Doctoral Degrees (Physics)

Permanent URI for this collection

https://scholar.sun.ac.za/handle/10019.1/3640

Browse

Browsing Doctoral Degrees (Physics) by Subject "Active network formation"

Now showing 1 - 1 of 1
  • Thumbnail Image
    Item
    Field theory of reversible and active network formation
    (Stellenbosch : Stellenbosch University, 2017-12) Pachong, Stanard Mebwe; Müller-Nedebock, Kristian; Stellenbosch University. Faculty of Science. Dept. of Physics.
    ENGLISH ABSTRACT : This dissertation presents a statistical physics analysis of randomly cross-linked polymer networks with both reversible and permanent cross-links. The theory used here is adapted from the field theory elaborated by Edwards (1988) for the permanent network and later used for a reversibly associated network by Fantoni and Müller-Nedebock (2011). The field theory automatically ensures cross linking constraints, includes the reversible link and enables the computation of the average numbers and fluctuations of cross-links in the network. The average density of cross-linkers is calculated. This contains statistical information about the behaviour of individual polymer chains and cross-linkers inside the network. For active cross-linkers moving in a preferential direction along filaments we show that the polarity of the polymer chains influences the elastic properties of the network. The response of the network under a small deformation is studied. We make use of the replica trick to calculate the free energy over the possible disorder in the system. We show that, when adding reversible cross linkers into a permanent polymer network, these make the network become softer. We study a special case of such networks to understand the biological network called "the contractile ring". We implement the Random Phase Approximation (RPA) along with a one dimensional Langevin dynamics simulation to investigate the stability of the ring. We calculate the explicit expression for the density-density correlation function which can be tested experimentally. Results show that the motor proteins pull and push the chains leading to a constant overtaking of the chains within the ring. It turns out that the energy generated by the network to maintain the chains connected is the one responsible for the contractile behaviour of the ring. Specifically, these observations only hold in the case of a finite periodic ring. The present consideration suggests that even in case of low ATP, the ring still contracts. The simulation and the analytical results confirm that the force generated by the motor protein sustains the polarisation current and therefore maintains the stability of the ring. On the other hand, the force generated to maintain the integrity of the ring render the ring unstable and interrupts the current flowing through it. The change of phase of the chain distribution within the ring therefore occurs due to the interplay of the two forces mentioned above.