Biofilament interacting with molecular motors
| dc.contributor.advisor | Muller-Nedebock, Kristian K. | en_ZA |
| dc.contributor.advisor | Touchette, Hugo | en_ZA |
| dc.contributor.author | Meylahn, Janusz Martin | en_ZA |
| dc.contributor.other | Stellenbosch University. Faculty of Science. Dept. of Physics. | en_ZA |
| dc.date.accessioned | 2015-12-14T07:43:38Z | |
| dc.date.available | 2015-12-14T07:43:38Z | |
| dc.date.issued | 2015-12 | |
| dc.description | Thesis (MSc)--Stellenbosch University, 2015. | en_ZA |
| dc.description.abstract | ENGLISH ABSTRACT: We study molecular motors moving along a filament or polymer using two different mathematical models in which motors are idealised as springs. In the first model we study the average and the fluctuations of the motor stretch by modelling the motion of the motors along the filament using a simple stochastic differential equation with linear friction. We use the notion of stochastic resetting to explicitly include the attachment and detachment dynamics of the motors to and from the filament and study the fluctuations around the most probable value of the mean stretch using methods from large deviation theory. The second model uses methods from field theory to model a dynamic network consisting of a single polymer and many molecular motors. In this case, we develop techniques to include the bias motion of the molecular motors in a weighting factor for the formation of specific networks rather than in the dynamical constraints of the partition function which allows us to study the steady-state of the network using a self-consistency argument and a saddlepoint approximation. | en_ZA |
| dc.description.abstract | AFRIKAANSE OPSOMMING: Ons beskou twee wiskundige modelle vir molekulêre motore wat langs ’n filament of polimeer beweeg. Die motore word as vere geïdealiseer. In die eerste model bestudeer ons die gemiddelde uitrekking van die motor, asook die fluktuasies in die uitrekking, deur die beweging van die motor met ’n eenvoudige stogastiese differensiaalvergelyking met lineêre wrywing te beskryf. Ons gebruik stogastiese hersetting om eksplisiet die aanheg en ontkoppeling dinamika van die motore aan die filament te modelleer en bestudeer dan die fluktuasies rondom die mees waarskynlike waarde van die gemiddelde uitrekking met metodes uit groot-afwykingsteorie. Die tweede model maak gebruik van metodes uit veldeteorie om ’n dinamiese netwerk van een polimeer en ’n aantal molekulêre motore te beskryf. Hier ontwikkel ons tegnieke om die voorkeur beweging van die motore deur ’n gewigsfaktor vir die vorming van spesifieke netwerke te bewerkstellig, eerder as om dit dinamies in die partisiefunksie af te dwing. Hierdie benadering laat ons dan toe om die bestendige toestand van die netwerk deur ’n selfkonsistensie argument en saalpuntbenadering te bestudeer. | af_ZA |
| dc.format.extent | ix, 79 pages : colour illustrations | en_ZA |
| dc.identifier.uri | http://hdl.handle.net/10019.1/97985 | |
| dc.language.iso | en_ZA | en_ZA |
| dc.publisher | Stellenbosch : Stellenbosch University | en_ZA |
| dc.rights.holder | Stellenbosch University | en_ZA |
| dc.subject | Molecular motors | en_ZA |
| dc.subject | Biofilaments | en_ZA |
| dc.subject | UCTD | en_ZA |
| dc.title | Biofilament interacting with molecular motors | en_ZA |
| dc.type | Thesis | en_ZA |