Applied and Computational Mathematics Seminar
Monday, October 20, 2014 - 2:00pm
1 hour (actually 50 minutes)
Given their ubiquity in physics, chemistry and materialsciences, cluster nucleation and growth have been extensively studied,often assuming infinitely large numbers of buildingblocks and unbounded cluster sizes. These assumptions lead to theuse of mass-action, mean field descriptions such as the well knownBecker Doering equations. In cellular biology, however, nucleationevents often take place in confined spaces, with a finite number ofcomponents, so that discrete and stochastic effects must be takeninto account. In this talk we examine finite sized homogeneousnucleation by considering a fully stochastic master equation, solvedvia Monte-Carlo simulations and via analytical insight. We findstriking differences between the mean cluster sizes obtained from ourdiscrete, stochastic treatment and those predicted by mean fieldones. We also study first assembly times and compare results obtained from processes where only monomer attachment anddetachment are allowed to those obtained from general coagulation-fragmentationevents between clusters of any size.