Numerical Simulations of Multiple Arms Star Polymer Translocation in the Presence of Constraints
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Date
2020-11-11
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Addis Ababa University
Abstract
Star polymers are branched macromolecules that each f-linear polymeric arms emerging
radially from or chemically connected to the branching point, and which can itself be
polymeric. Using an e_cient algorithm of Monte Carlo (MC) and Langevin Dynamics
(LD) simulations, we study the dynamics of star polymers translocation in the presence
of constraints. In this work, star polymers are modeled by a coarse-grained approach,
that is, a bead-spring model in which polymers are treated at the monomer level rather
than at the atomic level. By carrying out extensive simulation in terms of di_erent parameters
such as star polymer functionality, the total mass of the chain, the magnitude of
the pulling force, and dimensions of the constraints, we provide an in-depth description
of the translocation process. Our simulations were done by using the molecular dynamics
package ESPResSo, an extensible simulation package for research on soft matter.
In the _rst part of the dissertation, we carried out a two-dimensional (2D) MC simulation
of three and four arms star polymers. We have considered two di_erent cases:
one is the free di_usion of star polymers without using constraints, and the other is the
unforced translocation of the polymer through a nanopore where the common point is
initially located at the center of the pore. These tasks are done with computer simulation
using the bond uctuation algorithm. In the _rst case, we determine both the radius of
gyration and the self-di_usion coe_cient. The mean radius of gyration exhibits a power
scaling dependence on the total number of monomers, N, and functionality, where the
Abstract
exponent is found to be nearly 0:75. We also _nd that the self-di_usion coe_cient, D,
displays a scaling relation in terms of N as D _ N1, corresponding to the Rouse-type
model. As a second case, we analyze the kinetics of star-branched polymers translocation
in the absence of a driving force, focusing on the inuence of N upon the translocation
time, _ . Our simulation results satisfy the scaling law _ _ N_ with the scaling exponent
_ = 1 + 2_, where _ _ _2D = 0:75 is the Flory exponent in 2D.
In the second part of the dissertation, the unforced translocation of star polymers
through a nanopore has been studied using a three-dimensional (3D) LD simulation, in
which case, the central bead is initially placed just inside the pore. Star polymers of
various functionalities are considered with the total mass of the chain kept constant. In
the absence of a nanopore, the gyration radius of star polymers in terms of f is evaluated.
We observe that the gyration radius, Rg, decreases systematically as the functionality
increases. Our results also con_rm the scaling law Rgf1=2 _ (Nf1=2)_, where the Flory
scaling exponent is _ _ _3D = 0:6 in 3D. Here the results of the average exit time distributions
display narrow, highly peaked, and symmetric pro_les for smaller f; whereas, the
distributions become wider and asymmetric with a long tail when f increases. Moreover,
the impact of both the system temperature and coe_cient of friction on the translocation
dynamics is presented.
Besides, the dynamics of forced translocation of star-shaped polymers into a circular
nano-scaled pore is investigated via a 3D Langevin Dynamics approach. For forced
translocation, the branched-chain is initially placed in an open volume, and also the end
monomer of the leading arm is located inside a nanopore. The magnitude of a pulling
force, F, is applied directly at the end of the chain, which considerably a_ects the process
of translocation. Such a single-force setup mimics typical experimental situations in a
new sequencing technique based on a combination of magnetic and optical tweezers for
controlling the DNA motion. The e_ect of star's functionality upon the translocation time
Abstract
with constant molecular weight has been investigated for a given nanopore diameter. We
reveal that the dependence of mean exit time on the number of arms is non-monotonic.
The minimum mean escape time is also obtained at f = 5. Further, we explore the scaling
predictions of the polymer mass and the pulling force for various channel lengths, L, with
L=N < 1. In the limit of a strong driving force, the escape time illustrates a power-law
behavior as a function of N. In this regime, the scaling exponent for _ _ N_ is _ = 2.
Our results also verify that the exit time decays with the pulling force as _ _ F1.
Furthermore, a 3D Langevin Dynamics computer simulation is used to investigate
the dynamics of star polymer translocation out of a con_ned cylindrical cavity, where
the cylinder is connected to the wall with a circular nanopore along the tube axis. The
translocation is performed by applying an external pulling force that is exerted only on
the _rst monomer of the leading arm. In the present study, we have considered star
polymers of di_erent masses and functionalities. In this context, it is quite interesting to
understand the role of the polymer's functionality with constant mass but varying functionality.
We _nd that the exit time _rst decreases with f until a critical functionality
fc, and then increases with f. We have also found that the translocation dynamics are
signi_cantly a_ected by the pore radius. For larger pores, the translocation time decreases
as f increases, while for smaller pores, the exit time shows non-monotonic features with
a minimum value closer to fc. On the other side, our results display a scaling behavior
_ _ N2 under a strong pulling force, but _ _ F1 for a given N. Besides, we examine the
variations of _ on the tube dimensions, as well as the aspect ratio, a, de_ned to be the
ratio of the tube length to cavity diameter. These outcomes do not con_rm the scaling
law dependence in the regime of a strong driving force.
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Keywords
Numerical, Simulations, Multiple Arms Star Polymer, Translocation, Presence of Constraints