Polić, Dora (2014) Stochastic model of dyneindependent nuclear oscillations. Diploma thesis, Faculty of Science > Department of Physics.

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Abstract
During the meiotic prophase of the life cycle of fission yeast, oscillatory nuclear movement is crucial for proper chromosome pairing, recombination and spore viability. This movement is driven by dynein motors pulling on microtubules, consequently moving the nucleus back and forth inside the cell. A theoretical model (V ogel et a!„ 2009) of nuclear oscillations, based on loaddependent detachrnent and microtubule lengthdependent attachment of the motors, describes nuclear oscillations using large number of motors and a meanfield approximation. However, fluctuations in the number of active force generators are neglected. For small number of motors these fluctuations become important and lead to noisy oscillations. To verify that oscillations still occur in the presence of force fluctuations, we have performed stochastic computer simulations of individual force generators. We bave represented the dynamics of the system by a master equation for the probability P(N1 ,NT ,t) of finding a configuration of N1 and NT particles attached, both to the cell cortex and to the microtubule on the left and the right side of SPB, respectively, at time t. We have obtained our results by solving the equation numerically using Gillespie's algorithm. We have performed computer simulations for a different number of motors, starting with a large number of motors and ending with the situation where only one motor is present. In the limit of a large number of motors, we obtain results similar to those suggested by the meanfield approximation. On the contrary, as the number of particles decreases, the meanfield approximation is no longer valid. Using the method of autocorrelation we have determined the number of motors necessary for robust nucleus oscillations, Nuk = 20  40. We investigated how does friction of system influence oscillatory movement of nucleus. Last, we checked parametric space for attachrnent rate kon and constant of detachment ko. Comparing the results obtained by stochastic simulations to those measured experimentally, we have confirmed validity of our model which can now be used in other scientific experiments conducted on similar biological systems. As the cytoplasmic dynein is found in many eukaryotic cells, the frame that is used in this paper has a number of applications in other organisms, including humans.
Item Type:  Thesis (Diploma thesis) 

Keywords:  dyneindependent nuclear oscillations, stochastic model 
Supervisor:  Glunčić, Matko 
Date:  6 October 2014 
Number of Pages:  40 
Subjects:  NATURAL SCIENCES > Physics 
Divisions:  Faculty of Science > Department of Physics 
Depositing User:  Gordana Stubičan Ladešić 
Date Deposited:  21 Jun 2016 13:40 
Last Modified:  20 Jan 2017 14:01 
URI:  http://digre.pmf.unizg.hr/id/eprint/4888 
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