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36 3 Self-organization and cooperativity of weakly coupled molecular motors
V1/V1(0)
1
0.8
0.6
0.4
0.2
0
0 0.2 0.4 0.6 0.8 1
F/Fs
Fig. 3.8. Velocity-force curves for the mean field calculation (solid line) (Eq. 3.22), the corresponding
simulation with noise turned off in the U1 state (solid symbols), and simulation
with noise in both states (empty symbols). The parameters used are: τ = 0.05 and D = 0.25
(back and circles); τ = 0.05 and D = 0.025 (red and squares); τ = 0.175 and D = 0.25 (blue
and diamonds); τ = 0.175 and D = 0.025 (green and triangles). Both velocities and forces are
normalized to the analytical zero force velocity and the stall force (see text).
3.2.3 Hard-core repulsion
Significant deviations from mean field are expected generally for shortranged
repulsive interactions (Campas et al., 2006) and for small or moderate
noise strength in intermediate force range. In our model, we expect correlations
between motors to enhance the motor performance in general as in the
rigidly bound motors (see Fig. 3.5). However, not all the motor configurations
in short-range repulsive interactions contribute to increase the velocity with
respect to mean field, Fig. 3.9.
We will study the case of a hard-core potential between motors, modeled
by a truncated Lennard-Jones potential (see Fig. 3.3),
W(r)= 4ε
σ 6 σ 12
−
r6 r12
r ≤ 2 1/6 σ
(3.24)
ε r > 2 1/6 σ.
We analyze the dependence of the deviation from mean field with respect to
(i) β, the dimensionless parameter which is the ratio of the potential period
and the diffusive displacement in the state U2. Since the period of the potential
is fixed (ℓ ∼ 8 nm), varying β stands for varying noise intensity, Fig. 3.10. (ii)
the hard-core parameter σ, which represents effectively the size of the motor