Matematički modeli u biokemiji

master's thesis

• Author: Tamara Falak
• Mentor: Igor Pažanin (mentor)
• Committee member: Igor Pažanin (predsjednik povjerenstva)
• Committee member: Mea Bombardelli (član povjerenstva)
• Committee member: Vlado Volenec (član povjerenstva)
• Committee member: Juraj Šiftar (član povjerenstva)
• Granter: University of Zagreb; Faculty of Science; (Department of Mathematics); Zagreb
• Defense date and country: 2014-07-15, Croatia
• Scientific / art field, discipline and subdiscipline: NATURAL SCIENCES; Mathematics

Abstract

U ovom diplomskom radu prezentirani su matematički modeli biokemijskih reakcija kataliziranih enzimima. U Poglavlju 1 govorili smo o važnosti matematičkog modela te smo opisali glavna svojstva sustava običnih diferencijalnih jednadžbi. Poglavlje 2 posvećeno je uvođenju veoma korisnog modela za kemijske reakcije, zakona o djelovanju masa, koji opisuje brzinu interakcije kemijskih tvari u reakcijama i koji smo koristili u nastavku rada. U Poglavlju 3, koristeći matematički model kinetike enzima, promatrali smo tri fundamentalna enzimska svojstva: kompetitivnu (konkurentnu) inhibiciju, nekompetitivnu (alosteričku) inhibiciju te kooperativnost. Modele smo zapisali pomoću jednostavnih sustava običnih diferencijalnih jednadžbi.

Abstract (english)

In this work we present various mathematical models describing biochemical reactions catalyzed by the enzymes. Chapter 1 deals with the definition of the mathematical model and the main properties concerning the systems of ordinary differential equations. Chapter 2 introduces the law of mass action, a very useful model for chemical reactions, which describes the rate of interaction of chemical substances in the reactions, and which has later been extensively used in the work. Chapter 3, by using the mathematical model of kinetics of enzymes, examines three fundamental features of enzymes: competitive inhibition, noncompetitive (allosteric) inhibition and cooperation. Models are described by using simple systems of ordinary differential equations.

• Keywords: matematički modeli; sustav običnih diferencijalnih jednadžbi; kemijske reakcije; enzimi kinetika entima; kompetitivna inhibicija; konkurentna inhibicija; nekompetitivna inhibicija; alosterička inhibicija; kooperativnost
• Keywords (english): mathematical models; systems of ordinary differential equations; chemical reactions; enzymes; kinetics of enzymes; competitive inhibition; noncompetitive inhibition; allosteric inhibition; cooperation
• Language: croatian
• URN:NBN: urn:nbn:hr:217:709839
• Study programme: Title: Mathematics Education; specializations in: Mathematics Education; Course: Mathematics Education; Study programme type: university; Study level: graduate; Academic / professional title: magistar/magistra edukacije matematike (magistar/magistra edukacije matematike)
• Type of resource: Text
• File origin: Born digital
• Access conditions: Open access
• Created on: 2019-01-22 10:00:17