A driving and coupling "Pac-Man" mechanism for chromosome poleward translocation in anaphase A

Abstract

During mitosis, chromatid harnesses its kinetochore translocation at the depolymerizing microtubule ends for its poleward movement in anaphase A. The force generation mechanism for such movement remains unknown. Analysis of the current experimental results shows that the bending energy release from the bound tubulin subunits alone cannot provide sufficient driving force. Additional contribution from effective electrostatic attractions between the kinetochore and the microtubule is needed for kinetochore translocation. Interestingly, as the kinetochore moves to inside the microtubule, the microtubule tip is free to bend outward so that the instantaneous distance between the kinetochore and the microtubule tip is much closer than the rest of the microtubule. This close contact yields much larger electrostatic attraction than that from the rest of the microtubule under physiological ionic conditions. As a result, the effective electrostatic interaction hinders the further kinetochore poleward translocation until the microtubule tip dissociates. Thus, the kinetochore translocation is strongly coupled at the depolymerizing microtubule end. This driving-coupling mechanism indicates that the kinetochore velocity is largely controlled by the microtubule dissociation rate, which explains the insensitivity of kinetochore velocity to its viscous drag and the large redundancy in its stalling force.

Fig. 1.

Schematic illustrations of the theoretical model on kinetochore-microtubule systems. (A) The central notion of the driving–coupling mechanism. (B) The interaction notions within the microtubule. (C) The kinetochore and the tubulin subunit's coordinate definitions.

Fig. 2.

The kinetochore–microtubule dynamics. If not otherwise mentioned, the charge per kinetochore component q_kt = 6, the screening length λ_D = 1 nm, the binding energy is 12.5 k_BT, the bending energy is 3.0 k_BT, the lateral bond strength is 3.0 k_BT, k_off⁽⁰⁾ = 5 s⁻¹, and γ_kt = 5 pN·s/μm. The instantaneous kinetochore potential landscape is calculated from Eq. 1 (see Supporting Text). (A) Kinetochore translocation dynamics with zero electrostatic attraction q_kt = 0. (A Inset) The kinetochore potential landscape changes as the microtubule protofilaments flare out. An energy barrier (>3 k_BT) always remains, hindering the kinetochore translocation. (B) Kinetochore translocation dynamics with normal electrostatic attraction q_kt = 6. a, γ_kt = 5 pN·s/μm; b, γ_kt = 0.06 pN·s/μm; c, γ_kt = 0.03 pN·s/μm. (B Inset) k_offT_bind vs. time plot for B curve a. (C) The snapshots for the kinetochore–microtubule configuration and the corresponding kinetochore potential landscape during the kinetochore translocation in B curve a. Only the first a few tubulin subunits near the tip are shown for illustration purposes. (D) The kinetochore translocation dependence on the electrostatic attraction and the kinetochore diffusion. In a–c, γ_kt = 5, 2, and 0.15–0.02 pN·s/μm. (D Inset) The insensitivity of the kinetochore translocation velocity to the viscous drag.

Fig. 3.

Various factors affecting the kinetochore velocity. If not otherwise mentioned, q_kt = 6, λ_D = 1 nm, the binding energy is 12.5 k_BT, the bending energy is 3.0 k_BT, the lateral bond strength is 3.0 k_BT, k_off⁽⁰⁾ = 5 s⁻¹, and γ_kt = 5 pN·s/μm. (A) The dependence of kinetochore translocation velocity on the protofilament bare off-rate k_off⁽⁰⁾. (B) The kinetochore translocation dependence on the additional pulling force: a, q_kt = 6; b, q_kt = 3; c, q_kt = 0. (B Inset) The threshold pulling force depends on the kinetochore diffusion. (C) The velocity-load plot. (D) The stalling force dependence on the kinetochore charge q_kt. (D Inset) The dependence of the stalling force on the bending energy.

Fig. 4.

Phase diagram for sustained kinetochore translocation (bending energy vs. q_kt). If not otherwise mentioned, q_kt = 6, λ_D = 1 nm, the lateral bond is 3.0 k_BT, the binding energy is 12.5 k_BT, the bending energy is 3 k_BT, k_off⁽⁰⁾ = 5 s⁻¹, and γ_kt = 5 pN·s/μm. (Inset) Phase diagram (binding energy vs. kinetochore diffusion). The arrow is the probable routine in which the kinetochore stalls after it collects one or two kinetochores during the translocation along the microtubule (6).