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age-dependence
age dependence
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(a)
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(b)
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, as well as oscillations
. More importantly, oscillations ensue
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. The oscillations are reduced and eventually eliminated
and velocity. The regularity of oscillations, as characterized by the negative dip in the autocorrelation function, is reduced
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age-dependence
age dependence