Distribution of molecular motors on a growing microtubule

Abstract

U ovom radu smo konstruirali matematički model kako bismo opisali raspodjelu motora na rastućem mikrotubulu. Promatrali smo raspodjelu motora koji hodaju prema plus kraju mikrotubula, kinezin. Raspodjela motora nam je važna kako bismo mogli detaljnije proučavati mehanizme prijenosa tereta u stanicama i promjenu mikrotubula iz faze rasta u fazu smanjivanja, kao posljedicu akumulacije motora na kraju mikrotubula. Raspodjelu molekularnih motora na mikrotubulu smo dobili rješavanjem jednadžbe Laplaceovom metodom. Rješenje smo zatim prokomentirali za različite slučajeve, ovisno o relativnoj razlici brzina rasta mikrotubula i brzine molekularih modela koji hodaju po njemu. U metodičkom dijelu rada pisali smo o modelima u fizici te procesu modeliranja u istraživačkoj nastavi fizike. Ovakav pristup učenju gradiva fizike pokazao se kao jako koristan za sve učenike, neovisno o njihovoj dobi i sposobnostima.In this paper we have constructed a mathematical model to describe the distribution of the molecular motors on growing microtubules. We have observed distribution of molecular motors walking towards the plus end of the microtubule - kinesin. Distribution of the molecular motors is important to us so that we can study in detail the mechanisms of transfer of cargo in the cells and changes from growth phase to shrinking phase of mikroubules, as a result of the accumulation of the engine at the end of microtubules. We got the expression for distribution of molecular motors on microtubules by solving equation with Laplace method. The solution was then observed in three different cases, depending on the relative difference of the growth speed of microtubules and speed of molecular motors walking on it. In the methodological part of the paper we wrote about the models in physics and process of modeling in physics instruction and research. This approach to learning physics proved to be very beneficial for all students, regardless of age and ability