Browsing by Author "Dempers, Nadine"
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- ItemMotor protein transport on cytoskeleton networks(Stellenbosch : Stellenbosch University, 2022-04) Dempers, Nadine; Muller-Nedebock, Kristian; Stellenbosch University. Faculty of Science. Dept. of Physics.ENGLISH ABSTRACT: Motor proteins are able to propel themselves along the, sometimes branched and intersecting, directed filaments of the cytoskeleton, dragging various organelles and vesicles to their required destinations within a crowded intracellular environment [ 1 ]. Although sophisticated experimental techniques and various computational and mathematical models have lead to significant insights pertaining to this active transport process, various aspects thereof remain unclear [see e.g., 2]. This thesis aims to establish a mathematical framework providing a collective description of generic motor-driven transport along directed and branched filament networks. The discussion begins by introducing the reader to the intracellular structures that make up the system in consid- eration, along with mathematical models that describe their dynamics. The mathematical exploration begins with a set of Langevin equations that couple a cargo to an elastic tail of a motor protein that is propelled along a single filament. Various averages and correlation functions are calculated from the solutions of these equations, revealing the effects of the cargo on the motion of the motor protein. An effective time scale is presented, which exhibits the time the motor and cargo take, since the onset of motion, to settle into an —on average— constant progression along the filament. Diffusion and drift coefficients for this motion are also presented via a derivation of a Fokker-Planck equation. The system is then modified by including a bend in the filament. This is shown to temporarily adjust the average speed of the motor during the time that it is, on average, expected to move over the bend. A further investigation of the average fluctuations that the motor experiences reveals that this behaviour may indicate that in branched cytoskeleton networks a motor protein may be more likely to walk along certain branches, depending on the angles. The formalism is, however, not suitable to explicitly model branched filaments. The discussions that follow introduce a mathematical formalism for motor-driven transport on networks of filaments that models the attachment of a motor to a filament in a new way. The formalism consists of a Martin-Siggia-Rose (MSR) representation [see e.g., 3] of the Langevin dynamics of a motor and a cargo coupling, along with a Gaussian networking theory adapted from [ 4] that periodically attaches the diffusing motor to a set of discrete binding sites on the network. A series of approximation schemes dealt with the non-Gaussian functional integrals. This included a Random Phase Approximation (RPA) which introduced collective coordinates for the motors. After implementing a saddle point approximation and additional mathematical simplifications, results were obtained for two scenarios. The first being a correlation function for motor-driven transport on homogeneous networks, containing a parameter for the motor hopping speed and a diffusion coefficient in agreement with previous results. The final results present a generating functional which may be used to obtain averages and correlation functions for non-homogeneous networks. This allows for various possible avenues of further exploration, including quenched or annealed averaging over a distribution of possible network configurations.