- The dynamics of polymer chains in active fluids containing self-propelling particles are investigated through simulations. - At the optimal chain stiffness, where the elastic force is balanced with the self-propelling force, the diffusivity of the polymer chain shows a maximum. - The barrier crossing time of the polymer chain also exhibits a non-monotonic behavior with bending stiffness, which could be useful for polymer separation.

1. Dynamics of polymer chains in active fluids
Jaeoh Shin andVasily Zaburdaev
Max-Planck-Institute for the Physics of Complex Systems, Dresden
— DPG Spring Meeting Dresden, March 2017 —

2. Active fluids
• Fluids that contain self-propelling ‘particles’, such as motile
microorganisms and artificial swimmers
• Inherently out of equilibrium; exhibit peculiar phenomena
Spontaneous rotation of micron-sized gear
R. D. Leonardo et al. PNAS (2010)

3. Polymer dynamics in active fluids
• Relevant to many biological systems; biopolymer dynamics in the
cell
• The dynamics can be very different from that in equilibrium
3
Microtubule, myosin, C. Brangwynne et al. PRL (2007)

4. Polymer chains in the presence of Active particles
4
Us =
k
2
nX
i=2
(|ri ri 1| l0)2
Ub =

2
n 1X
i=2
✓2
i ,
UWCA(r) = 4✏[( /r)12
( /r)6
] + ✏
0
10
20
30
40
-10 0 10 20 30
Bead-spring model of polymer
U = Us + Ub + UWCA
d~ri
dt
= µrU +
p
2D~⇠i(t)
h~⇠i(t) · ~⇠i0 (t0
)i = 2 i,i0 (t t0
)

5. Active Brownian particle
⌧ = 1/Dr
5
d i(t)
dt
=
p
2Dr
~⇠i(t)
ˆn
d~ri
dt
= µrU + vaˆn( i, t) +
p
2D~⇠i(t)
U = UWCA
l = va⌧
101
102
10
3
10
4
105
100
101
102
103
MSD(t)
Time, t
t2
t1
Active
Passive

6. Simulation - Polymer chain with ABPs
n=32

7. Diffusive motion of Polymer centre of mass
7
At short times, the polymer chain moves super-diffusively.
Diffusivity at long times shows a non-monotonous behaviour as function
of the stiffness.
1
1.2
1.4
1.6
1.8
100
101
102
103
104
α(t)
Time, t
Scaling exponent of MSD
Mean squared displacement
n=32

8. ABPs accumulate in concave region of the polymer
flexible stiff
semiflexible

9. Chain conformation in Fourier modes
0
0.05
0.1
0.15
0.2
0.25
-20 -15 -10 -5 0 5 10 15 20PDF(a1)
Amplitude, a1
κ=30
90
360
1200
inactive, κ=30
b
0.2
0.3
0.4
0.5
PDF(a2)
κ=30
90
360
1200
inactive, κ=30
b
F. Gittes et al., J. Cell Biol. (1993)
⇥a1
⇥a2
...
- The distribution is much wider in the presence of ABPs.
- At the optimal stiffness, PDF of 1st mode shows a bimodal distribution,
indicating that the chain has preferentially bent conformations.

10. Amplitude of the Fourier modes
10
The fluctuations increase significantly in the presence of ABPs.
ha2
mi =
kBT

✓
L
m⇡
◆2
⇠ 1/m2
,
In equilibrium,
0.01
0.1
1
10
1 10
Variance,<am
2
>
Fourier modes, m
m-2
=90, Active
=90, equilibrium
Theory

11. Application: Polymer separation
11
Barrier crossing times also show a non-monotonous behaviour.
This finding can be employed for the polymer separation by its bending stiffness.
1000
1500
2000
2500
3000
3500
0 200 400 600 800 1000 1200
Crossingtime
Bending stiffness, κ
We consider barrier crossing of polymer chain

12. Summary
• We consider the dynamics of polymer chains in the presence of ABPs.
• The diffusive motion of the chain is dependent on the chain stiffness. At
the optimal chain stiffness, where the elastic force of the chain is
balanced with the self-propelling force, the diffusivity shows a maximum.
• The barrier crossing time of polymer also shows a non-monotonous
behaviour. This finding might be useful for polymer separation.
12

13. Acknowledgements
• A. G. Cherstvy (Potsdam)
• W. K. Kim (Berlin)

15. Velocity Autocorrelation function of Polymer COM
15
At short times, ACF decades as a power-law, with
—>
At longer times, it decays exponentially with the correlation time .
ACF(t) ⇠ t
MSD(t) ⇠ t2
10-3
10-2
10-1
100
100
101
102
Time, t
ACF(t)
t
-
exp(-t/⇥COM)
0.6 . . 0.9
⌧(= 1/Dr)
Nonthermal noise
{ , ⌧COM}
⌧COM
?

16. MSD: chain length dependence
10
-1
10
0
10
1
10
2
10
3
10
4
10
0
10
1
10
2
10
3
10
4
MSDx(t)
Time, t
24
32
40
48
56
0.5
1
1.5
0 20 40 60
D
n
1
1.2
1.4
1.6
1.8
10
0
10
1
10
2
10
3
10
4
α(t)
Time, t
10
20
30
0 20 40 60
τCOM
n
(B)
10
-1
10
0
10
1
10
2
10
3
10
4
10
0
10
1
10
2
10
3
10
4
MSDx(t)
Time, t
n=16
24
32
40
48
56
0.5
1
1.5
0 20 40 60
D
n
1
1.2
1.4
1.6
1.8
10
0
10
1
10
2
10
3
10
4
α(t)
Time, t
10
20
30
0 20 40 60
τCOM
n
(A)
(B)

17. Polymer motion
kappa=30, 360,1200

18. Passive particles vs. Active particles
Passive particles Active particles
P(~r) ⇠ exp(U(~r)/(kBT)) P(~r) =?