Field theory of reversible and active network formation

Pachong, Stanard Mebwe (2017-12)

Thesis (PhD)--Stellenbosch University, 2017.

Thesis

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.

AFRIKAANSE OPSOMMING : Hierdie proefskrif is 'n aanbieding van die statistiese fisika van 'n polimeernetwerk met lukraak geplaasde kruisverbindingspunte, wat beide permanent en tydelik is. Die teorie waarvan hier gebruik gemaak word is 'n aanpassing van Edwards (1988) se veldeteoretiese formulering vir die permanente netwerk en wat later deur Fantoni en Müller-Nedebock (2011) aangewend is vir omkeerbaar geassosieerde netwerke. Die veldeteorie verseker outomaties dat die verbindings bevredig word, en sluit nie-permanente knooppunte in en laat ook die berekening van gemiddelde getalle en fluktuasies van knooppunte in die netwerk toe. Die gemiddelde digtheid van knooppunte word bereken. Dit bevat statistiese inligting omtrent die gedrag van polimeerkettings en knooppunte binnekant die netwerk. Vir aktiewe knooppunte, wat in 'n voorkeurrigting op filamente beweeg, toon ons aan dat die polariteit van die polimeerkettings die elastiese eienskappe van die netwerk beïnvloed. Die gedrag van die netwerk onder klein vervorming word ondersoek. Ons maak gebruik van die replikametode om die vrye-energie te bereken, wat gemiddel word oor die wanorde in die stelsel. Ons toon aan dat die byvoeging van nie-permanente knooppunte in 'n permanente netwerk daartoe lei dat die netwerk sagter word. Ons ondersoek die spesiale geval van sulke netwerke om die biologiese netwerk, die sogenaamde kontraktiele ring, te verstaan. Ons maak gebruik van 'n kwadratiese kollektiewe koördinaatransformasie ("RPA") tesame met eendimensionele Langevin-dinamika simulasies om die stabiliteit van die ring te ondersoek. Ons bereken eksplisiet die digtheid-digtheid korrelasiefunksie wat eksperimenteel getoets kan word. Die resultate dui daarop dat die masjiene die filamente trek en stoot sodat filamente die hele tyd vir mekaar verbysteek. Die energie wat deur die netwerk gestoor word, is verantwoordelik vir die saamtrekking in die ring. Spesifiek geld hierdie gevolgtrekkings vir 'n eindige ring, wat periodies verloop. Die ondersoek dui aan dat, selfs in die geval van lae ATP-konsentrasies, die ring steeds sal saamtrek. Beide simulasies en analitiese resultate bevestig dat die krag wat deur die proteïenmasjientjies gegenereer word, die polarisasiestroom in die ring onderhou en dus ook vir die stabiliteit van die ring verantwoordelik is. Verder is die krag, wat die samehangendheid van die ring produseer, verantwoordelik daarvoor dat in sommige gevalle die ring onstabiel raak en die polarisasiestroom daarin onderbreek word. Die faseoorgang van die verdeling van kettings binne die ring is dus 'n gevolg van beide bogenoemde kragte.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/102782
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