Reverse engineering of force integration during mitosis in the Drosophila embryo

Abstract

The mitotic spindle is a complex macromolecular machine that coordinates accurate chromosome segregation. The spindle accomplishes its function using forces generated by microtubules (MTs) and multiple molecular motors, but how these forces are integrated remains unclear, since the temporal activation profiles and the mechanical characteristics of the relevant motors are largely unknown. Here, we developed a computational search algorithm that uses experimental measurements to 'reverse engineer' molecular mechanical machines. Our algorithm uses measurements of length time series for wild-type and experimentally perturbed spindles to identify mechanistic models for coordination of the mitotic force generators in Drosophila embryo spindles. The search eliminated thousands of possible models and identified six distinct strategies for MT-motor integration that agree with available data. Many features of these six predicted strategies are conserved, including a persistent kinesin-5-driven sliding filament mechanism combined with the anaphase B-specific inhibition of a kinesin-13 MT depolymerase on spindle poles. Such conserved features allow predictions of force-velocity characteristics and activation-deactivation profiles of key mitotic motors. Identified differences among the six predicted strategies regarding the mechanisms of prometaphase and anaphase spindle elongation suggest future experiments.

Figure 1

The spindle protein machinery. (A) A cartoon that shows all major components of the spindle. Four MT populations (astral (as), kinetochore (kt), chromosome arm (chr) and inter-polar (ip) MTs) extend from the poles creating the spindle. Molecular motors bind to MTs and either regulate their ends' kinetics, or slide them, or exert forces on the chromosomes and centrosomes. (B) Eight possible MT–motor combinations, with the respective velocities and forces acting on a single MT. asMT: cortical dynein pulling the MT generates an outward force F₁ on the spindle pole. chrMT are anchored at the pole, while MT polymerization and chromokinesins generate a pushing force F₂; a force F₃ is associated with such an MT if depolymerases are activated at the MT's minus end in addition to motor activity at the MT's plus end. ktMT: an inward force, F₄ is generated on an MT anchored at the pole while kt motors act on the MT plus end; modified force F₅ acts on an MT depolymerized at the minus end in addition to the plus end motor activity; force F₆ is exerted if ktMT is depolymerized at its minus end and anchored at its plus end. ipMT: an outward force, F₇ results from the combination of kinesin-5 and kinesin-14 actions on the MT anchored at the pole, while a force F₈ is exerted by these motors on an MT being depolymerized at its minus end. (C) The experimentally measured time series for spindle length (pole–pole distance) in wild type (WT) and inhibited spindles used in the optimization process (details in Supplementary Figure 1, referenced in Supplementary Table 2). Colors correspond to motor colors in the legend. Previous studies revealed that the double inhibition of kinesin-5 and kinesin-14 fully rescues metaphase spindle assembly (dashed blue line, not used here) (Sharp et al, 2000b). However, recent studies suggest that this effect results from the partial inhibition of kinesin-5, whereas a more complete inhibition leads to prometaphase spindle collapse even in kinesin-14 null mutants (green line, used here), suggesting that an additional unknown inward force also opposes kinesin-5 and contributes to the collapse (Brust-Mascher and Scholey, in preparation).

Figure 2

Iterative elimination of models that do not fit experimental data. Initial analysis identified ∼10 000 models (belonging to ∼1500 groups) that agree with WT data. (A–D) Four examples of the forces on the four MT populations (asMT—blue; ipMT—green; chrMT—red and ktMT—cyan) in different models. (E) Crosses illustrate projections of the points in the parameter space corresponding to all identified models onto a two-dimensional manifold in the parameter space (explained in the Supplementary information). The models corresponding to (A–D) are marked with red circles. The iterative process of addition of experimental data to the search reduced the number of identified groups of models (F) and the area they occupy in the two-dimensional projection of model space (G) (same projection as that in (E)). The probability density distributions of the parameter values governing the timing of kinesin-14 activity and force for each iteration are shown in (H) with the same color coding as that in (F).

Figure 3

Cluster analysis of all identified models. (A) Results of the cluster analysis for models that fit all available experimental data. Dendrogram shows the hierarchical tree of all ∼1000 models. Each imaginary vertical line across the panel corresponds to a specific model fitting all available experimental data. Time series (represented on the y axis of each panel running from top (early) to bottom (late)) for the forces on the four MT populations and cohesion forces from prometaphase (t=0) till the end of anaphase B (t=278 s) follow immediately below the dendrogram. Six identified clusters within the tree are color-coded. The forces (in picoNewtons) are color coded according to the bar shown at the upper left corner (extreme red (blue) corresponds to 1500 pN (−1500 pN)). The forces are abbreviated as follows: F_as—total force on astral MTs; F_ip—total force on inter-polar MTs; F_chr—total force on MTs reaching to the chromosome arms; F_kt—total force on the kinetochore fiber and F_coh—forces induced by the cohesion complex that hold sister chromatids together. For the reference, the time series for the pole–pole distance are shown immediately below the force bar. Time series for 10 motor switches' activity follow immediately below the force time series. White and black correspond to active and inactive motors, respectively. The switches are: P_dep—pole depolymerizer; P_chr—chromokinesin; P_dyn—dynein; P_k5—kinesin-5 sliding motor; P_k14—kinesin-14; P_kt—combined kt motors; P_mt—MT plus end depolymerization activity at the kinetochore; P_poly—MT plus end polymerization activity at the kinetochore; P_as—switch regulating the number of astral MTs; P_ovrlp—switch regulating the number of MTs at the overlap zone at the spindle equator. (B) The time series for the forces and switches predicted by a single selected model from group 1 as an illustrative example. The vertical bars (left) in the upper half of the panel represent the color-coded forces for each MT population, whereas the corresponding graphs (blue line, right) depict the change in magnitude of the corresponding force with time. The vertical bars in the lower half of the panel (left) represent the black–white switching ‘off' or ‘on' of the specific motors at the times indicated on the graphs (green line, right) for this particular model.

Figure 4

Constraints on the motors' mechanical properties. The predicted force–velocity relations of kinesin-5 (blue) and kinesin-14 (green). The main panel shows the force–velocity relation predicted in 50 resulting models randomly chosen from ∼1000 models that fit all available experimental data. The inset shows free load velocity measurements reported in Tao et al (2006).

Figure 5

Example of an identified model. The identified forces and main switches in one of the identified models (from group 1). (A) The pole–pole distance resulting from the net force acting on the spindle poles. (B) The MT populations' forces: asMT (blue), chrMT (red), ipMT (green) and ktMT (black). (C) The predicted sets of force generators acting in the spindle at sequential mitotic stages; roman numerals correspond to the stages in (A, B). (i) At the beginning of prometaphase, dynein pulling forces supported by pushing forces from the chromosome arms are balanced by inward forces resulting from MT minus end depolymerization at the poles. (ii) Recruitment of kinesin-5 to the antiparallel ipMT tips increases the net outward force. Then, downregulation of dynein (iii) followed by upregulation of kinesin-14 (iv) antagonizes kinesin-5, reduces the ipMT outward force (B) and decreases the total outward force resulting in the metaphase steady state. Upregulation of kt motors (v) changes the composition of the balance of forces (B) but has very small net effect on the total force (A). These changes followed by the degradation of cohesion (vi) are the only necessary transitions required for progression through anaphase A. Finally, anaphase B is the result of downregulation of chr-arm forces immediately followed by downregulation of depolymerization at the poles (vii).

Figure 6

Model prediction. Simulation result of dynamics of spindle length over time after complete (black line) and partial (color lines) inhibitions of kinesin-5. Partial inhibition is from 80% (blue line) to 0% (red lines).