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

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Abstract
The relation between the force pulling a kinetochore poleward and the length of the corresponding kinetochore fiber was investigated. It was recognized by Ostergren in 1950 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., meiotic bivalent or mitotic chromosome) with a single kinetochore fiber extending to each pole, the resultant force (RF) would equal 0 when the chromosome lay at the midpoint between the 2 poles. For special chromosomes that have unequal numbers of kinetochore fibers extending towards opposite poles, Ostergren''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. The force-length relationship was measured in living spindles by analyzing the metaphase positions of experimentally generated multivalent chromosomes having 3 or 4 kinetochore fibers. Multivalent chromosomes of varied configurations were generated by .gamma.-irradiation of nymphs of the grasshopper Melanoplus differentialis, and their behavior was analyzed in living 1st 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. Force (F) along a single kinetochore fiber is expressed by: F = kLexp, 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 = .SIGMA.KiLiexp, where kinetochore fiber lengths in opposite half-spindles are given the opposite sign. If forces on a metaphase chromosome are at equilibrium (RF = 0), then for asymmetrical orientations of multivalents the individual kinetochore fiber lengths (Li) can be measured and the exponent solved that yields a resultant force of 0. The value of the exponent relates how the magnitude of force along a kinetochore fiber varies with its length. For 6 trivalents and 1 naturally occurring quadrivalent an average value for exp = 1.06 .+-. 0.18 was calculated. This is consistent with Ostergren''s hypothesis and indicates that the magnitude of poleward traction force along a kinetochore fiber is directly proportional to the length of the fiber. The balance of forces along a kinetochore fiber may be a major factor regulating the extent of kinetochore microtubule assembly.