Traction force on a kinetochore at metaphase acts as a linear function of kinetochore fiber length

We are investigating the relation between the force pulling a kinetochore poleward and the length of the corresponding kinetochore fiber. It was recognized by Östergren in 1950 (Hereditas 36: 1-19) that the metaphase position of a chromosome could be achieved by a balance of traction forces if such forces were proportional to the distance from kinetochore to pole. For the typical chromosome (i.e., a meiotic bivalent or mitotic chromosome) with a single kinetochore fiber extending to each pole, the resultant force (RF) would equal zero when the chromosome lay at the midpoint between the two poles. For special chromosomes that have unequal numbers of kinetochore fibers extending towards opposite poles, Östergren’s proposal suggests that RF = 0 when the chromosome is shifted closer to the pole toward which the greater number of kinetochore fibers are pulling. We have measured the force-length relationship in living spindles by analyzing the metaphase positions of experimentally generated multivalent chromosomes having three or four kinetochore fibers. Multivalent chromosomes of varied configurations were generated by γ-irradiation of nymphs of the grasshopper Mclanoplus differentialis, and their behavior was analyzed in living first meiotic spermatocytes. The lengths of kinetochore fibers were determined from time-lapse photographs by measuring the kinetochore-to-pole distances for fully congressed chromosomes just before the onset of anaphase. In our analysis, force (F) along a single kinetochore fiber is expressed by: F = kL^exp, where k is a length-independent proportionality constant, L represents the kinetochore fiber length, and exp is an unknown exponent. The RF on a chromosome is then given by : RF = Ek_i L_i exp, where kinetochore fiber lengths in opposite half-spindles are given opposite sign. If forces on a metaphase chromosome are at equilibrium (RF = 0), then for asymmetrical orientations of multivalents we can measure the individual kinetochore fiber lengths (L I) and solve for the exponent that yields a resultant force of zero. The value of the exponent relates how the magnitude of force along a kinetochore fiber varies with its length. For six trivalents and one naturally occurring quadrivalent we calculated an average value for exp = 1.06 ± 0.18. This result is consistent with Östergren’s hypothesis and indicates that the magnitude of poleward traction force along a kinetochore fiber is directly proportional to the length of the fiber. Our finding suggests that the balance of forces along a kinetochore fiber may be a major factor regulating the extent of kinetochore microtubule assembly.