60
4 The Smoluchowski Model
Fig. 4.4 Mechanochemical coupling: The diffusion coefficient of the dynein along the microtubule and in solution are D ∗
dynein = 9 × 10 3 nm 2 /s, and D s
dynein ≈ 10 7 nm 2 /s respectively
k 12 = k 21 = 8, 400 s −1 . Details in Program 4.1
4.4 Program 4.1, Matlab Code
%Solution of the system of Fokker-Planck Equations with mechanochemical
%chemical coupling by the Crank-Nicholson scheme.
%V1(x)=(2A/pi)[sin(2pi*x/L)- 0.5sin(4pi*x/L) + (1/3)sin(6pi*x/L).
%V2(x)= 0.
%d21 = 2nd derivative of the potential at the state one.
%d22 = 2nd derivative of the potential at the state two.
%Intensity s0, Central Position x0, Standard deviation sigma,
%Thermal energy kBT, A=10kBT, (1 ATP 20kBT per molecule of 2 heads)
%Vo = A/kBT dimensionless Vo.
%L is the motor step per reaction cycle, 8nm.
%D∗ = 9x10 3 nm 2 /s dynein diffusion coefficient along the microtubule.
%Do 10 7 nm 2 /s dynein diffusion coefficient in solution.
%D = D ∗ /Do = 9x10 − 4 dimensionless diffusion coefficient.
%tau D = L 2 /Do = 6.4x10 − 6s.
%k12∗ = k21∗ = 84001/s transition rates.
%k12 = k21 = 5.376x10 − 2 dimensionless transitions rates.
%dt∗ = 7.1x10 − 7s from Wang et al. (2003).
%dt = dt ∗ /tau D = 0.111 dimensionless dt.