Fig. 2.
Ordered segregation requires extreme parameters to substantially reduce partitioning errors. (A) Upper: Segregating units with nonnegligible size (gray circles) exclude each other and thereby promote more even segregation. Lower: Simulation results (symbols) and analytical approximation (solid lines) plotted as a function of the average total volume fraction occupied by the segregating units, with x sampled from Poisson distributions for each 〈x〉 (circles and triangles) or assuming that synthesis occurs in a geometric burst with average burst size of 10 (diamonds). All results are truncated to ensure Kx < 1. The shaded area corresponds to the physiological regime for most cellular components (34) and shows that the effect should be minor. (B) Upper: Organelles (dots) compete for available binding sites (ends of astral, gray) and unbound organelles are partitioned independently. Lower: Simulation results (symbols) and analytical approximations (solid lines) when binding sites are distributed evenly between the two daughters. The circles and triangles correspond to v and x sampled from Poisson distributions, using 〈v〉 = 100, and diamonds show x and v sampled from processes where synthesis occurs in a geometrically distributed burst, with average burst sizes of 20 and 10 for v and x, respectively. The results show how modest the effects are when x and v are not exactly matched. (C) Upper: Among (x − δx,odd)/2 possible pairs in each cell, a fraction r of molecules (dots) binomially forms pairs, where δx,odd = 1 if x is odd and zero otherwise. Paired molecules segregate separately with probability p whereas unpaired molecules segregate independently. Under these assumptions, k = r(1 − Po/〈x〉), where Po is the probability that x is an odd number. Lower: Simulations (symbols), exact analytical results (Eq. 8, dashed line), and analytical approximations (k = r in Eq. 8, solid line) when x is sampled from a Poisson distribution of average 10. The results show that both r and p must approach 100% for efficient control. Derivations are given in SI Text.