Overview of “search and capture” • Two spindles on each side generate microtubules searching for kinetochores. • Once each pair of chromosome is amphitelically attached, a cell begins to break into two.
Formation of microtubule-kinetochore-centrosomes(MKC) complex and chromosome alignment • How many microtubules are attached to a kinetochore? (Minimum 1) • Two MKCcomplexes per sister chromatids. • Do all the MKC complex needed to be formed before chromosome alignment (wait for everyone) or chromosome align follows formation of a MKC complex (First-come-first-serve) • Freedom of movement of whole chromosomes?
Math Model: Amplitelic attachment of chromosomes to spindles Assumptions: • The number of chromosomes of a particular cell is N. (b) The time required for formation of two MKC complexes is denoted as Xn. • Assume X1, X2, … Xn are identically and independently distributed. Required time from “start” to “end” Start : when the spindles start to generate microtubules End: when the last kinetochore got captured
Questions • Does time T varies according to number of chromosome? • For example, a fruit fly has 8 but a goldfish has 100. Does Tf << Tg? • Are the “search and capture” times of different species available?
Math Model 2 Assumptions • The time required for n-th individual kinetochore to be properly connected is denoted as Xn. • Assume X1, X2, … Xn are identically but dependently distributed. • Let Y1 < Y2 <… <Yn and Zi= Yi – Yi-1 Required time from “start” to “end” Does the measurement of Zn available?
Why assume dependent? • Existenceof RanGTP -- Centromeres generate RanGTP to allow a bias in search and capture process. • Do fields of RanGTP actually around centromeres? • Does one field disappear once the chromosome is correctly attached?
Two dependent scenarios • Constant supply of monomers. 1 If RanGTP turns off when kinetochores are connected, the last kinetochore is the only target of all the MTs. (Police and theft) 2 More kinetochores (chromosomes) make the “smell” stronger and, thus, the trace easier