Redistribucija molekularnih motora tijekom oscilacija jezgre

master's thesis

• Title (english): Redistribution of molecular motors during nuclear oscillations
• Author: Agneza Bosilj
• Mentor: Matko Glunčić (mentor)
• Committee member: Matko Glunčić (predsjednik povjerenstva)
• Committee member: Danko Radić (član povjerenstva)
• Committee member: Mihael Grbić (član povjerenstva)
• Committee member: Vito Despoja (član povjerenstva)
• Committee member: Nikola Poljak (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Physics); Zagreb
• Defense date and country: 2015-06-01, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Physics

Abstract

Stanice kvasca S. pombe primjer su bioloških organizama kod kojih do miješanja genetskog materijala tijekom mejoze dolazi uslijed oscilacija jezgre. Takve oscilacije promatrane su eksperimentalno te je u dosadašnjim istraživanjima razvijen teorijski model koji opisuje mehanizme koji pokreću oscilacije. U ovom radu pronašli smo numerička rješenja za teorijski model, proveli analizu linearne stabilnosti i ispitali pojavu Hopfove bifurkacije u prostoru parametara čije vrijednosti nisu poznate iz eksperimenata: k_on c i f_c. Kao rezultat dobiven je bifurkacijski dijagram u kojem su prepoznata podru čja vrijednosti parametara u kojima će model kao rješenja davati stabilne i nestabilne periodične trajektorije. Utvrdeno je da za vrijednosti parametra f_c > 5:8pN sustav nikada neće pokazivati oscilatorno ponašanje, dok za f_c less or quivalent 1:75pN dolazi do pojave podkritične Hopfove bifurkacije. Unutar intervala 1:75pN less or quivalent f_c < 5:8pN promjenom parametra k_on c od nule prema većim vrijednostima sustav će brzo razviti stabilne oscilacije.

Abstract (english)

Yeast cells S. pombe are examples of biological organisms in which the mixing of genetic material during meiosis occurs due to oscillation of the nucleus. Such oscillations were observed experimentally and in previous research developed a theoretical model that describes the mechanisms that drive the oscillation. In this paper we found numerical solutions for the theoretical model, conducted the analysis of linear stability and examined the occurrence of Hopf bifurcation in the space of parameters whose values are not known from experiments: k_on c i f_c. This resulted in the bifurcation diagram in which the values of the parameters identified areas in which the model as solutions provide stable and unstable periodic orbits. It was found that for the value of the parameter fc > 5:8pN system will never show oscillatory behavior, while for f_c less or quivalent 1:75pN reported the occurrence of subcritical Hopf bifurcation. Within the interval 1:75pN less or quivalent f_c < 5:8pN changing parameter k_on c from zero to greater values, system will quickly develop a stable oscillations.

• Keywords: biološki sustav; citoskelet; proteinski motori; Hopfova bifurkacija
• Keywords (english): Hopf bifurcation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:681875
• Study programme: Title: Physics; specializations in: Research; Course: Research; Study programme type: university; Study level: integrated undergraduate and graduate; Academic / professional title: magistar/magistra fizike (magistar/magistra fizike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Access restricted to students and staff of home institution
• Created on: 2017-04-04 16:10:00