stochastic microtubule dynamics revisited
Post on 31-Dec-2015
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Stochastic Microtubule Dynamics Revisited
Richard Yamada
Yoichiro Mori
Maya Mincheva
(Alex Mogilner and Baochi Nguyen)
What are Microtubules?• Protein structures with a diameter of
approximately 24 nm, and with a length up to several millimeters in some cells
• Microtubules consist of polymers of tubulin, 13 protofilaments of which which are formed into a hollow cylinder
• Microtubules have plus and minus ends• Highly dynamic - capable of polymerizing and
depolymerizing within a time scale of seconds to minutes
Why Are Microtubules Important?
• Microtubules are involved in many fundamental biological functions/processes, among them:
1) segregating the chromosomes and to orient the plane of cleavage during cell division
2) organize cytoplasm by positioning the organelles
3) serve as the principal structural element of flagella and cilia
Kinetic Equations
• a - Polymerization rate
• b - Induced transition rate
• c - Spontaneous transition rate
€
dPkdt= aPk−1 + bPk+1 − (a+ b)Pk − ckPk + cPj
j= k+1
∞
∑
Integro-Differential Equations(Continuum Limit)
• The ensemble density of microtubules with caps of lengths x at time t is governed by a integro-differential equation:
€
∂t p = −v∂x p+ D(∂x )2 p− rxp+ r dyp(y, t)
x
∞
∫
v = vg − vAB
Numerical Methods
2 ways to simulate Kinetic Equations:• Trapezoidal rule for integration of ODEs
(Deterministic)• Gillespie Method (Stochastic)
all events (hydrolysis,induced,spontaneous) are possible but are weighted by rate constants along with a random number
( e.g. -log(random)/(rate constant))
Summary• No use of continuum limit equations -
instead our approach started from kinetic equations, using 2 numerical methods to investigate dynamic instability
• Incorporation of dilution washout effects
• Results are consistent with previous published results
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